LMFDB - Embedded newform 140.2.w.b.23.18

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			23.18
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41374 - 0.0366689i) q^{2} +(0.402205 + 0.107770i) q^{3} +(1.99731 - 0.103680i) q^{4} +(-2.22809 - 0.188711i) q^{5} +(0.572564 + 0.137611i) q^{6} +(2.30240 + 1.30345i) q^{7} +(2.81987 - 0.219816i) q^{8} +(-2.44792 - 1.41331i) q^{9} +(-3.15686 - 0.185086i) q^{10} +(-0.725638 + 0.418947i) q^{11} +(0.814501 + 0.173550i) q^{12} +(-1.16367 - 1.16367i) q^{13} +(3.30278 + 1.75831i) q^{14} +(-0.875811 - 0.316023i) q^{15} +(3.97850 - 0.414164i) q^{16} +(-4.94841 - 1.32592i) q^{17} +(-3.51255 - 1.90829i) q^{18} +(-2.91741 + 5.05309i) q^{19} +(-4.46976 - 0.145905i) q^{20} +(0.785561 + 0.772382i) q^{21} +(-1.01050 + 0.618890i) q^{22} +(-0.896861 - 3.34713i) q^{23} +(1.15786 + 0.215488i) q^{24} +(4.92878 + 0.840930i) q^{25} +(-1.68779 - 1.60245i) q^{26} +(-1.71555 - 1.71555i) q^{27} +(4.73374 + 2.36468i) q^{28} +5.00172i q^{29} +(-1.24976 - 0.414658i) q^{30} +(7.03267 - 4.06031i) q^{31} +(5.60937 - 0.731407i) 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} +(-3.93916 + 7.25073i) q^{38} +(-0.342623 - 0.593441i) q^{39} +(-6.32441 - 0.0423707i) q^{40} +0.0958388 q^{41} +(1.13890 + 1.06314i) q^{42} +(-4.87975 + 4.87975i) q^{43} +(-1.40589 + 0.912002i) q^{44} +(5.18749 + 3.61093i) q^{45} +(-1.39066 - 4.69908i) q^{46} +(5.28468 - 1.41603i) q^{47} +(1.64481 + 0.262186i) q^{48} +(3.60205 + 6.00210i) q^{49} +(6.99883 + 1.00812i) q^{50} +(-1.84738 - 1.06658i) q^{51} +(-2.44486 - 2.20356i) q^{52} +(3.43436 - 12.8172i) q^{53} +(-2.48825 - 2.36244i) q^{54} +(1.69585 - 0.796517i) q^{55} +(6.77898 + 3.16945i) q^{56} +(-1.71797 + 1.71797i) q^{57} +(0.183407 + 7.07112i) q^{58} +(4.46933 + 7.74111i) q^{59} +(-1.78203 - 0.540391i) q^{60} +(0.919379 - 1.59241i) q^{61} +(9.79346 - 5.99810i) q^{62} +(-3.79391 - 6.44473i) q^{63} +(7.90336 - 1.23971i) q^{64} +(2.37316 + 2.81235i) q^{65} +(-0.473126 + 0.140018i) q^{66} +(-0.138137 + 0.515535i) q^{67} +(-10.0210 - 2.13522i) q^{68} -1.44289i q^{69} +(-7.02708 - 4.54094i) q^{70} +13.6494i q^{71} +(-7.21350 - 3.44726i) q^{72} +(1.55074 - 5.78744i) q^{73} +(-0.295575 - 0.998755i) q^{74} +(1.89175 + 0.869402i) q^{75} +(-5.30306 + 10.3951i) q^{76} +(-2.21678 + 0.0187518i) q^{77} +(-0.506141 - 0.826407i) q^{78} +(5.30723 - 9.19239i) q^{79} +(-8.94262 + 0.172008i) q^{80} +(3.73481 + 6.46888i) q^{81} +(0.135491 - 0.00351430i) q^{82} +(4.36830 - 4.36830i) q^{83} +(1.64909 + 1.46124i) q^{84} +(10.7753 + 3.88809i) q^{85} +(-6.71975 + 7.07762i) q^{86} +(-0.539037 + 2.01171i) q^{87} +(-1.95412 + 1.34088i) q^{88} +(-2.50474 - 1.44611i) q^{89} +(7.46616 + 4.91469i) q^{90} +(-1.16244 - 4.19600i) q^{91} +(-2.13834 - 6.59227i) q^{92} +(3.26615 - 0.875163i) q^{93} +(7.41923 - 2.19567i) q^{94} +(7.45382 - 10.7082i) q^{95} +(2.33494 + 0.310349i) q^{96} +(4.24461 - 4.24461i) q^{97} +(5.31245 + 8.35332i) 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 $

$2$	1.41374	−	0.0366689i	0.999664	−	0.0259288i
$2$	1.41374	−	0.0366689i	0.999664	−	0.0259288i
$3$	0.402205	+	0.107770i	0.232213	+	0.0622213i	0.373049	−	0.927812i	$-0.378312\pi$
$3$	0.402205	+	0.107770i	0.232213	+	0.0622213i	−0.140836	+	0.990033i	$0.544979\pi$
$4$	1.99731	−	0.103680i	0.998655	−	0.0518402i
$5$	−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
$8$	2.81987	−	0.219816i	0.996975	−	0.0777167i
$9$	−2.44792	−	1.41331i	−0.815974	−	0.471103i
$10$	−3.15686	−	0.185086i	−0.998286	−	0.0585294i
$11$	−0.725638	+	0.418947i	−0.218788	+	0.126317i	−0.605389	−	0.795930i	$-0.706982\pi$
$11$	−0.725638	+	0.418947i	−0.218788	+	0.126317i	0.386601	+	0.922247i	$0.373649\pi$
$12$	0.814501	+	0.173550i	0.235126	+	0.0500996i
$13$	−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	$0.823289\pi$
$14$	3.30278	+	1.75831i	0.882705	+	0.469927i
$15$	−0.875811	−	0.316023i	−0.226133	−	0.0815967i
$16$	3.97850	−	0.414164i	0.994625	−	0.103541i
$17$	−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	$0.796709\pi$
$18$	−3.51255	−	1.90829i	−0.827915	−	0.449787i
$19$	−2.91741	+	5.05309i	−0.669299	+	1.15926i	0.308802	+	0.951126i	$0.400072\pi$
$19$	−2.91741	+	5.05309i	−0.669299	+	1.15926i	−0.978101	+	0.208133i	$0.933261\pi$
$20$	−4.46976	−	0.145905i	−0.999468	−	0.0326254i
$21$	0.785561	+	0.772382i	0.171423	+	0.168548i
$22$	−1.01050	+	0.618890i	−0.215439	+	0.131948i
$23$	−0.896861	−	3.34713i	−0.187008	−	0.697925i	−0.994192	−	0.107624i	$-0.965676\pi$
$23$	−0.896861	−	3.34713i	−0.187008	−	0.697925i	0.807183	−	0.590301i	$-0.200991\pi$
$24$	1.15786	+	0.215488i	0.236346	+	0.0439862i
$25$	4.92878	+	0.840930i	0.985755	+	0.168186i
$26$	−1.68779	−	1.60245i	−0.331003	−	0.314266i
$27$	−1.71555	−	1.71555i	−0.330159	−	0.330159i
$28$	4.73374	+	2.36468i	0.894593	+	0.446882i
$29$			5.00172i			0.928795i	0.885627	+	0.464398i	$0.153729\pi$
$29$			5.00172i			0.928795i	−0.885627	+	0.464398i	$0.846271\pi$
$30$	−1.24976	−	0.414658i	−0.228173	−	0.0757059i
$31$	7.03267	−	4.06031i	1.26310	−	0.729254i	0.289430	−	0.957199i	$-0.406534\pi$
$31$	7.03267	−	4.06031i	1.26310	−	0.729254i	0.973674	+	0.227945i	$0.0732008\pi$
$32$	5.60937	−	0.731407i	0.991606	−	0.129296i
$33$	−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	$0.935949\pi$
$38$	−3.93916	+	7.25073i	−0.639015	+	1.17622i
$39$	−0.342623	−	0.593441i	−0.0548637	−	0.0950266i
$40$	−6.32441	−	0.0423707i	−0.999978	−	0.00669940i
$41$	0.0958388			0.0149675			0.00748375	−	0.999972i	$-0.497618\pi$
$41$	0.0958388			0.0149675			0.00748375	+	0.999972i	$0.497618\pi$
$42$	1.13890	+	1.06314i	0.175736	+	0.164046i
$43$	−4.87975	+	4.87975i	−0.744155	+	0.744155i	−0.973375	−	0.229220i	$-0.926383\pi$
$43$	−4.87975	+	4.87975i	−0.744155	+	0.744155i	0.229220	+	0.973375i	$0.426383\pi$
$44$	−1.40589	+	0.912002i	−0.211946	+	0.137490i
$45$	5.18749	+	3.61093i	0.773305	+	0.538286i
$46$	−1.39066	−	4.69908i	−0.205042	−	0.692841i
$47$	5.28468	−	1.41603i	0.770850	−	0.206549i	0.148103	−	0.988972i	$-0.452683\pi$
$47$	5.28468	−	1.41603i	0.770850	−	0.206549i	0.622747	+	0.782423i	$0.286017\pi$
$48$	1.64481	+	0.262186i	0.237407	+	0.0378433i
$49$	3.60205	+	6.00210i	0.514579	+	0.857443i
$50$	6.99883	+	1.00812i	0.989785	+	0.142570i
$51$	−1.84738	−	1.06658i	−0.258684	−	0.149352i
$52$	−2.44486	−	2.20356i	−0.339040	−	0.305578i
$53$	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	$-0.281619\pi$
$54$	−2.48825	−	2.36244i	−0.338608	−	0.321487i
$55$	1.69585	−	0.796517i	0.228668	−	0.107402i
$56$	6.77898	+	3.16945i	0.905879	+	0.423536i
$57$	−1.71797	+	1.71797i	−0.227550	+	0.227550i
$58$	0.183407	+	7.07112i	0.0240826	+	0.928483i
$59$	4.46933	+	7.74111i	0.581858	+	1.00781i	0.995259	+	0.0972582i	$0.0310073\pi$
$59$	4.46933	+	7.74111i	0.581858	+	1.00781i	−0.413402	+	0.910549i	$0.635659\pi$
$60$	−1.78203	−	0.540391i	−0.230059	−	0.0697642i
$61$	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	$0.129110\pi$
$62$	9.79346	−	5.99810i	1.24377	−	0.761759i
$63$	−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
$66$	−0.473126	+	0.140018i	−0.0582377	+	0.0172351i
$67$	−0.138137	+	0.515535i	−0.0168761	+	0.0629826i	−0.973850	−	0.227190i	$-0.927046\pi$
$67$	−0.138137	+	0.515535i	−0.0168761	+	0.0629826i	0.956974	+	0.290173i	$0.0937128\pi$
$68$	−10.0210	−	2.13522i	−1.21522	−	0.258934i
$69$		−	1.44289i		−	0.173703i
$70$	−7.02708	−	4.54094i	−0.839897	−	0.542746i
$71$			13.6494i			1.61989i	0.586505	+	0.809946i	$0.300503\pi$
$71$			13.6494i			1.61989i	−0.586505	+	0.809946i	$0.699497\pi$
$72$	−7.21350	−	3.44726i	−0.850119	−	0.406263i
$73$	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	$-0.0306998\pi$
$74$	−0.295575	−	0.998755i	−0.0343599	−	0.116103i
$75$	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
$78$	−0.506141	−	0.826407i	−0.0573091	−	0.0935721i
$79$	5.30723	−	9.19239i	0.597110	−	1.03422i	−0.396136	−	0.918192i	$-0.629649\pi$
$79$	5.30723	−	9.19239i	0.597110	−	1.03422i	0.993245	−	0.116033i	$-0.0370177\pi$
$80$	−8.94262	+	0.172008i	−0.999815	+	0.0192311i
$81$	3.73481	+	6.46888i	0.414979	+	0.718764i
$82$	0.135491	−	0.00351430i	0.0149625	−	0.000388090i
$83$	4.36830	−	4.36830i	0.479483	−	0.479483i	−0.425483	−	0.904966i	$-0.639896\pi$
$83$	4.36830	−	4.36830i	0.479483	−	0.479483i	0.904966	+	0.425483i	$0.139896\pi$
$84$	1.64909	+	1.46124i	0.179931	+	0.159434i
$85$	10.7753	+	3.88809i	1.16874	+	0.421723i
$86$	−6.71975	+	7.07762i	−0.724610	+	0.763200i
$87$	−0.539037	+	2.01171i	−0.0577908	+	0.215678i
$88$	−1.95412	+	1.34088i	−0.208309	+	0.142939i
$89$	−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	$0.715653\pi$
$90$	7.46616	+	4.91469i	0.787002	+	0.518054i
$91$	−1.16244	−	4.19600i	−0.121857	−	0.439860i
$92$	−2.13834	−	6.59227i	−0.222937	−	0.687292i
$93$	3.26615	−	0.875163i	0.338684	−	0.0907502i
$94$	7.41923	−	2.19567i	0.765235	−	0.226466i
$95$	7.45382	−	10.7082i	0.764746	−	1.09864i
$96$	2.33494	+	0.310349i	0.238309	+	0.0316749i
$97$	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	$0.151429\pi$
$98$	5.31245	+	8.35332i	0.536638	+	0.843812i
$99$	2.36841			0.238034
$100$	9.93149	+	1.16858i	0.993149	+	0.116858i
$101$	−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	$0.860602\pi$
$102$	−2.65082	−	1.44013i	−0.262470	−	0.142594i
$103$	4.06549	+	15.1726i	0.400584	+	1.49500i	0.812057	+	0.583579i	$0.198348\pi$
$103$	4.06549	+	15.1726i	0.400584	+	1.49500i	−0.411472	+	0.911422i	$0.634985\pi$
$104$	−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	−0.841054	−	0.540951i	$-0.818064\pi$
$107$	−13.4365	+	3.60029i	−1.29895	+	0.348053i	−0.457899	+	0.889004i	$0.651398\pi$
$108$	−3.60437	−	3.24863i	−0.346830	−	0.312599i
$109$	−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	$0.503934\pi$
$110$	2.36828	−	1.18825i	0.225806	−	0.113295i
$111$		−	0.306675i		−	0.0291083i
$112$	9.69992	+	4.23220i	0.916557	+	0.399905i
$113$	−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	$0.871965\pi$
$114$	−2.36576	+	2.49175i	−0.221574	+	0.233374i
$115$	1.36665	+	7.62696i	0.127440	+	0.711217i
$116$	0.518580	+	9.98998i	0.0481490	+	0.927547i
$117$	1.20395	+	4.49319i	0.111305	+	0.415395i
$118$	6.60233	+	10.7800i	0.607793	+	0.992381i
$119$	−9.66492	−	9.50278i	−0.885982	−	0.871119i
$120$	−2.53914	−	0.698626i	−0.231791	−	0.0637755i
$121$	−5.14897	+	8.91827i	−0.468088	+	0.810752i
$122$	1.24137	−	2.28496i	0.112388	−	0.206871i
$123$	0.0385468	+	0.0103286i	0.00347565	+	0.000931297i
$124$	13.6254	−	8.83886i	1.22360	−	0.793753i
$125$	−10.8231	−	2.80378i	−0.968045	−	0.250778i
$126$	−5.59992	−	8.97205i	−0.498881	−	0.799293i
$127$	−4.54633	−	4.54633i	−0.403421	−	0.403421i	0.476016	−	0.879437i	$-0.342081\pi$
$127$	−4.54633	−	4.54633i	−0.403421	−	0.403421i	−0.879437	+	0.476016i	$0.842081\pi$
$128$	11.1278	−	2.04243i	0.983570	−	0.180527i
$129$	−2.48855	+	1.43677i	−0.219105	+	0.126500i
$130$	3.45815	+	3.88891i	0.303300	+	0.341080i
$131$	−11.9545	−	6.90194i	−1.04447	−	0.603025i	−0.123374	−	0.992360i	$-0.539371\pi$
$131$	−11.9545	−	6.90194i	−1.04447	−	0.603025i	−0.921096	+	0.389335i	$0.872705\pi$
$132$	−0.663741	+	0.215298i	−0.0577713	+	0.0187393i
$133$	−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
$136$	−14.2453	−	2.65119i	−1.22153	−	0.227338i
$137$	−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	$0.793927\pi$
$138$	−0.0529090	−	2.03986i	−0.00450391	−	0.173645i
$139$	−1.45615			−0.123509			−0.0617544	−	0.998091i	$-0.519670\pi$
$139$	−1.45615			−0.123509			−0.0617544	+	0.998091i	$0.519670\pi$
$140$	−10.1010	−	6.16202i	−0.853687	−	0.520786i
$141$	2.27813			0.191853
$142$	0.500510	+	19.2967i	0.0420019	+	1.61935i
$143$	1.33192	+	0.356886i	0.111380	+	0.0298443i
$144$	−10.3244	−	4.60901i	−0.860367	−	0.384084i
$145$	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
$148$	−0.454489	−	1.40114i	−0.0373588	−	0.115173i
$149$	−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	$0.823740\pi$
$150$	2.70632	+	1.15974i	0.220970	+	0.0946923i
$151$	−4.17078	+	2.40800i	−0.339414	+	0.195961i	−0.660013	−	0.751254i	$-0.729449\pi$
$151$	−4.17078	+	2.40800i	−0.339414	+	0.195961i	0.320599	+	0.947215i	$0.396116\pi$
$152$	−7.11596	+	14.8904i	−0.577181	+	1.20777i
$153$	10.2394	+	10.2394i	0.827805	+	0.827805i
$154$	−3.13326	+	0.107797i	−0.252485	+	0.00868653i
$155$	−16.4356	+	7.71960i	−1.32014	+	0.620053i
$156$	−0.745854	−	1.14976i	−0.0597161	−	0.0920547i
$157$	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	$0.528870\pi$
$158$	7.16596	−	13.1902i	0.570093	−	1.04936i
$159$	2.76263	−	4.78501i	0.219091	−	0.379476i
$160$	−12.6362	+	0.571090i	−0.998980	+	0.0451487i
$161$	2.29788	−	8.87543i	0.181098	−	0.699482i
$162$	5.51725	+	9.00835i	0.433476	+	0.707763i
$163$	−2.10452	−	7.85417i	−0.164839	−	0.615186i	−0.998061	−	0.0622476i	$-0.980173\pi$
$163$	−2.10452	−	7.85417i	−0.164839	−	0.615186i	0.833222	−	0.552938i	$-0.186494\pi$
$164$	0.191420	−	0.00993661i	0.0149474	−	0.000775919i
$165$	0.767918	−	0.137600i	0.0597824	−	0.0107122i
$166$	6.01545	−	6.33581i	0.466889	−	0.491754i
$167$	5.50649	+	5.50649i	0.426105	+	0.426105i	0.887299	−	0.461194i	$-0.152579\pi$
$167$	5.50649	+	5.50649i	0.426105	+	0.426105i	−0.461194	+	0.887299i	$0.652579\pi$
$168$	2.38496	+	2.00534i	0.184004	+	0.154715i
$169$		−	10.2918i		−	0.791674i
$170$	15.3760	+	5.10163i	1.17929	+	0.391277i
$171$	14.2832	−	8.24639i	1.09226	−	0.630617i
$172$	−9.24044	+	10.2523i	−0.704577	+	0.781731i
$173$	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
$178$	−3.59408	−	1.95258i	−0.269387	−	0.146352i
$179$	8.05255	+	13.9474i	0.601876	+	1.04248i	0.992537	+	0.121945i	$0.0389131\pi$
$179$	8.05255	+	13.9474i	0.601876	+	1.04248i	−0.390661	+	0.920535i	$0.627754\pi$
$180$	10.7354	+	6.67431i	0.800170	+	0.497474i
$181$	−3.83256			−0.284872			−0.142436	−	0.989804i	$-0.545493\pi$
$181$	−3.83256			−0.284872			−0.142436	+	0.989804i	$0.545493\pi$
$182$	−1.79725	−	5.88942i	−0.133221	−	0.436553i
$183$	0.541393	−	0.541393i	0.0400209	−	0.0400209i
$184$	−3.26479	−	9.24133i	−0.240683	−	0.681280i
$185$	0.290471	+	1.62105i	0.0213558	+	0.119182i
$186$	4.58539	−	1.35702i	0.336217	−	0.0995013i
$187$	4.14624	−	1.11098i	0.303203	−	0.0812431i
$188$	10.4083	−	3.37616i	0.759106	−	0.246232i
$189$	−1.71375	−	6.18602i	−0.124657	−	0.449967i
$190$	10.1451	−	15.4119i	0.736002	−	1.11810i
$191$	−2.42531	−	1.40025i	−0.175489	−	0.101319i	0.409682	−	0.912228i	$-0.365640\pi$
$191$	−2.42531	−	1.40025i	−0.175489	−	0.101319i	−0.585172	+	0.810909i	$0.698973\pi$
$192$	3.31237	+	0.353133i	0.239050	+	0.0254851i
$193$	−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	$0.982581\pi$
$194$	5.84513	−	6.15642i	0.419656	−	0.442005i
$195$	0.651407	+	1.38690i	0.0466482	+	0.0993178i
$196$	7.81672	+	11.6146i	0.558337	+	0.829614i
$197$	−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	$0.329410\pi$
$198$	3.34831	−	0.0868469i	0.237954	−	0.00617194i
$199$	−6.19859	−	10.7363i	−0.439406	−	0.761074i	0.558237	−	0.829681i	$-0.311478\pi$
$199$	−6.19859	−	10.7363i	−0.439406	−	0.761074i	−0.997644	+	0.0686071i	$0.978145\pi$
$200$	14.0834	+	1.28789i	0.995845	+	0.0910677i
$201$	−0.111119	+	0.192463i	−0.00783771	+	0.0135753i
$202$	−1.27028	−	2.07406i	−0.0893766	−	0.145931i
$203$	−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
$206$	6.30389	+	21.3010i	0.439213	+	1.48411i
$207$	−2.53508	+	9.46105i	−0.176200	+	0.657589i
$208$	−5.11160	−	4.14770i	−0.354426	−	0.287591i
$209$		−	4.88896i		−	0.338176i
$210$	−2.33695	−	2.58370i	−0.161265	−	0.178292i
$211$		−	0.877438i		−	0.0604053i	−0.999544	−	0.0302027i	$-0.990385\pi$
$211$		−	0.877438i		−	0.0604053i	0.999544	−	0.0302027i	$-0.00961527\pi$
$212$	5.53059	−	25.9560i	0.379842	−	1.78267i
$213$	−1.47101	+	5.48987i	−0.100792	+	0.376160i
$214$	−18.8636	+	5.58257i	−1.28949	+	0.381617i
$215$	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
$218$	−12.8595	+	7.87594i	−0.870957	+	0.533426i
$219$	1.24743	−	2.16061i	0.0842934	−	0.146000i
$220$	3.30455	−	1.76672i	0.222793	−	0.119112i
$221$	4.21537	+	7.30123i	0.283556	+	0.491134i
$222$	−0.0112454	−	0.433558i	−0.000754744	−	0.0290985i
$223$	12.6059	−	12.6059i	0.844153	−	0.844153i	−0.145243	−	0.989396i	$-0.546396\pi$
$223$	12.6059	−	12.6059i	0.844153	−	0.844153i	0.989396	+	0.145243i	$0.0463963\pi$
$224$	13.8683	+	5.62753i	0.926618	+	0.376005i
$225$	−10.8768	−	9.02441i	−0.725118	−	0.601628i
$226$	−8.15175	−	7.73957i	−0.542246	−	0.514828i
$227$	2.71787	−	10.1432i	0.180392	−	0.673230i	−0.815179	−	0.579210i	$-0.803361\pi$
$227$	2.71787	−	10.1432i	0.180392	−	0.673230i	0.995570	−	0.0940208i	$-0.0299720\pi$
$228$	−3.25320	+	3.60943i	−0.215448	+	0.239041i
$229$	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	$0.309996\pi$
$230$	2.21175	+	10.7324i	0.145839	+	0.707674i
$231$	−0.893620	−	0.231361i	−0.0587959	−	0.0152225i
$232$	1.09946	+	14.1042i	0.0721830	+	0.925986i
$233$	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	$0.275103\pi$
$234$	1.86682	+	6.30804i	0.122038	+	0.412370i
$235$	−12.0420	+	2.15776i	−0.785531	+	0.140756i
$236$	9.72925	+	14.9980i	0.633320	+	0.976288i
$237$	3.12526	−	3.12526i	0.203007	−	0.203007i
$238$	−14.0121	−	13.0800i	−0.908271	−	0.847853i
$239$	10.7078			0.692631			0.346315	−	0.938118i	$-0.387433\pi$
$239$	10.7078			0.692631			0.346315	+	0.938118i	$0.387433\pi$
$240$	−3.61530	−	0.894567i	−0.233367	−	0.0577440i
$241$	−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	$0.966056\pi$
$242$	−6.95227	+	12.7969i	−0.446909	+	0.822616i
$243$	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
$248$	18.9387	−	12.9955i	1.20261	−	0.825212i
$249$	2.22772	−	1.28618i	0.141176	−	0.0815080i
$250$	−15.4038	−	3.56695i	−0.974222	−	0.225593i
$251$			14.8357i			0.936420i	0.883617	+	0.468210i	$0.155101\pi$
$251$			14.8357i			0.936420i	−0.883617	+	0.468210i	$0.844899\pi$
$252$	−8.24582	−	12.4788i	−0.519438	−	0.786089i
$253$	2.05307	+	2.05307i	0.129075	+	0.129075i
$254$	−6.59403	−	6.26061i	−0.413746	−	0.392826i
$255$	3.91485	+	2.72506i	0.245157	+	0.170650i
$256$	15.6569	−	3.29550i	0.978559	−	0.205969i
$257$	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	$0.759612\pi$
$258$	−3.46547	+	2.12246i	−0.215751	+	0.132139i
$259$	0.488397	−	1.88641i	0.0303475	−	0.117216i
$260$	5.03152	+	5.37109i	0.312042	+	0.333101i
$261$	7.06897	−	12.2438i	0.437558	−	0.757873i
$262$	−17.1536	−	9.31917i	−1.05975	−	0.575740i
$263$	11.3208	+	3.03340i	0.698072	+	0.187048i	0.590367	−	0.807135i	$-0.298983\pi$
$263$	11.3208	+	3.03340i	0.698072	+	0.187048i	0.107705	+	0.994183i	$0.465650\pi$
$264$	−0.930462	+	0.328714i	−0.0572659	+	0.0202310i
$265$	−10.0708	+	27.9098i	−0.618645	+	1.71448i
$266$	−18.5204	+	11.5596i	−1.13556	+	0.708763i
$267$	−0.851570	−	0.851570i	−0.0521153	−	0.0521153i
$268$	−0.222452	+	1.04400i	−0.0135884	+	0.0637727i
$269$	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	$0.116061\pi$
$270$	5.09824	+	5.73329i	0.310269	+	0.348917i
$271$	−18.2735	−	10.5502i	−1.11003	−	0.640878i	−0.171195	−	0.985237i	$-0.554763\pi$
$271$	−18.2735	−	10.5502i	−1.11003	−	0.640878i	−0.938838	+	0.344359i	$0.888096\pi$
$272$	−20.2364	−	3.22573i	−1.22701	−	0.195588i
$273$	−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
$276$	−0.149599	−	2.88189i	−0.00900480	−	0.173469i
$277$	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	$0.552007\pi$
$278$	−2.05861	+	0.0533953i	−0.123467	+	0.00320244i
$279$	−22.9539			−1.37421
$280$	−14.5061	−	8.34109i	−0.866904	−	0.498476i
$281$	2.60091			0.155157			0.0775787	−	0.996986i	$-0.475281\pi$
$281$	2.60091			0.155157			0.0775787	+	0.996986i	$0.475281\pi$
$282$	3.22068	−	0.0835364i	0.191788	−	0.00497452i
$283$	−26.7711	−	7.17330i	−1.59138	−	0.426409i	−0.648954	−	0.760828i	$-0.724793\pi$
$283$	−26.7711	−	7.17330i	−1.59138	−	0.426409i	−0.942424	+	0.334419i	$0.891460\pi$
$284$	1.41518	+	27.2622i	0.0839755	+	1.61771i
$285$	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
$288$	−14.7650	−	6.13735i	−0.870036	−	0.361647i
$289$	8.00623	+	4.62240i	0.470955	+	0.271906i
$290$	0.925749	−	15.7897i	0.0543619	−	0.927203i
$291$	2.16465	−	1.24976i	0.126894	−	0.0732622i
$292$	2.49726	−	11.7201i	0.146141	−	0.685867i
$293$	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	$0.586082\pi$
$294$	1.23645	+	3.93227i	0.0721113	+	0.229334i
$295$	−8.49725	−	18.0913i	−0.494729	−	1.05332i
$296$	−0.693906	−	1.96418i	−0.0403325	−	0.114166i
$297$	1.96360	+	0.526145i	0.113940	+	0.0305300i
$298$	−14.3701	−	7.80696i	−0.832439	−	0.452245i
$299$	−2.85130	+	4.93859i	−0.164895	+	0.285606i
$300$	3.86855	+	1.54033i	0.223351	+	0.0889309i
$301$	−17.5956	+	4.87462i	−1.01419	+	0.280968i
$302$	−5.80810	+	3.55722i	−0.334218	+	0.204695i
$303$	−0.185342	−	0.691707i	−0.0106476	−	0.0397376i
$304$	−9.51409	+	21.3120i	−0.545670	+	1.22233i
$305$	−2.34897	+	3.37454i	−0.134501	+	0.193226i
$306$	14.8513	+	14.1003i	0.848990	+	0.806062i
$307$	−13.0364	−	13.0364i	−0.744028	−	0.744028i	0.229323	−	0.973350i	$-0.426349\pi$
$307$	−13.0364	−	13.0364i	−0.744028	−	0.744028i	−0.973350	+	0.229323i	$0.926349\pi$
$308$	−4.42566	+	0.267290i	−0.252175	+	0.0152303i
$309$			6.54063i			0.372083i
$310$	−22.9526	+	11.5162i	−1.30362	+	0.654075i
$311$	−10.1447	+	5.85707i	−0.575255	+	0.332124i	−0.759246	−	0.650804i	$-0.774432\pi$
$311$	−10.1447	+	5.85707i	−0.575255	+	0.332124i	0.183990	+	0.982928i	$0.441099\pi$
$312$	−1.09660	−	1.59811i	−0.0620829	−	0.0904754i
$313$	−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	$0.942510\pi$
$318$	3.73017	−	6.86605i	0.209178	−	0.385029i
$319$	−2.09546	−	3.62944i	−0.117323	−	0.203209i
$320$	−17.8434	+	1.27073i	−0.997474	+	0.0710359i
$321$	−5.79221			−0.323290
$322$	2.92315	−	12.6318i	0.162901	−	0.703942i
$323$	21.1365	−	21.1365i	1.17607	−	1.17607i
$324$	8.13027	+	12.5331i	0.451682	+	0.696285i
$325$	−4.75689	−	6.71402i	−0.263865	−	0.372427i
$326$	−3.26324	−	11.0266i	−0.180734	−	0.610705i
$327$	−4.28869	+	1.14915i	−0.237165	+	0.0635482i
$328$	0.270253	−	0.0210669i	0.0149222	−	0.00116323i
$329$	14.0131	+	3.62805i	0.772569	+	0.200021i
$330$	1.08059	−	0.222690i	0.0594845	−	0.0122587i
$331$	30.1984	+	17.4351i	1.65986	+	0.958318i	0.972780	+	0.231732i	$0.0744391\pi$
$331$	30.1984	+	17.4351i	1.65986	+	0.958318i	0.687075	+	0.726586i	$0.258894\pi$
$332$	8.27194	−	9.17775i	0.453982	−	0.503694i
$333$	−0.538813	+	2.01088i	−0.0295268	+	0.110195i
$334$	7.98665	+	7.58282i	0.437010	+	0.414913i
$335$	0.405069	−	1.12259i	0.0221313	−	0.0613336i
$336$	3.44525	+	2.74757i	0.187954	+	0.149892i
$337$	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	$0.0404240\pi$
$338$	−0.377387	−	14.5498i	−0.0205272	−	0.791407i
$339$	−1.65481	−	2.86622i	−0.0898771	−	0.155672i
$340$	21.9247	+	6.64854i	1.18903	+	0.360568i
$341$	−3.40211	+	5.89263i	−0.184235	+	0.319104i
$342$	19.8903	−	12.1820i	1.07554	−	0.658726i
$343$	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
$346$	4.24585	−	1.25653i	0.228258	−	0.0675516i
$347$	6.21524	−	23.1956i	0.333651	−	1.24520i	−0.571673	−	0.820482i	$-0.693705\pi$
$347$	6.21524	−	23.1956i	0.333651	−	1.24520i	0.905324	−	0.424722i	$-0.139628\pi$
$348$	−0.868049	+	4.07390i	−0.0465323	+	0.218384i
$349$		−	20.0084i		−	1.07102i	−0.844528	−	0.535512i	$-0.820119\pi$
$349$		−	20.0084i		−	1.07102i	0.844528	−	0.535512i	$-0.179881\pi$
$350$	14.8001	+	11.4437i	0.791096	+	0.611692i
$351$			3.99267i			0.213113i
$352$	−3.76395	+	2.88077i	−0.200619	+	0.153545i
$353$	−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	$0.869046\pi$
$354$	1.49372	+	5.04731i	0.0793902	+	0.268261i
$355$	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
$358$	11.8956	+	19.4227i	0.628704	+	1.02652i
$359$	−13.4523	+	23.3000i	−0.709984	+	1.22973i	0.254878	+	0.966973i	$0.417965\pi$
$359$	−13.4523	+	23.3000i	−0.709984	+	1.22973i	−0.964862	+	0.262756i	$0.915369\pi$
$360$	15.4218	+	9.04207i	0.812800	+	0.476559i
$361$	−7.52251	−	13.0294i	−0.395922	−	0.685756i
$362$	−5.41824	+	0.140536i	−0.284776	+	0.00738639i
$363$	−3.03206	+	3.03206i	−0.159142	+	0.159142i
$364$	−2.75681	−	8.26020i	−0.144496	−	0.432952i
$365$	−4.54734	+	12.6023i	−0.238019	+	0.659634i
$366$	0.745536	−	0.785240i	0.0389698	−	0.0410452i
$367$	−7.09214	+	26.4682i	−0.370207	+	1.38163i	0.490017	+	0.871713i	$0.336991\pi$
$367$	−7.09214	+	26.4682i	−0.370207	+	1.38163i	−0.860223	+	0.509917i	$0.829676\pi$
$368$	−4.95442	−	12.9451i	−0.258267	−	0.674811i
$369$	−0.234606	−	0.135450i	−0.0122131	−	0.00705123i
$370$	0.470092	+	2.28109i	0.0244389	+	0.118588i
$371$	24.6138	−	25.0337i	1.27788	−	1.29969i
$372$	6.43278	−	2.08661i	0.333524	−	0.108186i
$373$	−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	$0.608828\pi$
$374$	5.82096	−	1.72268i	0.300995	−	0.0890775i
$375$	−4.05092	−	2.29410i	−0.209189	−	0.118467i
$376$	14.5909	−	5.15467i	0.752466	−	0.265832i
$377$	5.82033	−	5.82033i	0.299762	−	0.299762i
$378$	−2.64963	−	8.68257i	−0.136282	−	0.446583i
$379$	20.4602			1.05097			0.525484	−	0.850803i	$-0.323884\pi$
$379$	20.4602			1.05097			0.525484	+	0.850803i	$0.323884\pi$
$380$	13.7774	−	22.1604i	0.706764	−	1.13681i
$381$	−1.33859	−	2.31851i	−0.0685783	−	0.118781i
$382$	−3.48010	−	1.89066i	−0.178057	−	0.0967345i
$383$	1.88076	+	7.01910i	0.0961024	+	0.358659i	0.997184	−	0.0749899i	$-0.0238925\pi$
$383$	1.88076	+	7.01910i	0.0961024	+	0.358659i	−0.901082	+	0.433649i	$0.857226\pi$
$384$	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
$388$	8.03773	−	8.91790i	0.408054	−	0.452738i
$389$	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	$0.288365\pi$
$390$	0.971775	+	1.93682i	0.0492077	+	0.0980749i
$391$			17.7521i			0.897764i
$392$	11.4767	+	16.1334i	0.579660	+	0.814858i
$393$	−4.06433	−	4.06433i	−0.205018	−	0.205018i
$394$	−6.74864	+	7.10805i	−0.339992	+	0.358098i
$395$	−13.5597	+	19.4799i	−0.682262	+	0.980142i
$396$	4.73044	−	0.245557i	0.237714	−	0.0123397i
$397$	−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	$-0.355776\pi$
$398$	−9.15687	−	14.9510i	−0.458992	−	0.749425i
$399$	−6.19472	+	1.71616i	−0.310124	+	0.0859155i
$400$	19.9574	+	1.30432i	0.997871	+	0.0652160i
$401$	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	$0.129712\pi$
$402$	−0.150035	+	0.276167i	−0.00748308	+	0.0137740i
$403$	−12.9085	−	3.45883i	−0.643020	−	0.172297i
$404$	−1.87190	−	2.88560i	−0.0931304	−	0.143564i
$405$	−7.10074	−	15.1180i	−0.352839	−	0.751222i
$406$	−8.79455	+	16.5196i	−0.436466	+	0.819853i
$407$	0.436364	+	0.436364i	0.0216298	+	0.0216298i
$408$	−5.44382	−	2.60155i	−0.269509	−	0.128796i
$409$	−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	$0.662199\pi$
$410$	−0.302549	−	0.0177384i	−0.0149418	−	0.000876040i
$411$	−5.18634	−	2.99434i	−0.255823	−	0.147700i
$412$	9.69314	+	29.8829i	0.477547	+	1.47222i
$413$	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
$416$	−7.37856	−	5.67633i	−0.361764	−	0.278305i
$417$	−0.585669	−	0.156930i	−0.0286803	−	0.00768487i
$418$	−0.179273	−	6.91170i	−0.00876851	−	0.338062i
$419$	28.1311			1.37429			0.687147	−	0.726518i	$-0.258863\pi$
$419$	28.1311			1.37429			0.687147	+	0.726518i	$0.258863\pi$
$420$	−3.39857	−	3.56698i	−0.165833	−	0.174051i
$421$	3.94616			0.192324			0.0961621	−	0.995366i	$-0.469343\pi$
$421$	3.94616			0.192324			0.0961621	+	0.995366i	$0.469343\pi$
$422$	−0.0321747	−	1.24047i	−0.00156624	−	0.0603850i
$423$	−14.9378	−	4.00256i	−0.726299	−	0.194611i
$424$	6.86702	−	36.8978i	0.333492	−	1.79191i
$425$	−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
$428$	−26.4635	+	8.58400i	−1.27916	+	0.414923i
$429$	0.497241	+	0.287082i	0.0240070	+	0.0138605i
$430$	16.3078	−	14.5015i	0.786434	−	0.699324i
$431$	−12.1350	+	7.00616i	−0.584523	+	0.337475i	−0.762929	−	0.646482i	$-0.776239\pi$
$431$	−12.1350	+	7.00616i	−0.584523	+	0.337475i	0.178406	+	0.983957i	$0.442906\pi$
$432$	−7.53586	−	6.11482i	−0.362569	−	0.294199i
$433$	−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	$0.774030\pi$
$434$	30.3666	−	1.04474i	1.45764	−	0.0501490i
$435$	1.58066	−	4.38056i	0.0757866	−	0.210032i
$436$	−17.8912	+	11.6061i	−0.856833	+	0.555829i
$437$	19.5299	+	5.23301i	0.934240	+	0.250329i
$438$	1.68431	−	3.10028i	0.0804795	−	0.148137i
$439$	−12.5163	+	21.6788i	−0.597369	+	1.03467i	0.395839	+	0.918320i	$0.370454\pi$
$439$	−12.5163	+	21.6788i	−0.597369	+	1.03467i	−0.993208	+	0.116354i	$0.962879\pi$
$440$	4.60699	−	2.61885i	0.219629	−	0.124849i
$441$	−0.334721	−	19.7835i	−0.0159391	−	0.942071i
$442$	6.22715	+	10.1675i	0.296196	+	0.483617i
$443$	1.13949	+	4.25262i	0.0541386	+	0.202048i	0.987698	−	0.156376i	$-0.0499810\pi$
$443$	1.13949	+	4.25262i	0.0541386	+	0.202048i	−0.933559	+	0.358424i	$0.883314\pi$
$444$	−0.0317962	−	0.612525i	−0.00150898	−	0.0290691i
$445$	5.30789	+	3.69474i	0.251618	+	0.175148i
$446$	17.3592	−	18.2837i	0.821982	−	0.865758i
$447$	−3.40482	−	3.40482i	−0.161042	−	0.161042i
$448$	19.8126	+	7.44732i	0.936055	+	0.351853i
$449$		−	24.2255i		−	1.14327i	−0.820507	−	0.571636i	$-0.806309\pi$
$449$		−	24.2255i		−	1.14327i	0.820507	−	0.571636i	$-0.193691\pi$
$450$	−15.7078	−	12.3593i	−0.740473	−	0.582624i
$451$	−0.0695443	+	0.0401514i	−0.00327471	+	0.00189066i
$452$	−11.8082	−	10.6428i	−0.555413	−	0.500595i
$453$	−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	$0.986957\pi$
$458$	33.8612	+	18.3960i	1.58223	+	0.859588i
$459$	6.21457	+	10.7640i	0.290071	+	0.502418i
$460$	3.52038	+	15.0917i	0.164139	+	0.703654i
$461$	12.3582			0.575580			0.287790	−	0.957693i	$-0.407079\pi$
$461$	12.3582			0.575580			0.287790	+	0.957693i	$0.407079\pi$
$462$	−1.27183	−	0.294316i	−0.0591708	−	0.0136928i
$463$	29.6788	−	29.6788i	1.37929	−	1.37929i	0.533471	−	0.845818i	$-0.320887\pi$
$463$	29.6788	−	29.6788i	1.37929	−	1.37929i	0.845818	−	0.533471i	$-0.179113\pi$
$464$	2.07153	+	19.8993i	0.0961684	+	0.923803i
$465$	−7.44244	+	1.33358i	−0.345135	+	0.0618434i
$466$	17.8107	−	5.27096i	0.825064	−	0.244172i
$467$	34.9600	−	9.36749i	1.61775	−	0.433476i	0.667413	−	0.744687i	$-0.267401\pi$
$467$	34.9600	−	9.36749i	1.61775	−	0.433476i	0.950341	+	0.311212i	$0.100735\pi$
$468$	2.87051	+	8.84947i	0.132689	+	0.409067i
$469$	−0.990018	+	1.00691i	−0.0457148	+	0.0464948i
$470$	−16.9451	+	3.49207i	−0.781617	+	0.161077i
$471$	1.53867	+	0.888349i	0.0708980	+	0.0409330i
$472$	14.3046	+	20.8465i	0.658421	+	0.959539i
$473$	1.49657	−	5.58529i	0.0688125	−	0.256812i
$474$	4.30370	−	4.53290i	0.197675	−	0.208203i
$475$	−18.6285	+	22.4522i	−0.854736	+	1.03018i
$476$	−20.2891	−	17.9779i	−0.929950	−	0.824018i
$477$	−26.5217	+	26.5217i	−1.21434	+	1.21434i
$478$	15.1380	−	0.392644i	0.692398	−	0.0179591i
$479$	−15.9325	−	27.5959i	−0.727974	−	1.26089i	−0.957738	−	0.287642i	$-0.907129\pi$
$479$	−15.9325	−	27.5959i	−0.727974	−	1.26089i	0.229764	−	0.973246i	$-0.426205\pi$
$480$	−5.14389	−	1.13211i	−0.234785	−	0.0516737i
$481$	−0.606023	+	1.04966i	−0.0276323	+	0.0478605i
$482$	−9.28749	−	15.1643i	−0.423034	−	0.690713i
$483$	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
$486$	4.16924	+	14.0880i	0.189121	+	0.639043i
$487$	−2.58469	+	9.64618i	−0.117123	+	0.437110i	−0.999437	−	0.0335518i	$-0.989318\pi$
$487$	−2.58469	+	9.64618i	−0.117123	+	0.437110i	0.882314	+	0.470662i	$0.155985\pi$
$488$	2.24249	−	4.69249i	0.101513	−	0.212419i
$489$		−	3.38579i		−	0.153111i
$490$	−10.2603	−	19.6145i	−0.463511	−	0.886091i
$491$			16.3501i			0.737871i	0.929455	+	0.368936i	$0.120278\pi$
$491$			16.3501i			0.737871i	−0.929455	+	0.368936i	$0.879722\pi$
$492$	0.0780608	+	0.0166328i	0.00351925	+	0.000749866i
$493$	6.63188	−	24.7505i	0.298685	−	1.11471i
$494$	13.0213	−	3.85357i	0.585856	−	0.173380i
$495$	−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
$498$	3.10225	−	1.90000i	0.139015	−	0.0851412i
$499$	−4.74809	+	8.22393i	−0.212554	+	0.368154i	−0.952513	−	0.304498i	$-0.901511\pi$
$499$	−4.74809	+	8.22393i	−0.212554	+	0.368154i	0.739959	+	0.672652i	$0.234845\pi$
$500$	−21.9077	−	4.47789i	−0.979743	−	0.200257i
$501$	1.62130	+	2.80817i	0.0724343	+	0.125460i
$502$	0.544008	+	20.9738i	0.0242803	+	0.936105i
$503$	−9.76866	+	9.76866i	−0.435563	+	0.435563i	−0.890516	−	0.454953i	$-0.849656\pi$
$503$	−9.76866	+	9.76866i	−0.435563	+	0.435563i	0.454953	+	0.890516i	$0.349656\pi$
$504$	−12.1150	−	17.3394i	−0.539645	−	0.772356i
$505$	1.63486	+	3.48075i	0.0727504	+	0.154891i
$506$	2.97778	+	2.82722i	0.132379	+	0.125685i
$507$	1.10915	−	4.13939i	0.0492589	−	0.183837i
$508$	−9.55180	−	8.60906i	−0.423792	−	0.381965i
$509$	−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	$0.810001\pi$
$510$	5.63449	+	3.70897i	0.249500	+	0.164236i
$511$	11.1140	−	11.3037i	0.491656	−	0.500045i
$512$	22.0140	−	5.23310i	0.972889	−	0.231273i
$513$	13.6738	−	3.66389i	0.603714	−	0.161765i
$514$	6.09429	+	20.5928i	0.268808	+	0.908308i
$515$	−6.19503	−	34.5731i	−0.272986	−	1.52347i
$516$	−4.82144	+	3.12768i	−0.212252	+	0.137688i
$517$	−3.24152	+	3.24152i	−0.142562	+	0.142562i
$518$	0.621293	−	2.68480i	0.0272981	−	0.117963i
$519$	1.30372			0.0572269
$520$	7.31021	+	7.40882i	0.320574	+	0.324898i
$521$	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	$0.450899\pi$
$522$	9.54470	−	17.5688i	0.417760	−	0.768964i
$523$	0.529969	+	1.97787i	0.0231739	+	0.0864862i	0.976544	−	0.215316i	$-0.0690783\pi$
$523$	0.529969	+	1.97787i	0.0231739	+	0.0864862i	−0.953370	+	0.301803i	$0.902412\pi$
$524$	−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
$528$	−1.30338	+	0.498835i	−0.0567221	+	0.0217090i
$529$	9.51967	−	5.49618i	0.413899	−	0.238964i
$530$	−13.2141	+	39.8264i	−0.573982	+	1.72995i
$531$		−	25.2662i		−	1.09646i
$532$	−25.7592	+	17.0213i	−1.11680	+	0.737968i
$533$	−0.111524	−	0.111524i	−0.00483066	−	0.00483066i
$534$	−1.23512	−	1.17267i	−0.0534490	−	0.0507464i
$535$	30.6171	−	5.48617i	1.32369	−	0.237188i
$536$	−0.276206	+	1.48411i	−0.0119303	+	0.0641036i
$537$	1.73565	+	6.47754i	0.0748989	+	0.279527i
$538$	24.9542	−	15.2834i	1.07585	−	0.658915i
$539$	−5.12835	−	2.84628i	−0.220894	−	0.122598i
$540$	7.41780	+	7.91842i	0.319211	+	0.340754i
$541$	−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	$0.197111\pi$
$542$	−26.2207	−	14.2451i	−1.12628	−	0.611881i
$543$	−1.54147	−	0.413036i	−0.0661509	−	0.0177251i
$544$	−28.7272	−	3.81829i	−1.23167	−	0.163708i
$545$	21.5812	−	10.1364i	0.924437	−	0.434196i
$546$	−0.0881585	−	2.56244i	−0.00377284	−	0.109662i
$547$	−13.7530	−	13.7530i	−0.588037	−	0.588037i	0.349062	−	0.937099i	$-0.386500\pi$
$547$	−13.7530	−	13.7530i	−0.588037	−	0.588037i	−0.937099	+	0.349062i	$0.886500\pi$
$548$	−28.1330	−	5.99445i	−1.20178	−	0.256070i
$549$	−4.50114	+	2.59873i	−0.192104	+	0.110911i
$550$	−5.50097	+	2.20061i	−0.234562	+	0.0938343i
$551$	−25.2741	−	14.5920i	−1.07671	−	0.621642i
$552$	−0.317170	−	4.06875i	−0.0134996	−	0.173178i
$553$	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
$556$	−2.90838	+	0.150974i	−0.123343	+	0.00640272i
$557$	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	$0.498033\pi$
$558$	−32.4508	+	0.841694i	−1.37375	+	0.0356317i
$559$	11.3568			0.480342
$560$	−20.8136	−	11.2602i	−0.879537	−	0.475830i
$561$	1.78737			0.0754628
$562$	3.67701	−	0.0953725i	0.155105	−	0.00402305i
$563$	7.45322	+	1.99709i	0.314116	+	0.0841671i	0.412433	−	0.910988i	$-0.364679\pi$
$563$	7.45322	+	1.99709i	0.314116	+	0.0841671i	−0.0983168	+	0.995155i	$0.531346\pi$
$564$	4.55013	−	0.236197i	0.191595	−	0.00994570i
$565$	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
$568$	3.00037	+	38.4897i	0.125893	+	1.61499i
$569$	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	$0.479954\pi$
$570$	5.74135	−	5.10540i	0.240479	−	0.213842i
$571$	−4.41042	+	2.54636i	−0.184570	+	0.106562i	−0.589438	−	0.807813i	$-0.700651\pi$
$571$	−4.41042	+	2.54636i	−0.184570	+	0.106562i	0.404868	+	0.914375i	$0.367318\pi$
$572$	2.69725	+	0.574718i	0.112778	+	0.0240302i
$573$	−0.824564	−	0.824564i	−0.0344467	−	0.0344467i
$574$	0.316534	+	0.168514i	0.0132119	+	0.00703364i
$575$	−1.60572	−	17.2515i	−0.0669633	−	0.719435i
$576$	−21.0989	−	8.13518i	−0.879121	−	0.338966i
$577$	−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	$0.718197\pi$
$578$	11.4882	+	6.24128i	0.477847	+	0.259603i
$579$	−1.80058	+	3.11870i	−0.0748295	+	0.129609i
$580$	0.729776	−	22.3564i	0.0303023	−	0.928301i
$581$	15.7514	−	4.36370i	0.653478	−	0.181037i
$582$	3.01442	−	1.84621i	0.124952	−	0.0765278i
$583$	2.87763	+	10.7395i	0.119179	+	0.444783i
$584$	3.10071	−	16.6607i	0.128308	−	0.689425i
$585$	−1.83459	−	10.2384i	−0.0758508	−	0.423307i
$586$	17.2921	+	16.4178i	0.714332	+	0.678213i
$587$	8.18830	+	8.18830i	0.337967	+	0.337967i	0.855602	−	0.517635i	$-0.173187\pi$
$587$	8.18830	+	8.18830i	0.337967	+	0.337967i	−0.517635	+	0.855602i	$0.673187\pi$
$588$	1.89221	+	5.51385i	0.0780334	+	0.227388i
$589$			47.3823i			1.95235i
$590$	−12.6763	−	25.2648i	−0.521874	−	1.04014i
$591$	−2.49925	+	1.44294i	−0.102805	+	0.0593547i
$592$	−1.05303	−	2.75139i	−0.0432791	−	0.113081i
$593$	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
$598$	−3.84990	+	7.08643i	−0.157434	+	0.289786i
$599$	−12.5631	−	21.7600i	−0.513315	−	0.889088i	−0.999881	−	0.0154439i	$-0.995084\pi$
$599$	−12.5631	−	21.7600i	−0.513315	−	0.889088i	0.486566	−	0.873644i	$-0.338249\pi$
$600$	5.52560	+	2.03577i	0.225582	+	0.0831098i
$601$	−23.9702			−0.977766			−0.488883	−	0.872349i	$-0.662595\pi$
$601$	−23.9702			−0.977766			−0.488883	+	0.872349i	$0.662595\pi$
$602$	−24.6968	+	7.53665i	−1.00657	+	0.307171i
$603$	1.06676	−	1.06676i	0.0434417	−	0.0434417i
$604$	−8.08069	+	5.24196i	−0.328799	+	0.213292i
$605$	13.1553	−	18.8991i	0.534841	−	0.768356i
$606$	−0.287390	−	0.971097i	−0.0116744	−	0.0394481i
$607$	−1.98316	+	0.531386i	−0.0804940	+	0.0215683i	−0.298841	−	0.954303i	$-0.596600\pi$
$607$	−1.98316	+	0.531386i	−0.0804940	+	0.0215683i	0.218347	+	0.975871i	$0.429933\pi$
$608$	−12.6689	+	30.4785i	−0.513793	+	1.23607i
$609$	−3.86324	+	3.92915i	−0.156546	+	0.159217i
$610$	−3.19708	+	4.85685i	−0.129446	+	0.196648i
$611$	−7.79739	−	4.50183i	−0.315449	−	0.182124i
$612$	21.5128	+	19.3896i	0.869605	+	0.783778i
$613$	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	$-0.181994\pi$
$614$	−18.9081	−	17.9521i	−0.763069	−	0.724486i
$615$	−0.0839366	−	0.0302872i	−0.00338465	−	0.00122130i
$616$	−6.24692	+	0.540162i	−0.251696	+	0.0217637i
$617$	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	$0.176876\pi$
$618$	0.239838	+	9.24673i	0.00964768	+	0.371958i
$619$	−13.8212	−	23.9391i	−0.555523	−	0.962194i	−0.997863	−	0.0653461i	$-0.979185\pi$
$619$	−13.8212	−	23.9391i	−0.555523	−	0.962194i	0.442340	−	0.896847i	$-0.354148\pi$
$620$	−32.0267	+	17.1225i	−1.28622	+	0.687656i
$621$	−4.20357	+	7.28080i	−0.168683	+	0.292168i
$622$	−14.1272	+	8.65236i	−0.566450	+	0.346928i
$623$	−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
$626$	−25.8984	+	7.66447i	−1.03511	+	0.306334i
$627$	0.526885	−	1.96636i	0.0210417	−	0.0785289i
$628$	8.34640	+	1.77841i	0.333058	+	0.0709664i
$629$			3.77309i			0.150443i
$630$	10.7840	+	21.0473i	0.429645	+	0.838544i
$631$			11.5488i			0.459750i	0.973220	+	0.229875i	$0.0738318\pi$
$631$			11.5488i			0.459750i	−0.973220	+	0.229875i	$0.926168\pi$
$632$	12.9451	−	27.0880i	0.514927	−	1.07750i
$633$	0.0945618	−	0.352910i	0.00375850	−	0.0140269i
$634$	−1.15898	−	3.91624i	−0.0460292	−	0.155534i
$635$	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
$638$	−3.09551	−	5.05423i	−0.122553	−	0.200099i
$639$	19.2909	−	33.4128i	0.763135	−	1.32179i
$640$	−25.1792	+	2.45077i	−0.995297	+	0.0968753i
$641$	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	$0.723585\pi$
$642$	−8.18867	+	0.212394i	−0.323181	+	0.00838253i
$643$	−18.4696	+	18.4696i	−0.728370	+	0.728370i	−0.970295	−	0.241925i	$-0.922221\pi$
$643$	−18.4696	+	18.4696i	−0.728370	+	0.728370i	0.241925	+	0.970295i	$0.422221\pi$
$644$	3.66937	−	17.9652i	0.144593	−	0.707929i
$645$	5.81585	−	2.73163i	0.228999	−	0.107558i
$646$	29.1064	−	30.6566i	1.14518	−	1.20617i
$647$	−8.66156	+	32.3254i	−0.340521	+	1.27084i	0.557237	+	0.830353i	$0.311861\pi$
$647$	−8.66156	+	32.3254i	−0.340521	+	1.27084i	−0.897758	+	0.440489i	$0.854805\pi$
$648$	11.9536	+	17.4204i	0.469584	+	0.684339i
$649$	−6.48624	−	3.74483i	−0.254607	−	0.146997i
$650$	−6.97120	−	9.31744i	−0.273433	−	0.365460i
$651$	8.66070	+	2.24228i	0.339440	+	0.0878821i
$652$	−5.01770	−	15.4690i	−0.196508	−	0.605813i
$653$	−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	$0.483384\pi$
$654$	−6.02095	+	1.78186i	−0.235438	+	0.0696763i
$655$	25.3332	+	17.6341i	0.989852	+	0.689021i
$656$	0.381295	−	0.0396930i	0.0148871	−	0.00154975i
$657$	−11.9755	+	11.9755i	−0.467210	+	0.467210i
$658$	19.9439	+	4.61526i	0.777496	+	0.179922i
$659$	21.6586			0.843698			0.421849	−	0.906666i	$-0.361381\pi$
$659$	21.6586			0.843698			0.421849	+	0.906666i	$0.361381\pi$
$660$	1.51950	−	0.354449i	0.0591466	−	0.0137969i
$661$	−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	$0.977730\pi$
$662$	43.3320	+	23.5413i	1.68415	+	0.914957i
$663$	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
$668$	11.5691	+	10.4273i	0.447621	+	0.403443i
$669$	6.42869	−	3.71161i	0.248548	−	0.143499i
$670$	0.531497	−	1.60190i	0.0205335	−	0.0618868i
$671$			1.54069i			0.0594775i
$672$	4.97143	+	3.75801i	0.191777	+	0.144969i
$673$	−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	$0.859216\pi$
$674$	21.8743	−	23.0392i	0.842565	−	0.887437i
$675$	−7.01292	−	9.89825i	−0.269928	−	0.380984i
$676$	−1.06705	−	20.5558i	−0.0410405	−	0.790609i
$677$	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	$0.831974\pi$
$678$	−2.44457	−	3.99141i	−0.0938833	−	0.153289i
$679$	15.3054	−	4.24015i	0.587368	−	0.162722i
$680$	31.2396	+	8.59534i	1.19798	+	0.329616i
$681$	2.18628	−	3.78675i	0.0837785	−	0.145109i
$682$	−4.59362	+	8.45539i	−0.175899	+	0.323774i
$683$	2.13814	+	0.572913i	0.0818137	+	0.0219219i	0.299494	−	0.954098i	$-0.403182\pi$
$683$	2.13814	+	0.572913i	0.0818137	+	0.0219219i	−0.217680	+	0.976020i	$0.569849\pi$
$684$	27.6729	−	17.9515i	1.05810	−	0.686392i
$685$	30.2506	+	10.9155i	1.15582	+	0.417059i
$686$	1.34325	+	26.1571i	0.0512856	+	0.998684i
$687$	8.02297	+	8.02297i	0.306095	+	0.306095i
$688$	−17.3931	+	21.4351i	−0.663105	+	0.817206i
$689$	−18.9114	+	10.9185i	−0.720467	+	0.415962i
$690$	−0.267058	+	4.55498i	−0.0101667	+	0.173405i
$691$	−19.0959	−	11.0250i	−0.726442	−	0.419411i	0.0906771	−	0.995880i	$-0.471097\pi$
$691$	−19.0959	−	11.0250i	−0.726442	−	0.419411i	−0.817119	+	0.576469i	$0.804430\pi$
$692$	5.95644	−	1.93210i	0.226430	−	0.0734473i
$693$	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
$696$	−1.07781	+	5.79126i	−0.0408542	+	0.219517i
$697$	−0.474249	−	0.127075i	−0.0179635	−	0.00481330i
$698$	−0.733685	−	28.2866i	−0.0277704	−	1.07066i
$699$	5.46890			0.206853
$700$	21.3430	+	15.6357i	0.806691	+	0.590974i
$701$	3.86536			0.145993			0.0729964	−	0.997332i	$-0.476744\pi$
$701$	3.86536			0.145993			0.0729964	+	0.997332i	$0.476744\pi$
$702$	0.146407	+	5.64459i	0.00552577	+	0.213041i
$703$	4.15093	+	1.11224i	0.156555	+	0.0419489i
$704$	−5.21561	+	4.21067i	−0.196571	+	0.158696i
$705$	−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
$708$	2.29681	+	7.08080i	0.0863192	+	0.266113i
$709$	−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	$0.870157\pi$
$710$	2.52633	−	43.0893i	0.0948113	−	1.61711i
$711$	−25.9834	+	15.0015i	−0.974452	+	0.562600i
$712$	−7.38093	−	3.52727i	−0.276612	−	0.132190i
$713$	−19.8977	−	19.8977i	−0.745175	−	0.745175i
$714$	−4.22610	−	6.77094i	−0.158158	−	0.253396i
$715$	−2.90028	−	1.04652i	−0.108464	−	0.0391377i
$716$	17.5295	+	27.0225i	0.655109	+	1.00988i
$717$	4.30673	+	1.15398i	0.160838	+	0.0430963i
$718$	−18.1636	+	33.4334i	−0.677860	+	1.24772i
$719$	−5.63438	+	9.75903i	−0.210127	+	0.363950i	−0.951754	−	0.306862i	$-0.900721\pi$
$719$	−5.63438	+	9.75903i	−0.210127	+	0.363950i	0.741627	+	0.670812i	$0.234054\pi$
$720$	22.1339	+	12.2176i	0.824883	+	0.455324i
$721$	−10.4163	+	40.2325i	−0.387924	+	1.49834i
$722$	−11.1126	−	18.1443i	−0.413569	−	0.675260i
$723$	−1.35511	−	5.05733i	−0.0503970	−	0.188084i
$724$	−7.65481	+	0.397361i	−0.284489	+	0.0147678i
$725$	−4.20610	+	24.6523i	−0.156210	+	0.915565i
$726$	−4.17536	+	4.39773i	−0.154962	+	0.163215i
$727$	−21.9895	−	21.9895i	−0.815544	−	0.815544i	0.169915	−	0.985459i	$-0.445651\pi$
$727$	−21.9895	−	21.9895i	−0.815544	−	0.815544i	−0.985459	+	0.169915i	$0.945651\pi$
$728$	−4.20029	−	11.5767i	−0.155673	−	0.429060i
$729$		−	18.0830i		−	0.669742i
$730$	−5.96664	+	17.9831i	−0.220835	+	0.665584i
$731$	30.6172	−	17.6768i	1.13242	−	0.653801i
$732$	1.02520	−	1.13746i	0.0378924	−	0.0420418i
$733$	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
$738$	−0.336638	−	0.182888i	−0.0123918	−	0.00673219i
$739$	15.6220	+	27.0581i	0.574665	+	0.995349i	0.996078	+	0.0884798i	$0.0282009\pi$
$739$	15.6220	+	27.0581i	0.574665	+	0.995349i	−0.421413	+	0.906869i	$0.638466\pi$
$740$	0.748232	+	3.20763i	0.0275056	+	0.117915i
$741$	3.99829			0.146881
$742$	33.8795	−	36.2937i	1.24375	−	1.33238i
$743$	−13.4261	+	13.4261i	−0.492557	+	0.492557i	−0.909111	−	0.416554i	$-0.863238\pi$
$743$	−13.4261	+	13.4261i	−0.492557	+	0.492557i	0.416554	+	0.909111i	$0.363238\pi$
$744$	9.01776	−	3.18580i	0.330607	−	0.116797i
$745$	21.2225	+	14.7726i	0.777531	+	0.541227i
$746$	−29.7356	+	8.80007i	−1.08870	+	0.322194i
$747$	−16.8670	+	4.51950i	−0.617131	+	0.165360i
$748$	8.16615	−	2.64886i	0.298584	−	0.0968520i
$749$	−35.6289	−	9.22443i	−1.30185	−	0.337053i
$750$	−5.81106	−	3.09471i	−0.212190	−	0.113003i
$751$	29.3693	+	16.9564i	1.07170	+	0.618748i	0.928646	−	0.370967i	$-0.120974\pi$
$751$	29.3693	+	16.9564i	1.07170	+	0.618748i	0.143056	+	0.989715i	$0.454307\pi$
$752$	20.4386	−	7.82238i	0.745320	−	0.285253i
$753$	−1.59885	+	5.96698i	−0.0582652	+	0.217449i
$754$	8.01500	−	8.44185i	0.291889	−	0.307434i
$755$	9.74730	−	4.57818i	0.354741	−	0.166617i
$756$	−4.06426	−	12.1777i	−0.147816	−	0.442900i
$757$	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	$0.161153\pi$
$758$	28.9253	−	0.750252i	1.05061	−	0.0272504i
$759$	0.604493	+	1.04701i	0.0219417	+	0.0380041i
$760$	18.6650	−	31.8342i	0.677050	−	1.15475i
$761$	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	$0.0199221\pi$
$762$	−1.97744	−	3.22869i	−0.0716351	−	0.116963i
$763$	−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
$766$	2.91629	+	9.85420i	0.105370	+	0.356047i
$767$	3.80726	−	14.2089i	0.137472	−	0.513054i
$768$	6.65245	+	0.361887i	0.240050	+	0.0130585i
$769$			38.3029i			1.38124i	0.723219	+	0.690619i	$0.242662\pi$
$769$			38.3029i			1.38124i	−0.723219	+	0.690619i	$0.757338\pi$
$770$	7.00153	+	0.351099i	0.252318	+	0.0126527i
$771$			6.32315i			0.227723i
$772$	−3.60463	+	16.9172i	−0.129734	+	0.608862i
$773$	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	$0.0751141\pi$
$774$	26.4523	−	7.82839i	0.950808	−	0.281386i
$775$	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
$778$	6.69829	−	4.10243i	0.240145	−	0.147079i
$779$	−0.279601	+	0.484282i	−0.0100177	+	0.0173512i
$780$	1.44486	+	2.70253i	0.0517342	+	0.0967660i
$781$	−5.71840	−	9.90456i	−0.204620	−	0.354413i
$782$	0.650951	+	25.0969i	0.0232780	+	0.897462i
$783$	8.58072	−	8.58072i	0.306650	−	0.306650i
$784$	16.8166	+	22.3875i	0.600594	+	0.799554i
$785$	−8.97465	−	3.23836i	−0.320319	−	0.115582i
$786$	−5.89493	−	5.59687i	−0.210265	−	0.199634i
$787$	−3.70435	+	13.8248i	−0.132046	+	0.492801i	−0.999993	−	0.00385583i	$-0.998773\pi$
$787$	−3.70435	+	13.8248i	−0.132046	+	0.492801i	0.867947	+	0.496657i	$0.165439\pi$
$788$	−9.28017	+	10.2964i	−0.330592	+	0.366794i
$789$	4.22637	+	2.44010i	0.150463	+	0.0868698i
$790$	−18.4555	+	28.0368i	−0.656619	+	0.997503i
$791$	−5.61441	−	20.2660i	−0.199625	−	0.720575i
$792$	6.67861	−	0.520614i	0.237314	−	0.0184992i
$793$	−2.92289	+	0.783185i	−0.103795	+	0.0278117i
$794$	−12.0770	−	40.8084i	−0.428597	−	1.44824i
$795$	−7.05837	+	10.1401i	−0.250335	+	0.359632i
$796$	−13.4937	−	20.8010i	−0.478270	−	0.737272i
$797$	−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	$0.329412\pi$
$798$	−8.69478	+	2.65336i	−0.307792	+	0.0939278i
$799$	−28.0283			−0.991569
$800$	28.2624	+	1.11215i	0.999227	+	0.0393205i
$801$	4.08761	+	7.07995i	0.144429	+	0.250158i
$802$	3.13201	−	5.76503i	0.110595	−	0.203570i
$803$	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
$808$	−2.75218	−	4.01085i	−0.0968215	−	0.141101i
$809$	−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	$0.548727\pi$
$810$	−10.5930	−	21.1126i	−0.372198	−	0.741820i
$811$		−	11.1150i		−	0.390299i	−0.980774	−	0.195149i	$-0.937481\pi$
$811$		−	11.1150i		−	0.390299i	0.980774	−	0.195149i	$-0.0625192\pi$
$812$	−11.8274	+	23.6768i	−0.415062	+	0.830894i
$813$	−6.21267	−	6.21267i	−0.217888	−	0.217888i
$814$	0.632906	+	0.600904i	0.0221833	+	0.0210617i
$815$	3.20689	+	17.8969i	0.112332	+	0.626903i
$816$	−7.79153	−	3.47829i	−0.272758	−	0.121764i
$817$	−10.4216	−	38.8940i	−0.364607	−	1.36073i
$818$	−41.8979	+	25.6608i	−1.46493	+	0.897207i
$819$	−3.08467	+	11.9144i	−0.107787	+	0.416322i
$820$	−0.428376	−	0.0139834i	−0.0149595	−	0.000488321i
$821$	−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	$0.242934\pi$
$822$	−7.44193	−	4.04303i	−0.259567	−	0.141017i
$823$	24.5214	+	6.57048i	0.854761	+	0.229033i	0.659487	−	0.751716i	$-0.270774\pi$
$823$	24.5214	+	6.57048i	0.854761	+	0.229033i	0.195274	+	0.980749i	$0.437440\pi$
$824$	14.7993	+	41.8911i	0.515559	+	1.45935i
$825$	−1.73696	+	0.161672i	−0.0604731	+	0.00562869i
$826$	1.14998	+	33.4257i	0.0400129	+	1.16303i
$827$	−17.3478	−	17.3478i	−0.603242	−	0.603242i	0.337929	−	0.941172i	$-0.390274\pi$
$827$	−17.3478	−	17.3478i	−0.603242	−	0.603242i	−0.941172	+	0.337929i	$0.890274\pi$
$828$	−4.08242	+	19.1595i	−0.141874	+	0.665839i
$829$	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	$0.227315\pi$
$830$	−14.5986	+	12.9816i	−0.506725	+	0.450597i
$831$	1.17942	+	0.680936i	0.0409135	+	0.0236214i
$832$	−10.6395	−	7.75428i	−0.368858	−	0.268831i
$833$	−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
$836$	−0.506889	−	9.76476i	−0.0175311	−	0.337721i
$837$	−19.0306	−	5.09924i	−0.657794	−	0.176255i
$838$	39.7700	−	1.03154i	1.37383	−	0.0356338i
$839$	3.21211			0.110894			0.0554472	−	0.998462i	$-0.482342\pi$
$839$	3.21211			0.110894			0.0554472	+	0.998462i	$0.482342\pi$
$840$	−4.93549	−	4.91815i	−0.170290	−	0.169692i
$841$	3.98283			0.137339
$842$	5.57884	−	0.144701i	0.192260	−	0.00498674i
$843$	1.04610	+	0.280301i	0.0360295	+	0.00965408i
$844$	−0.0909731	−	1.75252i	−0.00313142	−	0.0603241i
$845$	−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
$848$	8.35517	−	52.4156i	0.286918	−	1.79996i
$849$	−9.99440	−	5.77027i	−0.343007	−	0.198035i
$850$	−33.2964	−	14.2685i	−1.14206	−	0.489406i
$851$	−2.21021	+	1.27607i	−0.0757652	+	0.0437430i
$852$	−2.36886	+	11.1175i	−0.0811559	+	0.380879i
$853$	−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	$-0.528713\pi$
$854$	5.83645	−	3.64283i	0.199719	−	0.124655i
$855$	−33.3804	+	15.6783i	−1.14158	+	0.536187i
$856$	−37.0977	+	13.1059i	−1.26797	+	0.447951i
$857$	−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	$0.799040\pi$
$858$	0.713496	+	0.387626i	0.0243583	+	0.0132333i
$859$	−5.30651	+	9.19114i	−0.181056	+	0.313598i	−0.942240	−	0.334938i	$-0.891285\pi$
$859$	−5.30651	+	9.19114i	−0.181056	+	0.313598i	0.761185	+	0.648535i	$0.224618\pi$
$860$	22.5233	−	21.0993i	0.768037	−	0.719480i
$861$	0.0752872	+	0.0740242i	0.00256578	+	0.00252274i
$862$	−16.8988	+	10.3498i	−0.575576	+	0.352517i
$863$	−5.67140	−	21.1660i	−0.193057	−	0.720498i	−0.992761	−	0.120104i	$-0.961677\pi$
$863$	−5.67140	−	21.1660i	−0.193057	−	0.720498i	0.799705	−	0.600394i	$-0.204989\pi$
$864$	−10.8780	−	8.36842i	−0.370075	−	0.284699i
$865$	−6.89133	+	1.23483i	−0.234312	+	0.0419856i
$866$	−3.21919	−	3.05642i	−0.109393	−	0.103861i
$867$	2.72198	+	2.72198i	0.0924434	+	0.0924434i
$868$	42.8922	−	2.59049i	1.45585	−	0.0879271i
$869$			8.89379i			0.301701i
$870$	2.07400	−	6.25092i	0.0703153	−	0.211926i
$871$	0.760656	−	0.439165i	0.0257739	−	0.0148805i
$872$	−24.8679	+	17.0640i	−0.842133	+	0.577859i
$873$	−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	$0.854899\pi$
$878$	−16.8998	+	31.1071i	−0.570340	+	1.04981i
$879$	3.51032	+	6.08006i	0.118400	+	0.205075i
$880$	6.41704	−	3.87130i	0.216318	−	0.130502i
$881$	27.2610			0.918447			0.459224	−	0.888321i	$-0.348128\pi$
$881$	27.2610			0.918447			0.459224	+	0.888321i	$0.348128\pi$
$882$	−1.19865	−	27.9564i	−0.0403605	−	0.941341i
$883$	−29.9932	+	29.9932i	−1.00935	+	1.00935i	−0.00939636	+	0.999956i	$0.502991\pi$
$883$	−29.9932	+	29.9932i	−1.00935	+	1.00935i	−0.999956	+	0.00939636i	$0.997009\pi$
$884$	9.17640	+	14.1458i	0.308636	+	0.475774i
$885$	−1.46792	−	8.19216i	−0.0493437	−	0.275376i
$886$	1.76687	+	5.97030i	0.0593592	+	0.200576i
$887$	21.8561	−	5.85632i	0.733855	−	0.196636i	0.127510	−	0.991837i	$-0.459302\pi$
$887$	21.8561	−	5.85632i	0.733855	−	0.196636i	0.606345	+	0.795201i	$0.292635\pi$
$888$	−0.0674121	−	0.864784i	−0.00226220	−	0.0290202i
$889$	−4.54155	−	16.3933i	−0.152319	−	0.549815i
$890$	7.63946	+	5.02877i	0.256075	+	0.168565i
$891$	−5.42024	−	3.12937i	−0.181585	−	0.104838i
$892$	23.8709	−	26.4849i	0.799257	−	0.886780i
$893$	−8.26224	+	30.8351i	−0.276485	+	1.03186i
$894$	−4.93837	−	4.68867i	−0.165164	−	0.156813i
$895$	−15.3098	−	32.5957i	−0.511749	−	1.08956i
$896$	28.2829	+	9.80205i	0.944864	+	0.327464i
$897$	−1.67904	+	1.67904i	−0.0560615	+	0.0560615i
$898$	−0.888322	−	34.2485i	−0.0296437	−	1.14289i
$899$	20.3085	+	35.1754i	0.677327	+	1.17317i
$900$	−22.6599	−	16.8969i	−0.755331	−	0.563228i
$901$	−33.9892	+	58.8710i	−1.13234	+	1.96128i
$902$	−0.0968451	+	0.0593137i	−0.00322459	+	0.00197493i
$903$	−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
$906$	−2.71941	+	0.804791i	−0.0903462	+	0.0267374i
$907$	1.07561	−	4.01423i	0.0357151	−	0.133290i	−0.945766	−	0.324847i	$-0.894687\pi$
$907$	1.07561	−	4.01423i	0.0357151	−	0.133290i	0.981481	+	0.191557i	$0.0613537\pi$
$908$	4.37678	−	20.5410i	0.145249	−	0.681677i
$909$			4.86119i			0.161235i
$910$	2.89305	+	13.4613i	0.0959036	+	0.446239i
$911$			29.4464i			0.975603i	0.872955	+	0.487801i	$0.162201\pi$
$911$			29.4464i			0.975603i	−0.872955	+	0.487801i	$0.837799\pi$
$912$	−6.12341	+	7.54646i	−0.202767	+	0.249888i
$913$	−1.33972	+	4.99989i	−0.0443381	+	0.165472i
$914$	−3.75829	−	12.6993i	−0.124313	−	0.420057i
$915$	−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
$918$	9.18048	+	14.9895i	0.303001	+	0.494728i
$919$	4.57597	−	7.92582i	0.150947	−	0.261449i	−0.780629	−	0.624995i	$-0.785101\pi$
$919$	4.57597	−	7.92582i	0.150947	−	0.261449i	0.931576	+	0.363547i	$0.118434\pi$
$920$	5.53030	+	21.2066i	0.182329	+	0.699162i
$921$	−3.83837	−	6.64825i	−0.126479	−	0.219067i
$922$	17.4713	−	0.453163i	0.575387	−	0.0149241i
$923$	15.8834	−	15.8834i	0.522809	−	0.522809i
$924$	−1.80883	−	0.369449i	−0.0595060	−	0.0121540i
$925$	−0.341285	−	3.66667i	−0.0112214	−	0.120559i
$926$	40.8697	−	43.0463i	1.34306	−	1.41459i
$927$	11.4916	−	42.8871i	0.377433	−	1.40860i
$928$	3.65829	+	28.0565i	0.120089	+	0.920999i
$929$	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	$0.502383\pi$
$930$	−10.4728	+	2.15824i	−0.343415	+	0.0707716i
$931$	−40.8378	+	0.690945i	−1.33841	+	0.0226448i
$932$	24.9864	−	8.10485i	0.818456	−	0.265483i
$933$	−4.71148	+	1.26244i	−0.154247	+	0.0413303i
$934$	49.0807	−	14.5251i	1.60597	−	0.475277i
$935$	−9.44786	+	1.69293i	−0.308978	+	0.0553647i
$936$	4.38265	+	12.4056i	0.143251	+	0.405489i
$937$	−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	$0.300177\pi$
$938$	−1.36270	+	1.45981i	−0.0444939	+	0.0476645i
$939$	−7.95230			−0.259514
$940$	−23.8278	+	5.55823i	−0.777178	+	0.181289i
$941$	−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	$0.928991\pi$
$942$	2.20785	+	1.19947i	0.0719355	+	0.0390809i
$943$	−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	−0.524070	−	0.851675i	$-0.675587\pi$
$947$	−16.9897	+	4.55237i	−0.552091	+	0.147932i	−0.0280205	+	0.999607i	$0.508920\pi$
$948$	5.91808	−	6.56614i	0.192210	−	0.213258i
$949$	−8.53920	+	4.93011i	−0.277194	+	0.160038i
$950$	−25.5126	+	32.4247i	−0.827737	+	1.05200i
$951$		−	1.20251i		−	0.0389940i
$952$	−29.3427	−	24.6721i	−0.951003	−	0.799628i
$953$	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	$0.654670\pi$
$954$	−36.5222	+	38.4672i	−1.18245	+	1.24542i
$955$	5.13957	+	3.57757i	0.166312	+	0.115768i
$956$	21.3868	−	1.11019i	0.691699	−	0.0359061i
$957$	−0.451656	−	1.68560i	−0.0146000	−	0.0544878i
$958$	−23.5363	−	38.4291i	−0.760423	−	1.24159i
$959$	−27.1334	−	26.6782i	−0.876183	−	0.861484i
$960$	−7.31362	−	1.41189i	−0.236046	−	0.0455686i
$961$	17.4723	−	30.2629i	0.563622	−	0.976222i
$962$	−0.818267	+	1.50617i	−0.0263820	+	0.0485609i
$963$	37.9798	+	10.1766i	1.22388	+	0.327938i
$964$	−13.6861	−	21.0977i	−0.440801	−	0.679512i
$965$	6.56378	−	18.1906i	0.211296	−	0.585575i
$966$	2.53703	−	4.76553i	0.0816278	−	0.153329i
$967$	21.8531	+	21.8531i	0.702748	+	0.702748i	0.965000	−	0.262251i	$-0.0844649\pi$
$967$	21.8531	+	21.8531i	0.702748	+	0.702748i	−0.262251	+	0.965000i	$0.584465\pi$
$968$	−12.5590	+	26.2802i	−0.403663	+	0.844678i
$969$	10.7791	−	6.22331i	0.346274	−	0.199922i
$970$	−14.1853	+	12.6140i	−0.455461	+	0.405012i
$971$	49.5916	+	28.6317i	1.59147	+	0.918836i	0.993055	+	0.117650i	$0.0375362\pi$
$971$	49.5916	+	28.6317i	1.59147	+	0.918836i	0.598416	+	0.801186i	$0.295797\pi$
$972$	6.41081	+	19.7638i	0.205627	+	0.633925i
$973$	−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
$976$	2.99823	−	6.71618i	0.0959710	−	0.214980i
$977$	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	$0.456598\pi$
$978$	−0.124153	−	4.78662i	−0.00396998	−	0.153059i
$979$	2.42338			0.0774516
$980$	−15.2246	−	27.3535i	−0.486330	−	0.873775i
$981$	30.1401			0.962300
$982$	0.599541	+	23.1148i	0.0191321	+	0.737623i
$983$	13.7291	+	3.67869i	0.437889	+	0.117332i	0.471027	−	0.882119i	$-0.343883\pi$
$983$	13.7291	+	3.67869i	0.437889	+	0.117332i	−0.0331380	+	0.999451i	$0.510550\pi$
$984$	0.110967	+	0.0206521i	0.00353751	+	0.000658364i
$985$	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
$988$	18.2674	−	5.92542i	0.581164	−	0.188513i
$989$	20.7096	+	11.9567i	0.658527	+	0.380201i
$990$	−7.47672	−	0.438360i	−0.237626	−	0.0139320i
$991$	40.1223	−	23.1646i	1.27453	−	0.735848i	0.298689	−	0.954350i	$-0.403451\pi$
$991$	40.1223	−	23.1646i	1.27453	−	0.735848i	0.975836	+	0.218503i	$0.0701172\pi$
$992$	36.4791	−	27.9195i	1.15821	−	0.886446i
$993$	10.2670	+	10.2670i	0.325812	+	0.325812i
$994$	−23.9999	+	45.0811i	−0.761231	+	1.42989i
$995$	11.7850	+	25.0911i	0.373609	+	0.795442i
$996$	4.31610	−	2.79986i	0.136761	−	0.0887170i
$997$	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	$0.323448\pi$
$998$	−6.41099	+	11.8006i	−0.202936	+	0.373541i
$999$	−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.23.18	yes	72
4.3	odd	2	inner	140.2.w.b.23.4	✓	72
5.2	odd	4	inner	140.2.w.b.107.8	yes	72
5.3	odd	4		700.2.be.e.107.11		72
5.4	even	2		700.2.be.e.443.1		72
7.2	even	3		980.2.k.k.883.7		36
7.3	odd	6		980.2.x.m.263.6		72
7.4	even	3	inner	140.2.w.b.123.6	yes	72
7.5	odd	6		980.2.k.j.883.7		36
7.6	odd	2		980.2.x.m.863.18		72
20.3	even	4		700.2.be.e.107.13		72
20.7	even	4	inner	140.2.w.b.107.6	yes	72
20.19	odd	2		700.2.be.e.443.15		72
28.3	even	6		980.2.x.m.263.8		72
28.11	odd	6	inner	140.2.w.b.123.8	yes	72
28.19	even	6		980.2.k.j.883.15		36
28.23	odd	6		980.2.k.k.883.15		36
28.27	even	2		980.2.x.m.863.4		72
35.2	odd	12		980.2.k.k.687.15		36
35.4	even	6		700.2.be.e.543.13		72
35.12	even	12		980.2.k.j.687.15		36
35.17	even	12		980.2.x.m.67.4		72
35.18	odd	12		700.2.be.e.207.15		72
35.27	even	4		980.2.x.m.667.8		72
35.32	odd	12	inner	140.2.w.b.67.4	yes	72
140.27	odd	4		980.2.x.m.667.6		72
140.39	odd	6		700.2.be.e.543.11		72
140.47	odd	12		980.2.k.j.687.7		36
140.67	even	12	inner	140.2.w.b.67.18	yes	72
140.87	odd	12		980.2.x.m.67.18		72
140.107	even	12		980.2.k.k.687.7		36
140.123	even	12		700.2.be.e.207.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.4	✓	72	4.3	odd	2	inner
140.2.w.b.23.18	yes	72	1.1	even	1	trivial
140.2.w.b.67.4	yes	72	35.32	odd	12	inner
140.2.w.b.67.18	yes	72	140.67	even	12	inner
140.2.w.b.107.6	yes	72	20.7	even	4	inner
140.2.w.b.107.8	yes	72	5.2	odd	4	inner
140.2.w.b.123.6	yes	72	7.4	even	3	inner
140.2.w.b.123.8	yes	72	28.11	odd	6	inner
700.2.be.e.107.11		72	5.3	odd	4
700.2.be.e.107.13		72	20.3	even	4
700.2.be.e.207.1		72	140.123	even	12
700.2.be.e.207.15		72	35.18	odd	12
700.2.be.e.443.1		72	5.4	even	2
700.2.be.e.443.15		72	20.19	odd	2
700.2.be.e.543.11		72	140.39	odd	6
700.2.be.e.543.13		72	35.4	even	6
980.2.k.j.687.7		36	140.47	odd	12
980.2.k.j.687.15		36	35.12	even	12
980.2.k.j.883.7		36	7.5	odd	6
980.2.k.j.883.15		36	28.19	even	6
980.2.k.k.687.7		36	140.107	even	12
980.2.k.k.687.15		36	35.2	odd	12
980.2.k.k.883.7		36	7.2	even	3
980.2.k.k.883.15		36	28.23	odd	6
980.2.x.m.67.4		72	35.17	even	12
980.2.x.m.67.18		72	140.87	odd	12
980.2.x.m.263.6		72	7.3	odd	6
980.2.x.m.263.8		72	28.3	even	6
980.2.x.m.667.6		72	140.27	odd	4
980.2.x.m.667.8		72	35.27	even	4
980.2.x.m.863.4		72	28.27	even	2
980.2.x.m.863.18		72	7.6	odd	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+(1.41374 - 0.0366689i) q^{2} +(0.402205 + 0.107770i) q^{3} +(1.99731 - 0.103680i) q^{4} +(-2.22809 - 0.188711i) q^{5} +(0.572564 + 0.137611i) q^{6} +(2.30240 + 1.30345i) q^{7} +(2.81987 - 0.219816i) q^{8} +(-2.44792 - 1.41331i) q^{9} +(-3.15686 - 0.185086i) q^{10} +(-0.725638 + 0.418947i) q^{11} +(0.814501 + 0.173550i) q^{12} +(-1.16367 - 1.16367i) q^{13} +(3.30278 + 1.75831i) q^{14} +(-0.875811 - 0.316023i) q^{15} +(3.97850 - 0.414164i) q^{16} +(-4.94841 - 1.32592i) q^{17} +(-3.51255 - 1.90829i) q^{18} +(-2.91741 + 5.05309i) q^{19} +(-4.46976 - 0.145905i) q^{20} +(0.785561 + 0.772382i) q^{21} +(-1.01050 + 0.618890i) q^{22} +(-0.896861 - 3.34713i) q^{23} +(1.15786 + 0.215488i) q^{24} +(4.92878 + 0.840930i) q^{25} +(-1.68779 - 1.60245i) q^{26} +(-1.71555 - 1.71555i) q^{27} +(4.73374 + 2.36468i) q^{28} +5.00172i q^{29} +(-1.24976 - 0.414658i) q^{30} +(7.03267 - 4.06031i) q^{31} +(5.60937 - 0.731407i) 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} +(-3.93916 + 7.25073i) q^{38} +(-0.342623 - 0.593441i) q^{39} +(-6.32441 - 0.0423707i) q^{40} +0.0958388 q^{41} +(1.13890 + 1.06314i) q^{42} +(-4.87975 + 4.87975i) q^{43} +(-1.40589 + 0.912002i) q^{44} +(5.18749 + 3.61093i) q^{45} +(-1.39066 - 4.69908i) q^{46} +(5.28468 - 1.41603i) q^{47} +(1.64481 + 0.262186i) q^{48} +(3.60205 + 6.00210i) q^{49} +(6.99883 + 1.00812i) q^{50} +(-1.84738 - 1.06658i) q^{51} +(-2.44486 - 2.20356i) q^{52} +(3.43436 - 12.8172i) q^{53} +(-2.48825 - 2.36244i) q^{54} +(1.69585 - 0.796517i) q^{55} +(6.77898 + 3.16945i) q^{56} +(-1.71797 + 1.71797i) q^{57} +(0.183407 + 7.07112i) q^{58} +(4.46933 + 7.74111i) q^{59} +(-1.78203 - 0.540391i) q^{60} +(0.919379 - 1.59241i) q^{61} +(9.79346 - 5.99810i) q^{62} +(-3.79391 - 6.44473i) q^{63} +(7.90336 - 1.23971i) q^{64} +(2.37316 + 2.81235i) q^{65} +(-0.473126 + 0.140018i) q^{66} +(-0.138137 + 0.515535i) q^{67} +(-10.0210 - 2.13522i) q^{68} -1.44289i q^{69} +(-7.02708 - 4.54094i) q^{70} +13.6494i q^{71} +(-7.21350 - 3.44726i) q^{72} +(1.55074 - 5.78744i) q^{73} +(-0.295575 - 0.998755i) q^{74} +(1.89175 + 0.869402i) q^{75} +(-5.30306 + 10.3951i) q^{76} +(-2.21678 + 0.0187518i) q^{77} +(-0.506141 - 0.826407i) q^{78} +(5.30723 - 9.19239i) q^{79} +(-8.94262 + 0.172008i) q^{80} +(3.73481 + 6.46888i) q^{81} +(0.135491 - 0.00351430i) q^{82} +(4.36830 - 4.36830i) q^{83} +(1.64909 + 1.46124i) q^{84} +(10.7753 + 3.88809i) q^{85} +(-6.71975 + 7.07762i) q^{86} +(-0.539037 + 2.01171i) q^{87} +(-1.95412 + 1.34088i) q^{88} +(-2.50474 - 1.44611i) q^{89} +(7.46616 + 4.91469i) q^{90} +(-1.16244 - 4.19600i) q^{91} +(-2.13834 - 6.59227i) q^{92} +(3.26615 - 0.875163i) q^{93} +(7.41923 - 2.19567i) q^{94} +(7.45382 - 10.7082i) q^{95} +(2.33494 + 0.310349i) q^{96} +(4.24461 - 4.24461i) q^{97} +(5.31245 + 8.35332i) 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

Groups

Database

Properties

Related objects

Downloads

Learn more