LMFDB - Embedded newform 140.2.w.b.23.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(23,140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			23.4
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24267 + 0.675113i) q^{2} +(-0.402205 - 0.107770i) q^{3} +(1.08845 - 1.67788i) q^{4} +(-2.22809 - 0.188711i) q^{5} +(0.572564 - 0.137611i) q^{6} +(-2.30240 - 1.30345i) q^{7} +(-0.219816 + 2.81987i) q^{8} +(-2.44792 - 1.41331i) q^{9} +(2.89618 - 1.26971i) q^{10} +(0.725638 - 0.418947i) q^{11} +(-0.618604 + 0.557549i) q^{12} +(-1.16367 - 1.16367i) q^{13} +(3.74109 + 0.0653744i) q^{14} +(0.875811 + 0.316023i) q^{15} +(-1.63057 - 3.65256i) q^{16} +(-4.94841 - 1.32592i) q^{17} +(3.99610 + 0.103649i) q^{18} +(2.91741 - 5.05309i) q^{19} +(-2.74179 + 3.53307i) q^{20} +(0.785561 + 0.772382i) q^{21} +(-0.618890 + 1.01050i) q^{22} +(0.896861 + 3.34713i) q^{23} +(0.392310 - 1.11048i) q^{24} +(4.92878 + 0.840930i) q^{25} +(2.23166 + 0.660445i) q^{26} +(1.71555 + 1.71555i) q^{27} +(-4.69306 + 2.44442i) q^{28} +5.00172i q^{29} +(-1.30169 + 0.198560i) q^{30} +(-7.03267 + 4.06031i) q^{31} +(4.49215 + 3.43810i) q^{32} +(-0.337005 + 0.0903002i) q^{33} +(7.04437 - 1.69305i) q^{34} +(4.88397 + 3.33869i) q^{35} +(-5.03579 + 2.56901i) q^{36} +(-0.190621 - 0.711408i) q^{37} +(-0.213956 + 8.24889i) q^{38} +(0.342623 + 0.593441i) q^{39} +(1.02191 - 6.24145i) q^{40} +0.0958388 q^{41} +(-1.49764 - 0.429472i) q^{42} +(4.87975 - 4.87975i) q^{43} +(0.0868733 - 1.67354i) q^{44} +(5.18749 + 3.61093i) q^{45} +(-3.37419 - 3.55389i) q^{46} +(-5.28468 + 1.41603i) q^{47} +(0.262186 + 1.64481i) q^{48} +(3.60205 + 6.00210i) q^{49} +(-6.69255 + 2.28248i) q^{50} +(1.84738 + 1.06658i) q^{51} +(-3.21908 + 0.685908i) q^{52} +(3.43436 - 12.8172i) q^{53} +(-3.29006 - 0.973671i) q^{54} +(-1.69585 + 0.796517i) q^{55} +(4.18166 - 6.20594i) q^{56} +(-1.71797 + 1.71797i) q^{57} +(-3.37672 - 6.21547i) q^{58} +(-4.46933 - 7.74111i) q^{59} +(1.48352 - 1.12553i) q^{60} +(0.919379 - 1.59241i) q^{61} +(5.99810 - 9.79346i) q^{62} +(3.79391 + 6.44473i) q^{63} +(-7.90336 - 1.23971i) q^{64} +(2.37316 + 2.81235i) q^{65} +(0.357822 - 0.339730i) q^{66} +(0.138137 - 0.515535i) q^{67} +(-7.61081 + 6.85965i) q^{68} -1.44289i q^{69} +(-8.32314 - 0.851644i) q^{70} -13.6494i q^{71} +(4.52344 - 6.59216i) q^{72} +(1.55074 - 5.78744i) q^{73} +(0.717160 + 0.755353i) q^{74} +(-1.89175 - 0.869402i) q^{75} +(-5.30306 - 10.3951i) q^{76} +(-2.21678 + 0.0187518i) q^{77} +(-0.826407 - 0.506141i) q^{78} +(-5.30723 + 9.19239i) q^{79} +(2.94379 + 8.44595i) q^{80} +(3.73481 + 6.46888i) q^{81} +(-0.119096 + 0.0647020i) q^{82} +(-4.36830 + 4.36830i) q^{83} +(2.15101 - 0.477382i) q^{84} +(10.7753 + 3.88809i) q^{85} +(-2.76953 + 9.35829i) q^{86} +(0.539037 - 2.01171i) q^{87} +(1.02187 + 2.13830i) q^{88} +(-2.50474 - 1.44611i) q^{89} +(-8.88411 - 0.985047i) q^{90} +(1.16244 + 4.19600i) q^{91} +(6.59227 + 2.13834i) q^{92} +(3.26615 - 0.875163i) q^{93} +(5.61112 - 5.32740i) q^{94} +(-7.45382 + 10.7082i) q^{95} +(-1.43624 - 1.86694i) q^{96} +(4.24461 - 4.24461i) q^{97} +(-8.52825 - 5.02683i) q^{98} -2.36841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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 $

$2$	−1.24267	+	0.675113i	−0.878699	+	0.477377i
$2$	−1.24267	+	0.675113i	−0.878699	+	0.477377i
$3$	−0.402205	−	0.107770i	−0.232213	−	0.0622213i	0.140836	−	0.990033i	$-0.455021\pi$
$3$	−0.402205	−	0.107770i	−0.232213	−	0.0622213i	−0.373049	+	0.927812i	$0.621688\pi$
$4$	1.08845	−	1.67788i	0.544223	−	0.838941i
$5$	−2.22809	−	0.188711i	−0.996432	−	0.0843941i
$5$	−2.22809	−	0.188711i	−0.996432	−	0.0843941i
$6$	0.572564	−	0.137611i	0.233748	−	0.0561793i
$7$	−2.30240	−	1.30345i	−0.870224	−	0.492657i
$7$	−2.30240	−	1.30345i	−0.870224	−	0.492657i
$8$	−0.219816	+	2.81987i	−0.0777167	+	0.996975i
$9$	−2.44792	−	1.41331i	−0.815974	−	0.471103i
$10$	2.89618	−	1.26971i	0.915852	−	0.401517i
$11$	0.725638	−	0.418947i	0.218788	−	0.126317i	−0.386601	−	0.922247i	$-0.626351\pi$
$11$	0.725638	−	0.418947i	0.218788	−	0.126317i	0.605389	+	0.795930i	$0.293018\pi$
$12$	−0.618604	+	0.557549i	−0.178575	+	0.160951i
$13$	−1.16367	−	1.16367i	−0.322743	−	0.322743i	0.527075	−	0.849819i	$-0.323289\pi$
$13$	−1.16367	−	1.16367i	−0.322743	−	0.322743i	−0.849819	+	0.527075i	$0.823289\pi$
$14$	3.74109	+	0.0653744i	0.999847	+	0.0174720i
$15$	0.875811	+	0.316023i	0.226133	+	0.0815967i
$16$	−1.63057	−	3.65256i	−0.407643	−	0.913141i
$17$	−4.94841	−	1.32592i	−1.20016	−	0.321583i	−0.397269	−	0.917702i	$-0.630042\pi$
$17$	−4.94841	−	1.32592i	−1.20016	−	0.321583i	−0.802896	+	0.596119i	$0.796709\pi$
$18$	3.99610	+	0.103649i	0.941889	+	0.0244303i
$19$	2.91741	−	5.05309i	0.669299	−	1.15926i	−0.308802	−	0.951126i	$-0.599928\pi$
$19$	2.91741	−	5.05309i	0.669299	−	1.15926i	0.978101	−	0.208133i	$-0.0667387\pi$
$20$	−2.74179	+	3.53307i	−0.613083	+	0.790019i
$21$	0.785561	+	0.772382i	0.171423	+	0.168548i
$22$	−0.618890	+	1.01050i	−0.131948	+	0.215439i
$23$	0.896861	+	3.34713i	0.187008	+	0.697925i	0.994192	+	0.107624i	$0.0343242\pi$
$23$	0.896861	+	3.34713i	0.187008	+	0.697925i	−0.807183	+	0.590301i	$0.799009\pi$
$24$	0.392310	−	1.11048i	0.0800799	−	0.226675i
$25$	4.92878	+	0.840930i	0.985755	+	0.168186i
$26$	2.23166	+	0.660445i	0.437664	+	0.129524i
$27$	1.71555	+	1.71555i	0.330159	+	0.330159i
$28$	−4.69306	+	2.44442i	−0.886905	+	0.461951i
$29$			5.00172i			0.928795i	0.885627	+	0.464398i	$0.153729\pi$
$29$			5.00172i			0.928795i	−0.885627	+	0.464398i	$0.846271\pi$
$30$	−1.30169	+	0.198560i	−0.237655	+	0.0362519i
$31$	−7.03267	+	4.06031i	−1.26310	+	0.729254i	−0.973674	−	0.227945i	$-0.926799\pi$
$31$	−7.03267	+	4.06031i	−1.26310	+	0.729254i	−0.289430	+	0.957199i	$0.593466\pi$
$32$	4.49215	+	3.43810i	0.794108	+	0.607776i
$33$	−0.337005	+	0.0903002i	−0.0586650	+	0.0157192i
$34$	7.04437	−	1.69305i	1.20810	−	0.290356i
$35$	4.88397	+	3.33869i	0.825542	+	0.564341i
$36$	−5.03579	+	2.56901i	−0.839299	+	0.428169i
$37$	−0.190621	−	0.711408i	−0.0313379	−	0.116955i	0.948485	−	0.316822i	$-0.102616\pi$
$37$	−0.190621	−	0.711408i	−0.0313379	−	0.116955i	−0.979823	+	0.199867i	$0.935949\pi$
$38$	−0.213956	+	8.24889i	−0.0347083	+	1.33815i
$39$	0.342623	+	0.593441i	0.0548637	+	0.0950266i
$40$	1.02191	−	6.24145i	0.161578	−	0.986860i
$41$	0.0958388			0.0149675			0.00748375	−	0.999972i	$-0.497618\pi$
$41$	0.0958388			0.0149675			0.00748375	+	0.999972i	$0.497618\pi$
$42$	−1.49764	−	0.429472i	−0.231090	−	0.0662690i
$43$	4.87975	−	4.87975i	0.744155	−	0.744155i	−0.229220	−	0.973375i	$-0.573617\pi$
$43$	4.87975	−	4.87975i	0.744155	−	0.744155i	0.973375	+	0.229220i	$0.0736174\pi$
$44$	0.0868733	−	1.67354i	0.0130966	−	0.252295i
$45$	5.18749	+	3.61093i	0.773305	+	0.538286i
$46$	−3.37419	−	3.55389i	−0.497497	−	0.523992i
$47$	−5.28468	+	1.41603i	−0.770850	+	0.206549i	−0.622747	−	0.782423i	$-0.713983\pi$
$47$	−5.28468	+	1.41603i	−0.770850	+	0.206549i	−0.148103	+	0.988972i	$0.547317\pi$
$48$	0.262186	+	1.64481i	0.0378433	+	0.237407i
$49$	3.60205	+	6.00210i	0.514579	+	0.857443i
$50$	−6.69255	+	2.28248i	−0.946470	+	0.322792i
$51$	1.84738	+	1.06658i	0.258684	+	0.149352i
$52$	−3.21908	+	0.685908i	−0.446407	+	0.0951183i
$53$	3.43436	−	12.8172i	0.471745	−	1.76058i	−0.161752	−	0.986832i	$-0.551714\pi$
$53$	3.43436	−	12.8172i	0.471745	−	1.76058i	0.633497	−	0.773745i	$-0.281619\pi$
$54$	−3.29006	−	0.973671i	−0.447720	−	0.132500i
$55$	−1.69585	+	0.796517i	−0.228668	+	0.107402i
$56$	4.18166	−	6.20594i	0.558798	−	0.829304i
$57$	−1.71797	+	1.71797i	−0.227550	+	0.227550i
$58$	−3.37672	−	6.21547i	−0.443385	−	0.816131i
$59$	−4.46933	−	7.74111i	−0.581858	−	1.00781i	−0.995259	−	0.0972582i	$-0.968993\pi$
$59$	−4.46933	−	7.74111i	−0.581858	−	1.00781i	0.413402	−	0.910549i	$-0.364341\pi$
$60$	1.48352	−	1.12553i	0.191522	−	0.145306i
$61$	0.919379	−	1.59241i	0.117714	−	0.203887i	−0.801147	−	0.598467i	$-0.795777\pi$
$61$	0.919379	−	1.59241i	0.117714	−	0.203887i	0.918862	+	0.394580i	$0.129110\pi$
$62$	5.99810	−	9.79346i	0.761759	−	1.24377i
$63$	3.79391	+	6.44473i	0.477988	+	0.811960i
$64$	−7.90336	−	1.23971i	−0.987920	−	0.154963i
$65$	2.37316	+	2.81235i	0.294354	+	0.348830i
$66$	0.357822	−	0.339730i	0.0440449	−	0.0418178i
$67$	0.138137	−	0.515535i	0.0168761	−	0.0629826i	−0.956974	−	0.290173i	$-0.906287\pi$
$67$	0.138137	−	0.515535i	0.0168761	−	0.0629826i	0.973850	+	0.227190i	$0.0729539\pi$
$68$	−7.61081	+	6.85965i	−0.922946	+	0.831855i
$69$		−	1.44289i		−	0.173703i
$70$	−8.32314	−	0.851644i	−0.994806	−	0.101791i
$71$		−	13.6494i		−	1.61989i	−0.586505	−	0.809946i	$-0.699497\pi$
$71$		−	13.6494i		−	1.61989i	0.586505	−	0.809946i	$-0.300503\pi$
$72$	4.52344	−	6.59216i	0.533093	−	0.776894i
$73$	1.55074	−	5.78744i	0.181500	−	0.677368i	−0.813852	−	0.581072i	$-0.802634\pi$
$73$	1.55074	−	5.78744i	0.181500	−	0.677368i	0.995353	−	0.0962967i	$-0.0306998\pi$
$74$	0.717160	+	0.755353i	0.0833681	+	0.0878080i
$75$	−1.89175	−	0.869402i	−0.218440	−	0.100390i
$76$	−5.30306	−	10.3951i	−0.608303	−	1.19240i
$77$	−2.21678	+	0.0187518i	−0.252626	+	0.00213696i
$78$	−0.826407	−	0.506141i	−0.0935721	−	0.0573091i
$79$	−5.30723	+	9.19239i	−0.597110	+	1.03422i	0.396136	+	0.918192i	$0.370351\pi$
$79$	−5.30723	+	9.19239i	−0.597110	+	1.03422i	−0.993245	+	0.116033i	$0.962982\pi$
$80$	2.94379	+	8.44595i	0.329125	+	0.944286i
$81$	3.73481	+	6.46888i	0.414979	+	0.718764i
$82$	−0.119096	+	0.0647020i	−0.0131519	+	0.00714514i
$83$	−4.36830	+	4.36830i	−0.479483	+	0.479483i	−0.904966	−	0.425483i	$-0.860104\pi$
$83$	−4.36830	+	4.36830i	−0.479483	+	0.479483i	0.425483	+	0.904966i	$0.360104\pi$
$84$	2.15101	−	0.477382i	0.234694	−	0.0520867i
$85$	10.7753	+	3.88809i	1.16874	+	0.421723i
$86$	−2.76953	+	9.35829i	−0.298646	+	1.00913i
$87$	0.539037	−	2.01171i	0.0577908	−	0.215678i
$88$	1.02187	+	2.13830i	0.108932	+	0.227943i
$89$	−2.50474	−	1.44611i	−0.265502	−	0.153288i	0.361340	−	0.932434i	$-0.382319\pi$
$89$	−2.50474	−	1.44611i	−0.265502	−	0.153288i	−0.626842	+	0.779147i	$0.715653\pi$
$90$	−8.88411	−	0.985047i	−0.936467	−	0.103833i
$91$	1.16244	+	4.19600i	0.121857	+	0.439860i
$92$	6.59227	+	2.13834i	0.687292	+	0.222937i
$93$	3.26615	−	0.875163i	0.338684	−	0.0907502i
$94$	5.61112	−	5.32740i	0.578743	−	0.549480i
$95$	−7.45382	+	10.7082i	−0.764746	+	1.09864i
$96$	−1.43624	−	1.86694i	−0.146586	−	0.190544i
$97$	4.24461	−	4.24461i	0.430975	−	0.430975i	−0.457985	−	0.888960i	$-0.651429\pi$
$97$	4.24461	−	4.24461i	0.430975	−	0.430975i	0.888960	+	0.457985i	$0.151429\pi$
$98$	−8.52825	−	5.02683i	−0.861483	−	0.507786i
$99$	−2.36841			−0.238034
$100$	6.77569	−	7.35460i	0.677569	−	0.735460i
$101$	−0.859895	−	1.48938i	−0.0855628	−	0.148199i	0.820068	−	0.572266i	$-0.193935\pi$
$101$	−0.859895	−	1.48938i	−0.0855628	−	0.148199i	−0.905631	+	0.424067i	$0.860602\pi$
$102$	−3.01574	−	0.0782209i	−0.298603	−	0.00774502i
$103$	−4.06549	−	15.1726i	−0.400584	−	1.49500i	−0.812057	−	0.583579i	$-0.801652\pi$
$103$	−4.06549	−	15.1726i	−0.400584	−	1.49500i	0.411472	−	0.911422i	$-0.365015\pi$
$104$	3.53719	−	3.02560i	0.346850	−	0.296685i
$105$	−1.60454	−	1.86918i	−0.156587	−	0.182413i
$106$	4.38529	+	18.2461i	0.425937	+	1.77222i
$107$	13.4365	−	3.60029i	1.29895	−	0.348053i	0.457899	−	0.889004i	$-0.348602\pi$
$107$	13.4365	−	3.60029i	1.29895	−	0.348053i	0.841054	+	0.540951i	$0.181936\pi$
$108$	4.74579	−	1.01121i	0.456663	−	0.0973038i
$109$	−9.23440	+	5.33148i	−0.884495	+	0.510664i	−0.872138	−	0.489260i	$-0.837267\pi$
$109$	−9.23440	+	5.33148i	−0.884495	+	0.510664i	−0.0123573	+	0.999924i	$0.503934\pi$
$110$	1.56964	−	2.13469i	0.149659	−	0.203535i
$111$			0.306675i			0.0291083i
$112$	−1.00670	+	10.5350i	−0.0951241	+	0.995465i
$113$	−5.62032	−	5.62032i	−0.528715	−	0.528715i	0.391474	−	0.920189i	$-0.371965\pi$
$113$	−5.62032	−	5.62032i	−0.528715	−	0.528715i	−0.920189	+	0.391474i	$0.871965\pi$
$114$	0.975040	−	3.29468i	0.0913209	−	0.308575i
$115$	−1.36665	−	7.62696i	−0.127440	−	0.711217i
$116$	8.39229	+	5.44409i	0.779204	+	0.505472i
$117$	1.20395	+	4.49319i	0.111305	+	0.415395i
$118$	10.7800	+	6.60233i	0.992381	+	0.607793i
$119$	9.66492	+	9.50278i	0.885982	+	0.871119i
$120$	−1.08366	+	2.40021i	−0.0989242	+	0.219108i
$121$	−5.14897	+	8.91827i	−0.468088	+	0.810752i
$122$	−0.0674252	+	2.59952i	−0.00610439	+	0.235350i
$123$	−0.0385468	−	0.0103286i	−0.00347565	−	0.000931297i
$124$	−0.841950	+	16.2194i	−0.0756093	+	1.45655i
$125$	−10.8231	−	2.80378i	−0.968045	−	0.250778i
$126$	−9.06549	−	5.44734i	−0.807618	−	0.485288i
$127$	4.54633	+	4.54633i	0.403421	+	0.403421i	0.879437	−	0.476016i	$-0.157919\pi$
$127$	4.54633	+	4.54633i	0.403421	+	0.403421i	−0.476016	+	0.879437i	$0.657919\pi$
$128$	10.6582	−	3.79512i	0.942060	−	0.335444i
$129$	−2.48855	+	1.43677i	−0.219105	+	0.126500i
$130$	−4.84770	−	1.89267i	−0.425172	−	0.165998i
$131$	11.9545	+	6.90194i	1.04447	+	0.603025i	0.921096	−	0.389335i	$-0.127295\pi$
$131$	11.9545	+	6.90194i	1.04447	+	0.603025i	0.123374	+	0.992360i	$0.460629\pi$
$132$	−0.215298	+	0.663741i	−0.0187393	+	0.0577713i
$133$	−13.3035	+	7.83154i	−1.15356	+	0.679081i
$134$	0.176386	+	0.733896i	0.0152374	+	0.0633990i
$135$	−3.49867	−	4.14616i	−0.301117	−	0.356844i
$136$	4.82667	−	13.6624i	0.413884	−	1.17154i
$137$	−13.8922	−	3.72240i	−1.18689	−	0.318026i	−0.389235	−	0.921139i	$-0.627260\pi$
$137$	−13.8922	−	3.72240i	−1.18689	−	0.318026i	−0.797656	+	0.603112i	$0.793927\pi$
$138$	0.974111	+	1.79303i	0.0829218	+	0.152633i
$139$	1.45615			0.123509			0.0617544	−	0.998091i	$-0.480330\pi$
$139$	1.45615			0.123509			0.0617544	+	0.998091i	$0.480330\pi$
$140$	10.9179	−	4.56075i	0.922727	−	0.385454i
$141$	2.27813			0.191853
$142$	9.21492	+	16.9617i	0.773299	+	1.42340i
$143$	−1.33192	−	0.356886i	−0.111380	−	0.0298443i
$144$	−1.17068	+	11.2457i	−0.0975569	+	0.937142i
$145$	0.943879	−	11.1443i	0.0783849	−	0.925482i
$146$	1.98012	+	8.23879i	0.163876	+	0.681847i
$147$	−0.801913	−	2.80227i	−0.0661407	−	0.231127i
$148$	−1.40114	−	0.454489i	−0.115173	−	0.0373588i
$149$	−10.0147	−	5.78197i	−0.820433	−	0.473677i	0.0301327	−	0.999546i	$-0.490407\pi$
$149$	−10.0147	−	5.78197i	−0.820433	−	0.473677i	−0.850566	+	0.525869i	$0.823740\pi$
$150$	2.93776	−	0.196766i	0.239867	−	0.0160659i
$151$	4.17078	−	2.40800i	0.339414	−	0.195961i	−0.320599	−	0.947215i	$-0.603884\pi$
$151$	4.17078	−	2.40800i	0.339414	−	0.195961i	0.660013	+	0.751254i	$0.270551\pi$
$152$	13.6078	+	9.33746i	1.10374	+	0.757368i
$153$	10.2394	+	10.2394i	0.827805	+	0.827805i
$154$	2.74206	−	1.51988i	0.220962	−	0.122475i
$155$	16.4356	−	7.71960i	1.32014	−	0.620053i
$156$	1.36865	+	0.0710467i	0.109580	+	0.00568829i
$157$	4.12149	+	1.10435i	0.328931	+	0.0881368i	0.419505	−	0.907753i	$-0.362204\pi$
$157$	4.12149	+	1.10435i	0.328931	+	0.0881368i	−0.0905743	+	0.995890i	$0.528870\pi$
$158$	0.389220	−	15.0061i	0.0309647	−	1.19382i
$159$	−2.76263	+	4.78501i	−0.219091	+	0.379476i
$160$	−9.36012	−	8.50812i	−0.739982	−	0.672626i
$161$	2.29788	−	8.87543i	0.181098	−	0.699482i
$162$	−9.00835	−	5.51725i	−0.707763	−	0.433476i
$163$	2.10452	+	7.85417i	0.164839	+	0.615186i	0.998061	+	0.0622476i	$0.0198268\pi$
$163$	2.10452	+	7.85417i	0.164839	+	0.615186i	−0.833222	+	0.552938i	$0.813506\pi$
$164$	0.104315	−	0.160806i	0.00814566	−	0.0125569i
$165$	0.767918	−	0.137600i	0.0597824	−	0.0107122i
$166$	2.47925	−	8.37743i	0.192427	−	0.650215i
$167$	−5.50649	−	5.50649i	−0.426105	−	0.426105i	0.461194	−	0.887299i	$-0.347421\pi$
$167$	−5.50649	−	5.50649i	−0.426105	−	0.426105i	−0.887299	+	0.461194i	$0.847421\pi$
$168$	−2.35070	+	2.04540i	−0.181360	+	0.157806i
$169$		−	10.2918i		−	0.791674i
$170$	−16.0150	+	2.44293i	−1.22829	+	0.187364i
$171$	−14.2832	+	8.24639i	−1.09226	+	0.630617i
$172$	−2.87630	−	13.4990i	−0.219316	−	1.02929i
$173$	3.02430	−	0.810358i	0.229933	−	0.0616104i	−0.142013	−	0.989865i	$-0.545357\pi$
$173$	3.02430	−	0.810358i	0.229933	−	0.0616104i	0.371946	+	0.928254i	$0.378691\pi$
$174$	0.688290	+	2.86380i	0.0521791	+	0.217104i
$175$	−10.2519	−	8.36055i	−0.774970	−	0.631998i
$176$	−2.71344	−	1.96732i	−0.204533	−	0.148292i
$177$	0.963323	+	3.59517i	0.0724078	+	0.270230i
$178$	4.08885	+	0.106055i	0.306472	+	0.00794914i
$179$	−8.05255	−	13.9474i	−0.601876	−	1.04248i	−0.992537	−	0.121945i	$-0.961087\pi$
$179$	−8.05255	−	13.9474i	−0.601876	−	1.04248i	0.390661	−	0.920535i	$-0.372246\pi$
$180$	11.7050	−	4.77369i	0.872440	−	0.355810i
$181$	−3.83256			−0.284872			−0.142436	−	0.989804i	$-0.545493\pi$
$181$	−3.83256			−0.284872			−0.142436	+	0.989804i	$0.545493\pi$
$182$	−4.27731	−	4.42945i	−0.317055	−	0.328333i
$183$	−0.541393	+	0.541393i	−0.0400209	+	0.0400209i
$184$	−9.63562	+	1.79328i	−0.710348	+	0.132202i
$185$	0.290471	+	1.62105i	0.0213558	+	0.119182i
$186$	−3.46791	+	3.29256i	−0.254279	+	0.241422i
$187$	−4.14624	+	1.11098i	−0.303203	+	0.0812431i
$188$	−3.37616	+	10.4083i	−0.246232	+	0.759106i
$189$	−1.71375	−	6.18602i	−0.124657	−	0.449967i
$190$	2.03337	−	18.3389i	0.147516	−	1.33044i
$191$	2.42531	+	1.40025i	0.175489	+	0.101319i	0.585172	−	0.810909i	$-0.301027\pi$
$191$	2.42531	+	1.40025i	0.175489	+	0.101319i	−0.409682	+	0.912228i	$0.634360\pi$
$192$	3.04516	+	1.35036i	0.219766	+	0.0974541i
$193$	−2.23839	+	8.35378i	−0.161123	+	0.601318i	0.837380	+	0.546621i	$0.184086\pi$
$193$	−2.23839	+	8.35378i	−0.161123	+	0.601318i	−0.998503	+	0.0546973i	$0.982581\pi$
$194$	−2.40905	+	8.14024i	−0.172960	+	0.584435i
$195$	−0.651407	−	1.38690i	−0.0466482	−	0.0993178i
$196$	13.9915	+	0.489142i	0.999389	+	0.0349387i
$197$	−4.90073	+	4.90073i	−0.349162	+	0.349162i	−0.859798	−	0.510635i	$-0.829410\pi$
$197$	−4.90073	+	4.90073i	−0.349162	+	0.349162i	0.510635	+	0.859798i	$0.329410\pi$
$198$	2.94314	−	1.59894i	0.209160	−	0.113632i
$199$	6.19859	+	10.7363i	0.439406	+	0.761074i	0.997644	−	0.0686071i	$-0.0218555\pi$
$199$	6.19859	+	10.7363i	0.439406	+	0.761074i	−0.558237	+	0.829681i	$0.688522\pi$
$200$	−3.45474	+	13.7137i	−0.244287	+	0.969703i
$201$	−0.111119	+	0.192463i	−0.00783771	+	0.0135753i
$202$	2.07406	+	1.27028i	0.145931	+	0.0893766i
$203$	6.51947	−	11.5159i	0.457577	−	0.808260i
$204$	3.80037	−	1.93876i	0.266079	−	0.135740i
$205$	−0.213538	−	0.0180858i	−0.0149141	−	0.00126317i
$206$	15.2953	+	16.1098i	1.06567	+	1.12243i
$207$	2.53508	−	9.46105i	0.176200	−	0.657589i
$208$	−2.35293	+	6.14782i	−0.163146	+	0.426274i
$209$		−	4.88896i		−	0.338176i
$210$	3.25582	+	1.23952i	0.224673	+	0.0855352i
$211$			0.877438i			0.0604053i	0.999544	+	0.0302027i	$0.00961527\pi$
$211$			0.877438i			0.0604053i	−0.999544	+	0.0302027i	$0.990385\pi$
$212$	−17.7676	−	19.7133i	−1.22029	−	1.35391i
$213$	−1.47101	+	5.48987i	−0.100792	+	0.376160i
$214$	−14.2665	+	13.5451i	−0.975235	+	0.925924i
$215$	−11.7934	+	9.95166i	−0.804302	+	0.678698i
$216$	−5.21475	+	4.46054i	−0.354819	+	0.303501i
$217$	21.4844	−	0.181737i	1.45846	−	0.0123371i
$218$	7.87594	−	12.8595i	0.533426	−	0.870957i
$219$	−1.24743	+	2.16061i	−0.0842934	+	0.146000i
$220$	−0.509376	+	3.71240i	−0.0343421	+	0.250290i
$221$	4.21537	+	7.30123i	0.283556	+	0.491134i
$222$	−0.207040	−	0.381095i	−0.0138956	−	0.0255774i
$223$	−12.6059	+	12.6059i	−0.844153	+	0.844153i	−0.989396	−	0.145243i	$-0.953604\pi$
$223$	−12.6059	+	12.6059i	−0.844153	+	0.844153i	0.145243	+	0.989396i	$0.453604\pi$
$224$	−5.86133	−	13.7712i	−0.391627	−	0.920124i
$225$	−10.8768	−	9.02441i	−0.725118	−	0.601628i
$226$	10.7785	+	3.18984i	0.716978	+	0.212185i
$227$	−2.71787	+	10.1432i	−0.180392	+	0.673230i	0.815179	+	0.579210i	$0.196639\pi$
$227$	−2.71787	+	10.1432i	−0.180392	+	0.673230i	−0.995570	+	0.0940208i	$0.970028\pi$
$228$	1.01263	+	4.75246i	0.0670632	+	0.314739i
$229$	23.5981	+	13.6244i	1.55941	+	0.900324i	0.997314	+	0.0732513i	$0.0233375\pi$
$229$	23.5981	+	13.6244i	1.55941	+	0.900324i	0.562094	+	0.827073i	$0.309996\pi$
$230$	6.84734	+	8.55513i	0.451500	+	0.564109i
$231$	0.893620	+	0.231361i	0.0587959	+	0.0152225i
$232$	−14.1042	−	1.09946i	−0.925986	−	0.0721830i
$233$	12.6865	−	3.39933i	0.831118	−	0.222697i	0.181917	−	0.983314i	$-0.441770\pi$
$233$	12.6865	−	3.39933i	0.831118	−	0.222697i	0.649201	+	0.760617i	$0.275103\pi$
$234$	−4.52951	−	4.77074i	−0.296104	−	0.311873i
$235$	12.0420	−	2.15776i	0.785531	−	0.140756i
$236$	−17.8533	−	0.926765i	−1.16215	−	0.0603272i
$237$	3.12526	−	3.12526i	0.203007	−	0.203007i
$238$	−18.4257	−	5.28389i	−1.19436	−	0.342503i
$239$	−10.7078			−0.692631			−0.346315	−	0.938118i	$-0.612567\pi$
$239$	−10.7078			−0.692631			−0.346315	+	0.938118i	$0.612567\pi$
$240$	−0.273781	−	3.71425i	−0.0176725	−	0.239754i
$241$	−6.28701	−	10.8894i	−0.404982	−	0.701449i	0.589337	−	0.807887i	$-0.299389\pi$
$241$	−6.28701	−	10.8894i	−0.404982	−	0.701449i	−0.994319	+	0.106438i	$0.966056\pi$
$242$	0.377614	−	14.5586i	0.0242739	−	0.935861i
$243$	−2.68881	−	10.0348i	−0.172487	−	0.643732i
$244$	−1.67118	−	3.27586i	−0.106987	−	0.209716i
$245$	−6.89304	−	14.0530i	−0.440380	−	0.897812i
$246$	0.0548738	−	0.0131884i	0.00349863	−	0.000840864i
$247$	−9.27501	+	2.48523i	−0.590155	+	0.158132i
$248$	−9.90367	−	20.7237i	−0.628884	−	1.31596i
$249$	2.22772	−	1.28618i	0.141176	−	0.0815080i
$250$	15.3423	−	3.82262i	0.970335	−	0.241764i
$251$		−	14.8357i		−	0.936420i	−0.883617	−	0.468210i	$-0.844899\pi$
$251$		−	14.8357i		−	0.936420i	0.883617	−	0.468210i	$-0.155101\pi$
$252$	14.9430	+	0.649002i	0.941318	+	0.0408833i
$253$	2.05307	+	2.05307i	0.129075	+	0.129075i
$254$	−8.71886	−	2.58029i	−0.547070	−	0.161902i
$255$	−3.91485	−	2.72506i	−0.245157	−	0.170650i
$256$	−10.6825	+	11.9116i	−0.667654	+	0.744472i
$257$	3.93031	+	14.6681i	0.245166	+	0.914972i	0.973300	+	0.229537i	$0.0737212\pi$
$257$	3.93031	+	14.6681i	0.245166	+	0.914972i	−0.728134	+	0.685435i	$0.759612\pi$
$258$	2.12246	−	3.46547i	0.132139	−	0.215751i
$259$	−0.488397	+	1.88641i	−0.0303475	+	0.117216i
$260$	7.30185	−	0.920788i	0.452842	−	0.0571049i
$261$	7.06897	−	12.2438i	0.437558	−	0.757873i
$262$	−19.5151	−	0.506173i	−1.20564	−	0.0312715i
$263$	−11.3208	−	3.03340i	−0.698072	−	0.187048i	−0.107705	−	0.994183i	$-0.534350\pi$
$263$	−11.3208	−	3.03340i	−0.698072	−	0.187048i	−0.590367	+	0.807135i	$0.701017\pi$
$264$	−0.180556	−	0.970160i	−0.0111124	−	0.0597092i
$265$	−10.0708	+	27.9098i	−0.618645	+	1.71448i
$266$	11.2446	−	18.7133i	0.689451	−	1.14739i
$267$	0.851570	+	0.851570i	0.0521153	+	0.0521153i
$268$	−0.714651	−	0.792909i	−0.0436543	−	0.0484346i
$269$	17.9195	−	10.3458i	1.09257	−	0.630797i	0.158313	−	0.987389i	$-0.449395\pi$
$269$	17.9195	−	10.3458i	1.09257	−	0.630797i	0.934260	+	0.356592i	$0.116061\pi$
$270$	7.14680	+	2.79030i	0.434941	+	0.169812i
$271$	18.2735	+	10.5502i	1.11003	+	0.640878i	0.938838	−	0.344359i	$-0.111904\pi$
$271$	18.2735	+	10.5502i	1.11003	+	0.640878i	0.171195	+	0.985237i	$0.445237\pi$
$272$	3.22573	+	20.2364i	0.195588	+	1.22701i
$273$	−0.0153356	−	1.81293i	−0.000928151	−	0.109723i
$274$	19.7764	−	4.75309i	1.19474	−	0.287145i
$275$	3.92881	−	1.45469i	0.236916	−	0.0877209i
$276$	−2.42099	−	1.57050i	−0.145727	−	0.0945331i
$277$	3.15920	+	0.846505i	0.189818	+	0.0508616i	0.352476	−	0.935821i	$-0.385340\pi$
$277$	3.15920	+	0.846505i	0.189818	+	0.0508616i	−0.162658	+	0.986683i	$0.552007\pi$
$278$	−1.80951	+	0.983064i	−0.108527	+	0.0589603i
$279$	22.9539			1.37421
$280$	−10.4882	+	13.0383i	−0.626792	+	0.779186i
$281$	2.60091			0.155157			0.0775787	−	0.996986i	$-0.475281\pi$
$281$	2.60091			0.155157			0.0775787	+	0.996986i	$0.475281\pi$
$282$	−2.83095	+	1.53799i	−0.168581	+	0.0915861i
$283$	26.7711	+	7.17330i	1.59138	+	0.426409i	0.942424	−	0.334419i	$-0.108540\pi$
$283$	26.7711	+	7.17330i	1.59138	+	0.426409i	0.648954	+	0.760828i	$0.275207\pi$
$284$	−22.9022	−	14.8567i	−1.35899	−	0.881582i
$285$	4.15199	−	3.50359i	0.245942	−	0.207535i
$286$	1.89607	−	0.455703i	0.112117	−	0.0269463i
$287$	−0.220659	−	0.124921i	−0.0130251	−	0.00737384i
$288$	−6.13735	−	14.7650i	−0.361647	−	0.870036i
$289$	8.00623	+	4.62240i	0.470955	+	0.271906i
$290$	6.35072	+	14.4859i	0.372927	+	0.850639i
$291$	−2.16465	+	1.24976i	−0.126894	+	0.0732622i
$292$	−8.02274	−	8.90127i	−0.469495	−	0.520907i
$293$	11.9223	+	11.9223i	0.696506	+	0.696506i	0.963655	−	0.267149i	$-0.0860815\pi$
$293$	11.9223	+	11.9223i	0.696506	+	0.696506i	−0.267149	+	0.963655i	$0.586082\pi$
$294$	2.88836	+	2.94090i	0.168452	+	0.171517i
$295$	8.49725	+	18.0913i	0.494729	+	1.05332i
$296$	2.04798	−	0.381149i	0.119037	−	0.0221538i
$297$	1.96360	+	0.526145i	0.113940	+	0.0305300i
$298$	16.3484	+	0.424037i	0.947036	+	0.0245638i
$299$	2.85130	−	4.93859i	0.164895	−	0.285606i
$300$	−3.51782	+	2.22783i	−0.203101	+	0.128624i
$301$	−17.5956	+	4.87462i	−1.01419	+	0.280968i
$302$	−3.55722	+	5.80810i	−0.204695	+	0.334218i
$303$	0.185342	+	0.691707i	0.0106476	+	0.0397376i
$304$	−23.2138	−	2.41657i	−1.33140	−	0.138600i
$305$	−2.34897	+	3.37454i	−0.134501	+	0.193226i
$306$	−19.6369	−	5.81141i	−1.12257	−	0.332216i
$307$	13.0364	+	13.0364i	0.744028	+	0.744028i	0.973350	−	0.229323i	$-0.0736511\pi$
$307$	13.0364	+	13.0364i	0.744028	+	0.744028i	−0.229323	+	0.973350i	$0.573651\pi$
$308$	−2.38138	+	3.73991i	−0.135692	+	0.213101i
$309$			6.54063i			0.372083i
$310$	−15.2124	+	20.6888i	−0.864009	+	1.17505i
$311$	10.1447	−	5.85707i	0.575255	−	0.332124i	−0.183990	−	0.982928i	$-0.558901\pi$
$311$	10.1447	−	5.85707i	0.575255	−	0.332124i	0.759246	+	0.650804i	$0.225568\pi$
$312$	−1.74874	+	0.835706i	−0.0990031	+	0.0473126i
$313$	−18.4473	+	4.94295i	−1.04270	+	0.279392i	−0.739234	−	0.673449i	$-0.764812\pi$
$313$	−18.4473	+	4.94295i	−1.04270	+	0.279392i	−0.303471	+	0.952841i	$0.598145\pi$
$314$	−5.86721	+	1.41013i	−0.331106	+	0.0795783i
$315$	−7.23699	−	15.0754i	−0.407758	−	0.849403i
$316$	9.64711	+	18.9103i	0.542693	+	1.06379i
$317$	−0.747448	−	2.78952i	−0.0419809	−	0.156675i	0.941754	−	0.336304i	$-0.109177\pi$
$317$	−0.747448	−	2.78952i	−0.0419809	−	0.156675i	−0.983734	+	0.179629i	$0.942510\pi$
$318$	0.202605	−	7.81126i	0.0113615	−	0.438034i
$319$	2.09546	+	3.62944i	0.117323	+	0.203209i
$320$	17.3755	+	4.25363i	0.971318	+	0.237785i
$321$	−5.79221			−0.323290
$322$	3.13642	+	12.5805i	0.174786	+	0.701086i
$323$	−21.1365	+	21.1365i	−1.17607	+	1.17607i
$324$	14.9191	+	0.774453i	0.828841	+	0.0430252i
$325$	−4.75689	−	6.71402i	−0.263865	−	0.372427i
$326$	−7.91767	−	8.33933i	−0.438519	−	0.461873i
$327$	4.28869	−	1.14915i	0.237165	−	0.0635482i
$328$	−0.0210669	+	0.270253i	−0.00116323	+	0.0149222i
$329$	14.0131	+	3.62805i	0.772569	+	0.200021i
$330$	−0.861371	+	0.689423i	−0.0474169	+	0.0379515i
$331$	−30.1984	−	17.4351i	−1.65986	−	0.958318i	−0.972780	−	0.231732i	$-0.925561\pi$
$331$	−30.1984	−	17.4351i	−1.65986	−	0.958318i	−0.687075	−	0.726586i	$-0.741106\pi$
$332$	2.57483	+	12.0841i	0.141312	+	0.663203i
$333$	−0.538813	+	2.01088i	−0.0295268	+	0.110195i
$334$	10.5602	+	3.12523i	0.577831	+	0.171005i
$335$	−0.405069	+	1.12259i	−0.0221313	+	0.0613336i
$336$	1.54026	−	4.12874i	0.0840281	−	0.225241i
$337$	15.8847	−	15.8847i	0.865292	−	0.865292i	−0.126655	−	0.991947i	$-0.540424\pi$
$337$	15.8847	−	15.8847i	0.865292	−	0.865292i	0.991947	+	0.126655i	$0.0404240\pi$
$338$	6.94810	+	12.7892i	0.377927	+	0.695642i
$339$	1.65481	+	2.86622i	0.0898771	+	0.155672i
$340$	18.2521	−	13.8477i	0.989857	−	0.750996i
$341$	−3.40211	+	5.89263i	−0.184235	+	0.319104i
$342$	12.1820	−	19.8903i	0.658726	−	1.07554i
$343$	−0.469928	−	18.5143i	−0.0253737	−	0.999678i
$344$	12.6876	+	14.8329i	0.684071	+	0.799738i
$345$	−0.272288	+	3.21488i	−0.0146595	+	0.173083i
$346$	−3.21111	+	3.04875i	−0.172630	+	0.163902i
$347$	−6.21524	+	23.1956i	−0.333651	+	1.24520i	0.571673	+	0.820482i	$0.306295\pi$
$347$	−6.21524	+	23.1956i	−0.333651	+	1.24520i	−0.905324	+	0.424722i	$0.860372\pi$
$348$	−2.78870	−	3.09408i	−0.149490	−	0.165860i
$349$		−	20.0084i		−	1.07102i	−0.844528	−	0.535512i	$-0.820119\pi$
$349$		−	20.0084i		−	1.07102i	0.844528	−	0.535512i	$-0.179881\pi$
$350$	18.3840	+	3.46821i	0.982666	+	0.185384i
$351$		−	3.99267i		−	0.213113i
$352$	4.70006	+	0.612842i	0.250514	+	0.0326646i
$353$	−6.06381	+	22.6305i	−0.322744	+	1.20450i	0.593816	+	0.804601i	$0.297621\pi$
$353$	−6.06381	+	22.6305i	−0.322744	+	1.20450i	−0.916560	+	0.399897i	$0.869046\pi$
$354$	−3.62424	−	3.81725i	−0.192626	−	0.202885i
$355$	−2.57580	+	30.4122i	−0.136709	+	1.61411i
$356$	−5.15268	+	2.62865i	−0.273092	+	0.139318i
$357$	−2.86316	−	4.86365i	−0.151534	−	0.257412i
$358$	19.4227	+	11.8956i	1.02652	+	0.628704i
$359$	13.4523	−	23.3000i	0.709984	−	1.22973i	−0.254878	−	0.966973i	$-0.582035\pi$
$359$	13.4523	−	23.3000i	0.709984	−	1.22973i	0.964862	−	0.262756i	$-0.0846313\pi$
$360$	−11.3227	+	13.8343i	−0.596756	+	0.729132i
$361$	−7.52251	−	13.0294i	−0.395922	−	0.685756i
$362$	4.76260	−	2.58741i	0.250317	−	0.135991i
$363$	3.03206	−	3.03206i	0.159142	−	0.159142i
$364$	8.30565	+	2.61667i	0.435334	+	0.137151i
$365$	−4.54734	+	12.6023i	−0.238019	+	0.659634i
$366$	0.307270	−	1.03827i	0.0160613	−	0.0542714i
$367$	7.09214	−	26.4682i	0.370207	−	1.38163i	−0.490017	−	0.871713i	$-0.663009\pi$
$367$	7.09214	−	26.4682i	0.370207	−	1.38163i	0.860223	−	0.509917i	$-0.170324\pi$
$368$	10.7632	−	8.73358i	0.561071	−	0.455270i
$369$	−0.234606	−	0.135450i	−0.0122131	−	0.00705123i
$370$	−1.45535	−	1.81833i	−0.0756602	−	0.0945305i
$371$	−24.6138	+	25.0337i	−1.27788	+	1.29969i
$372$	2.08661	−	6.43278i	0.108186	−	0.333524i
$373$	−21.1806	+	5.67531i	−1.09669	+	0.293857i	−0.761415	−	0.648265i	$-0.775495\pi$
$373$	−21.1806	+	5.67531i	−1.09669	+	0.293857i	−0.335272	+	0.942121i	$0.608828\pi$
$374$	4.40236	−	4.17976i	0.227641	−	0.216130i
$375$	4.05092	+	2.29410i	0.209189	+	0.118467i
$376$	−2.83135	−	15.2134i	−0.146016	−	0.784570i
$377$	5.82033	−	5.82033i	0.299762	−	0.299762i
$378$	6.30589	+	6.53019i	0.324340	+	0.335877i
$379$	−20.4602			−1.05097			−0.525484	−	0.850803i	$-0.676116\pi$
$379$	−20.4602			−1.05097			−0.525484	+	0.850803i	$0.676116\pi$
$380$	9.85403	+	24.1619i	0.505501	+	1.23948i
$381$	−1.33859	−	2.31851i	−0.0685783	−	0.118781i
$382$	−3.95918	−	0.102691i	−0.202569	−	0.00525415i
$383$	−1.88076	−	7.01910i	−0.0961024	−	0.358659i	0.901082	−	0.433649i	$-0.142774\pi$
$383$	−1.88076	−	7.01910i	−0.0961024	−	0.358659i	−0.997184	+	0.0749899i	$0.976108\pi$
$384$	−4.69577	+	0.377776i	−0.239630	+	0.0192783i
$385$	4.94273	+	0.376550i	0.251905	+	0.0191908i
$386$	−2.85817	−	11.8921i	−0.145477	−	0.605294i
$387$	−18.8418	+	5.04866i	−0.957785	+	0.256638i
$388$	−2.50193	−	11.7420i	−0.127016	−	0.596109i
$389$	4.81003	−	2.77707i	0.243878	−	0.140803i	−0.373080	−	0.927799i	$-0.621698\pi$
$389$	4.81003	−	2.77707i	0.243878	−	0.140803i	0.616958	+	0.786996i	$0.288365\pi$
$390$	1.74579	+	1.28368i	0.0884018	+	0.0650016i
$391$		−	17.7521i		−	0.897764i
$392$	−17.7169	+	8.83797i	−0.894841	+	0.446385i
$393$	−4.06433	−	4.06433i	−0.205018	−	0.205018i
$394$	2.78143	−	9.39852i	0.140126	−	0.473491i
$395$	13.5597	−	19.4799i	0.682262	−	0.980142i
$396$	−2.57788	+	3.97391i	−0.129543	+	0.199696i
$397$	−7.78865	−	29.0677i	−0.390901	−	1.45886i	−0.828650	−	0.559766i	$-0.810891\pi$
$397$	−7.78865	−	29.0677i	−0.390901	−	1.45886i	0.437749	−	0.899097i	$-0.355776\pi$
$398$	−14.9510	−	9.15687i	−0.749425	−	0.458992i
$399$	6.19472	−	1.71616i	0.310124	−	0.0859155i
$400$	−4.96518	−	19.3739i	−0.248259	−	0.968694i
$401$	2.31962	−	4.01770i	0.115836	−	0.200634i	−0.802277	−	0.596951i	$-0.796379\pi$
$401$	2.31962	−	4.01770i	0.115836	−	0.200634i	0.918114	+	0.396317i	$0.129712\pi$
$402$	0.00814920	−	0.314185i	0.000406445	−	0.0156701i
$403$	12.9085	+	3.45883i	0.643020	+	0.172297i
$404$	−3.43496	−	0.178309i	−0.170895	−	0.00887118i
$405$	−7.10074	−	15.1180i	−0.352839	−	0.751222i
$406$	−0.326984	+	18.7119i	−0.0162279	+	0.928654i
$407$	−0.436364	−	0.436364i	−0.0216298	−	0.0216298i
$408$	−3.41371	+	4.97491i	−0.169004	+	0.246295i
$409$	−30.0868	+	17.3706i	−1.48770	+	0.858922i	−0.999901	−	0.0140366i	$-0.995532\pi$
$409$	−30.0868	+	17.3706i	−1.48770	+	0.858922i	−0.487795	+	0.872958i	$0.662199\pi$
$410$	0.277566	−	0.121687i	0.0137080	−	0.00600970i
$411$	5.18634	+	2.99434i	0.255823	+	0.147700i
$412$	−29.8829	−	9.69314i	−1.47222	−	0.477547i
$413$	0.200044	+	23.6486i	0.00984353	+	1.16367i
$414$	3.23702	+	13.4684i	0.159091	+	0.661936i
$415$	10.5573	−	8.90861i	0.518238	−	0.437307i
$416$	−1.22657	−	9.22818i	−0.0601374	−	0.452449i
$417$	−0.585669	−	0.156930i	−0.0286803	−	0.00768487i
$418$	3.30060	+	6.07535i	0.161437	+	0.297155i
$419$	−28.1311			−1.37429			−0.687147	−	0.726518i	$-0.741137\pi$
$419$	−28.1311			−1.37429			−0.687147	+	0.726518i	$0.741137\pi$
$420$	−4.88272	+	0.657733i	−0.238253	+	0.0320941i
$421$	3.94616			0.192324			0.0961621	−	0.995366i	$-0.469343\pi$
$421$	3.94616			0.192324			0.0961621	+	0.995366i	$0.469343\pi$
$422$	−0.592370	−	1.09036i	−0.0288361	−	0.0530781i
$423$	14.9378	+	4.00256i	0.726299	+	0.194611i
$424$	35.3879	+	12.5019i	1.71859	+	0.607145i
$425$	−23.2746	−	10.6964i	−1.12898	−	0.518853i
$426$	−1.87831	−	7.81518i	−0.0910044	−	0.378647i
$427$	−4.19240	+	2.46800i	−0.202884	+	0.119435i
$428$	8.58400	−	26.4635i	0.414923	−	1.27916i
$429$	0.497241	+	0.287082i	0.0240070	+	0.0138605i
$430$	7.93677	−	20.3285i	0.382745	−	0.980326i
$431$	12.1350	−	7.00616i	0.584523	−	0.337475i	−0.178406	−	0.983957i	$-0.557094\pi$
$431$	12.1350	−	7.00616i	0.584523	−	0.337475i	0.762929	+	0.646482i	$0.223761\pi$
$432$	3.46884	−	9.06351i	0.166894	−	0.436069i
$433$	−2.21951	−	2.21951i	−0.106663	−	0.106663i	0.651761	−	0.758424i	$-0.274030\pi$
$433$	−2.21951	−	2.21951i	−0.106663	−	0.106663i	−0.758424	+	0.651761i	$0.774030\pi$
$434$	−26.5753	+	14.7302i	−1.27565	+	0.707073i
$435$	−1.58066	+	4.38056i	−0.0757866	+	0.210032i
$436$	−1.10554	+	21.2973i	−0.0529458	+	1.01995i
$437$	19.5299	+	5.23301i	0.934240	+	0.250329i
$438$	0.0914837	−	3.52707i	0.00437126	−	0.168530i
$439$	12.5163	−	21.6788i	0.597369	−	1.03467i	−0.395839	−	0.918320i	$-0.629546\pi$
$439$	12.5163	−	21.6788i	0.597369	−	1.03467i	0.993208	−	0.116354i	$-0.0371206\pi$
$440$	−1.87330	−	4.95716i	−0.0893061	−	0.236323i
$441$	−0.334721	−	19.7835i	−0.0159391	−	0.942071i
$442$	−10.1675	−	6.22715i	−0.483617	−	0.296196i
$443$	−1.13949	−	4.25262i	−0.0541386	−	0.202048i	0.933559	−	0.358424i	$-0.116686\pi$
$443$	−1.13949	−	4.25262i	−0.0541386	−	0.202048i	−0.987698	+	0.156376i	$0.950019\pi$
$444$	0.514564	+	0.333799i	0.0244201	+	0.0158414i
$445$	5.30789	+	3.69474i	0.251618	+	0.175148i
$446$	7.15454	−	24.1753i	0.338777	−	1.14474i
$447$	3.40482	+	3.40482i	0.161042	+	0.161042i
$448$	16.5808	+	13.1559i	0.783368	+	0.621558i
$449$		−	24.2255i		−	1.14327i	−0.820507	−	0.571636i	$-0.806309\pi$
$449$		−	24.2255i		−	1.14327i	0.820507	−	0.571636i	$-0.193691\pi$
$450$	19.6087	+	3.87130i	0.924363	+	0.182495i
$451$	0.0695443	−	0.0401514i	0.00327471	−	0.00189066i
$452$	−15.5476	+	3.31282i	−0.731299	+	0.155822i
$453$	−1.93702	+	0.519023i	−0.0910091	+	0.0243858i
$454$	−3.47042	−	14.4395i	−0.162875	−	0.677681i
$455$	−1.79820	−	9.56844i	−0.0843009	−	0.448575i
$456$	−4.46681	−	5.22209i	−0.209178	−	0.244547i
$457$	−2.42378	−	9.04568i	−0.113380	−	0.423139i	0.885781	−	0.464104i	$-0.153624\pi$
$457$	−2.42378	−	9.04568i	−0.113380	−	0.423139i	−0.999161	+	0.0409647i	$0.986957\pi$
$458$	−38.5226	−	0.999182i	−1.80004	−	0.0466887i
$459$	−6.21457	−	10.7640i	−0.290071	−	0.502418i
$460$	−14.2846	−	6.00845i	−0.666025	−	0.280146i
$461$	12.3582			0.575580			0.287790	−	0.957693i	$-0.407079\pi$
$461$	12.3582			0.575580			0.287790	+	0.957693i	$0.407079\pi$
$462$	−1.26667	+	0.315789i	−0.0589307	+	0.0146919i
$463$	−29.6788	+	29.6788i	−1.37929	+	1.37929i	−0.533471	+	0.845818i	$0.679113\pi$
$463$	−29.6788	+	29.6788i	−1.37929	+	1.37929i	−0.845818	+	0.533471i	$0.820887\pi$
$464$	18.2691	−	8.15567i	0.848121	−	0.378617i
$465$	−7.44244	+	1.33358i	−0.345135	+	0.0618434i
$466$	−13.4701	+	12.7890i	−0.623992	+	0.592440i
$467$	−34.9600	+	9.36749i	−1.61775	+	0.433476i	−0.950341	−	0.311212i	$-0.899265\pi$
$467$	−34.9600	+	9.36749i	−1.61775	+	0.433476i	−0.667413	+	0.744687i	$0.732599\pi$
$468$	8.84947	+	2.87051i	0.409067	+	0.132689i
$469$	−0.990018	+	1.00691i	−0.0457148	+	0.0464948i
$470$	−13.5074	+	10.8111i	−0.623051	+	0.498677i
$471$	−1.53867	−	0.888349i	−0.0708980	−	0.0409330i
$472$	22.8114	−	10.9013i	1.04998	−	0.501774i
$473$	1.49657	−	5.58529i	0.0688125	−	0.256812i
$474$	−1.77375	+	5.99356i	−0.0814713	+	0.275293i
$475$	18.6285	−	22.4522i	0.854736	−	1.03018i
$476$	26.4643	−	5.87334i	1.21299	−	0.269204i
$477$	−26.5217	+	26.5217i	−1.21434	+	1.21434i
$478$	13.3062	−	7.22898i	0.608614	−	0.330646i
$479$	15.9325	+	27.5959i	0.727974	+	1.26089i	0.957738	+	0.287642i	$0.0928714\pi$
$479$	15.9325	+	27.5959i	0.727974	+	1.26089i	−0.229764	+	0.973246i	$0.573795\pi$
$480$	2.84776	+	4.43075i	0.129982	+	0.202235i
$481$	−0.606023	+	1.04966i	−0.0276323	+	0.0478605i
$482$	15.1643	+	9.28749i	0.690713	+	0.423034i
$483$	−1.88072	+	3.32209i	−0.0855759	+	0.151160i
$484$	9.35944	+	18.3464i	0.425429	+	0.833928i
$485$	−10.2584	+	8.65638i	−0.465810	+	0.393066i
$486$	10.1159	+	10.6547i	0.458867	+	0.483305i
$487$	2.58469	−	9.64618i	0.117123	−	0.437110i	−0.882314	−	0.470662i	$-0.844015\pi$
$487$	2.58469	−	9.64618i	0.117123	−	0.437110i	0.999437	+	0.0335518i	$0.0106819\pi$
$488$	4.28830	+	2.94257i	0.194122	+	0.133204i
$489$		−	3.38579i		−	0.153111i
$490$	18.0531	+	12.8096i	0.815556	+	0.578679i
$491$		−	16.3501i		−	0.737871i	−0.929455	−	0.368936i	$-0.879722\pi$
$491$		−	16.3501i		−	0.737871i	0.929455	−	0.368936i	$-0.120278\pi$
$492$	−0.0592862	+	0.0534349i	−0.00267283	+	0.00240903i
$493$	6.63188	−	24.7505i	0.298685	−	1.11471i
$494$	9.84794	−	9.35000i	0.443080	−	0.420676i
$495$	5.27703	+	0.446944i	0.237185	+	0.0200887i
$496$	26.2978	+	19.0666i	1.18081	+	0.856117i
$497$	−17.7913	+	31.4264i	−0.798050	+	1.40967i
$498$	−1.90000	+	3.10225i	−0.0851412	+	0.139015i
$499$	4.74809	−	8.22393i	0.212554	−	0.368154i	−0.739959	−	0.672652i	$-0.765155\pi$
$499$	4.74809	−	8.22393i	0.212554	−	0.368154i	0.952513	+	0.304498i	$0.0984886\pi$
$500$	−16.4847	+	15.1081i	−0.737220	+	0.675653i
$501$	1.62130	+	2.80817i	0.0724343	+	0.125460i
$502$	10.0158	+	18.4358i	0.447025	+	0.822831i
$503$	9.76866	−	9.76866i	0.435563	−	0.435563i	−0.454953	−	0.890516i	$-0.650344\pi$
$503$	9.76866	−	9.76866i	0.435563	−	0.435563i	0.890516	+	0.454953i	$0.150344\pi$
$504$	−19.0073	+	9.28169i	−0.846652	+	0.413440i
$505$	1.63486	+	3.48075i	0.0727504	+	0.154891i
$506$	−3.93733	−	1.16523i	−0.175036	−	0.0518007i
$507$	−1.10915	+	4.13939i	−0.0492589	+	0.183837i
$508$	12.5766	−	2.67977i	0.557998	−	0.118896i
$509$	−17.0075	−	9.81931i	−0.753846	−	0.435233i	0.0732360	−	0.997315i	$-0.476667\pi$
$509$	−17.0075	−	9.81931i	−0.753846	−	0.435233i	−0.827082	+	0.562082i	$0.810001\pi$
$510$	6.70458	+	0.743386i	0.296884	+	0.0329177i
$511$	−11.1140	+	11.3037i	−0.491656	+	0.500045i
$512$	5.23310	−	22.0140i	0.231273	−	0.972889i
$513$	13.6738	−	3.66389i	0.603714	−	0.161765i
$514$	−14.7867	−	15.5742i	−0.652214	−	0.686948i
$515$	6.19503	+	34.5731i	0.272986	+	1.52347i
$516$	−0.297929	+	5.73933i	−0.0131156	+	0.252660i
$517$	−3.24152	+	3.24152i	−0.142562	+	0.142562i
$518$	−0.666623	−	2.67390i	−0.0292897	−	0.117484i
$519$	−1.30372			−0.0572269
$520$	−8.45214	+	6.07381i	−0.370651	+	0.266354i
$521$	21.2862	+	36.8688i	0.932565	+	1.61525i	0.778920	+	0.627124i	$0.215768\pi$
$521$	21.2862	+	36.8688i	0.932565	+	1.61525i	0.153645	+	0.988126i	$0.450899\pi$
$522$	−0.518422	+	19.9873i	−0.0226907	+	0.874822i
$523$	−0.529969	−	1.97787i	−0.0231739	−	0.0864862i	0.953370	−	0.301803i	$-0.0975884\pi$
$523$	−0.529969	−	1.97787i	−0.0231739	−	0.0864862i	−0.976544	+	0.215316i	$0.930922\pi$
$524$	24.5925	−	12.5459i	1.07433	−	0.548069i
$525$	3.22233	+	4.46750i	0.140634	+	0.194978i
$526$	16.1159	−	3.87332i	0.702687	−	0.168885i
$527$	40.1842	−	10.7673i	1.75045	−	0.469032i
$528$	0.879339	+	1.08369i	0.0382683	+	0.0471616i
$529$	9.51967	−	5.49618i	0.413899	−	0.238964i
$530$	−6.32758	−	41.4815i	−0.274853	−	1.80184i
$531$			25.2662i			1.09646i
$532$	−1.33969	+	30.8458i	−0.0580831	+	1.33734i
$533$	−0.111524	−	0.111524i	−0.00483066	−	0.00483066i
$534$	−1.63312	−	0.483313i	−0.0706722	−	0.0209150i
$535$	−30.6171	+	5.48617i	−1.32369	+	0.237188i
$536$	1.42338	+	0.502852i	0.0614805	+	0.0217199i
$537$	1.73565	+	6.47754i	0.0748989	+	0.279527i
$538$	−15.2834	+	24.9542i	−0.658915	+	1.07585i
$539$	5.12835	+	2.84628i	0.220894	+	0.122598i
$540$	−10.7649	+	1.35749i	−0.463246	+	0.0584169i
$541$	−2.22119	+	3.84722i	−0.0954965	+	0.165405i	−0.909816	−	0.415012i	$-0.863777\pi$
$541$	−2.22119	+	3.84722i	−0.0954965	+	0.165405i	0.814319	+	0.580417i	$0.197111\pi$
$542$	−29.8304	−	0.773727i	−1.28133	−	0.0332344i
$543$	1.54147	+	0.413036i	0.0661509	+	0.0177251i
$544$	−17.6704	−	22.9694i	−0.757610	−	0.984804i
$545$	21.5812	−	10.1364i	0.924437	−	0.434196i
$546$	1.24299	+	2.24251i	0.0531950	+	0.0959707i
$547$	13.7530	+	13.7530i	0.588037	+	0.588037i	0.937099	−	0.349062i	$-0.113500\pi$
$547$	13.7530	+	13.7530i	0.588037	+	0.588037i	−0.349062	+	0.937099i	$0.613500\pi$
$548$	−21.3667	+	19.2578i	−0.912738	+	0.822654i
$549$	−4.50114	+	2.59873i	−0.192104	+	0.110911i
$550$	−3.90013	+	4.46008i	−0.166302	+	0.190179i
$551$	25.2741	+	14.5920i	1.07671	+	0.621642i
$552$	4.06875	+	0.317170i	0.173178	+	0.0134996i
$553$	24.2011	−	14.2468i	1.02914	−	0.605837i
$554$	−4.49732	+	1.08089i	−0.191073	+	0.0459227i
$555$	0.0578729	−	0.683299i	0.00245657	−	0.0290044i
$556$	1.58494	−	2.44324i	0.0672163	−	0.103617i
$557$	12.0723	+	3.23476i	0.511519	+	0.137061i	0.505341	−	0.862920i	$-0.331367\pi$
$557$	12.0723	+	3.23476i	0.511519	+	0.137061i	0.00617797	+	0.999981i	$0.498033\pi$
$558$	−28.5241	+	15.4965i	−1.20752	+	0.656018i
$559$	−11.3568			−0.480342
$560$	4.23109	−	23.2830i	0.178796	−	0.983886i
$561$	1.78737			0.0754628
$562$	−3.23207	+	1.75591i	−0.136337	+	0.0740685i
$563$	−7.45322	−	1.99709i	−0.314116	−	0.0841671i	0.0983168	−	0.995155i	$-0.468654\pi$
$563$	−7.45322	−	1.99709i	−0.314116	−	0.0841671i	−0.412433	+	0.910988i	$0.635321\pi$
$564$	2.47962	−	3.82243i	0.104411	−	0.160953i
$565$	11.4620	+	13.5832i	0.482208	+	0.571449i
$566$	−38.1104	+	9.15950i	−1.60190	+	0.385003i
$567$	−0.167167	−	19.7620i	−0.00702037	−	0.829928i
$568$	38.4897	+	3.00037i	1.61499	+	0.125893i
$569$	22.8689	+	13.2033i	0.958712	+	0.553513i	0.895776	−	0.444505i	$-0.146620\pi$
$569$	22.8689	+	13.2033i	0.958712	+	0.553513i	0.0629358	+	0.998018i	$0.479954\pi$
$570$	−2.79422	+	7.15685i	−0.117037	+	0.299768i
$571$	4.41042	−	2.54636i	0.184570	−	0.106562i	−0.404868	−	0.914375i	$-0.632682\pi$
$571$	4.41042	−	2.54636i	0.184570	−	0.106562i	0.589438	+	0.807813i	$0.299349\pi$
$572$	−2.04853	+	1.84635i	−0.0856534	+	0.0771997i
$573$	−0.824564	−	0.824564i	−0.0344467	−	0.0344467i
$574$	0.358541	+	0.00626540i	0.0149652	+	0.000261513i
$575$	1.60572	+	17.2515i	0.0669633	+	0.719435i
$576$	17.5947	+	14.2046i	0.733114	+	0.591858i
$577$	−19.0781	−	5.11195i	−0.794230	−	0.212813i	−0.161181	−	0.986925i	$-0.551530\pi$
$577$	−19.0781	−	5.11195i	−0.794230	−	0.212813i	−0.633049	+	0.774111i	$0.718197\pi$
$578$	−13.0697	−	0.338997i	−0.543629	−	0.0141004i
$579$	1.80058	−	3.11870i	0.0748295	−	0.129609i
$580$	−17.6714	−	13.7137i	−0.733766	−	0.569428i
$581$	15.7514	−	4.36370i	0.653478	−	0.181037i
$582$	1.84621	−	3.01442i	0.0765278	−	0.124952i
$583$	−2.87763	−	10.7395i	−0.119179	−	0.444783i
$584$	15.9790	+	5.64506i	0.661214	+	0.233594i
$585$	−1.83459	−	10.2384i	−0.0758508	−	0.423307i
$586$	−22.8643	−	6.76654i	−0.944515	−	0.279523i
$587$	−8.18830	−	8.18830i	−0.337967	−	0.337967i	0.517635	−	0.855602i	$-0.326813\pi$
$587$	−8.18830	−	8.18830i	−0.337967	−	0.337967i	−0.855602	+	0.517635i	$0.826813\pi$
$588$	−5.57471	−	1.70460i	−0.229897	−	0.0702965i
$589$			47.3823i			1.95235i
$590$	−22.7729	−	16.7449i	−0.937547	−	0.689376i
$591$	2.49925	−	1.44294i	0.102805	−	0.0593547i
$592$	−2.28764	+	1.85626i	−0.0940215	+	0.0762918i
$593$	6.09096	−	1.63207i	0.250126	−	0.0670210i	−0.131578	−	0.991306i	$-0.542004\pi$
$593$	6.09096	−	1.63207i	0.250126	−	0.0670210i	0.381703	+	0.924285i	$0.375338\pi$
$594$	−2.79531	+	0.671828i	−0.114693	+	0.0275654i
$595$	−19.7410	−	22.9969i	−0.809304	−	0.942783i
$596$	−20.6019	+	10.5101i	−0.843886	+	0.430509i
$597$	−1.33605	−	4.98620i	−0.0546808	−	0.204072i
$598$	−0.209108	+	8.06198i	−0.00855106	+	0.329679i
$599$	12.5631	+	21.7600i	0.513315	+	0.889088i	0.999881	+	0.0154439i	$0.00491615\pi$
$599$	12.5631	+	21.7600i	0.513315	+	0.889088i	−0.486566	+	0.873644i	$0.661751\pi$
$600$	2.86744	−	5.14338i	0.117063	−	0.209978i
$601$	−23.9702			−0.977766			−0.488883	−	0.872349i	$-0.662595\pi$
$601$	−23.9702			−0.977766			−0.488883	+	0.872349i	$0.662595\pi$
$602$	18.5746	−	17.9366i	0.757043	−	0.731039i
$603$	−1.06676	+	1.06676i	−0.0434417	+	0.0434417i
$604$	0.499326	−	9.61906i	0.0203173	−	0.391394i
$605$	13.1553	−	18.8991i	0.534841	−	0.768356i
$606$	−0.697300	−	0.734435i	−0.0283259	−	0.0298344i
$607$	1.98316	−	0.531386i	0.0804940	−	0.0215683i	−0.218347	−	0.975871i	$-0.570067\pi$
$607$	1.98316	−	0.531386i	0.0804940	−	0.0215683i	0.298841	+	0.954303i	$0.403400\pi$
$608$	30.4785	−	12.6689i	1.23607	−	0.513793i
$609$	−3.86324	+	3.92915i	−0.156546	+	0.159217i
$610$	0.640788	−	5.77925i	0.0259447	−	0.233995i
$611$	7.79739	+	4.50183i	0.315449	+	0.182124i
$612$	28.3255	−	6.03546i	1.14499	−	0.243969i
$613$	9.48807	−	35.4100i	0.383220	−	1.43020i	−0.457735	−	0.889089i	$-0.651339\pi$
$613$	9.48807	−	35.4100i	0.383220	−	1.43020i	0.840954	−	0.541106i	$-0.181994\pi$
$614$	−25.0010	−	7.39888i	−1.00896	−	0.298595i
$615$	0.0839366	+	0.0302872i	0.00338465	+	0.00122130i
$616$	0.434407	−	6.25516i	0.0175027	−	0.252028i
$617$	7.99905	−	7.99905i	0.322029	−	0.322029i	−0.527516	−	0.849545i	$-0.676876\pi$
$617$	7.99905	−	7.99905i	0.322029	−	0.322029i	0.849545	+	0.527516i	$0.176876\pi$
$618$	−4.41566	−	8.12783i	−0.177624	−	0.326949i
$619$	13.8212	+	23.9391i	0.555523	+	0.962194i	0.997863	+	0.0653461i	$0.0208151\pi$
$619$	13.8212	+	23.9391i	0.555523	+	0.962194i	−0.442340	+	0.896847i	$0.645852\pi$
$620$	4.93672	−	35.9794i	0.198264	−	1.44497i
$621$	−4.20357	+	7.28080i	−0.168683	+	0.292168i
$622$	−8.65236	+	14.1272i	−0.346928	+	0.566450i
$623$	3.88197	+	6.59432i	0.155528	+	0.264196i
$624$	1.60891	−	2.21910i	0.0644079	−	0.0888352i
$625$	23.5857	+	8.28952i	0.943427	+	0.331581i
$626$	19.5868	−	18.5965i	0.782848	−	0.743264i
$627$	−0.526885	+	1.96636i	−0.0210417	+	0.0785289i
$628$	6.33899	−	5.71335i	0.252953	−	0.227988i
$629$			3.77309i			0.150443i
$630$	19.1708	+	13.8479i	0.763782	+	0.551715i
$631$		−	11.5488i		−	0.459750i	−0.973220	−	0.229875i	$-0.926168\pi$
$631$		−	11.5488i		−	0.459750i	0.973220	−	0.229875i	$-0.0738318\pi$
$632$	−24.7547	−	16.9863i	−0.984691	−	0.675680i
$633$	0.0945618	−	0.352910i	0.00375850	−	0.0140269i
$634$	2.81207	+	2.96183i	0.111681	+	0.117629i
$635$	−9.27169	−	10.9876i	−0.367936	−	0.436029i
$636$	5.02171	+	9.84358i	0.199124	+	0.390324i
$637$	2.79286	−	11.1760i	0.110657	−	0.442811i
$638$	−5.05423	−	3.09551i	−0.200099	−	0.122553i
$639$	−19.2909	+	33.4128i	−0.763135	+	1.32179i
$640$	−24.4636	+	6.44455i	−0.967009	+	0.254743i
$641$	8.55730	+	14.8217i	0.337993	+	0.585421i	0.984055	−	0.177864i	$-0.0569186\pi$
$641$	8.55730	+	14.8217i	0.337993	+	0.585421i	−0.646062	+	0.763285i	$0.723585\pi$
$642$	7.19780	−	3.91040i	0.284074	−	0.154331i
$643$	18.4696	−	18.4696i	0.728370	−	0.728370i	−0.241925	−	0.970295i	$-0.577779\pi$
$643$	18.4696	−	18.4696i	0.728370	−	0.728370i	0.970295	+	0.241925i	$0.0777789\pi$
$644$	−12.3908	−	13.5160i	−0.488266	−	0.532604i
$645$	5.81585	−	2.73163i	0.228999	−	0.107558i
$646$	11.9961	−	40.5352i	0.471981	−	1.59484i
$647$	8.66156	−	32.3254i	0.340521	−	1.27084i	−0.557237	−	0.830353i	$-0.688139\pi$
$647$	8.66156	−	32.3254i	0.340521	−	1.27084i	0.897758	−	0.440489i	$-0.145195\pi$
$648$	−19.0624	+	9.10972i	−0.748841	+	0.357864i
$649$	−6.48624	−	3.74483i	−0.254607	−	0.146997i
$650$	10.4440	+	5.13185i	0.409646	+	0.201288i
$651$	−8.66070	−	2.24228i	−0.339440	−	0.0878821i
$652$	15.4690	+	5.01770i	0.605813	+	0.196508i
$653$	−10.2716	+	2.75226i	−0.401958	+	0.107704i	−0.454133	−	0.890934i	$-0.650051\pi$
$653$	−10.2716	+	2.75226i	−0.401958	+	0.107704i	0.0521757	+	0.998638i	$0.483384\pi$
$654$	−4.55361	+	4.32337i	−0.178060	+	0.169057i
$655$	−25.3332	−	17.6341i	−0.989852	−	0.689021i
$656$	−0.156272	−	0.350057i	−0.00610141	−	0.0136674i
$657$	−11.9755	+	11.9755i	−0.467210	+	0.467210i
$658$	−19.8630	+	4.95199i	−0.774341	+	0.193049i
$659$	−21.6586			−0.843698			−0.421849	−	0.906666i	$-0.638619\pi$
$659$	−21.6586			−0.843698			−0.421849	+	0.906666i	$0.638619\pi$
$660$	0.604960	−	1.43825i	0.0235480	−	0.0559837i
$661$	−11.2670	−	19.5150i	−0.438236	−	0.759046i	0.559318	−	0.828953i	$-0.311063\pi$
$661$	−11.2670	−	19.5150i	−0.438236	−	0.759046i	−0.997554	+	0.0699068i	$0.977730\pi$
$662$	49.2972	+	1.27865i	1.91599	+	0.0496961i
$663$	−0.908584	−	3.39088i	−0.0352865	−	0.131691i
$664$	−11.3578	−	13.2783i	−0.440769	−	0.515296i
$665$	31.1192	−	14.9389i	1.20675	−	0.579305i
$666$	−0.688004	−	2.86261i	−0.0266596	−	0.110924i
$667$	−16.7414	+	4.48584i	−0.648229	+	0.173693i
$668$	−15.2328	+	3.24573i	−0.589373	+	0.125581i
$669$	6.42869	−	3.71161i	0.248548	−	0.143499i
$670$	−0.254509	−	1.66847i	−0.00983253	−	0.0644587i
$671$		−	1.54069i		−	0.0594775i
$672$	0.873332	+	6.17050i	0.0336895	+	0.238032i
$673$	−12.3425	−	12.3425i	−0.475769	−	0.475769i	0.428007	−	0.903776i	$-0.359216\pi$
$673$	−12.3425	−	12.3425i	−0.475769	−	0.475769i	−0.903776	+	0.428007i	$0.859216\pi$
$674$	−9.01541	+	30.4633i	−0.347261	+	1.17340i
$675$	7.01292	+	9.89825i	0.269928	+	0.380984i
$676$	−17.2683	−	11.2020i	−0.664167	−	0.430847i
$677$	3.54145	+	13.2169i	0.136109	+	0.507966i	0.999991	+	0.00427157i	$0.00135969\pi$
$677$	3.54145	+	13.2169i	0.136109	+	0.507966i	−0.863882	+	0.503695i	$0.831974\pi$
$678$	−3.99141	−	2.44457i	−0.153289	−	0.0938833i
$679$	−15.3054	+	4.24015i	−0.587368	+	0.162722i
$680$	−13.3325	+	29.5303i	−0.511278	+	1.13243i
$681$	2.18628	−	3.78675i	0.0837785	−	0.145109i
$682$	0.249503	−	9.61940i	0.00955398	−	0.368346i
$683$	−2.13814	−	0.572913i	−0.0818137	−	0.0219219i	0.217680	−	0.976020i	$-0.430151\pi$
$683$	−2.13814	−	0.572913i	−0.0818137	−	0.0219219i	−0.299494	+	0.954098i	$0.596818\pi$
$684$	−1.70998	+	32.9412i	−0.0653826	+	1.25954i
$685$	30.2506	+	10.9155i	1.15582	+	0.417059i
$686$	13.0832	+	22.6899i	0.499519	+	0.866303i
$687$	−8.02297	−	8.02297i	−0.306095	−	0.306095i
$688$	−25.7804	−	9.86681i	−0.982868	−	0.376169i
$689$	−18.9114	+	10.9185i	−0.720467	+	0.415962i
$690$	−1.83204	−	4.17885i	−0.0697447	−	0.159086i
$691$	19.0959	+	11.0250i	0.726442	+	0.419411i	0.817119	−	0.576469i	$-0.195570\pi$
$691$	19.0959	+	11.0250i	0.726442	+	0.419411i	−0.0906771	+	0.995880i	$0.528903\pi$
$692$	1.93210	−	5.95644i	0.0734473	−	0.226430i
$693$	5.45301	+	3.08709i	0.207143	+	0.117269i
$694$	−7.93616	−	33.0204i	−0.301252	−	1.25344i
$695$	−3.24443	−	0.274791i	−0.123068	−	0.0104234i
$696$	5.55428	+	1.96222i	0.210535	+	0.0743778i
$697$	−0.474249	−	0.127075i	−0.0179635	−	0.00481330i
$698$	13.5079	+	24.8638i	0.511282	+	0.941107i
$699$	−5.46890			−0.206853
$700$	−25.1866	+	8.10145i	−0.951965	+	0.306206i
$701$	3.86536			0.145993			0.0729964	−	0.997332i	$-0.476744\pi$
$701$	3.86536			0.145993			0.0729964	+	0.997332i	$0.476744\pi$
$702$	2.69550	+	4.96156i	0.101735	+	0.187262i
$703$	−4.15093	−	1.11224i	−0.156555	−	0.0419489i
$704$	−6.25435	+	2.41151i	−0.235720	+	0.0908873i
$705$	−5.07587	−	0.429908i	−0.191168	−	0.0161913i
$706$	−7.74281	−	32.2159i	−0.291404	−	1.21246i
$707$	0.0384883	+	4.54997i	0.00144750	+	0.171119i
$708$	7.08080	+	2.29681i	0.266113	+	0.0863192i
$709$	−27.5158	−	15.8862i	−1.03338	−	0.596620i	−0.115427	−	0.993316i	$-0.536823\pi$
$709$	−27.5158	−	15.8862i	−1.03338	−	0.596620i	−0.917950	+	0.396696i	$0.870157\pi$
$710$	−17.3308	−	39.5312i	−0.650414	−	1.48358i
$711$	25.9834	−	15.0015i	0.974452	−	0.562600i
$712$	4.62844	−	6.74517i	0.173458	−	0.252786i
$713$	−19.8977	−	19.8977i	−0.745175	−	0.745175i
$714$	6.84147	+	4.11095i	0.256035	+	0.153848i
$715$	2.90028	+	1.04652i	0.108464	+	0.0391377i
$716$	−32.1669	−	1.66978i	−1.20213	−	0.0624027i
$717$	4.30673	+	1.15398i	0.160838	+	0.0430963i
$718$	−0.986561	+	38.0360i	−0.0368181	+	1.41949i
$719$	5.63438	−	9.75903i	0.210127	−	0.363950i	−0.741627	−	0.670812i	$-0.765946\pi$
$719$	5.63438	−	9.75903i	0.210127	−	0.363950i	0.951754	+	0.306862i	$0.0992790\pi$
$720$	4.73058	−	24.8355i	0.176298	−	0.925565i
$721$	−10.4163	+	40.2325i	−0.387924	+	1.49834i
$722$	18.1443	+	11.1126i	0.675260	+	0.413569i
$723$	1.35511	+	5.05733i	0.0503970	+	0.188084i
$724$	−4.17153	+	6.43058i	−0.155034	+	0.238991i
$725$	−4.20610	+	24.6523i	−0.156210	+	0.915565i
$726$	−1.72086	+	5.81483i	−0.0638672	+	0.215809i
$727$	21.9895	+	21.9895i	0.815544	+	0.815544i	0.985459	−	0.169915i	$-0.0543492\pi$
$727$	21.9895	+	21.9895i	0.815544	+	0.815544i	−0.169915	+	0.985459i	$0.554349\pi$
$728$	−12.0877	+	2.35560i	−0.448000	+	0.0873042i
$729$		−	18.0830i		−	0.669742i
$730$	−2.85714	−	18.7304i	−0.105747	−	0.693244i
$731$	−30.6172	+	17.6768i	−1.13242	+	0.653801i
$732$	0.319117	+	1.49767i	0.0117949	+	0.0553555i
$733$	39.0339	−	10.4591i	1.44175	−	0.386316i	0.548604	−	0.836082i	$-0.315159\pi$
$733$	39.0339	−	10.4591i	1.44175	−	0.386316i	0.893146	+	0.449766i	$0.148493\pi$
$734$	9.05587	+	37.6792i	0.334258	+	1.39077i
$735$	1.25792	+	6.39503i	0.0463989	+	0.235884i
$736$	−7.47894	+	18.1193i	−0.275677	+	0.667887i
$737$	−0.115744	−	0.431964i	−0.00426350	−	0.0159116i
$738$	0.382981	+	0.00993359i	0.0140977	+	0.000365660i
$739$	−15.6220	−	27.0581i	−0.574665	−	0.995349i	−0.996078	−	0.0884798i	$-0.971799\pi$
$739$	−15.6220	−	27.0581i	−0.574665	−	0.995349i	0.421413	−	0.906869i	$-0.361534\pi$
$740$	3.03610	+	1.27705i	0.111609	+	0.0469454i
$741$	3.99829			0.146881
$742$	13.6861	−	47.7257i	0.502434	−	1.75207i
$743$	13.4261	−	13.4261i	0.492557	−	0.492557i	−0.416554	−	0.909111i	$-0.636762\pi$
$743$	13.4261	−	13.4261i	0.492557	−	0.492557i	0.909111	+	0.416554i	$0.136762\pi$
$744$	1.74989	+	9.40251i	0.0641542	+	0.344713i
$745$	21.2225	+	14.7726i	0.777531	+	0.541227i
$746$	22.4889	−	21.3518i	0.823378	−	0.781745i
$747$	16.8670	−	4.51950i	0.617131	−	0.165360i
$748$	−2.64886	+	8.16615i	−0.0968520	+	0.298584i
$749$	−35.6289	−	9.22443i	−1.30185	−	0.337053i
$750$	−6.58273	−	0.115975i	−0.240367	−	0.00423480i
$751$	−29.3693	−	16.9564i	−1.07170	−	0.618748i	−0.143056	−	0.989715i	$-0.545693\pi$
$751$	−29.3693	−	16.9564i	−1.07170	−	0.618748i	−0.928646	+	0.370967i	$0.879026\pi$
$752$	13.7892	+	16.9937i	0.502840	+	0.619696i
$753$	−1.59885	+	5.96698i	−0.0582652	+	0.217449i
$754$	−3.30336	+	11.1621i	−0.120301	+	0.406501i
$755$	−9.74730	+	4.57818i	−0.354741	+	0.166617i
$756$	−12.2447	−	3.85767i	−0.445337	−	0.140302i
$757$	10.7202	−	10.7202i	0.389633	−	0.389633i	−0.484924	−	0.874556i	$-0.661153\pi$
$757$	10.7202	−	10.7202i	0.389633	−	0.389633i	0.874556	+	0.484924i	$0.161153\pi$
$758$	25.4252	−	13.8129i	0.923484	−	0.501708i
$759$	−0.604493	−	1.04701i	−0.0219417	−	0.0380041i
$760$	−28.5573	−	23.3727i	−1.03588	−	0.847815i
$761$	12.2719	−	21.2555i	0.444854	−	0.770510i	−0.553188	−	0.833057i	$-0.686589\pi$
$761$	12.2719	−	21.2555i	0.444854	−	0.770510i	0.998042	+	0.0625464i	$0.0199221\pi$
$762$	3.22869	+	1.97744i	0.116963	+	0.0716351i
$763$	28.2106	−	0.238633i	1.02129	−	0.00863911i
$764$	4.98927	−	2.54528i	0.180506	−	0.0920851i
$765$	−20.8820	−	24.7465i	−0.754990	−	0.894713i
$766$	7.07584	+	7.45268i	0.255661	+	0.269276i
$767$	−3.80726	+	14.2089i	−0.137472	+	0.513054i
$768$	5.58025	−	3.63963i	0.201360	−	0.131334i
$769$			38.3029i			1.38124i	0.723219	+	0.690619i	$0.242662\pi$
$769$			38.3029i			1.38124i	−0.723219	+	0.690619i	$0.757338\pi$
$770$	−6.39638	+	2.86897i	−0.230510	+	0.103391i
$771$		−	6.32315i		−	0.227723i
$772$	11.5803	+	12.8484i	0.416784	+	0.462423i
$773$	0.371576	−	1.38674i	0.0133647	−	0.0498776i	−0.958922	−	0.283672i	$-0.908447\pi$
$773$	0.371576	−	1.38674i	0.0133647	−	0.0498776i	0.972286	+	0.233794i	$0.0751141\pi$
$774$	20.0057	−	18.9942i	0.719091	−	0.682731i
$775$	−38.0769	+	14.0984i	−1.36776	+	0.506429i
$776$	11.0362	+	12.9023i	0.396178	+	0.463166i
$777$	0.399734	−	0.706087i	0.0143404	−	0.0253307i
$778$	−4.10243	+	6.69829i	−0.147079	+	0.240145i
$779$	0.279601	−	0.484282i	0.0100177	−	0.0173512i
$780$	−3.03607	−	0.416578i	−0.108709	−	0.0149159i
$781$	−5.71840	−	9.90456i	−0.204620	−	0.354413i
$782$	11.9847	+	22.0600i	0.428572	+	0.788864i
$783$	−8.58072	+	8.58072i	−0.306650	+	0.306650i
$784$	16.0497	−	22.9436i	0.573202	−	0.819414i
$785$	−8.97465	−	3.23836i	−0.320319	−	0.115582i
$786$	7.79449	+	2.30673i	0.278020	+	0.0822783i
$787$	3.70435	−	13.8248i	0.132046	−	0.492801i	−0.867947	−	0.496657i	$-0.834561\pi$
$787$	3.70435	−	13.8248i	0.132046	−	0.492801i	0.999993	+	0.00385583i	$0.00122735\pi$
$788$	2.88867	+	13.5570i	0.102905	+	0.482949i
$789$	4.22637	+	2.44010i	0.150463	+	0.0868698i
$790$	−3.69903	+	33.3614i	−0.131605	+	1.18695i
$791$	5.61441	+	20.2660i	0.199625	+	0.720575i
$792$	0.520614	−	6.67861i	0.0184992	−	0.237314i
$793$	−2.92289	+	0.783185i	−0.103795	+	0.0278117i
$794$	29.3027	+	30.8632i	1.03991	+	1.09529i
$795$	7.05837	−	10.1401i	0.250335	−	0.359632i
$796$	24.7610	+	1.28534i	0.877631	+	0.0455578i
$797$	−9.85742	+	9.85742i	−0.349168	+	0.349168i	−0.859800	−	0.510632i	$-0.829412\pi$
$797$	−9.85742	+	9.85742i	−0.349168	+	0.349168i	0.510632	+	0.859800i	$0.329412\pi$
$798$	−6.53938	+	6.31475i	−0.231491	+	0.223540i
$799$	28.0283			0.991569
$800$	19.2496	+	20.7232i	0.680577	+	0.732677i
$801$	4.08761	+	7.07995i	0.144429	+	0.250158i
$802$	−0.170116	+	6.55867i	−0.00600699	+	0.231595i
$803$	−1.29936	−	4.84926i	−0.0458533	−	0.171127i
$804$	0.201984	+	0.395930i	0.00712342	+	0.0139634i
$805$	−6.79477	+	19.3416i	−0.239484	+	0.681703i
$806$	−18.3761	+	4.41654i	−0.647271	+	0.155566i
$807$	−8.32229	+	2.22995i	−0.292959	+	0.0784980i
$808$	4.38889	−	2.09740i	0.154400	−	0.0737864i
$809$	−30.8498	+	17.8112i	−1.08462	+	0.626207i	−0.932140	−	0.362099i	$-0.882060\pi$
$809$	−30.8498	+	17.8112i	−1.08462	+	0.626207i	−0.152483	+	0.988306i	$0.548727\pi$
$810$	19.0302	+	13.9929i	0.668655	+	0.491660i
$811$			11.1150i			0.390299i	0.980774	+	0.195149i	$0.0625192\pi$
$811$			11.1150i			0.390299i	−0.980774	+	0.195149i	$0.937481\pi$
$812$	−12.2263	−	23.4734i	−0.429058	−	0.823754i
$813$	−6.21267	−	6.21267i	−0.217888	−	0.217888i
$814$	0.836851	+	0.247661i	0.0293316	+	0.00868050i
$815$	−3.20689	−	17.8969i	−0.112332	−	0.626903i
$816$	0.883481	−	8.48680i	0.0309280	−	0.297098i
$817$	−10.4216	−	38.8940i	−0.364607	−	1.36073i
$818$	25.6608	−	41.8979i	0.897207	−	1.46493i
$819$	3.08467	−	11.9144i	0.107787	−	0.416322i
$820$	−0.262770	+	0.338605i	−0.00917632	+	0.0118246i
$821$	−6.79984	+	11.7777i	−0.237316	+	0.411043i	−0.959943	−	0.280195i	$-0.909601\pi$
$821$	−6.79984	+	11.7777i	−0.237316	+	0.411043i	0.722627	+	0.691238i	$0.242934\pi$
$822$	−8.46641	−	0.219598i	−0.295300	−	0.00765936i
$823$	−24.5214	−	6.57048i	−0.854761	−	0.229033i	−0.195274	−	0.980749i	$-0.562560\pi$
$823$	−24.5214	−	6.57048i	−0.854761	−	0.229033i	−0.659487	+	0.751716i	$0.729226\pi$
$824$	43.6785	−	8.12897i	1.52161	−	0.283186i
$825$	−1.73696	+	0.161672i	−0.0604731	+	0.00562869i
$826$	−16.2141	−	29.2524i	−0.564160	−	1.01782i
$827$	17.3478	+	17.3478i	0.603242	+	0.603242i	0.941172	−	0.337929i	$-0.109726\pi$
$827$	17.3478	+	17.3478i	0.603242	+	0.603242i	−0.337929	+	0.941172i	$0.609726\pi$
$828$	−13.1152	−	14.5514i	−0.455786	−	0.505696i
$829$	16.3045	−	9.41343i	0.566280	−	0.326942i	−0.189382	−	0.981903i	$-0.560649\pi$
$829$	16.3045	−	9.41343i	0.566280	−	0.326942i	0.755662	+	0.654962i	$0.227315\pi$
$830$	−7.10490	+	18.1978i	−0.246615	+	0.631655i
$831$	−1.17942	−	0.680936i	−0.0409135	−	0.0236214i
$832$	7.75428	+	10.6395i	0.268831	+	0.368858i
$833$	−9.86610	−	34.4769i	−0.341840	−	1.19455i
$834$	0.833737	−	0.200381i	0.0288700	−	0.00693864i
$835$	11.2298	+	13.3081i	0.388624	+	0.460546i
$836$	−8.20309	−	5.32136i	−0.283710	−	0.184043i
$837$	−19.0306	−	5.09924i	−0.657794	−	0.176255i
$838$	34.9576	−	18.9917i	1.20759	−	0.656056i
$839$	−3.21211			−0.110894			−0.0554472	−	0.998462i	$-0.517658\pi$
$839$	−3.21211			−0.110894			−0.0554472	+	0.998462i	$0.517658\pi$
$840$	5.62356	−	4.11373i	0.194031	−	0.141937i
$841$	3.98283			0.137339
$842$	−4.90377	+	2.66410i	−0.168995	+	0.0918111i
$843$	−1.04610	−	0.280301i	−0.0360295	−	0.00965408i
$844$	1.47224	+	0.955043i	0.0506765	+	0.0328739i
$845$	−1.94217	+	22.9310i	−0.0668126	+	0.788849i
$846$	−21.2649	+	5.11082i	−0.731101	+	0.175714i
$847$	23.4795	−	13.8220i	0.806764	−	0.474929i
$848$	−52.4156	+	8.35517i	−1.79996	+	0.286918i
$849$	−9.99440	−	5.77027i	−0.343007	−	0.198035i
$850$	36.1439	−	2.42085i	1.23972	−	0.0830346i
$851$	2.21021	−	1.27607i	0.0757652	−	0.0437430i
$852$	7.61024	+	8.44360i	0.260723	+	0.289273i
$853$	−31.7184	−	31.7184i	−1.08602	−	1.08602i	−0.995934	−	0.0900831i	$-0.971287\pi$
$853$	−31.7184	−	31.7184i	−1.08602	−	1.08602i	−0.0900831	−	0.995934i	$-0.528713\pi$
$854$	3.54358	−	5.89724i	0.121259	−	0.201799i
$855$	33.3804	−	15.6783i	1.14158	−	0.536187i
$856$	7.19881	+	38.6805i	0.246050	+	1.32207i
$857$	−35.4579	−	9.50091i	−1.21122	−	0.324545i	−0.403978	−	0.914769i	$-0.632373\pi$
$857$	−35.4579	−	9.50091i	−1.21122	−	0.324545i	−0.807240	+	0.590224i	$0.799040\pi$
$858$	−0.811718	−	0.0210540i	−0.0277116	−	0.000718771i
$859$	5.30651	−	9.19114i	0.181056	−	0.313598i	−0.761185	−	0.648535i	$-0.775382\pi$
$859$	5.30651	−	9.19114i	0.181056	−	0.313598i	0.942240	+	0.334938i	$0.108715\pi$
$860$	3.86126	+	30.6198i	0.131668	+	1.04412i
$861$	0.0752872	+	0.0740242i	0.00256578	+	0.00252274i
$862$	−10.3498	+	16.8988i	−0.352517	+	0.575576i
$863$	5.67140	+	21.1660i	0.193057	+	0.720498i	0.992761	+	0.120104i	$0.0383228\pi$
$863$	5.67140	+	21.1660i	0.193057	+	0.720498i	−0.799705	+	0.600394i	$0.795011\pi$
$864$	1.80828	+	13.6048i	0.0615191	+	0.462844i
$865$	−6.89133	+	1.23483i	−0.234312	+	0.0419856i
$866$	4.25653	+	1.25969i	0.144643	+	0.0428061i
$867$	−2.72198	−	2.72198i	−0.0924434	−	0.0924434i
$868$	23.0796	−	36.2461i	0.783374	−	1.23027i
$869$			8.89379i			0.301701i
$870$	−0.993141	−	6.51070i	−0.0336706	−	0.220733i
$871$	−0.760656	+	0.439165i	−0.0257739	+	0.0148805i
$872$	−13.0042	−	27.2118i	−0.440379	−	0.921507i
$873$	−16.3894	+	4.39154i	−0.554698	+	0.148631i
$874$	−27.8020	+	6.68197i	−0.940417	+	0.226021i
$875$	21.2644	+	20.5627i	0.718868	+	0.695147i
$876$	2.26749	+	4.44474i	0.0766114	+	0.150174i
$877$	2.95602	+	11.0320i	0.0998175	+	0.372524i	0.997706	−	0.0676994i	$-0.0215659\pi$
$877$	2.95602	+	11.0320i	0.0998175	+	0.372524i	−0.897888	+	0.440224i	$0.854899\pi$
$878$	−0.917916	+	35.3895i	−0.0309782	+	1.19434i
$879$	−3.51032	−	6.08006i	−0.118400	−	0.205075i
$880$	5.67453	+	4.89541i	0.191288	+	0.165024i
$881$	27.2610			0.918447			0.459224	−	0.888321i	$-0.348128\pi$
$881$	27.2610			0.918447			0.459224	+	0.888321i	$0.348128\pi$
$882$	13.7720	+	24.3583i	0.463729	+	0.820187i
$883$	29.9932	−	29.9932i	1.00935	−	1.00935i	0.00939636	−	0.999956i	$-0.497009\pi$
$883$	29.9932	−	29.9932i	1.00935	−	1.00935i	0.999956	−	0.00939636i	$-0.00299100\pi$
$884$	16.8388	+	0.874102i	0.566350	+	0.0293992i
$885$	−1.46792	−	8.19216i	−0.0493437	−	0.275376i
$886$	4.28700	+	4.51531i	0.144024	+	0.151695i
$887$	−21.8561	+	5.85632i	−0.733855	+	0.196636i	−0.606345	−	0.795201i	$-0.707365\pi$
$887$	−21.8561	+	5.85632i	−0.733855	+	0.196636i	−0.127510	+	0.991837i	$0.540698\pi$
$888$	−0.864784	−	0.0674121i	−0.0290202	−	0.00226220i
$889$	−4.54155	−	16.3933i	−0.152319	−	0.549815i
$890$	−9.09032	−	1.00791i	−0.304708	−	0.0337852i
$891$	5.42024	+	3.12937i	0.181585	+	0.104838i
$892$	7.43038	+	34.8720i	0.248787	+	1.16760i
$893$	−8.26224	+	30.8351i	−0.276485	+	1.03186i
$894$	−6.52969	−	1.93242i	−0.218386	−	0.0646298i
$895$	15.3098	+	32.5957i	0.511749	+	1.08956i
$896$	−29.4861	−	5.15453i	−0.985062	−	0.172201i
$897$	−1.67904	+	1.67904i	−0.0560615	+	0.0560615i
$898$	16.3549	+	30.1042i	0.545772	+	1.00459i
$899$	−20.3085	−	35.1754i	−0.677327	−	1.17317i
$900$	−26.9807	+	8.42735i	−0.899355	+	0.280912i
$901$	−33.9892	+	58.8710i	−1.13234	+	1.96128i
$902$	−0.0593137	+	0.0968451i	−0.00197493	+	0.00322459i
$903$	7.60237	−	0.0643086i	0.252991	−	0.00214005i
$904$	17.0840	−	14.6131i	0.568206	−	0.486026i
$905$	8.53929	+	0.723246i	0.283856	+	0.0240415i
$906$	2.05667	−	1.95268i	0.0683284	−	0.0648734i
$907$	−1.07561	+	4.01423i	−0.0357151	+	0.133290i	−0.981481	−	0.191557i	$-0.938646\pi$
$907$	−1.07561	+	4.01423i	−0.0357151	+	0.133290i	0.945766	+	0.324847i	$0.105313\pi$
$908$	14.0609	+	15.6006i	0.466627	+	0.517725i
$909$			4.86119i			0.161235i
$910$	8.69434	+	10.6764i	0.288215	+	0.353919i
$911$		−	29.4464i		−	0.975603i	−0.872955	−	0.487801i	$-0.837799\pi$
$911$		−	29.4464i		−	0.975603i	0.872955	−	0.487801i	$-0.162201\pi$
$912$	9.07626	+	3.47371i	0.300545	+	0.115026i
$913$	−1.33972	+	4.99989i	−0.0443381	+	0.165472i
$914$	9.11881	+	9.60445i	0.301624	+	0.317687i
$915$	1.30844	−	1.10411i	0.0432557	−	0.0365006i
$916$	48.5454	−	24.7655i	1.60398	−	0.818274i
$917$	−18.5277	−	31.4731i	−0.611838	−	1.03933i
$918$	14.9895	+	9.18048i	0.494728	+	0.303001i
$919$	−4.57597	+	7.92582i	−0.150947	+	0.261449i	−0.931576	−	0.363547i	$-0.881566\pi$
$919$	−4.57597	+	7.92582i	−0.150947	+	0.261449i	0.780629	+	0.624995i	$0.214899\pi$
$920$	21.8075	−	2.17724i	0.718970	−	0.0717815i
$921$	−3.83837	−	6.64825i	−0.126479	−	0.219067i
$922$	−15.3572	+	8.34320i	−0.505762	+	0.274769i
$923$	−15.8834	+	15.8834i	−0.522809	+	0.522809i
$924$	1.36085	−	1.24756i	0.0447688	−	0.0410419i
$925$	−0.341285	−	3.66667i	−0.0112214	−	0.120559i
$926$	16.8443	−	56.9174i	0.553539	−	1.87042i
$927$	−11.4916	+	42.8871i	−0.377433	+	1.40860i
$928$	−17.1964	+	22.4685i	−0.564500	+	0.737564i
$929$	26.0531	+	15.0417i	0.854773	+	0.493504i	0.862259	−	0.506468i	$-0.169049\pi$
$929$	26.0531	+	15.0417i	0.854773	+	0.493504i	−0.00748525	+	0.999972i	$0.502383\pi$
$930$	8.34815	−	6.68168i	0.273747	−	0.219101i
$931$	40.8378	−	0.690945i	1.33841	−	0.0226448i
$932$	8.10485	−	24.9864i	0.265483	−	0.818456i
$933$	−4.71148	+	1.26244i	−0.154247	+	0.0413303i
$934$	37.1195	−	35.2426i	1.21459	−	1.15317i
$935$	9.44786	−	1.69293i	0.308978	−	0.0553647i
$936$	−12.9349	+	2.40730i	−0.422789	+	0.0786850i
$937$	−6.79581	+	6.79581i	−0.222009	+	0.222009i	−0.809344	−	0.587335i	$-0.800177\pi$
$937$	−6.79581	+	6.79581i	−0.222009	+	0.222009i	0.587335	+	0.809344i	$0.300177\pi$
$938$	0.550485	−	1.91963i	0.0179740	−	0.0626781i
$939$	7.95230			0.259514
$940$	9.48656	−	22.5536i	0.309417	−	0.735617i
$941$	−9.08044	−	15.7278i	−0.296014	−	0.512711i	0.679206	−	0.733947i	$-0.262324\pi$
$941$	−9.08044	−	15.7278i	−0.296014	−	0.512711i	−0.975220	+	0.221236i	$0.928991\pi$
$942$	2.51179	+	0.0651496i	0.0818384	+	0.00212269i
$943$	0.0859540	+	0.320785i	0.00279905	+	0.0104462i
$944$	−20.9873	+	28.9470i	−0.683080	+	0.942144i
$945$	2.65102	+	14.1064i	0.0862378	+	0.458882i
$946$	1.91096	+	7.95101i	0.0621306	+	0.258510i
$947$	16.9897	−	4.55237i	0.552091	−	0.147932i	0.0280205	−	0.999607i	$-0.491080\pi$
$947$	16.9897	−	4.55237i	0.552091	−	0.147932i	0.524070	+	0.851675i	$0.324413\pi$
$948$	−1.84214	−	8.64549i	−0.0598300	−	0.280792i
$949$	−8.53920	+	4.93011i	−0.277194	+	0.160038i
$950$	−7.99129	+	40.4770i	−0.259272	+	1.31325i
$951$			1.20251i			0.0389940i
$952$	−28.9211	+	25.1650i	−0.937340	+	0.815602i
$953$	12.8804	+	12.8804i	0.417238	+	0.417238i	0.884251	−	0.467013i	$-0.154670\pi$
$953$	12.8804	+	12.8804i	0.417238	+	0.417238i	−0.467013	+	0.884251i	$0.654670\pi$
$954$	15.0525	−	50.8628i	0.487343	−	1.64674i
$955$	−5.13957	−	3.57757i	−0.166312	−	0.115768i
$956$	−11.6549	+	17.9664i	−0.376945	+	0.581076i
$957$	−0.451656	−	1.68560i	−0.0146000	−	0.0544878i
$958$	−38.4291	−	23.5363i	−1.24159	−	0.760423i
$959$	27.1334	+	26.6782i	0.876183	+	0.861484i
$960$	−6.53007	−	3.58339i	−0.210757	−	0.115653i
$961$	17.4723	−	30.2629i	0.563622	−	0.976222i
$962$	0.0444444	−	1.71351i	0.00143294	−	0.0552459i
$963$	−37.9798	−	10.1766i	−1.22388	−	0.327938i
$964$	−25.1142	−	1.30368i	−0.808875	−	0.0419887i
$965$	6.56378	−	18.1906i	0.211296	−	0.585575i
$966$	0.0943277	−	5.39796i	0.00303494	−	0.173676i
$967$	−21.8531	−	21.8531i	−0.702748	−	0.702748i	0.262251	−	0.965000i	$-0.415535\pi$
$967$	−21.8531	−	21.8531i	−0.702748	−	0.702748i	−0.965000	+	0.262251i	$0.915535\pi$
$968$	−24.0166	−	16.4798i	−0.771922	−	0.529681i
$969$	10.7791	−	6.22331i	0.346274	−	0.199922i
$970$	6.90374	−	17.6826i	0.221666	−	0.567753i
$971$	−49.5916	−	28.6317i	−1.59147	−	0.918836i	−0.993055	−	0.117650i	$-0.962464\pi$
$971$	−49.5916	−	28.6317i	−1.59147	−	0.918836i	−0.598416	−	0.801186i	$-0.704203\pi$
$972$	−19.7638	−	6.41081i	−0.633925	−	0.205627i
$973$	−3.35263	−	1.89801i	−0.107480	−	0.0608475i
$974$	3.30035	+	13.7319i	0.105750	+	0.440000i
$975$	1.18967	+	3.21306i	0.0381000	+	0.102900i
$976$	−7.31550	−	0.761547i	−0.234163	−	0.0243765i
$977$	23.4116	+	6.27313i	0.749004	+	0.200695i	0.613076	−	0.790024i	$-0.289932\pi$
$977$	23.4116	+	6.27313i	0.749004	+	0.200695i	0.135928	+	0.990719i	$0.456598\pi$
$978$	2.28579	+	4.20741i	0.0730914	+	0.134538i
$979$	−2.42338			−0.0774516
$980$	−31.0819	−	3.73019i	−0.992875	−	0.119157i
$981$	30.1401			0.962300
$982$	11.0382	+	20.3178i	0.352243	+	0.648366i
$983$	−13.7291	−	3.67869i	−0.437889	−	0.117332i	0.0331380	−	0.999451i	$-0.489450\pi$
$983$	−13.7291	−	3.67869i	−0.437889	−	0.117332i	−0.471027	+	0.882119i	$0.656117\pi$
$984$	0.0375985	−	0.106427i	0.00119860	−	0.00339276i
$985$	11.8441	−	9.99445i	0.377384	−	0.318450i
$986$	8.46817	+	35.2339i	0.269682	+	1.12208i
$987$	−5.24515	−	2.96942i	−0.166955	−	0.0945176i
$988$	−5.92542	+	18.2674i	−0.188513	+	0.581164i
$989$	20.7096	+	11.9567i	0.658527	+	0.380201i
$990$	−6.85933	+	3.00718i	−0.218004	+	0.0955746i
$991$	−40.1223	+	23.1646i	−1.27453	+	0.735848i	−0.975836	−	0.218503i	$-0.929883\pi$
$991$	−40.1223	+	23.1646i	−1.27453	+	0.735848i	−0.298689	+	0.954350i	$0.596549\pi$
$992$	−45.5516	−	5.93948i	−1.44626	−	0.188579i
$993$	10.2670	+	10.2670i	0.325812	+	0.325812i
$994$	0.892324	−	51.0638i	0.0283028	−	1.61964i
$995$	−11.7850	−	25.0911i	−0.373609	−	0.795442i
$996$	0.266702	−	5.13778i	0.00845079	−	0.162797i
$997$	44.4512	+	11.9107i	1.40778	+	0.377214i	0.881133	−	0.472869i	$-0.156781\pi$
$997$	44.4512	+	11.9107i	1.40778	+	0.377214i	0.526649	+	0.850083i	$0.323448\pi$
$998$	−0.348214	+	13.4251i	−0.0110225	+	0.424965i
$999$	0.893438	−	1.54748i	0.0282671	−	0.0489601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.23.4	✓	72
4.3	odd	2	inner	140.2.w.b.23.18	yes	72
5.2	odd	4	inner	140.2.w.b.107.6	yes	72
5.3	odd	4		700.2.be.e.107.13		72
5.4	even	2		700.2.be.e.443.15		72
7.2	even	3		980.2.k.k.883.15		36
7.3	odd	6		980.2.x.m.263.8		72
7.4	even	3	inner	140.2.w.b.123.8	yes	72
7.5	odd	6		980.2.k.j.883.15		36
7.6	odd	2		980.2.x.m.863.4		72
20.3	even	4		700.2.be.e.107.11		72
20.7	even	4	inner	140.2.w.b.107.8	yes	72
20.19	odd	2		700.2.be.e.443.1		72
28.3	even	6		980.2.x.m.263.6		72
28.11	odd	6	inner	140.2.w.b.123.6	yes	72
28.19	even	6		980.2.k.j.883.7		36
28.23	odd	6		980.2.k.k.883.7		36
28.27	even	2		980.2.x.m.863.18		72
35.2	odd	12		980.2.k.k.687.7		36
35.4	even	6		700.2.be.e.543.11		72
35.12	even	12		980.2.k.j.687.7		36
35.17	even	12		980.2.x.m.67.18		72
35.18	odd	12		700.2.be.e.207.1		72
35.27	even	4		980.2.x.m.667.6		72
35.32	odd	12	inner	140.2.w.b.67.18	yes	72
140.27	odd	4		980.2.x.m.667.8		72
140.39	odd	6		700.2.be.e.543.13		72
140.47	odd	12		980.2.k.j.687.15		36
140.67	even	12	inner	140.2.w.b.67.4	yes	72
140.87	odd	12		980.2.x.m.67.4		72
140.107	even	12		980.2.k.k.687.15		36
140.123	even	12		700.2.be.e.207.15		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.4	✓	72	1.1	even	1	trivial
140.2.w.b.23.18	yes	72	4.3	odd	2	inner
140.2.w.b.67.4	yes	72	140.67	even	12	inner
140.2.w.b.67.18	yes	72	35.32	odd	12	inner
140.2.w.b.107.6	yes	72	5.2	odd	4	inner
140.2.w.b.107.8	yes	72	20.7	even	4	inner
140.2.w.b.123.6	yes	72	28.11	odd	6	inner
140.2.w.b.123.8	yes	72	7.4	even	3	inner
700.2.be.e.107.11		72	20.3	even	4
700.2.be.e.107.13		72	5.3	odd	4
700.2.be.e.207.1		72	35.18	odd	12
700.2.be.e.207.15		72	140.123	even	12
700.2.be.e.443.1		72	20.19	odd	2
700.2.be.e.443.15		72	5.4	even	2
700.2.be.e.543.11		72	35.4	even	6
700.2.be.e.543.13		72	140.39	odd	6
980.2.k.j.687.7		36	35.12	even	12
980.2.k.j.687.15		36	140.47	odd	12
980.2.k.j.883.7		36	28.19	even	6
980.2.k.j.883.15		36	7.5	odd	6
980.2.k.k.687.7		36	35.2	odd	12
980.2.k.k.687.15		36	140.107	even	12
980.2.k.k.883.7		36	28.23	odd	6
980.2.k.k.883.15		36	7.2	even	3
980.2.x.m.67.4		72	140.87	odd	12
980.2.x.m.67.18		72	35.17	even	12
980.2.x.m.263.6		72	28.3	even	6
980.2.x.m.263.8		72	7.3	odd	6
980.2.x.m.667.6		72	35.27	even	4
980.2.x.m.667.8		72	140.27	odd	4
980.2.x.m.863.4		72	7.6	odd	2
980.2.x.m.863.18		72	28.27	even	2

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 $\F_{q}$
Belyi maps

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+(-1.24267 + 0.675113i) q^{2} +(-0.402205 - 0.107770i) q^{3} +(1.08845 - 1.67788i) q^{4} +(-2.22809 - 0.188711i) q^{5} +(0.572564 - 0.137611i) q^{6} +(-2.30240 - 1.30345i) q^{7} +(-0.219816 + 2.81987i) q^{8} +(-2.44792 - 1.41331i) q^{9} +(2.89618 - 1.26971i) q^{10} +(0.725638 - 0.418947i) q^{11} +(-0.618604 + 0.557549i) q^{12} +(-1.16367 - 1.16367i) q^{13} +(3.74109 + 0.0653744i) q^{14} +(0.875811 + 0.316023i) q^{15} +(-1.63057 - 3.65256i) q^{16} +(-4.94841 - 1.32592i) q^{17} +(3.99610 + 0.103649i) q^{18} +(2.91741 - 5.05309i) q^{19} +(-2.74179 + 3.53307i) q^{20} +(0.785561 + 0.772382i) q^{21} +(-0.618890 + 1.01050i) q^{22} +(0.896861 + 3.34713i) q^{23} +(0.392310 - 1.11048i) q^{24} +(4.92878 + 0.840930i) q^{25} +(2.23166 + 0.660445i) q^{26} +(1.71555 + 1.71555i) q^{27} +(-4.69306 + 2.44442i) q^{28} +5.00172i q^{29} +(-1.30169 + 0.198560i) q^{30} +(-7.03267 + 4.06031i) q^{31} +(4.49215 + 3.43810i) q^{32} +(-0.337005 + 0.0903002i) q^{33} +(7.04437 - 1.69305i) q^{34} +(4.88397 + 3.33869i) q^{35} +(-5.03579 + 2.56901i) q^{36} +(-0.190621 - 0.711408i) q^{37} +(-0.213956 + 8.24889i) q^{38} +(0.342623 + 0.593441i) q^{39} +(1.02191 - 6.24145i) q^{40} +0.0958388 q^{41} +(-1.49764 - 0.429472i) q^{42} +(4.87975 - 4.87975i) q^{43} +(0.0868733 - 1.67354i) q^{44} +(5.18749 + 3.61093i) q^{45} +(-3.37419 - 3.55389i) q^{46} +(-5.28468 + 1.41603i) q^{47} +(0.262186 + 1.64481i) q^{48} +(3.60205 + 6.00210i) q^{49} +(-6.69255 + 2.28248i) q^{50} +(1.84738 + 1.06658i) q^{51} +(-3.21908 + 0.685908i) q^{52} +(3.43436 - 12.8172i) q^{53} +(-3.29006 - 0.973671i) q^{54} +(-1.69585 + 0.796517i) q^{55} +(4.18166 - 6.20594i) q^{56} +(-1.71797 + 1.71797i) q^{57} +(-3.37672 - 6.21547i) q^{58} +(-4.46933 - 7.74111i) q^{59} +(1.48352 - 1.12553i) q^{60} +(0.919379 - 1.59241i) q^{61} +(5.99810 - 9.79346i) q^{62} +(3.79391 + 6.44473i) q^{63} +(-7.90336 - 1.23971i) q^{64} +(2.37316 + 2.81235i) q^{65} +(0.357822 - 0.339730i) q^{66} +(0.138137 - 0.515535i) q^{67} +(-7.61081 + 6.85965i) q^{68} -1.44289i q^{69} +(-8.32314 - 0.851644i) q^{70} -13.6494i q^{71} +(4.52344 - 6.59216i) q^{72} +(1.55074 - 5.78744i) q^{73} +(0.717160 + 0.755353i) q^{74} +(-1.89175 - 0.869402i) q^{75} +(-5.30306 - 10.3951i) q^{76} +(-2.21678 + 0.0187518i) q^{77} +(-0.826407 - 0.506141i) q^{78} +(-5.30723 + 9.19239i) q^{79} +(2.94379 + 8.44595i) q^{80} +(3.73481 + 6.46888i) q^{81} +(-0.119096 + 0.0647020i) q^{82} +(-4.36830 + 4.36830i) q^{83} +(2.15101 - 0.477382i) q^{84} +(10.7753 + 3.88809i) q^{85} +(-2.76953 + 9.35829i) q^{86} +(0.539037 - 2.01171i) q^{87} +(1.02187 + 2.13830i) q^{88} +(-2.50474 - 1.44611i) q^{89} +(-8.88411 - 0.985047i) q^{90} +(1.16244 + 4.19600i) q^{91} +(6.59227 + 2.13834i) q^{92} +(3.26615 - 0.875163i) q^{93} +(5.61112 - 5.32740i) q^{94} +(-7.45382 + 10.7082i) q^{95} +(-1.43624 - 1.86694i) q^{96} +(4.24461 - 4.24461i) q^{97} +(-8.52825 - 5.02683i) q^{98} -2.36841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100}) \) 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

Fields

Representations

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Database

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