LMFDB - Embedded newform 820.2.bk.c.43.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(43,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			43.17
Character	$\chi$	$=$	820.43
Dual form			820.2.bk.c.267.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30056 + 0.555460i) q^{2} -1.73013i q^{3} +(1.38293 - 1.44482i) q^{4} +(1.62837 - 1.53246i) q^{5} +(0.961018 + 2.25014i) q^{6} +(-1.40474 + 4.32334i) q^{7} +(-0.996046 + 2.64724i) q^{8} +0.00664869 q^{9} +(-1.26657 + 2.89755i) q^{10} +(-0.524708 - 3.31288i) q^{11} +(-2.49973 - 2.39265i) q^{12} +(-1.69550 - 5.21822i) q^{13} +(-0.574491 - 6.40306i) q^{14} +(-2.65135 - 2.81728i) q^{15} +(-0.175015 - 3.99617i) q^{16} +(4.71763 + 3.42756i) q^{17} +(-0.00864704 + 0.00369308i) q^{18} +(-0.330761 + 0.168531i) q^{19} +(0.0377873 - 4.47198i) q^{20} +(7.47995 + 2.43038i) q^{21} +(2.52259 + 4.01715i) q^{22} +(-2.48132 - 1.26429i) q^{23} +(4.58007 + 1.72329i) q^{24} +(0.303149 - 4.99080i) q^{25} +(5.10362 + 5.84484i) q^{26} -5.20189i q^{27} +(4.30380 + 8.00848i) q^{28} +(3.02368 + 0.478905i) q^{29} +(5.01314 + 2.19134i) q^{30} +(2.23580 - 3.07732i) q^{31} +(2.44733 + 5.10006i) q^{32} +(-5.73171 + 0.907813i) q^{33} +(-8.03945 - 1.83730i) q^{34} +(4.33791 + 9.19269i) q^{35} +(0.00919467 - 0.00960617i) q^{36} +(0.490485 - 3.09680i) q^{37} +(0.336564 - 0.402910i) q^{38} +(-9.02820 + 2.93344i) q^{39} +(2.43486 + 5.83708i) q^{40} +(2.45027 - 5.91576i) q^{41} +(-11.0781 + 0.993945i) q^{42} +(1.07119 - 2.10232i) q^{43} +(-5.51215 - 3.82336i) q^{44} +(0.0108265 - 0.0101888i) q^{45} +(3.92937 + 0.266023i) q^{46} +(-4.74323 + 1.54117i) q^{47} +(-6.91389 + 0.302800i) q^{48} +(-11.0549 - 8.03185i) q^{49} +(2.37792 + 6.65924i) q^{50} +(5.93013 - 8.16212i) q^{51} +(-9.88415 - 4.76673i) q^{52} +(-3.05367 + 2.21862i) q^{53} +(2.88944 + 6.76539i) q^{54} +(-5.93126 - 4.59048i) q^{55} +(-10.0458 - 8.02494i) q^{56} +(0.291581 + 0.572260i) q^{57} +(-4.19850 + 1.05669i) q^{58} +(-0.610546 - 1.87907i) q^{59} +(-7.73710 - 0.0653770i) q^{60} +(-3.93490 - 1.27853i) q^{61} +(-1.19848 + 5.24414i) q^{62} +(-0.00933968 + 0.0287446i) q^{63} +(-6.01578 - 5.27355i) q^{64} +(-10.7576 - 5.89888i) q^{65} +(6.95019 - 4.36440i) q^{66} +(5.83060 + 8.02513i) q^{67} +(11.4764 - 2.07606i) q^{68} +(-2.18739 + 4.29300i) q^{69} +(-10.7479 - 9.54614i) q^{70} +(-0.960600 - 6.06499i) q^{71} +(-0.00662240 + 0.0176007i) q^{72} +(-1.33173 + 1.33173i) q^{73} +(1.08224 + 4.30003i) q^{74} +(-8.63474 - 0.524488i) q^{75} +(-0.213922 + 0.710958i) q^{76} +(15.0598 + 2.38524i) q^{77} +(10.1123 - 8.82993i) q^{78} +(5.38411 - 5.38411i) q^{79} +(-6.40895 - 6.23902i) q^{80} -8.98001 q^{81} +(0.0992377 + 9.05484i) q^{82} +(6.44284 - 6.44284i) q^{83} +(13.8557 - 7.44614i) q^{84} +(12.9346 - 1.64825i) q^{85} +(-0.225391 + 3.32921i) q^{86} +(0.828567 - 5.23137i) q^{87} +(9.29262 + 1.91075i) q^{88} +(-4.00873 + 2.04255i) q^{89} +(-0.00842106 + 0.0192649i) q^{90} +24.9419 q^{91} +(-5.25816 + 1.83663i) q^{92} +(-5.32416 - 3.86823i) q^{93} +(5.31281 - 4.63906i) q^{94} +(-0.280333 + 0.781308i) q^{95} +(8.82376 - 4.23420i) q^{96} +(11.9882 - 8.70996i) q^{97} +(18.8390 + 4.30538i) q^{98} +(-0.00348862 - 0.0220263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.30056	+	0.555460i	−0.919637	+	0.392769i
$2$	−1.30056	+	0.555460i	−0.919637	+	0.392769i
$3$		−	1.73013i		−	0.998891i	−0.866345	−	0.499446i	$-0.833537\pi$
$3$		−	1.73013i		−	0.998891i	0.866345	−	0.499446i	$-0.166463\pi$
$4$	1.38293	−	1.44482i	0.691464	−	0.722411i
$5$	1.62837	−	1.53246i	0.728227	−	0.685336i
$5$	1.62837	−	1.53246i	0.728227	−	0.685336i
$6$	0.961018	+	2.25014i	0.392334	+	0.918617i
$7$	−1.40474	+	4.32334i	−0.530942	+	1.63407i	0.221316	+	0.975202i	$0.428965\pi$
$7$	−1.40474	+	4.32334i	−0.530942	+	1.63407i	−0.752258	+	0.658869i	$0.771035\pi$
$8$	−0.996046	+	2.64724i	−0.352156	+	0.935941i
$9$	0.00664869			0.00221623
$10$	−1.26657	+	2.89755i	−0.400526	+	0.916285i
$11$	−0.524708	−	3.31288i	−0.158205	−	0.998870i	−0.931214	−	0.364474i	$-0.881249\pi$
$11$	−0.524708	−	3.31288i	−0.158205	−	0.998870i	0.773008	−	0.634396i	$-0.218751\pi$
$12$	−2.49973	−	2.39265i	−0.721610	−	0.690698i
$13$	−1.69550	−	5.21822i	−0.470248	−	1.44727i	−0.852261	−	0.523117i	$-0.824769\pi$
$13$	−1.69550	−	5.21822i	−0.470248	−	1.44727i	0.382013	−	0.924157i	$-0.375231\pi$
$14$	−0.574491	−	6.40306i	−0.153539	−	1.71129i
$15$	−2.65135	−	2.81728i	−0.684576	−	0.727420i
$16$	−0.175015	−	3.99617i	−0.0437539	−	0.999042i
$17$	4.71763	+	3.42756i	1.14419	+	0.831305i	0.987698	−	0.156373i	$-0.0499803\pi$
$17$	4.71763	+	3.42756i	1.14419	+	0.831305i	0.156496	+	0.987679i	$0.449980\pi$
$18$	−0.00864704	+	0.00369308i	−0.00203813	+	0.000870467i
$19$	−0.330761	+	0.168531i	−0.0758819	+	0.0386637i	−0.491520	−	0.870866i	$-0.663558\pi$
$19$	−0.330761	+	0.168531i	−0.0758819	+	0.0386637i	0.415638	+	0.909530i	$0.363558\pi$
$20$	0.0377873	−	4.47198i	0.00844950	−	0.999964i
$21$	7.47995	+	2.43038i	1.63226	+	0.530353i
$22$	2.52259	+	4.01715i	0.537817	+	0.856459i
$23$	−2.48132	−	1.26429i	−0.517390	−	0.263624i	0.175739	−	0.984437i	$-0.443769\pi$
$23$	−2.48132	−	1.26429i	−0.517390	−	0.263624i	−0.693129	+	0.720813i	$0.743769\pi$
$24$	4.58007	+	1.72329i	0.934904	+	0.351765i
$25$	0.303149	−	4.99080i	0.0606298	−	0.998160i
$26$	5.10362	+	5.84484i	1.00090	+	1.14627i
$27$		−	5.20189i		−	1.00111i
$28$	4.30380	+	8.00848i	0.813342	+	1.51346i
$29$	3.02368	+	0.478905i	0.561484	+	0.0889303i	0.430724	−	0.902484i	$-0.358258\pi$
$29$	3.02368	+	0.478905i	0.561484	+	0.0889303i	0.130760	+	0.991414i	$0.458258\pi$
$30$	5.01314	+	2.19134i	0.915270	+	0.400082i
$31$	2.23580	−	3.07732i	0.401562	−	0.552703i	−0.559573	−	0.828781i	$-0.689035\pi$
$31$	2.23580	−	3.07732i	0.401562	−	0.552703i	0.961135	+	0.276078i	$0.0890349\pi$
$32$	2.44733	+	5.10006i	0.432631	+	0.901571i
$33$	−5.73171	+	0.907813i	−0.997762	+	0.158030i
$34$	−8.03945	−	1.83730i	−1.37875	−	0.315095i
$35$	4.33791	+	9.19269i	0.733241	+	1.55385i
$36$	0.00919467	−	0.00960617i	0.00153244	−	0.00160103i
$37$	0.490485	−	3.09680i	0.0806352	−	0.509111i	−0.914004	−	0.405705i	$-0.867026\pi$
$37$	0.490485	−	3.09680i	0.0806352	−	0.509111i	0.994639	−	0.103406i	$-0.0329740\pi$
$38$	0.336564	−	0.402910i	0.0545978	−	0.0653607i
$39$	−9.02820	+	2.93344i	−1.44567	+	0.469726i
$40$	2.43486	+	5.83708i	0.384985	+	0.922923i
$41$	2.45027	−	5.91576i	0.382668	−	0.923886i
$41$	2.45027	−	5.91576i	0.382668	−	0.923886i
$42$	−11.0781	+	0.993945i	−1.70939	+	0.153369i
$43$	1.07119	−	2.10232i	0.163355	−	0.320601i	−0.794791	−	0.606883i	$-0.792419\pi$
$43$	1.07119	−	2.10232i	0.163355	−	0.320601i	0.958145	+	0.286282i	$0.0924195\pi$
$44$	−5.51215	−	3.82336i	−0.830987	−	0.576394i
$45$	0.0108265	−	0.0101888i	0.00161392	−	0.00151886i
$46$	3.92937	+	0.266023i	0.579355	+	0.0392229i
$47$	−4.74323	+	1.54117i	−0.691871	+	0.224803i	−0.633785	−	0.773509i	$-0.718500\pi$
$47$	−4.74323	+	1.54117i	−0.691871	+	0.224803i	−0.0580861	+	0.998312i	$0.518500\pi$
$48$	−6.91389	+	0.302800i	−0.997935	+	0.0437054i
$49$	−11.0549	−	8.03185i	−1.57927	−	1.14741i
$50$	2.37792	+	6.65924i	0.336289	+	0.941759i
$51$	5.93013	−	8.16212i	0.830384	−	1.14293i
$52$	−9.88415	−	4.76673i	−1.37069	−	0.661026i
$53$	−3.05367	+	2.21862i	−0.419454	+	0.304751i	−0.777418	−	0.628984i	$-0.783471\pi$
$53$	−3.05367	+	2.21862i	−0.419454	+	0.304751i	0.357964	+	0.933735i	$0.383471\pi$
$54$	2.88944	+	6.76539i	0.393203	+	0.920653i
$55$	−5.93126	−	4.59048i	−0.799771	−	0.618980i
$56$	−10.0458	−	8.02494i	−1.34242	−	1.07238i
$57$	0.291581	+	0.572260i	0.0386209	+	0.0757977i
$58$	−4.19850	+	1.05669i	−0.551291	+	0.138750i
$59$	−0.610546	−	1.87907i	−0.0794863	−	0.244634i	0.903415	−	0.428767i	$-0.141052\pi$
$59$	−0.610546	−	1.87907i	−0.0794863	−	0.244634i	−0.982901	+	0.184134i	$0.941052\pi$
$60$	−7.73710	−	0.0653770i	−0.998856	−	0.00844013i
$61$	−3.93490	−	1.27853i	−0.503812	−	0.163699i	0.0460740	−	0.998938i	$-0.485329\pi$
$61$	−3.93490	−	1.27853i	−0.503812	−	0.163699i	−0.549886	+	0.835239i	$0.685329\pi$
$62$	−1.19848	+	5.24414i	−0.152207	+	0.666007i
$63$	−0.00933968	+	0.0287446i	−0.00117669	+	0.00362148i
$64$	−6.01578	−	5.27355i	−0.751973	−	0.659194i
$65$	−10.7576	−	5.89888i	−1.33432	−	0.731667i
$66$	6.95019	−	4.36440i	0.855510	−	0.537221i
$67$	5.83060	+	8.02513i	0.712321	+	0.980425i	0.999744	+	0.0226218i	$0.00720135\pi$
$67$	5.83060	+	8.02513i	0.712321	+	0.980425i	−0.287423	+	0.957804i	$0.592799\pi$
$68$	11.4764	−	2.07606i	1.39171	−	0.251759i
$69$	−2.18739	+	4.29300i	−0.263331	+	0.516817i
$70$	−10.7479	−	9.54614i	−1.28462	−	1.14098i
$71$	−0.960600	−	6.06499i	−0.114002	−	0.719782i	−0.976787	−	0.214211i	$-0.931282\pi$
$71$	−0.960600	−	6.06499i	−0.114002	−	0.719782i	0.862785	−	0.505571i	$-0.168718\pi$
$72$	−0.00662240	+	0.0176007i	−0.000780458	+	0.00207426i
$73$	−1.33173	+	1.33173i	−0.155868	+	0.155868i	−0.780733	−	0.624865i	$-0.785154\pi$
$73$	−1.33173	+	1.33173i	−0.155868	+	0.155868i	0.624865	+	0.780733i	$0.285154\pi$
$74$	1.08224	+	4.30003i	0.125808	+	0.499868i
$75$	−8.63474	−	0.524488i	−0.997054	−	0.0605626i
$76$	−0.213922	+	0.710958i	−0.0245385	+	0.0815525i
$77$	15.0598	+	2.38524i	1.71622	+	0.271823i
$78$	10.1123	−	8.82993i	1.14500	−	0.999792i
$79$	5.38411	−	5.38411i	0.605760	−	0.605760i	−0.336075	−	0.941835i	$-0.609100\pi$
$79$	5.38411	−	5.38411i	0.605760	−	0.605760i	0.941835	+	0.336075i	$0.109100\pi$
$80$	−6.40895	−	6.23902i	−0.716542	−	0.697544i
$81$	−8.98001			−0.997779
$82$	0.0992377	+	9.05484i	0.0109590	+	0.999940i
$83$	6.44284	−	6.44284i	0.707193	−	0.707193i	−0.258751	−	0.965944i	$-0.583311\pi$
$83$	6.44284	−	6.44284i	0.707193	−	0.707193i	0.965944	+	0.258751i	$0.0833109\pi$
$84$	13.8557	−	7.44614i	1.51178	−	0.812441i
$85$	12.9346	−	1.64825i	1.40296	−	0.178778i
$86$	−0.225391	+	3.32921i	−0.0243045	+	0.358998i
$87$	0.828567	−	5.23137i	0.0888317	−	0.560862i
$88$	9.29262	+	1.91075i	0.990597	+	0.203687i
$89$	−4.00873	+	2.04255i	−0.424925	+	0.216510i	−0.653357	−	0.757050i	$-0.726640\pi$
$89$	−4.00873	+	2.04255i	−0.424925	+	0.216510i	0.228432	+	0.973560i	$0.426640\pi$
$90$	−0.00842106	+	0.0192649i	−0.000887657	+	0.00203070i
$91$	24.9419			2.61462
$92$	−5.25816	+	1.83663i	−0.548201	+	0.191482i
$93$	−5.32416	−	3.86823i	−0.552090	−	0.401117i
$94$	5.31281	−	4.63906i	0.547975	−	0.478483i
$95$	−0.280333	+	0.781308i	−0.0287616	+	0.0801606i
$96$	8.82376	−	4.23420i	0.900572	−	0.432151i
$97$	11.9882	−	8.70996i	1.21722	−	0.884362i	0.221354	−	0.975194i	$-0.428952\pi$
$97$	11.9882	−	8.70996i	1.21722	−	0.884362i	0.995866	+	0.0908314i	$0.0289524\pi$
$98$	18.8390	+	4.30538i	1.90302	+	0.434909i
$99$	−0.00348862	−	0.0220263i	−0.000350620	−	0.00221373i
$100$	−6.79158	−	7.33992i	−0.679158	−	0.733992i
$101$	−14.1767	+	7.22338i	−1.41063	+	0.718753i	−0.982725	−	0.185069i	$-0.940749\pi$
$101$	−14.1767	+	7.22338i	−1.41063	+	0.718753i	−0.427907	+	0.903823i	$0.640749\pi$
$102$	−3.17877	+	13.9093i	−0.314746	+	1.37723i
$103$	−3.26366	+	1.66292i	−0.321578	+	0.163852i	−0.607326	−	0.794452i	$-0.707758\pi$
$103$	−3.26366	+	1.66292i	−0.321578	+	0.163852i	0.285748	+	0.958305i	$0.407758\pi$
$104$	15.5027	+	0.709183i	1.52016	+	0.0695411i
$105$	15.9046	−	7.50515i	1.55213	−	0.732428i
$106$	2.73913	−	4.58165i	0.266048	−	0.445009i
$107$	−13.3180	+	6.78585i	−1.28750	+	0.656012i	−0.957626	−	0.288014i	$-0.907005\pi$
$107$	−13.3180	+	6.78585i	−1.28750	+	0.656012i	−0.329871	+	0.944026i	$0.607005\pi$
$108$	−7.51581	−	7.19385i	−0.723209	−	0.692229i
$109$	12.0752	−	12.0752i	1.15659	−	1.15659i	0.171386	−	0.985204i	$-0.445176\pi$
$109$	12.0752	−	12.0752i	1.15659	−	1.15659i	0.985204	−	0.171386i	$-0.0548244\pi$
$110$	10.2638	+	2.67564i	0.978615	+	0.255112i
$111$	−5.35787	−	0.848603i	−0.508546	−	0.0805458i
$112$	17.5227	+	4.85693i	1.65574	+	0.458936i
$113$	2.94600	+	18.6003i	0.277136	+	1.74977i	0.596942	+	0.802285i	$0.296382\pi$
$113$	2.94600	+	18.6003i	0.277136	+	1.74977i	−0.319806	+	0.947483i	$0.603618\pi$
$114$	−0.697087	−	0.582299i	−0.0652882	−	0.0545373i
$115$	−5.97797	+	1.74378i	−0.557448	+	0.162608i
$116$	4.87347	−	3.70639i	0.452490	−	0.344130i
$117$	−0.0112729	−	0.0346943i	−0.00104218	−	0.00320749i
$118$	1.83780	+	2.10471i	0.169183	+	0.193754i
$119$	−21.4456	+	15.5811i	−1.96591	+	1.42832i
$120$	10.0989	−	4.21262i	0.921900	−	0.384558i
$121$	−0.238209	+	0.0773987i	−0.0216553	+	0.00703625i
$122$	5.82776	−	0.522874i	0.527620	−	0.0473388i
$123$	−10.2350	−	4.23928i	−0.922862	−	0.382243i
$124$	−1.35422	−	7.48605i	−0.121612	−	0.672267i
$125$	−7.15455	−	8.59141i	−0.639923	−	0.768439i
$126$	−0.00381961	−	0.0425720i	−0.000340278	−	0.00379261i
$127$	−20.8452	−	3.30155i	−1.84971	−	0.292965i	−0.869950	−	0.493141i	$-0.835849\pi$
$127$	−20.8452	−	3.30155i	−1.84971	−	0.292965i	−0.979760	+	0.200176i	$0.935849\pi$
$128$	10.7532	+	3.51706i	0.950453	+	0.310867i
$129$	−3.63729	−	1.85329i	−0.320246	−	0.163173i
$130$	17.2675	+	1.69646i	1.51446	+	0.148789i
$131$	14.3433	+	10.4210i	1.25318	+	0.910490i	0.998402	−	0.0565095i	$-0.0179971\pi$
$131$	14.3433	+	10.4210i	1.25318	+	0.910490i	0.254779	+	0.966999i	$0.417997\pi$
$132$	−6.61492	+	9.53673i	−0.575755	+	0.830066i
$133$	−0.263985	−	1.66674i	−0.0228904	−	0.144525i
$134$	−12.0407	−	7.19852i	−1.04016	−	0.621858i
$135$	−7.97168	−	8.47059i	−0.686093	−	0.729032i
$136$	−13.7726	+	9.07470i	−1.18099	+	0.778149i
$137$	−6.17111			−0.527233			−0.263617	−	0.964628i	$-0.584915\pi$
$137$	−6.17111			−0.527233			−0.263617	+	0.964628i	$0.584915\pi$
$138$	0.460254	−	6.79833i	0.0391794	−	0.578712i
$139$	4.17600	−	12.8524i	0.354204	−	1.09013i	−0.602266	−	0.798296i	$-0.705735\pi$
$139$	4.17600	−	12.8524i	0.354204	−	1.09013i	0.956470	−	0.291832i	$-0.0942648\pi$
$140$	19.2808	+	6.44533i	1.62953	+	0.544730i
$141$	2.66642	+	8.20641i	0.224553	+	0.691104i
$142$	4.61818	+	7.35433i	0.387549	+	0.617161i
$143$	−16.3977	+	8.35503i	−1.37124	+	0.698683i
$144$	−0.00116362	−	0.0265693i	−9.69686e−5	−	0.00221411i
$145$	5.65756	−	3.85384i	0.469835	−	0.320044i
$146$	0.992280	−	2.47173i	0.0821216	−	0.204562i
$147$	−13.8962	+	19.1264i	−1.14614	+	1.57752i
$148$	−3.79601	−	4.99132i	−0.312030	−	0.410284i
$149$	−2.39884	+	15.1457i	−0.196521	+	1.24078i	0.670273	+	0.742115i	$0.266177\pi$
$149$	−2.39884	+	15.1457i	−0.196521	+	1.24078i	−0.866793	+	0.498667i	$0.833823\pi$
$150$	11.5214	−	4.11412i	0.940715	−	0.335917i
$151$	−3.17225	+	6.22588i	−0.258154	+	0.506655i	−0.983312	−	0.181927i	$-0.941767\pi$
$151$	−3.17225	+	6.22588i	−0.258154	+	0.506655i	0.725158	+	0.688582i	$0.241767\pi$
$152$	−0.116690	−	1.04347i	−0.00946478	−	0.0846366i
$153$	0.0313661	+	0.0227888i	0.00253580	+	0.00184236i
$154$	−20.9111	+	5.26296i	−1.68506	+	0.424101i
$155$	−1.07515	−	8.43727i	−0.0863585	−	0.677698i
$156$	−8.24706	+	17.1009i	−0.660294	+	1.36917i
$157$	−5.24987	−	1.70579i	−0.418985	−	0.136137i	0.0919342	−	0.995765i	$-0.470695\pi$
$157$	−5.24987	−	1.70579i	−0.418985	−	0.136137i	−0.510920	+	0.859628i	$0.670695\pi$
$158$	−4.01172	+	9.99304i	−0.319155	+	0.795003i
$159$	3.83850	+	5.28325i	0.304413	+	0.418989i
$160$	11.8008	+	4.55433i	0.932933	+	0.360051i
$161$	8.95158	−	8.95158i	0.705484	−	0.705484i
$162$	11.6791	−	4.98803i	0.917594	−	0.391897i
$163$	10.5950	−	10.5950i	0.829861	−	0.829861i	−0.157636	−	0.987497i	$-0.550387\pi$
$163$	10.5950	−	10.5950i	0.829861	−	0.829861i	0.987497	+	0.157636i	$0.0503874\pi$
$164$	−5.15867	−	11.7213i	−0.402824	−	0.915277i
$165$	−7.94213	+	10.2618i	−0.618294	+	0.798884i
$166$	−4.80058	+	11.9581i	−0.372597	+	0.928125i
$167$	16.4442			1.27249			0.636244	−	0.771488i	$-0.280487\pi$
$167$	16.4442			1.27249			0.636244	+	0.771488i	$0.280487\pi$
$168$	−13.8842	+	17.3805i	−1.07119	+	1.34093i
$169$	−13.8379	+	10.0538i	−1.06445	+	0.773369i
$170$	−15.9068	+	9.32831i	−1.21999	+	0.715449i
$171$	−0.00219913	+	0.00112051i	−0.000168172	+	8.56878e-5i
$172$	−1.55611	−	4.45504i	−0.118652	−	0.339693i
$173$	6.52709	−	6.52709i	0.496245	−	0.496245i	−0.414022	−	0.910267i	$-0.635876\pi$
$173$	6.52709	−	6.52709i	0.496245	−	0.496245i	0.910267	+	0.414022i	$0.135876\pi$
$174$	1.82821	+	7.26396i	0.138596	+	0.550679i
$175$	21.1511	+	8.32140i	1.59887	+	0.629038i
$176$	−13.1470	+	2.67663i	−0.990991	+	0.201758i
$177$	−3.25103	+	1.05632i	−0.244362	+	0.0793982i
$178$	4.07906	−	4.88316i	0.305738	−	0.366008i
$179$	17.6535	+	2.79605i	1.31949	+	0.208986i	0.776161	−	0.630535i	$-0.217165\pi$
$179$	17.6535	+	2.79605i	1.31949	+	0.208986i	0.543327	+	0.839521i	$0.317165\pi$
$180$	0.000251236	−	0.0297328i	1.87260e−5	−	0.00221615i
$181$	3.82099	+	24.1248i	0.284012	+	1.79318i	0.556317	+	0.830970i	$0.312214\pi$
$181$	3.82099	+	24.1248i	0.284012	+	1.79318i	−0.272305	+	0.962211i	$0.587786\pi$
$182$	−32.4385	+	13.8542i	−2.40450	+	1.02694i
$183$	−2.21202	+	6.80789i	−0.163517	+	0.503254i
$184$	5.81840	−	5.30935i	0.428938	−	0.391411i
$185$	−3.94702	−	5.79437i	−0.290191	−	0.426010i
$186$	9.07305	+	2.07352i	0.665269	+	0.152038i
$187$	8.87970	−	17.4274i	0.649348	−	1.27442i
$188$	−4.33284	+	8.98445i	−0.316005	+	0.655258i
$189$	22.4896	+	7.30731i	1.63588	+	0.531528i
$190$	−0.0693941	−	1.17185i	−0.00503438	−	0.0850153i
$191$	−12.4200	+	12.4200i	−0.898676	+	0.898676i	−0.995319	−	0.0966428i	$-0.969190\pi$
$191$	−12.4200	+	12.4200i	−0.898676	+	0.898676i	0.0966428	+	0.995319i	$0.469190\pi$
$192$	−9.12393	+	10.4081i	−0.658463	+	0.751139i
$193$	5.29076	−	3.84396i	0.380837	−	0.276695i	−0.380853	−	0.924636i	$-0.624370\pi$
$193$	5.29076	−	3.84396i	0.380837	−	0.276695i	0.761691	+	0.647941i	$0.224370\pi$
$194$	−10.7534	+	17.9868i	−0.772050	+	1.29138i
$195$	−10.2058	+	18.6120i	−0.730855	+	1.33284i
$196$	−26.8927	+	4.86487i	−1.92091	+	0.347490i
$197$	−1.24697	−	7.87304i	−0.0888428	−	0.560931i	−0.991452	−	0.130471i	$-0.958351\pi$
$197$	−1.24697	−	7.87304i	−0.0888428	−	0.560931i	0.902609	−	0.430460i	$-0.141649\pi$
$198$	0.0167719	+	0.0267088i	0.00119193	+	0.00189811i
$199$	6.42371	−	12.6072i	0.455365	−	0.893704i	−0.543172	−	0.839622i	$-0.682777\pi$
$199$	6.42371	−	12.6072i	0.455365	−	0.893704i	0.998536	−	0.0540823i	$-0.0172233\pi$
$200$	12.9099	+	5.77358i	0.912869	+	0.408254i
$201$	13.8845	−	10.0877i	0.979338	−	0.711531i
$202$	14.4254	−	17.2690i	1.01497	−	1.21505i
$203$	−6.31796	+	12.3997i	−0.443434	+	0.870288i
$204$	−3.59186	−	19.8556i	−0.251480	−	1.39017i
$205$	−5.07571	−	13.3879i	−0.354503	−	0.935055i
$206$	3.32091	−	3.97556i	0.231379	−	0.276991i
$207$	−0.0164975	−	0.00840590i	−0.00114666	−	0.000584250i
$208$	−20.5562	+	7.68878i	−1.42531	+	0.533121i
$209$	0.731877	+	1.00734i	0.0506250	+	0.0696793i
$210$	−16.5161	+	18.5953i	−1.13972	+	1.28320i
$211$	10.0218	+	5.10637i	0.689930	+	0.351537i	0.763549	−	0.645750i	$-0.223455\pi$
$211$	10.0218	+	5.10637i	0.689930	+	0.351537i	−0.0736196	+	0.997286i	$0.523455\pi$
$212$	−1.01750	+	7.48020i	−0.0698820	+	0.513742i
$213$	−10.4932	+	1.66196i	−0.718984	+	0.113876i
$214$	13.5516	−	16.2230i	0.926368	−	1.10898i
$215$	−1.47744	−	5.06490i	−0.100760	−	0.345423i
$216$	13.7707	+	5.18133i	0.936976	+	0.352545i
$217$	10.1636	+	13.9890i	0.689949	+	0.949634i
$218$	−8.99723	+	22.4118i	−0.609370	+	1.51792i
$219$	2.30407	+	2.30407i	0.155695	+	0.155695i
$220$	−14.8349	+	2.22130i	−1.00017	+	0.149760i
$221$	9.88701	−	30.4291i	0.665072	−	2.04688i
$222$	7.43961	−	1.87242i	0.499314	−	0.125668i
$223$	−0.538270	−	0.274262i	−0.0360452	−	0.0183660i	0.435875	−	0.900007i	$-0.356439\pi$
$223$	−0.538270	−	0.274262i	−0.0360452	−	0.0183660i	−0.471920	+	0.881641i	$0.656439\pi$
$224$	−25.4872	+	3.41640i	−1.70293	+	0.228268i
$225$	0.00201554	−	0.0331823i	0.000134370	−	0.00221215i
$226$	−14.1632	−	22.5545i	−0.942120	−	1.50030i
$227$	4.15500	+	1.35004i	0.275777	+	0.0896054i	0.443640	−	0.896205i	$-0.353687\pi$
$227$	4.15500	+	1.35004i	0.275777	+	0.0896054i	−0.167863	+	0.985810i	$0.553687\pi$
$228$	1.23005	+	0.370113i	0.0814621	+	0.0245113i
$229$	−15.8132	+	2.50456i	−1.04496	+	0.165506i	−0.655236	−	0.755424i	$-0.727431\pi$
$229$	−15.8132	+	2.50456i	−1.04496	+	0.165506i	−0.389727	+	0.920930i	$0.627431\pi$
$230$	6.80613	−	5.58842i	0.448783	−	0.368489i
$231$	4.12677	−	26.0554i	0.271521	−	1.71432i
$232$	−4.27951	+	7.52741i	−0.280963	+	0.494199i
$233$	8.30902	+	25.5725i	0.544342	+	1.67531i	0.722550	+	0.691319i	$0.242970\pi$
$233$	8.30902	+	25.5725i	0.544342	+	1.67531i	−0.178208	+	0.983993i	$0.557030\pi$
$234$	0.0339324	+	0.0388605i	0.00221823	+	0.00254039i
$235$	−5.36194	+	9.77839i	−0.349774	+	0.637872i
$236$	−3.55926	−	1.71649i	−0.231688	−	0.111734i
$237$	−9.31522	−	9.31522i	−0.605088	−	0.605088i
$238$	19.2366	−	32.1764i	1.24693	−	2.08568i
$239$	10.7221	+	21.0433i	0.693556	+	1.36118i	0.921834	+	0.387585i	$0.126690\pi$
$239$	10.7221	+	21.0433i	0.693556	+	1.36118i	−0.228278	+	0.973596i	$0.573310\pi$
$240$	−10.7943	+	11.0883i	−0.696770	+	0.715748i
$241$	5.83821	+	8.03560i	0.376072	+	0.517619i	0.954539	−	0.298087i	$-0.0963487\pi$
$241$	5.83821	+	8.03560i	0.376072	+	0.517619i	−0.578467	+	0.815706i	$0.696349\pi$
$242$	0.266814	−	0.232977i	0.0171514	−	0.0149764i
$243$		−	0.0690951i		−	0.00443245i
$244$	−7.28893	+	3.91712i	−0.466626	+	0.250768i
$245$	−30.3099	+	3.86236i	−1.93643	+	0.246757i
$246$	15.6661	−	0.171694i	0.998831	−	0.0109468i
$247$	1.44024	+	1.44024i	0.0916403	+	0.0916403i
$248$	5.91944	+	8.98386i	0.375885	+	0.570476i
$249$	−11.1469	−	11.1469i	−0.706409	−	0.706409i
$250$	14.0771	+	7.19961i	0.890316	+	0.455343i
$251$	−2.22455	+	1.61623i	−0.140412	+	0.102016i	−0.655774	−	0.754957i	$-0.727658\pi$
$251$	−2.22455	+	1.61623i	−0.140412	+	0.102016i	0.515362	+	0.856973i	$0.327658\pi$
$252$	0.0286147	+	0.0532459i	0.00180255	+	0.00335417i
$253$	−2.88648	+	8.88368i	−0.181472	+	0.558512i
$254$	28.9443	−	7.28478i	1.81613	−	0.457088i
$255$	−2.85168	−	22.3786i	−0.178579	−	1.40140i
$256$	−15.9387	+	1.39878i	−0.996171	+	0.0874239i
$257$	−6.41959	+	8.83581i	−0.400443	+	0.551163i	−0.960855	−	0.277051i	$-0.910643\pi$
$257$	−6.41959	+	8.83581i	−0.400443	+	0.551163i	0.560412	+	0.828214i	$0.310643\pi$
$258$	5.75996	+	0.389955i	0.358599	+	0.0242775i
$259$	12.6995	+	6.47073i	0.789110	+	0.402072i
$260$	−23.3998	+	7.38506i	−1.45120	+	0.458002i
$261$	0.0201035	+	0.00318409i	0.00124438	+	0.000197090i
$262$	−24.4429	−	5.58607i	−1.51008	−	0.345109i
$263$	2.01160	+	1.46151i	0.124040	+	0.0901205i	0.648076	−	0.761576i	$-0.275574\pi$
$263$	2.01160	+	1.46151i	0.124040	+	0.0901205i	−0.524035	+	0.851696i	$0.675574\pi$
$264$	3.30584	−	16.0774i	0.203461	−	0.989498i
$265$	−1.57255	+	8.29234i	−0.0966009	+	0.509395i
$266$	1.26914	+	2.02107i	0.0778157	+	0.123919i
$267$	3.53388	+	6.93563i	0.216270	+	0.424454i
$268$	19.6582	+	2.67401i	1.20081	+	0.163341i
$269$	4.96767	−	1.61409i	0.302884	−	0.0984130i	−0.153632	−	0.988128i	$-0.549097\pi$
$269$	4.96767	−	1.61409i	0.302884	−	0.0984130i	0.456516	+	0.889715i	$0.349097\pi$
$270$	15.0727	+	6.58858i	0.917298	+	0.400968i
$271$	23.1925	+	7.53571i	1.40885	+	0.457762i	0.912041	−	0.410100i	$-0.134506\pi$
$271$	23.1925	+	7.53571i	1.40885	+	0.457762i	0.496806	+	0.867862i	$0.334506\pi$
$272$	12.8715	−	19.4523i	0.780446	−	1.17947i
$273$		−	43.1527i		−	2.61172i
$274$	8.02591	−	3.42780i	0.484863	−	0.207081i
$275$	−16.6930	+	1.61442i	−1.00662	+	0.0973531i
$276$	3.17761	+	9.09731i	0.191270	+	0.547594i
$277$	2.96870	−	0.470196i	0.178372	−	0.0282514i	−0.0666094	−	0.997779i	$-0.521218\pi$
$277$	2.96870	−	0.470196i	0.178372	−	0.0282514i	0.244981	+	0.969528i	$0.421218\pi$
$278$	1.70784	+	19.0350i	0.102430	+	1.14164i
$279$	0.0148652	−	0.0204601i	0.000889954	−	0.00122492i
$280$	−28.6560	+	2.32716i	−1.71253	+	0.139074i
$281$	4.24760	−	8.33639i	0.253391	−	0.497308i	−0.728912	−	0.684608i	$-0.759974\pi$
$281$	4.24760	−	8.33639i	0.253391	−	0.497308i	0.982303	+	0.187300i	$0.0599736\pi$
$282$	−8.02618	−	9.19186i	−0.477952	−	0.547367i
$283$	1.42810	−	9.01667i	0.0848917	−	0.535985i	−0.908190	−	0.418559i	$-0.862535\pi$
$283$	1.42810	−	9.01667i	0.0848917	−	0.535985i	0.993082	−	0.117427i	$-0.0374645\pi$
$284$	−10.0913	−	6.99955i	−0.598806	−	0.415347i
$285$	1.35177	+	0.485013i	0.0800717	+	0.0287297i
$286$	16.6853	−	19.9745i	0.986624	−	1.18112i
$287$	22.1339	+	18.9035i	1.30652	+	1.11584i
$288$	0.0162715	+	0.0339087i	0.000958810	+	0.00199809i
$289$	5.25459	+	16.1720i	0.309094	+	0.951292i
$290$	−5.21737	+	8.15471i	−0.306374	+	0.478861i
$291$	−15.0694	−	20.7412i	−0.883382	−	1.21587i
$292$	0.0824239	+	3.76581i	0.00482349	+	0.220377i
$293$	16.0572	−	5.21729i	0.938069	−	0.304797i	0.200211	−	0.979753i	$-0.435837\pi$
$293$	16.0572	−	5.21729i	0.938069	−	0.304797i	0.737858	+	0.674956i	$0.235837\pi$
$294$	7.44887	−	32.5939i	0.434427	−	1.90091i
$295$	−3.87378	−	2.12417i	−0.225540	−	0.123674i
$296$	7.70943	+	4.38299i	0.448102	+	0.254756i
$297$	−17.2332	+	2.72948i	−0.999974	+	0.158380i
$298$	−5.29297	−	21.0304i	−0.306614	−	1.21826i
$299$	−2.39029	+	15.0917i	−0.138234	+	0.872774i
$300$	−12.6990	+	11.7503i	−0.733178	+	0.678405i
$301$	7.58433	+	7.58433i	0.437154	+	0.437154i
$302$	0.667478	−	9.85921i	0.0384091	−	0.567334i
$303$	12.4974	+	24.5275i	0.717956	+	1.40907i
$304$	0.731368	+	1.29228i	0.0419468	+	0.0741175i
$305$	−8.36674	+	3.94816i	−0.479078	+	0.226071i
$306$	−0.0534518	−	0.0122157i	−0.00305564	−	0.000698323i
$307$	3.66941	+	7.20162i	0.209424	+	0.411018i	0.971695	−	0.236241i	$-0.0759153\pi$
$307$	3.66941	+	7.20162i	0.209424	+	0.411018i	−0.762270	+	0.647259i	$0.775915\pi$
$308$	24.2728	−	18.4601i	1.38307	−	1.05186i
$309$	2.87707	+	5.64656i	0.163671	+	0.321222i
$310$	6.08487	+	10.3760i	0.345597	+	0.589317i
$311$	19.1762	−	3.03721i	1.08738	−	0.172225i	0.413091	−	0.910690i	$-0.364449\pi$
$311$	19.1762	−	3.03721i	1.08738	−	0.172225i	0.674292	+	0.738465i	$0.264449\pi$
$312$	1.22698	−	26.8217i	0.0694640	−	1.51848i
$313$	−7.13276	−	9.81741i	−0.403168	−	0.554913i	0.558368	−	0.829593i	$-0.311428\pi$
$313$	−7.13276	−	9.81741i	−0.403168	−	0.554913i	−0.961535	+	0.274681i	$0.911428\pi$
$314$	7.77529	−	0.697609i	0.438785	−	0.0393684i
$315$	0.0288414	+	0.0611193i	0.00162503	+	0.00344369i
$316$	−0.333234	−	15.2249i	−0.0187459	−	0.856469i
$317$	−13.0073	+	17.9031i	−0.730566	+	1.00554i	0.268541	+	0.963268i	$0.413459\pi$
$317$	−13.0073	+	17.9031i	−0.730566	+	1.00554i	−0.999106	+	0.0422689i	$0.986541\pi$
$318$	−7.92684	−	4.73906i	−0.444515	−	0.265753i
$319$		−	10.2684i		−	0.574919i
$320$	−17.8774	+	0.631661i	−0.999376	+	0.0353109i
$321$	11.7404	+	23.0418i	0.655285	+	1.28607i
$322$	−6.66986	+	16.6143i	−0.371696	+	0.925881i
$323$	−2.13806	−	0.338636i	−0.118965	−	0.0188422i
$324$	−12.4187	+	12.9745i	−0.689929	+	0.720806i
$325$	−26.5571	+	6.88002i	−1.47312	+	0.381635i
$326$	−7.89433	+	19.6645i	−0.437227	+	1.08911i
$327$	−20.8916	−	20.8916i	−1.15531	−	1.15531i
$328$	13.2199	+	12.3788i	0.729945	+	0.683506i
$329$		−	22.6716i		−	1.24992i
$330$	4.62920	−	17.7577i	0.254829	−	0.977530i
$331$	22.7143	+	22.7143i	1.24849	+	1.24849i	0.956385	+	0.292108i	$0.0943565\pi$
$331$	22.7143	+	22.7143i	1.24849	+	1.24849i	0.292108	+	0.956385i	$0.405643\pi$
$332$	−0.398761	−	18.2187i	−0.0218848	−	0.999883i
$333$	0.00326108	−	0.0205897i	0.000178706	−	0.00112831i
$334$	−21.3867	+	9.13407i	−1.17023	+	0.499794i
$335$	21.7925	+	4.13270i	1.19065	+	0.225794i
$336$	8.40312	−	30.3165i	0.458428	−	1.65390i
$337$	6.24735	+	6.24735i	0.340315	+	0.340315i	0.856486	−	0.516171i	$-0.172643\pi$
$337$	6.24735	+	6.24735i	0.340315	+	0.340315i	−0.516171	+	0.856486i	$0.672643\pi$
$338$	12.4125	−	20.7620i	0.675153	−	1.12930i
$339$	32.1809	−	5.09696i	1.74783	−	0.276829i
$340$	15.5062	−	20.9676i	0.840944	−	1.13713i
$341$	−11.3679	−	5.79224i	−0.615607	−	0.313668i
$342$	0.00223771	−	0.00267883i	0.000121001	−	0.000144854i
$343$	24.5101	−	17.8076i	1.32342	−	0.961523i
$344$	4.49841	+	4.92970i	0.242538	+	0.265792i
$345$	3.01697	+	10.3427i	0.162428	+	0.556830i
$346$	−4.86336	+	12.1144i	−0.261456	+	0.651276i
$347$	−9.85220	−	3.20117i	−0.528894	−	0.171848i	0.0323839	−	0.999476i	$-0.489690\pi$
$347$	−9.85220	−	3.20117i	−0.528894	−	0.171848i	−0.561278	+	0.827627i	$0.689690\pi$
$348$	−6.41254	−	8.43174i	−0.343748	−	0.451989i
$349$	−9.16956	+	28.2210i	−0.490835	+	1.51064i	0.332512	+	0.943099i	$0.392104\pi$
$349$	−9.16956	+	28.2210i	−0.490835	+	1.51064i	−0.823348	+	0.567537i	$0.807896\pi$
$350$	−32.1306	+	0.926090i	−1.71745	+	0.0495016i
$351$	−27.1446	+	8.81982i	−1.44887	+	0.470767i
$352$	15.6117	−	10.7837i	0.832108	−	0.574775i
$353$	−3.15716	+	1.60866i	−0.168039	+	0.0856201i	−0.535987	−	0.844226i	$-0.680060\pi$
$353$	−3.15716	+	1.60866i	−0.168039	+	0.0856201i	0.367948	+	0.929846i	$0.380060\pi$
$354$	3.64143	−	3.17963i	0.193540	−	0.168996i
$355$	−10.8585	−	8.40394i	−0.576312	−	0.446035i
$356$	−2.59267	+	8.61661i	−0.137411	+	0.456679i
$357$	26.9574	+	37.1036i	1.42673	+	1.96373i
$358$	−24.5126	+	6.16940i	−1.29553	+	0.326063i
$359$	1.28820	+	0.935930i	0.0679884	+	0.0493965i	0.621260	−	0.783604i	$-0.286621\pi$
$359$	1.28820	+	0.935930i	0.0679884	+	0.0493965i	−0.553272	+	0.833001i	$0.686621\pi$
$360$	0.0161886	+	0.0388089i	0.000853215	+	0.00204541i
$361$	−11.0869	+	15.2598i	−0.583522	+	0.803149i
$362$	−18.3698	−	29.2534i	−0.965495	−	1.53752i
$363$	0.133910	+	0.412132i	0.00702845	+	0.0216313i
$364$	34.4929	−	36.0366i	1.80792	−	1.88883i
$365$	−0.127724	+	4.20938i	−0.00668540	+	0.220329i
$366$	−0.904641	−	10.0828i	−0.0472863	−	0.527035i
$367$	−21.4899	−	10.9496i	−1.12176	−	0.571566i	−0.208126	−	0.978102i	$-0.566737\pi$
$367$	−21.4899	−	10.9496i	−1.12176	−	0.571566i	−0.913635	+	0.406536i	$0.866737\pi$
$368$	−4.61806	+	10.1370i	−0.240733	+	0.528429i
$369$	0.0162911	−	0.0393320i	0.000848079	−	0.00204754i
$370$	8.35189	+	5.34353i	0.434194	+	0.277797i
$371$	−5.30225	−	16.3186i	−0.275279	−	0.847222i
$372$	−12.9518	+	2.34297i	−0.671521	+	0.121478i
$373$	−15.6635	−	2.48085i	−0.811023	−	0.128453i	−0.262870	−	0.964831i	$-0.584669\pi$
$373$	−15.6635	−	2.48085i	−0.811023	−	0.128453i	−0.548153	+	0.836378i	$0.684669\pi$
$374$	−1.86840	+	27.5977i	−0.0966124	+	1.42705i
$375$	−14.8643	+	12.3783i	−0.767587	+	0.639213i
$376$	0.644630	−	14.0916i	0.0332442	−	0.726717i
$377$	−2.62763	−	16.5902i	−0.135330	−	0.854440i
$378$	−33.3080	+	2.98844i	−1.71318	+	0.153709i
$379$	−4.04407	−	2.93819i	−0.207730	−	0.150924i	0.479056	−	0.877784i	$-0.340979\pi$
$379$	−4.04407	−	2.93819i	−0.207730	−	0.150924i	−0.686786	+	0.726860i	$0.740979\pi$
$380$	0.741170	+	1.48553i	0.0380212	+	0.0762059i
$381$	−5.71211	+	36.0649i	−0.292640	+	1.84766i
$382$	9.25415	−	23.0517i	0.473483	−	1.17943i
$383$	22.8153			1.16581			0.582903	−	0.812542i	$-0.301917\pi$
$383$	22.8153			1.16581			0.582903	+	0.812542i	$0.301917\pi$
$384$	6.08498	−	18.6044i	0.310523	−	0.949400i
$385$	28.1781	−	19.1944i	1.43609	−	0.978239i
$386$	−4.74580	+	7.93812i	−0.241555	+	0.404040i
$387$	0.00712199	−	0.0139777i	0.000362031	−	0.000710526i
$388$	3.99454	−	29.3661i	0.202792	−	1.49084i
$389$	3.92738	−	12.0872i	0.199126	−	0.612847i	−0.800777	−	0.598962i	$-0.795580\pi$
$389$	3.92738	−	12.0872i	0.199126	−	0.612847i	0.999904	−	0.0138854i	$-0.00441999\pi$
$390$	2.93510	−	29.8751i	0.148624	−	1.51278i
$391$	−7.37249	−	14.4693i	−0.372843	−	0.731746i
$392$	32.2734	−	21.2649i	1.63006	−	1.07404i
$393$	18.0297	−	24.8158i	0.909480	−	1.25179i
$394$	5.99492	+	9.54675i	0.302020	+	0.480958i
$395$	0.516381	−	17.0182i	0.0259820	−	0.856280i
$396$	−0.0366486	−	0.0254204i	−0.00184166	−	0.00127742i
$397$	8.73535	−	2.83829i	0.438415	−	0.142450i	−0.0814895	−	0.996674i	$-0.525968\pi$
$397$	8.73535	−	2.83829i	0.438415	−	0.142450i	0.519904	+	0.854225i	$0.325968\pi$
$398$	−1.35163	+	19.9646i	−0.0677509	+	1.00074i
$399$	−2.88367	+	0.456729i	−0.144364	+	0.0228651i
$400$	−19.9971	−	0.337968i	−0.999857	−	0.0168984i
$401$		−	31.0429i		−	1.55021i	−0.631833	−	0.775105i	$-0.717697\pi$
$401$		−	31.0429i		−	1.55021i	0.631833	−	0.775105i	$-0.282303\pi$
$402$	−12.4544	+	20.8320i	−0.621168	+	1.03900i
$403$	−19.8489	−	6.44931i	−0.988746	−	0.321263i
$404$	−9.16885	+	30.4722i	−0.456167	+	1.51605i
$405$	−14.6227	+	13.7615i	−0.726610	+	0.683814i
$406$	1.32937	−	19.6360i	0.0659757	−	0.974516i
$407$	−10.5167			−0.521292
$408$	15.7004	+	23.8283i	0.777287	+	1.17968i
$409$			10.9610i			0.541985i	0.962582	+	0.270992i	$0.0873518\pi$
$409$			10.9610i			0.541985i	−0.962582	+	0.270992i	$0.912648\pi$
$410$	14.0378	+	14.5925i	0.693275	+	0.720673i
$411$			10.6768i			0.526649i
$412$	−2.11079	+	7.01511i	−0.103991	+	0.345609i
$413$	8.98151			0.441951
$414$	0.0261252	+	0.00176870i	0.00128398	+	8.69269e-5i
$415$	0.617921	−	20.3647i	0.0303326	−	0.999662i
$416$	22.4638	−	21.4179i	1.10138	−	1.05010i
$417$	−22.2364	−	7.22503i	−1.08892	−	0.353811i
$418$	−1.51139	−	0.903584i	−0.0739245	−	0.0441957i
$419$			7.32461i			0.357831i	0.983864	+	0.178915i	$0.0572588\pi$
$419$			7.32461i			0.357831i	−0.983864	+	0.178915i	$0.942741\pi$
$420$	11.1513	−	33.3583i	0.544126	−	1.62772i
$421$	22.4897	−	3.56201i	1.09608	−	0.173602i	0.417896	−	0.908495i	$-0.362768\pi$
$421$	22.4897	−	3.56201i	1.09608	−	0.173602i	0.678183	+	0.734893i	$0.262768\pi$
$422$	−15.8704	−	1.07444i	−0.772558	−	0.0523029i
$423$	−0.0315363	+	0.0102468i	−0.00153335	+	0.000498214i
$424$	−2.83163	−	10.2936i	−0.137516	−	0.499904i
$425$	18.5364	−	22.5057i	0.899148	−	1.09169i
$426$	12.7239	−	7.99005i	0.616477	−	0.387119i
$427$	11.0550	−	15.2159i	0.534990	−	0.736351i
$428$	−8.61348	+	28.6264i	−0.416348	+	1.38371i
$429$	14.4553	+	28.3701i	0.697908	+	1.36972i
$430$	4.73485	+	5.76657i	0.228335	+	0.278089i
$431$	−0.738065	+	2.27153i	−0.0355513	+	0.109416i	−0.967257	−	0.253797i	$-0.918320\pi$
$431$	−0.738065	+	2.27153i	−0.0355513	+	0.109416i	0.931706	+	0.363213i	$0.118320\pi$
$432$	−20.7877	+	0.910412i	−1.00015	+	0.0438022i
$433$	5.79877	−	11.3807i	0.278671	−	0.546923i	−0.708669	−	0.705541i	$-0.750704\pi$
$433$	5.79877	−	11.3807i	0.278671	−	0.546923i	0.987340	+	0.158618i	$0.0507040\pi$
$434$	−20.9887	−	12.5481i	−1.00749	−	0.602327i
$435$	−6.66764	−	9.78832i	−0.319689	−	0.469314i
$436$	−0.747357	−	34.1455i	−0.0357919	−	1.63527i
$437$	1.03380			0.0494532
$438$	−4.27641	−	1.71677i	−0.204335	−	0.0820306i
$439$	−4.05470	+	25.6004i	−0.193520	+	1.22184i	0.679324	+	0.733839i	$0.262273\pi$
$439$	−4.05470	+	25.6004i	−0.193520	+	1.22184i	−0.872844	+	0.488000i	$0.837727\pi$
$440$	18.0599	−	11.1291i	0.860973	−	0.530561i
$441$	−0.0735006	−	0.0534013i	−0.00350003	−	0.00254292i
$442$	4.04345	+	45.0668i	0.192327	+	2.14361i
$443$	−0.238709	−	1.50715i	−0.0113414	−	0.0716069i	0.981368	−	0.192135i	$-0.0615412\pi$
$443$	−0.238709	−	1.50715i	−0.0113414	−	0.0716069i	−0.992710	+	0.120528i	$0.961541\pi$
$444$	−8.63563	+	6.56760i	−0.409829	+	0.311685i
$445$	−3.39756	+	9.46924i	−0.161060	+	0.448885i
$446$	0.852396	+	0.0577080i	0.0403621	+	0.00273255i
$447$	26.2040	+	4.15030i	1.23941	+	0.196303i
$448$	31.2500	−	18.6003i	1.47642	−	0.878783i
$449$	11.9737	+	36.8514i	0.565075	+	1.73912i	0.667728	+	0.744406i	$0.267267\pi$
$449$	11.9737	+	36.8514i	0.565075	+	1.73912i	−0.102652	+	0.994717i	$0.532733\pi$
$450$	0.0158101	+	0.0442752i	0.000745295	+	0.00208715i
$451$	−20.8838	−	5.01339i	−0.983382	−	0.236071i
$452$	30.9482	+	21.4664i	1.45568	+	1.00970i
$453$	10.7716	+	5.48840i	0.506093	+	0.257867i
$454$	−6.15373	+	0.552121i	−0.288809	+	0.0259123i
$455$	40.6145	−	38.2224i	1.90404	−	1.79189i
$456$	−1.80534	+	0.201888i	−0.0845428	+	0.00945429i
$457$	−9.72311	−	29.9247i	−0.454828	−	1.39982i	−0.871337	−	0.490685i	$-0.836747\pi$
$457$	−9.72311	−	29.9247i	−0.454828	−	1.39982i	0.416509	−	0.909131i	$-0.363253\pi$
$458$	19.1748	−	12.0409i	0.895981	−	0.562635i
$459$	17.8298	−	24.5406i	0.832224	−	1.14546i
$460$	−5.74766	+	11.0486i	−0.267986	+	0.515144i
$461$	17.1200	+	12.4384i	0.797356	+	0.579313i	0.910137	−	0.414307i	$-0.135976\pi$
$461$	17.1200	+	12.4384i	0.797356	+	0.579313i	−0.112781	+	0.993620i	$0.535976\pi$
$462$	9.10560	+	36.1789i	0.423631	+	1.68320i
$463$	17.9574	+	24.7162i	0.834550	+	1.14866i	0.987059	+	0.160357i	$0.0512646\pi$
$463$	17.9574	+	24.7162i	0.834550	+	1.14866i	−0.152509	+	0.988302i	$0.548735\pi$
$464$	1.38459	−	12.1670i	0.0642781	−	0.564837i
$465$	−14.5976	+	1.86016i	−0.676947	+	0.0862628i
$466$	−25.0109	−	28.6434i	−1.15861	−	1.32688i
$467$	12.8717	−	6.55847i	0.595632	−	0.303490i	−0.130063	−	0.991506i	$-0.541518\pi$
$467$	12.8717	−	6.55847i	0.595632	−	0.303490i	0.725696	+	0.688016i	$0.241518\pi$
$468$	−0.0657167	−	0.0316925i	−0.00303775	−	0.00146499i
$469$	−42.8859	+	13.9345i	−1.98029	+	0.643434i
$470$	1.54204	−	15.6958i	0.0711290	−	0.723991i
$471$	−2.95123	+	9.08296i	−0.135986	+	0.418521i
$472$	5.58248	+	0.255375i	0.256954	+	0.0117546i
$473$	−7.52680	−	2.44561i	−0.346083	−	0.112449i
$474$	17.2893	+	6.94080i	0.794122	+	0.318801i
$475$	0.740837	+	1.70185i	0.0339919	+	0.0780865i
$476$	−7.14577	+	52.5326i	−0.327526	+	2.40783i
$477$	−0.0203029	+	0.0147509i	−0.000929606	+	0.000675398i
$478$	−25.6335	−	21.4125i	−1.17245	−	0.979384i
$479$	−8.81985	−	4.49394i	−0.402989	−	0.205333i	0.240735	−	0.970591i	$-0.422612\pi$
$479$	−8.81985	−	4.49394i	−0.402989	−	0.205333i	−0.643724	+	0.765258i	$0.722612\pi$
$480$	7.87958	−	20.4169i	0.359652	−	0.931898i
$481$	−16.9914	+	2.69117i	−0.774741	+	0.122707i
$482$	−12.0564	−	7.20792i	−0.549155	−	0.328312i
$483$	−15.4874	−	15.4874i	−0.704701	−	0.704701i
$484$	−0.217599	+	0.451206i	−0.00989084	+	0.0205094i
$485$	6.17358	−	32.5544i	0.280328	−	1.47822i
$486$	0.0383795	+	0.0898625i	0.00174093	+	0.00407625i
$487$	2.99256	−	18.8943i	0.135606	−	0.856181i	−0.822291	−	0.569068i	$-0.807304\pi$
$487$	2.99256	−	18.8943i	0.135606	−	0.856181i	0.957897	−	0.287114i	$-0.0926958\pi$
$488$	7.30391	−	9.14316i	0.330633	−	0.413892i
$489$	−18.3307	−	18.3307i	−0.828941	−	0.828941i
$490$	37.2745	−	21.8592i	1.68389	−	0.987497i
$491$		−	21.2787i		−	0.960295i	−0.877188	−	0.480147i	$-0.840583\pi$
$491$		−	21.2787i		−	0.960295i	0.877188	−	0.480147i	$-0.159417\pi$
$492$	−20.2793	+	8.92516i	−0.914263	+	0.402377i
$493$	12.6232	+	12.6232i	0.568518	+	0.568518i
$494$	−2.67312	−	1.07313i	−0.120269	−	0.0482823i
$495$	−0.0394351	−	0.0305207i	−0.00177248	−	0.00137180i
$496$	−12.6888	−	8.39607i	−0.569743	−	0.376995i
$497$	27.5704	+	4.36673i	1.23670	+	0.195875i
$498$	20.6890	+	8.30563i	0.927096	+	0.372184i
$499$	−2.89370	−	5.67921i	−0.129540	−	0.254236i	0.817122	−	0.576465i	$-0.195568\pi$
$499$	−2.89370	−	5.67921i	−0.129540	−	0.254236i	−0.946662	+	0.322228i	$0.895568\pi$
$500$	−22.3073	−	1.54426i	−0.997612	−	0.0690616i
$501$		−	28.4505i		−	1.27108i
$502$	1.99542	−	3.33766i	0.0890598	−	0.148967i
$503$	−14.7841	+	20.3485i	−0.659189	+	0.907295i	−0.999454	−	0.0330341i	$-0.989483\pi$
$503$	−14.7841	+	20.3485i	−0.659189	+	0.907295i	0.340266	+	0.940329i	$0.389483\pi$
$504$	−0.0667911	−	0.0533553i	−0.00297511	−	0.00237664i
$505$	−12.0153	+	33.4875i	−0.534674	+	1.49017i
$506$	−1.18047	−	13.1571i	−0.0524785	−	0.584905i
$507$	17.3944	+	23.9413i	0.772512	+	1.06327i
$508$	−33.5975	+	25.5517i	−1.49065	+	1.13367i
$509$	−1.77379	+	0.280940i	−0.0786217	+	0.0124525i	−0.195621	−	0.980679i	$-0.562672\pi$
$509$	−1.77379	+	0.280940i	−0.0786217	+	0.0124525i	0.117000	+	0.993132i	$0.462672\pi$
$510$	16.1392	+	27.5208i	0.714656	+	1.21864i
$511$	−3.88681	−	7.62829i	−0.171942	−	0.337456i
$512$	19.9524	−	10.6725i	0.881778	−	0.471664i
$513$	0.876682	+	1.72059i	0.0387065	+	0.0759657i
$514$	3.44115	−	15.0574i	0.151783	−	0.664152i
$515$	−2.76608	+	7.70926i	−0.121888	+	0.339711i
$516$	−7.70780	+	2.69227i	−0.339317	+	0.118520i
$517$	7.59452	+	14.9051i	0.334006	+	0.655525i
$518$	−20.1108	−	1.36152i	−0.883616	−	0.0598217i
$519$	−11.2927	−	11.2927i	−0.495695	−	0.495695i
$520$	26.3308	−	22.6024i	1.15468	−	0.991181i
$521$	−2.24203	+	14.1556i	−0.0982253	+	0.620170i	0.888638	+	0.458610i	$0.151653\pi$
$521$	−2.24203	+	14.1556i	−0.0982253	+	0.620170i	−0.986863	+	0.161560i	$0.948347\pi$
$522$	−0.0279146	+	0.00702560i	−0.00122179	+	0.000307502i
$523$	−27.3760	+	4.33593i	−1.19707	+	0.189597i	−0.722973	−	0.690876i	$-0.757225\pi$
$523$	−27.3760	+	4.33593i	−1.19707	+	0.189597i	−0.474095	+	0.880473i	$0.657225\pi$
$524$	34.8923	−	6.31198i	1.52428	−	0.275740i
$525$	14.3971	−	36.5942i	0.628341	−	1.59710i
$526$	−3.42802	−	0.783425i	−0.149469	−	0.0341590i
$527$	21.0954	−	6.85431i	0.918929	−	0.298578i
$528$	4.63091	+	22.7460i	0.201535	+	0.989892i
$529$	−8.96057	−	12.3332i	−0.389590	−	0.536224i
$530$	−2.56086	−	11.6582i	−0.111237	−	0.506400i
$531$	−0.00405933	−	0.0124933i	−0.000176160	−	0.000542165i
$532$	−2.77321	−	1.92357i	−0.120234	−	0.0833973i
$533$	−35.0242	−	2.75585i	−1.51706	−	0.119369i
$534$	−8.44850	−	7.05730i	−0.365602	−	0.305399i
$535$	−11.2875	+	31.4591i	−0.488002	+	1.36009i
$536$	−27.0520	+	7.44160i	−1.16847	+	0.321428i
$537$	4.83752	−	30.5429i	0.208755	−	1.31802i
$538$	−5.56420	+	4.85857i	−0.239890	+	0.209468i
$539$	−20.8079	+	40.8379i	−0.896261	+	1.75901i
$540$	−23.2627	−	0.196566i	−1.00107	−	0.00845884i
$541$	−22.8867	+	31.5009i	−0.983977	+	1.35433i	−0.0493179	+	0.998783i	$0.515705\pi$
$541$	−22.8867	+	31.5009i	−0.983977	+	1.35433i	−0.934659	+	0.355545i	$0.884295\pi$
$542$	−34.3491	+	3.08185i	−1.47542	+	0.132377i
$543$	41.7390	−	6.61081i	1.79119	−	0.283697i
$544$	−5.93515	+	32.4486i	−0.254467	+	1.39122i
$545$	1.15811	−	38.1674i	0.0496079	−	1.63491i
$546$	23.9696	+	56.1229i	1.02580	+	2.40184i
$547$		−	28.3024i		−	1.21012i	−0.796179	−	0.605061i	$-0.793149\pi$
$547$		−	28.3024i		−	1.21012i	0.796179	−	0.605061i	$-0.206851\pi$
$548$	−8.53420	+	8.91614i	−0.364563	+	0.380879i
$549$	−0.0261619	−	0.00850053i	−0.00111656	−	0.000362794i
$550$	20.8135	−	11.3719i	0.887491	−	0.484901i
$551$	−1.08083	+	0.351182i	−0.0460448	+	0.0149609i
$552$	−9.18587	−	10.0666i	−0.390977	−	0.428463i
$553$	15.7141	+	30.8407i	0.668231	+	1.31148i
$554$	−3.59981	+	2.26052i	−0.152941	+	0.0960401i
$555$	−10.0250	+	6.82887i	−0.425538	+	0.289869i
$556$	−12.7943	−	23.8076i	−0.542600	−	1.00967i
$557$	28.5137	+	20.7164i	1.20816	+	0.877783i	0.995063	−	0.0992469i	$-0.0316434\pi$
$557$	28.5137	+	20.7164i	1.20816	+	0.877783i	0.213102	+	0.977030i	$0.431643\pi$
$558$	−0.00796829	+	0.0348667i	−0.000337325	+	0.00147602i
$559$	−12.7866	−	2.02520i	−0.540815	−	0.0856567i
$560$	35.9763	−	18.9439i	1.52028	−	0.800525i
$561$	−30.1517	−	15.3630i	−1.27300	−	0.648628i
$562$	−0.893747	+	13.2014i	−0.0377004	+	0.556867i
$563$	0.0918430	−	0.126411i	0.00387072	−	0.00532759i	−0.807077	−	0.590446i	$-0.798952\pi$
$563$	0.0918430	−	0.126411i	0.00387072	−	0.00532759i	0.810948	+	0.585118i	$0.198952\pi$
$564$	15.5443	+	7.49638i	0.654532	+	0.315654i
$565$	33.3013	+	25.7735i	1.40100	+	1.08430i
$566$	3.15106	+	12.5200i	0.132449	+	0.526255i
$567$	12.6146	−	38.8237i	0.529762	−	1.63044i
$568$	17.0123	+	3.49807i	0.713820	+	0.146776i
$569$	−14.2950	+	10.3859i	−0.599276	+	0.435399i	−0.845622	−	0.533783i	$-0.820770\pi$
$569$	−14.2950	+	10.3859i	−0.599276	+	0.435399i	0.246346	+	0.969182i	$0.420770\pi$
$570$	−2.02746	+	0.120061i	−0.0849210	+	0.00502880i
$571$	−32.4481	−	32.4481i	−1.35791	−	1.35791i	−0.876490	−	0.481419i	$-0.840121\pi$
$571$	−32.4481	−	32.4481i	−1.35791	−	1.35791i	−0.481419	−	0.876490i	$-0.659879\pi$
$572$	−10.6053	+	35.2461i	−0.443429	+	1.47371i
$573$	21.4881	+	21.4881i	0.897680	+	0.897680i
$574$	−39.2866	−	12.2907i	−1.63979	−	0.513002i
$575$	−7.06205	+	12.0005i	−0.294508	+	0.500455i
$576$	−0.0399971	−	0.0350622i	−0.00166654	−	0.00146093i
$577$		−	28.6405i		−	1.19232i	−0.802865	−	0.596160i	$-0.796692\pi$
$577$		−	28.6405i		−	1.19232i	0.802865	−	0.596160i	$-0.203308\pi$
$578$	−15.8168	−	18.1139i	−0.657892	−	0.753441i
$579$	−6.65056	−	9.15371i	−0.276388	−	0.380415i
$580$	2.25591	−	13.5037i	0.0936714	−	0.560713i
$581$	18.8041	+	36.9051i	0.780125	+	1.53108i
$582$	31.1196	+	18.6048i	1.28995	+	0.771194i
$583$	8.95230	+	8.95230i	0.370766	+	0.370766i
$584$	−2.19895	−	4.85189i	−0.0909934	−	0.200773i
$585$	−0.0715239	−	0.0392199i	−0.00295715	−	0.00162154i
$586$	−17.9854	+	15.7045i	−0.742968	+	0.648748i
$587$	2.56994	+	7.90947i	0.106073	+	0.326459i	0.989981	−	0.141202i	$-0.0450968\pi$
$587$	2.56994	+	7.90947i	0.106073	+	0.326459i	−0.883908	+	0.467661i	$0.845097\pi$
$588$	8.41685	+	46.5279i	0.347105	+	1.91878i
$589$	−0.220893	+	1.39466i	−0.00910172	+	0.0574660i
$590$	6.21799	+	0.610891i	0.255991	+	0.0251500i
$591$	−13.6214	+	2.15742i	−0.560309	+	0.0887442i
$592$	−12.4612	−	1.41807i	−0.512151	−	0.0582824i
$593$	−13.7920	−	4.48128i	−0.566368	−	0.184024i	0.0118162	−	0.999930i	$-0.496239\pi$
$593$	−13.7920	−	4.48128i	−0.566368	−	0.184024i	−0.578185	+	0.815906i	$0.696239\pi$
$594$	20.8968	−	13.1222i	0.857406	−	0.538411i
$595$	−11.0438	+	58.2362i	−0.452753	+	2.38745i
$596$	18.5654	+	24.4113i	0.760467	+	0.999925i
$597$	−21.8122	−	11.1139i	−0.892713	−	0.454860i
$598$	−5.27410	−	20.9554i	−0.215674	−	0.856929i
$599$	11.5083	−	35.4190i	0.470218	−	1.44718i	−0.382083	−	0.924128i	$-0.624793\pi$
$599$	11.5083	−	35.4190i	0.470218	−	1.44718i	0.852300	−	0.523053i	$-0.175207\pi$
$600$	9.98904	−	22.3358i	0.407801	−	0.911856i
$601$	9.49204	+	9.49204i	0.387189	+	0.387189i	0.873683	−	0.486495i	$-0.161725\pi$
$601$	9.49204	+	9.49204i	0.387189	+	0.387189i	−0.486495	+	0.873683i	$0.661725\pi$
$602$	−14.0767	−	5.65111i	−0.573723	−	0.230322i
$603$	0.0387658	+	0.0533566i	0.00157867	+	0.00217285i
$604$	4.60830	+	13.1933i	0.187509	+	0.536827i
$605$	−0.269281	+	0.491078i	−0.0109478	+	0.0199652i
$606$	−29.8777	−	24.9578i	−1.21370	−	1.01384i
$607$	−18.6797	+	2.95857i	−0.758185	+	0.120085i	−0.523545	−	0.851998i	$-0.675391\pi$
$607$	−18.6797	+	2.95857i	−0.758185	+	0.120085i	−0.234639	+	0.972082i	$0.575391\pi$
$608$	−1.66900	−	1.27445i	−0.0676870	−	0.0516858i
$609$	21.4531	+	10.9309i	0.869323	+	0.442942i
$610$	8.68844	−	9.78222i	0.351785	−	0.396070i
$611$	16.0843	+	22.1382i	0.650702	+	0.895615i
$612$	0.0763028	−	0.0138031i	0.00308436	−	0.000557957i
$613$	11.6830	+	5.95277i	0.471871	+	0.240430i	0.673720	−	0.738986i	$-0.264695\pi$
$613$	11.6830	+	5.95277i	0.471871	+	0.240430i	−0.201850	+	0.979417i	$0.564695\pi$
$614$	−8.77251	−	7.32795i	−0.354030	−	0.295732i
$615$	−23.1629	+	8.78165i	−0.934018	+	0.354110i
$616$	−21.3145	+	37.4911i	−0.858787	+	1.51056i
$617$	21.4828	−	42.1625i	0.864867	−	1.69740i	0.161133	−	0.986933i	$-0.448485\pi$
$617$	21.4828	−	42.1625i	0.864867	−	1.69740i	0.703733	−	0.710464i	$-0.251515\pi$
$618$	−6.87824	−	5.74561i	−0.276684	−	0.231123i
$619$	0.445971	−	0.324017i	0.0179251	−	0.0130233i	−0.578787	−	0.815479i	$-0.696474\pi$
$619$	0.445971	−	0.324017i	0.0179251	−	0.0130233i	0.596712	+	0.802456i	$0.296474\pi$
$620$	−13.6772	−	10.1147i	−0.549290	−	0.406218i
$621$	−6.57672	+	12.9075i	−0.263915	+	0.517962i
$622$	−23.2528	+	14.6017i	−0.932353	+	0.585475i
$623$	−3.19943	−	20.2004i	−0.128182	−	0.809312i
$624$	13.3026	+	35.5648i	0.532530	+	1.42373i
$625$	−24.8162	−	3.02591i	−0.992648	−	0.121037i
$626$	14.7298	+	8.80619i	0.588720	+	0.351966i
$627$	1.74283	−	1.26624i	0.0696020	−	0.0505688i
$628$	−9.72476	+	5.22614i	−0.388060	+	0.208546i
$629$	12.9284	−	12.9284i	0.515489	−	0.515489i
$630$	−0.0714594	−	0.0634693i	−0.00284701	−	0.00252868i
$631$	−15.8804	−	5.15984i	−0.632187	−	0.205410i	−0.0246435	−	0.999696i	$-0.507845\pi$
$631$	−15.8804	−	5.15984i	−0.632187	−	0.205410i	−0.607544	+	0.794286i	$0.707845\pi$
$632$	8.89022	+	19.6159i	0.353634	+	0.780278i
$633$	8.83468	−	17.3390i	0.351147	−	0.689165i
$634$	6.97244	−	30.5091i	0.276911	−	1.21167i
$635$	−39.0030	+	26.5682i	−1.54779	+	1.05433i
$636$	12.9417	+	1.76040i	0.513173	+	0.0698045i
$637$	−23.1684	+	71.3049i	−0.917964	+	2.82520i
$638$	5.70367	+	13.3547i	0.225810	+	0.528717i
$639$	−0.00638673	−	0.0403242i	−0.000252655	−	0.00159520i
$640$	22.8998	−	10.7517i	0.905194	−	0.424998i
$641$	−11.4602	−	1.81512i	−0.452651	−	0.0716929i	−0.0740536	−	0.997254i	$-0.523594\pi$
$641$	−11.4602	−	1.81512i	−0.452651	−	0.0716929i	−0.378598	+	0.925561i	$0.623594\pi$
$642$	−28.0679	−	23.4460i	−1.10775	−	0.925341i
$643$	11.1496	−	3.62274i	0.439699	−	0.142867i	−0.0807980	−	0.996730i	$-0.525747\pi$
$643$	11.1496	−	3.62274i	0.439699	−	0.142867i	0.520497	+	0.853864i	$0.325747\pi$
$644$	−0.554033	−	25.3128i	−0.0218319	−	0.997466i
$645$	−8.76294	+	2.55616i	−0.345040	+	0.100649i
$646$	2.96878	−	0.747190i	0.116805	−	0.0293978i
$647$	−8.26066	+	8.26066i	−0.324760	+	0.324760i	−0.850590	−	0.525830i	$-0.823755\pi$
$647$	−8.26066	+	8.26066i	−0.324760	+	0.324760i	0.525830	+	0.850590i	$0.323755\pi$
$648$	8.94451	−	23.7723i	0.351373	−	0.933863i
$649$	−5.90476	+	3.00862i	−0.231782	+	0.118099i
$650$	30.7176	−	23.6993i	1.20484	−	0.929563i
$651$	24.2028	−	17.5843i	0.948581	−	0.689184i
$652$	−0.655744	−	29.9599i	−0.0256809	−	1.17332i
$653$	−45.1969			−1.76869			−0.884347	−	0.466831i	$-0.845396\pi$
$653$	−45.1969			−1.76869			−0.884347	+	0.466831i	$0.845396\pi$
$654$	38.7753	+	15.5664i	1.51623	+	0.608694i
$655$	39.3260	−	5.01127i	1.53659	−	0.195807i
$656$	−24.0692	−	8.75634i	−0.939745	−	0.341877i
$657$	−0.00885429	+	0.00885429i	−0.000345439	+	0.000345439i
$658$	12.5931	+	29.4858i	0.490932	+	1.14948i
$659$	−34.4536	+	34.4536i	−1.34212	+	1.34212i	−0.448173	+	0.893947i	$0.647925\pi$
$659$	−34.4536	+	34.4536i	−1.34212	+	1.34212i	−0.893947	+	0.448173i	$0.852075\pi$
$660$	3.84313	+	25.6664i	0.149594	+	0.999062i
$661$	−15.6989	−	21.6077i	−0.610616	−	0.840441i	0.386012	−	0.922494i	$-0.373852\pi$
$661$	−15.6989	−	21.6077i	−0.610616	−	0.840441i	−0.996628	+	0.0820528i	$0.973852\pi$
$662$	−42.1583	−	16.9245i	−1.63853	−	0.657791i
$663$	−52.6463	−	17.1058i	−2.04461	−	0.664335i
$664$	10.6384	+	23.4731i	0.412849	+	0.910933i
$665$	−2.98407	−	2.30951i	−0.115717	−	0.0895591i
$666$	0.00719548	+	0.0285895i	0.000278819	+	0.00110782i
$667$	−6.89724	−	5.01114i	−0.267062	−	0.194032i
$668$	22.7411	−	23.7589i	0.879880	−	0.919258i
$669$	−0.474509	+	0.931277i	−0.0183456	+	0.0360053i
$670$	−30.6381	+	6.73002i	−1.18365	+	0.260003i
$671$	−2.17093	+	13.7067i	−0.0838077	+	0.529141i
$672$	5.91082	+	44.0961i	0.228015	+	1.70104i
$673$	12.4593	−	17.1487i	0.480270	−	0.661035i	−0.498287	−	0.867012i	$-0.666037\pi$
$673$	12.4593	−	17.1487i	0.480270	−	0.661035i	0.978557	+	0.205977i	$0.0660374\pi$
$674$	−11.5952	−	4.65492i	−0.446631	−	0.179301i
$675$	−25.9616	−	1.57695i	−0.999263	−	0.0606968i
$676$	−4.61085	+	33.8969i	−0.177340	+	1.30373i
$677$	−1.21442	+	0.618779i	−0.0466740	+	0.0237816i	−0.477172	−	0.878810i	$-0.658338\pi$
$677$	−1.21442	+	0.618779i	−0.0466740	+	0.0237816i	0.430498	+	0.902592i	$0.358338\pi$
$678$	−39.0222	+	24.5041i	−1.49864	+	0.941075i
$679$	20.8158	+	64.0645i	0.798837	+	2.45857i
$680$	−8.52017	+	35.8828i	−0.326733	+	1.37604i
$681$	2.33575	−	7.18869i	0.0895060	−	0.275471i
$682$	18.0021	+	1.21876i	0.689334	+	0.0466686i
$683$	−7.94393			−0.303966			−0.151983	−	0.988383i	$-0.548566\pi$
$683$	−7.94393			−0.303966			−0.151983	+	0.988383i	$0.548566\pi$
$684$	−0.00142230	+	0.00472694i	−5.43830e−5	+	0.000180739i
$685$	−10.0488	+	9.45696i	−0.383946	+	0.361332i
$686$	−21.9855	+	36.7744i	−0.839412	+	1.40405i
$687$	4.33321	+	27.3588i	0.165322	+	1.04380i
$688$	−8.58872	−	3.91271i	−0.327442	−	0.149171i
$689$	16.7548	+	12.1730i	0.638305	+	0.463756i
$690$	−9.66869	−	11.7755i	−0.368081	−	0.448285i
$691$	23.4913	+	11.9694i	0.893650	+	0.455337i	0.839603	−	0.543201i	$-0.182788\pi$
$691$	23.4913	+	11.9694i	0.893650	+	0.455337i	0.0540472	+	0.998538i	$0.482788\pi$
$692$	−0.403975	−	18.4570i	−0.0153568	−	0.701629i
$693$	0.100128	+	0.0158587i	0.00380354	+	0.000602422i
$694$	14.5915	−	1.30917i	0.553887	−	0.0496955i
$695$	−12.8957	−	27.3280i	−0.489163	−	1.03661i
$696$	13.0234	+	7.40410i	0.493651	+	0.280652i
$697$	31.8361	−	19.5099i	1.20588	−	0.738991i
$698$	−3.75004	−	41.7965i	−0.141941	−	1.58202i
$699$	44.2438	−	14.3757i	1.67345	−	0.543738i
$700$	41.2734	−	19.0517i	1.55999	−	0.720085i
$701$	−11.6754	+	8.48264i	−0.440972	+	0.320385i	−0.786021	−	0.618200i	$-0.787862\pi$
$701$	−11.6754	+	8.48264i	−0.440972	+	0.320385i	0.345049	+	0.938585i	$0.387862\pi$
$702$	30.4042	−	26.5485i	1.14753	−	1.00201i
$703$	0.359674	+	1.10696i	0.0135654	+	0.0417499i
$704$	−14.3141	+	22.6966i	−0.539483	+	0.855411i
$705$	16.9179	+	9.27685i	0.637164	+	0.349387i
$706$	3.21255	−	3.84584i	0.120906	−	0.144740i
$707$	−11.3146	−	71.4377i	−0.425530	−	2.68669i
$708$	−2.96975	+	6.15798i	−0.111610	+	0.231431i
$709$	−41.9172	−	6.63903i	−1.57423	−	0.249334i	−0.692619	−	0.721304i	$-0.743543\pi$
$709$	−41.9172	−	6.63903i	−1.57423	−	0.249334i	−0.881615	+	0.471970i	$0.843543\pi$
$710$	18.7903	+	4.89837i	0.705186	+	0.183833i
$711$	0.0357973	−	0.0357973i	0.00134250	−	0.00134250i
$712$	−1.41425	−	12.6466i	−0.0530011	−	0.473950i
$713$	−9.43837	+	4.80909i	−0.353470	+	0.180102i
$714$	−55.6693	−	33.2819i	−2.08337	−	1.24554i
$715$	−13.8977	+	38.7338i	−0.519744	+	1.44856i
$716$	28.4534	−	21.6395i	1.06335	−	0.808705i
$717$	36.4077	−	18.5507i	1.35967	−	0.692787i
$718$	−2.19525	−	0.501694i	−0.0819261	−	0.0187231i
$719$	6.47131	−	3.29730i	0.241339	−	0.122968i	−0.329138	−	0.944282i	$-0.606758\pi$
$719$	6.47131	−	3.29730i	0.241339	−	0.122968i	0.570477	+	0.821313i	$0.306758\pi$
$720$	−0.0426111	−	0.0414813i	−0.00158802	−	0.00154592i
$721$	−2.60478	−	16.4459i	−0.0970069	−	0.612477i
$722$	5.94301	−	26.0047i	0.221176	−	0.967795i
$723$	13.9026	−	10.1009i	0.517045	−	0.375655i
$724$	40.1402	+	27.8422i	1.49180	+	1.03475i
$725$	3.30674	−	14.9454i	0.122809	−	0.555059i
$726$	−0.403081	−	0.461623i	−0.0149597	−	0.0171324i
$727$	33.9361	+	24.6560i	1.25862	+	0.914441i	0.998689	−	0.0511857i	$-0.0163000\pi$
$727$	33.9361	+	24.6560i	1.25862	+	0.914441i	0.259931	+	0.965627i	$0.416300\pi$
$728$	−24.8433	+	66.0273i	−0.920754	+	2.44713i
$729$	−27.0596			−1.00221
$730$	−2.17203	−	5.54550i	−0.0803903	−	0.205248i
$731$	12.2593	−	6.24643i	0.453427	−	0.231033i
$732$	6.77712	+	12.6108i	0.250490	+	0.466109i
$733$	1.93326	−	12.2061i	0.0714066	−	0.450843i	−0.925917	−	0.377727i	$-0.876706\pi$
$733$	1.93326	−	12.2061i	0.0714066	−	0.450843i	0.997323	−	0.0731160i	$-0.0232943\pi$
$734$	34.0310	+	2.30393i	1.25611	+	0.0850397i
$735$	6.68239	+	52.4401i	0.246484	+	1.93428i
$736$	0.375370	−	15.7490i	0.0138363	−	0.580516i
$737$	23.5269	−	23.5269i	0.866624	−	0.866624i
$738$	0.000659801		0.0602028i	2.42876e−5		0.00221610i
$739$	11.2656			0.414413			0.207206	−	0.978297i	$-0.433563\pi$
$739$	11.2656			0.414413			0.207206	+	0.978297i	$0.433563\pi$
$740$	−13.8303	−	2.31046i	−0.508411	−	0.0849341i
$741$	2.49180	−	2.49180i	0.0915387	−	0.0915387i
$742$	15.9603	+	18.2782i	0.585920	+	0.671015i
$743$	−29.5101	−	4.67394i	−1.08262	−	0.171470i	−0.410462	−	0.911878i	$-0.634633\pi$
$743$	−29.5101	−	4.67394i	−1.08262	−	0.171470i	−0.672158	+	0.740407i	$0.734633\pi$
$744$	15.5433	−	10.2414i	0.569843	−	0.375468i
$745$	19.3039	+	28.3388i	0.707241	+	1.03825i
$746$	21.7493	−	5.47392i	0.796300	−	0.200415i
$747$	0.0428364	−	0.0428364i	0.00156730	−	0.00156730i
$748$	−12.8995	−	36.9304i	−0.471651	−	1.35031i
$749$	−10.6293	−	67.1105i	−0.388385	−	2.45217i
$750$	12.4563	−	24.3553i	0.454838	−	0.889329i
$751$	−24.2120	+	47.5187i	−0.883508	+	1.73398i	−0.236280	+	0.971685i	$0.575928\pi$
$751$	−24.2120	+	47.5187i	−0.883508	+	1.73398i	−0.647228	+	0.762297i	$0.724072\pi$
$752$	6.98891	+	18.6850i	0.254859	+	0.681373i
$753$	2.79629	+	3.84876i	0.101902	+	0.140257i
$754$	12.6326	+	20.1171i	0.460053	+	0.732622i
$755$	4.37532	+	14.9993i	0.159234	+	0.545882i
$756$	41.6592	−	22.3879i	1.51513	−	0.814241i
$757$	−5.04189	+	15.5173i	−0.183251	+	0.563988i	−0.999914	−	0.0131270i	$-0.995821\pi$
$757$	−5.04189	+	15.5173i	−0.183251	+	0.563988i	0.816663	+	0.577115i	$0.195821\pi$
$758$	6.89161	+	1.57498i	0.250314	+	0.0572058i
$759$	15.3699	+	4.99399i	0.557893	+	0.181270i
$760$	−1.78909	−	1.52033i	−0.0648970	−	0.0551482i
$761$	7.77260	+	23.9216i	0.281756	+	0.867157i	0.987352	+	0.158543i	$0.0506795\pi$
$761$	7.77260	+	23.9216i	0.281756	+	0.867157i	−0.705596	+	0.708615i	$0.749320\pi$
$762$	−12.6036	−	50.0775i	−0.456581	−	1.81412i
$763$	35.2426	+	69.1675i	1.27587	+	2.50403i
$764$	0.768697	+	35.1205i	0.0278105	+	1.27062i
$765$	0.0859983	−	0.0109587i	0.00310927	−	0.000396212i
$766$	−29.6727	+	12.6730i	−1.07212	+	0.457893i
$767$	−8.77020	+	6.37193i	−0.316674	+	0.230077i
$768$	2.42008	+	27.5761i	0.0873270	+	0.995067i
$769$	16.4639	−	22.6606i	0.593703	−	0.817161i	−0.401411	−	0.915898i	$-0.631480\pi$
$769$	16.4639	−	22.6606i	0.593703	−	0.817161i	0.995114	+	0.0987366i	$0.0314801\pi$
$770$	−25.9857	+	40.6154i	−0.936458	+	1.46368i
$771$	15.2871	+	11.1067i	0.550552	+	0.399999i
$772$	1.76291	−	12.9601i	0.0634485	−	0.466445i
$773$	35.7235	−	11.6073i	1.28488	−	0.417484i	0.414586	−	0.910010i	$-0.363926\pi$
$773$	35.7235	−	11.6073i	1.28488	−	0.417484i	0.870298	+	0.492526i	$0.163926\pi$
$774$	−0.00149855	+	0.0221349i	−5.38643e−5	+	0.000795621i
$775$	−14.6805	−	12.0913i	−0.527339	−	0.434334i
$776$	11.1165	+	40.4113i	0.399060	+	1.45068i
$777$	11.1952	−	21.9718i	0.401626	−	0.788235i
$778$	1.60617	+	17.9017i	0.0575839	+	0.641808i
$779$	0.186537	+	2.36965i	0.00668337	+	0.0849016i
$780$	12.7771	+	40.4847i	0.457494	+	1.44959i
$781$	−19.5885	+	6.36470i	−0.700933	+	0.227747i
$782$	17.6255	+	14.7232i	0.630288	+	0.526499i
$783$	2.49121	−	15.7289i	0.0890286	−	0.562105i
$784$	−30.1619	+	45.5829i	−1.07721	+	1.62796i
$785$	−11.1628	+	5.26756i	−0.398416	+	0.188007i
$786$	−9.66463	+	42.2893i	−0.344726	+	1.50841i
$787$	8.61292	−	1.36415i	0.307017	−	0.0486268i	−0.00102477	−	0.999999i	$-0.500326\pi$
$787$	8.61292	−	1.36415i	0.307017	−	0.0486268i	0.308042	+	0.951373i	$0.400326\pi$
$788$	−13.0996	−	9.08621i	−0.466654	−	0.323683i
$789$	2.52860	−	3.48032i	0.0900206	−	0.123903i
$790$	8.78135	+	22.4201i	0.312427	+	0.797672i
$791$	−84.5538	−	13.3920i	−3.00639	−	0.476165i
$792$	0.0617837	+	0.0127040i	0.00219539	+	0.000451416i
$793$			22.7009i			0.806133i
$794$	−9.78432	+	8.54350i	−0.347232	+	0.303198i
$795$	14.3468	+	2.72071i	0.508830	+	0.0964938i
$796$	−9.33168	−	26.7160i	−0.330752	−	0.946925i
$797$	−30.0763	−	15.3246i	−1.06536	−	0.542827i	−0.168753	−	0.985658i	$-0.553974\pi$
$797$	−30.0763	−	15.3246i	−1.06536	−	0.542827i	−0.896605	+	0.442832i	$0.853974\pi$
$798$	3.49671	−	2.19577i	0.123782	−	0.0777294i
$799$	−27.6593	−	8.98704i	−0.978515	−	0.317939i
$800$	26.1953	−	10.6681i	0.926143	−	0.377173i
$801$	−0.0266528	+	0.0135803i	−0.000941732	+	0.000479836i
$802$	17.2431	+	40.3733i	0.608875	+	1.42563i
$803$	5.11064	+	3.71310i	0.180351	+	0.131032i
$804$	4.62639	−	34.0112i	0.163160	−	1.19948i
$805$	0.858531	−	28.2944i	0.0302592	−	0.997246i
$806$	29.3971	−	2.63755i	1.03547	−	0.0929037i
$807$	−2.79259	−	8.59472i	−0.0983039	−	0.302548i
$808$	−5.00141	−	44.7239i	−0.175949	−	1.57338i
$809$	5.42911	+	34.2781i	0.190877	+	1.20515i	0.878018	+	0.478628i	$0.158866\pi$
$809$	5.42911	+	34.2781i	0.190877	+	1.20515i	−0.687140	+	0.726525i	$0.741134\pi$
$810$	11.3738	−	26.0200i	0.399636	−	0.914250i
$811$	−7.89730			−0.277312			−0.138656	−	0.990341i	$-0.544278\pi$
$811$	−7.89730			−0.277312			−0.138656	+	0.990341i	$0.544278\pi$
$812$	9.17805	+	26.2762i	0.322086	+	0.922114i
$813$	13.0378	−	40.1261i	0.457254	−	1.40728i
$814$	13.6776	−	5.84159i	0.479400	−	0.204748i
$815$	1.01614	−	33.4888i	0.0355940	−	1.17306i
$816$	−33.6551	−	22.2693i	−1.17816	−	0.779581i
$817$			0.875896i			0.0306437i
$818$	−6.08837	−	14.2554i	−0.212875	−	0.498429i
$819$	0.165831			0.00579460
$820$	−26.3625	−	11.1811i	−0.920620	−	0.390460i
$821$	42.4541			1.48166			0.740829	−	0.671693i	$-0.234433\pi$
$821$	42.4541			1.48166			0.740829	+	0.671693i	$0.234433\pi$
$822$	−5.93054	−	13.8859i	−0.206851	−	0.484326i
$823$			23.9428i			0.834594i	0.908770	+	0.417297i	$0.137022\pi$
$823$			23.9428i			0.834594i	−0.908770	+	0.417297i	$0.862978\pi$
$824$	−1.15139	−	10.2960i	−0.0401106	−	0.358680i
$825$	2.79315	+	28.8810i	0.0972451	+	1.00551i
$826$	−11.6810	+	4.98887i	−0.406435	+	0.173585i
$827$	−3.38484	+	10.4175i	−0.117702	+	0.362251i	−0.992501	−	0.122236i	$-0.960994\pi$
$827$	−3.38484	+	10.4175i	−0.117702	+	0.362251i	0.874799	+	0.484487i	$0.160994\pi$
$828$	−0.0349599	+	0.0122112i	−0.00121494	+	0.000424368i
$829$	4.75367			0.165102			0.0825509	−	0.996587i	$-0.473693\pi$
$829$	4.75367			0.165102			0.0825509	+	0.996587i	$0.473693\pi$
$830$	10.5081	+	26.8288i	0.364742	+	0.931240i
$831$	−0.813501	−	5.13624i	−0.0282200	−	0.178174i
$832$	−17.3188	+	40.3330i	−0.600421	+	1.39830i
$833$	−24.6233	−	75.7826i	−0.853146	−	2.62571i
$834$	32.9330	−	2.95479i	1.14038	−	0.102316i
$835$	26.7771	−	25.2000i	0.926660	−	0.872081i
$836$	2.46756	+	0.335651i	0.0853424	+	0.0116087i
$837$	−16.0079	−	11.6304i	−0.553313	−	0.402006i
$838$	−4.06853	−	9.52612i	−0.140545	−	0.329074i
$839$	38.3002	−	19.5149i	1.32227	−	0.673730i	0.356785	−	0.934187i	$-0.383873\pi$
$839$	38.3002	−	19.5149i	1.32227	−	0.673730i	0.965486	+	0.260456i	$0.0838730\pi$
$840$	4.02628	+	49.5787i	0.138920	+	1.71063i
$841$	−18.6673	−	6.06538i	−0.643701	−	0.209151i
$842$	−27.2707	+	17.1247i	−0.939809	+	0.590157i
$843$	−14.4230	−	7.34891i	−0.496756	−	0.253110i
$844$	21.2372	−	7.41798i	0.731016	−	0.255337i
$845$	−7.12609	+	37.5772i	−0.245145	+	1.29270i
$846$	0.0353233	−	0.0308437i	0.00121444	−	0.00106043i
$847$		−	1.13858i		−	0.0391222i
$848$	9.40042	+	11.8147i	0.322812	+	0.405718i
$849$	−15.6000	−	2.47080i	−0.535391	−	0.0847976i
$850$	−11.6068	+	39.5663i	−0.398109	+	1.35711i
$851$	−5.13231	+	7.06402i	−0.175933	+	0.242152i
$852$	−12.1101	+	17.4592i	−0.414887	+	0.598143i
$853$	−32.3052	+	5.11665i	−1.10611	+	0.175191i	−0.682665	−	0.730731i	$-0.739179\pi$
$853$	−32.3052	+	5.11665i	−1.10611	+	0.175191i	−0.423445	+	0.905922i	$0.639179\pi$
$854$	−5.92592	+	25.9299i	−0.202781	+	0.887303i
$855$	−0.00186385	+	0.00519468i	−6.37423e−5	+	0.000177654i
$856$	−4.69846	−	42.0149i	−0.160590	−	1.43604i
$857$	−8.70713	+	54.9747i	−0.297430	+	1.87790i	0.157720	+	0.987484i	$0.449586\pi$
$857$	−8.70713	+	54.9747i	−0.297430	+	1.87790i	−0.455150	+	0.890415i	$0.650414\pi$
$858$	−34.5585	−	28.8678i	−1.17981	−	0.985530i
$859$	−36.1753	+	11.7541i	−1.23428	+	0.401043i	−0.852265	−	0.523111i	$-0.824771\pi$
$859$	−36.1753	+	11.7541i	−1.23428	+	0.401043i	−0.382020	+	0.924154i	$0.624771\pi$
$860$	−9.36106	−	4.86977i	−0.319210	−	0.166058i
$861$	32.7054	−	38.2945i	1.11460	−	1.30507i
$862$	−0.301844	−	3.36424i	−0.0102808	−	0.114586i
$863$	0.861211	−	1.69022i	0.0293160	−	0.0575358i	−0.875884	−	0.482522i	$-0.839721\pi$
$863$	0.861211	−	1.69022i	0.0293160	−	0.0575358i	0.905200	+	0.424986i	$0.139721\pi$
$864$	26.5300	−	12.7308i	0.902567	−	0.433109i
$865$	0.626002	−	20.6310i	0.0212847	−	0.701474i
$866$	−1.22013	+	18.0223i	−0.0414617	+	0.612424i
$867$	27.9796	−	9.09113i	0.950237	−	0.308751i
$868$	34.2671	+	4.66120i	1.16310	+	0.158211i
$869$	−20.6620	−	15.0118i	−0.700910	−	0.509241i
$870$	14.1087	+	9.02673i	0.478330	+	0.306035i
$871$	31.9911	−	44.0320i	1.08398	−	1.49197i
$872$	19.9384	+	43.9933i	0.675201	+	1.48980i
$873$	0.0797060	−	0.0579098i	0.00269764	−	0.00195995i
$874$	−1.34452	+	0.574233i	−0.0454790	+	0.0194237i
$875$	47.1939	−	18.8629i	1.59545	−	0.637682i
$876$	6.51534	−	0.142604i	0.220133	−	0.00481814i
$877$	12.9005	+	25.3186i	0.435618	+	0.854949i	0.999575	+	0.0291450i	$0.00927846\pi$
$877$	12.9005	+	25.3186i	0.435618	+	0.854949i	−0.563957	+	0.825804i	$0.690722\pi$
$878$	−8.94658	−	35.5471i	−0.301932	−	1.19966i
$879$	−9.02659	−	27.7810i	−0.304459	−	0.937029i
$880$	−17.3063	+	24.5057i	−0.583395	+	0.826088i
$881$	45.6728	+	14.8400i	1.53876	+	0.499972i	0.951033	−	0.309090i	$-0.100024\pi$
$881$	45.6728	+	14.8400i	1.53876	+	0.499972i	0.587723	+	0.809062i	$0.300024\pi$
$882$	0.125254	+	0.0286251i	0.00421754	+	0.000963859i
$883$	14.3450	−	44.1493i	0.482747	−	1.48574i	−0.352470	−	0.935823i	$-0.614658\pi$
$883$	14.3450	−	44.1493i	0.482747	−	1.48574i	0.835217	−	0.549920i	$-0.185342\pi$
$884$	−30.2915	−	56.3662i	−1.01881	−	1.89580i
$885$	−3.67510	+	6.70215i	−0.123537	+	0.225290i
$886$	1.14762	+	1.82755i	0.0385550	+	0.0613978i
$887$	23.4780	+	32.3147i	0.788315	+	1.08502i	0.994316	+	0.106471i	$0.0339550\pi$
$887$	23.4780	+	32.3147i	0.788315	+	1.08502i	−0.206001	+	0.978552i	$0.566045\pi$
$888$	7.58314	−	13.3383i	0.254474	−	0.447605i
$889$	43.5558	−	85.4830i	1.46081	−	2.86701i
$890$	−0.841037	−	14.2025i	−0.0281916	−	0.476070i
$891$	4.71188	+	29.7497i	0.157854	+	0.996651i
$892$	−1.14065	+	0.398419i	−0.0381917	+	0.0133400i
$893$	1.30914	−	1.30914i	0.0438088	−	0.0438088i
$894$	−36.3853	+	9.15753i	−1.21691	+	0.306274i
$895$	33.0312	−	22.5003i	1.10411	−	0.752102i
$896$	−30.3109	+	41.5490i	−1.01261	+	1.38806i
$897$	26.1106	+	4.13551i	0.871806	+	0.138081i
$898$	−36.0420	−	41.2766i	−1.20274	−	1.37742i
$899$	8.23410	−	8.23410i	0.274623	−	0.274623i
$900$	−0.0451551	−	0.0488009i	−0.00150517	−	0.00162670i
$901$	−22.0105			−0.733277
$902$	29.9455	−	5.07991i	0.997076	−	0.169143i
$903$	13.1219	−	13.1219i	0.436669	−	0.436669i
$904$	−52.1738	−	10.7280i	−1.73528	−	0.356807i
$905$	43.1922	+	33.4285i	1.43576	+	1.11120i
$906$	−17.0577	−	1.15482i	−0.566705	−	0.0383665i
$907$	7.84491	−	49.5308i	0.260486	−	1.64464i	−0.416854	−	0.908973i	$-0.636868\pi$
$907$	7.84491	−	49.5308i	0.260486	−	1.64464i	0.677340	−	0.735670i	$-0.263132\pi$
$908$	7.69663	−	4.13622i	0.255422	−	0.137265i
$909$	−0.0942564	+	0.0480260i	−0.00312629	+	0.00159292i
$910$	−31.5908	+	72.2704i	−1.04722	+	2.39574i
$911$	21.2435			0.703827			0.351914	−	0.936032i	$-0.385531\pi$
$911$	21.2435			0.703827			0.351914	+	0.936032i	$0.385531\pi$
$912$	2.23582	−	1.26536i	0.0740353	−	0.0419003i
$913$	−24.7249	−	17.9637i	−0.818276	−	0.594512i
$914$	29.2675	+	33.5181i	0.968082	+	1.10868i
$915$	6.83083	+	14.4756i	0.225820	+	0.478547i
$916$	−18.2498	+	26.3108i	−0.602992	+	0.869334i
$917$	−65.2023	+	47.3723i	−2.15317	+	1.56437i
$918$	−9.55746	+	41.8204i	−0.315443	+	1.38028i
$919$	0.894894	+	5.65014i	0.0295198	+	0.186381i	0.998042	−	0.0625461i	$-0.0199221\pi$
$919$	0.894894	+	5.65014i	0.0295198	+	0.186381i	−0.968522	+	0.248927i	$0.919922\pi$
$920$	1.33813	−	17.5620i	0.0441167	−	0.579002i
$921$	12.4597	−	6.34856i	0.410562	−	0.209192i
$922$	−29.1746	−	6.66745i	−0.960814	−	0.219581i
$923$	−30.0197	+	15.2958i	−0.988112	+	0.503468i
$924$	−31.9383	−	41.9952i	−1.05069	−	1.38154i
$925$	−15.3068	−	3.38670i	−0.503285	−	0.111354i
$926$	−37.0835	−	22.1704i	−1.21864	−	0.728564i
$927$	−0.0216991	+	0.0110562i	−0.000712691	+	0.000363134i
$928$	4.95751	+	16.5930i	0.162738	+	0.544692i
$929$	−16.0940	+	16.0940i	−0.528026	+	0.528026i	−0.919983	−	0.391957i	$-0.871798\pi$
$929$	−16.0940	+	16.0940i	−0.528026	+	0.528026i	0.391957	+	0.919983i	$0.371798\pi$
$930$	17.9518	−	10.5276i	0.588664	−	0.345214i
$931$	5.01015	+	0.793530i	0.164201	+	0.0260069i
$932$	48.4385	+	23.3599i	1.58666	+	0.765180i
$933$	−5.25478	−	33.1774i	−0.172034	−	1.08618i
$934$	−13.0975	+	15.6794i	−0.428564	+	0.513046i
$935$	−12.2473	−	41.9859i	−0.400531	−	1.37309i
$936$	0.103073	+	0.00471514i	0.00336903	+	0.000154119i
$937$	−10.8600	−	33.4237i	−0.354781	−	1.09190i	−0.956136	−	0.292922i	$-0.905372\pi$
$937$	−10.8600	−	33.4237i	−0.354781	−	1.09190i	0.601355	−	0.798982i	$-0.294628\pi$
$938$	48.0357	−	41.9440i	1.56842	−	1.36952i
$939$	−16.9854	+	12.3406i	−0.554297	+	0.402721i
$940$	6.71284	+	21.2699i	0.218949	+	0.693746i
$941$	4.04299	−	1.31365i	0.131798	−	0.0428236i	−0.242375	−	0.970183i	$-0.577927\pi$
$941$	4.04299	−	1.31365i	0.131798	−	0.0428236i	0.374173	+	0.927359i	$0.377927\pi$
$942$	−1.20696	−	13.4523i	−0.0393247	−	0.438298i
$943$	−13.5591	+	11.5810i	−0.441547	+	0.377130i
$944$	−7.40222	+	2.76871i	−0.240922	+	0.0901139i
$945$	47.8194	−	22.5654i	1.55557	−	0.734051i
$946$	11.1475	−	1.00017i	0.362437	−	0.0325183i
$947$	−27.3389	−	4.33006i	−0.888395	−	0.140708i	−0.304476	−	0.952520i	$-0.598481\pi$
$947$	−27.3389	−	4.33006i	−0.888395	−	0.140708i	−0.583919	+	0.811812i	$0.698481\pi$
$948$	−26.3411	+	0.576539i	−0.855519	+	0.0187251i
$949$	9.20724	+	4.69132i	0.298880	+	0.152287i
$950$	−1.90882	−	1.80186i	−0.0619302	−	0.0584602i
$951$	30.9747	+	22.5044i	1.00442	+	0.729756i
$952$	−19.8862	−	72.2911i	−0.644516	−	2.34297i
$953$	1.71538	+	10.8305i	0.0555666	+	0.350834i	0.999770	+	0.0214694i	$0.00683445\pi$
$953$	1.71538	+	10.8305i	0.0555666	+	0.350834i	−0.944203	+	0.329364i	$0.893166\pi$
$954$	0.0182117	−	0.0304619i	0.000589624	−	0.000986242i
$955$	−1.19118	+	39.2573i	−0.0385456	+	1.27034i
$956$	45.2318	+	13.6099i	1.46290	+	0.440176i
$957$	−17.7656			−0.574281
$958$	13.9670	+	0.945579i	0.451253	+	0.0305503i
$959$	8.66880	−	26.6798i	0.279930	−	0.861536i
$960$	1.09286	+	30.9302i	0.0352717	+	0.998268i
$961$	5.10845	+	15.7222i	0.164789	+	0.507168i
$962$	20.6035	−	12.9381i	0.664285	−	0.417140i
$963$	−0.0885471	+	0.0451170i	−0.00285339	+	0.00145387i
$964$	19.6838	+	2.67750i	0.633974	+	0.0862366i
$965$	2.72459	−	14.3672i	0.0877075	−	0.462498i
$966$	28.7450	+	11.5397i	0.924855	+	0.371284i
$967$	−13.0042	+	17.8988i	−0.418188	+	0.575587i	−0.965192	−	0.261544i	$-0.915768\pi$
$967$	−13.0042	+	17.8988i	−0.418188	+	0.575587i	0.547003	+	0.837130i	$0.315768\pi$
$968$	0.0323738	−	0.707689i	0.00104053	−	0.0227460i
$969$	−0.585884	+	3.69913i	−0.0188213	+	0.118833i
$970$	10.0536	+	45.7683i	0.322800	+	1.46953i
$971$	11.1799	−	21.9417i	0.358778	−	0.704142i	−0.639108	−	0.769117i	$-0.720697\pi$
$971$	11.1799	−	21.9417i	0.358778	−	0.704142i	0.997887	+	0.0649742i	$0.0206965\pi$
$972$	−0.0998300	−	0.0955536i	−0.00320205	−	0.00306488i
$973$	49.6992	+	36.1086i	1.59328	+	1.15759i
$974$	6.60300	+	26.2354i	0.211574	+	0.840638i
$975$	11.9033	+	45.9472i	0.381212	+	1.47149i
$976$	−4.42054	+	15.9483i	−0.141498	+	0.510492i
$977$	4.56066	+	1.48185i	0.145909	+	0.0474086i	0.381061	−	0.924550i	$-0.375559\pi$
$977$	4.56066	+	1.48185i	0.145909	+	0.0474086i	−0.235152	+	0.971959i	$0.575559\pi$
$978$	34.0221	+	13.6582i	1.08791	+	0.436742i
$979$	8.87014	+	12.2087i	0.283491	+	0.390192i
$980$	−36.3360	+	49.1337i	−1.16071	+	1.56952i
$981$	0.0802839	−	0.0802839i	0.00256327	−	0.00256327i
$982$	11.8195	+	27.6743i	0.377174	+	0.883123i
$983$	−28.8420	+	28.8420i	−0.919917	+	0.919917i	−0.997023	−	0.0771060i	$-0.975432\pi$
$983$	−28.8420	+	28.8420i	−0.919917	+	0.919917i	0.0771060	+	0.997023i	$0.475432\pi$
$984$	21.4170	−	22.8721i	0.682748	−	0.729136i
$985$	−14.0956	−	10.9093i	−0.449124	−	0.347598i
$986$	−23.4289	−	9.40555i	−0.746127	−	0.299534i
$987$	−39.2248			−1.24854
$988$	4.07264	−	0.0891396i	0.129568	−	0.00283591i
$989$	−5.31591	+	3.86224i	−0.169036	+	0.122812i
$990$	0.0682408	+	0.0177895i	0.00216884	+	0.000565386i
$991$	−31.2153	+	15.9050i	−0.991587	+	0.505239i	−0.873008	−	0.487706i	$-0.837834\pi$
$991$	−31.2153	+	15.9050i	−0.991587	+	0.505239i	−0.118579	+	0.992945i	$0.537834\pi$
$992$	21.1662	+	3.87151i	0.672029	+	0.122920i
$993$	39.2988	−	39.2988i	1.24711	−	1.24711i
$994$	−38.2826	+	9.63506i	−1.21425	+	0.305606i
$995$	−8.85991	−	30.3733i	−0.280878	−	0.962897i
$996$	−31.5208	+	0.689908i	−0.998774	+	0.0218606i
$997$	−4.22394	+	1.37244i	−0.133774	+	0.0434657i	−0.375139	−	0.926969i	$-0.622405\pi$
$997$	−4.22394	+	1.37244i	−0.133774	+	0.0434657i	0.241365	+	0.970434i	$0.422405\pi$
$998$	6.91801	+	5.77883i	0.218986	+	0.182926i
$999$	−16.1092	−	2.55145i	−0.509673	−	0.0807243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bk.c.43.17	✓	960
4.3	odd	2	inner	820.2.bk.c.43.69	yes	960
5.2	odd	4		820.2.bv.c.207.45	yes	960
20.7	even	4		820.2.bv.c.207.8	yes	960
41.21	even	20		820.2.bv.c.103.8	yes	960
164.103	odd	20		820.2.bv.c.103.45	yes	960
205.62	odd	20	inner	820.2.bk.c.267.69	yes	960
820.267	even	20	inner	820.2.bk.c.267.17	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.17	✓	960	1.1	even	1	trivial
820.2.bk.c.43.69	yes	960	4.3	odd	2	inner
820.2.bk.c.267.17	yes	960	820.267	even	20	inner
820.2.bk.c.267.69	yes	960	205.62	odd	20	inner
820.2.bv.c.103.8	yes	960	41.21	even	20
820.2.bv.c.103.45	yes	960	164.103	odd	20
820.2.bv.c.207.8	yes	960	20.7	even	4
820.2.bv.c.207.45	yes	960	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30056 + 0.555460i) q^{2} -1.73013i q^{3} +(1.38293 - 1.44482i) q^{4} +(1.62837 - 1.53246i) q^{5} +(0.961018 + 2.25014i) q^{6} +(-1.40474 + 4.32334i) q^{7} +(-0.996046 + 2.64724i) q^{8} +0.00664869 q^{9} +(-1.26657 + 2.89755i) q^{10} +(-0.524708 - 3.31288i) q^{11} +(-2.49973 - 2.39265i) q^{12} +(-1.69550 - 5.21822i) q^{13} +(-0.574491 - 6.40306i) q^{14} +(-2.65135 - 2.81728i) q^{15} +(-0.175015 - 3.99617i) q^{16} +(4.71763 + 3.42756i) q^{17} +(-0.00864704 + 0.00369308i) q^{18} +(-0.330761 + 0.168531i) q^{19} +(0.0377873 - 4.47198i) q^{20} +(7.47995 + 2.43038i) q^{21} +(2.52259 + 4.01715i) q^{22} +(-2.48132 - 1.26429i) q^{23} +(4.58007 + 1.72329i) q^{24} +(0.303149 - 4.99080i) q^{25} +(5.10362 + 5.84484i) q^{26} -5.20189i q^{27} +(4.30380 + 8.00848i) q^{28} +(3.02368 + 0.478905i) q^{29} +(5.01314 + 2.19134i) q^{30} +(2.23580 - 3.07732i) q^{31} +(2.44733 + 5.10006i) q^{32} +(-5.73171 + 0.907813i) q^{33} +(-8.03945 - 1.83730i) q^{34} +(4.33791 + 9.19269i) q^{35} +(0.00919467 - 0.00960617i) q^{36} +(0.490485 - 3.09680i) q^{37} +(0.336564 - 0.402910i) q^{38} +(-9.02820 + 2.93344i) q^{39} +(2.43486 + 5.83708i) q^{40} +(2.45027 - 5.91576i) q^{41} +(-11.0781 + 0.993945i) q^{42} +(1.07119 - 2.10232i) q^{43} +(-5.51215 - 3.82336i) q^{44} +(0.0108265 - 0.0101888i) q^{45} +(3.92937 + 0.266023i) q^{46} +(-4.74323 + 1.54117i) q^{47} +(-6.91389 + 0.302800i) q^{48} +(-11.0549 - 8.03185i) q^{49} +(2.37792 + 6.65924i) q^{50} +(5.93013 - 8.16212i) q^{51} +(-9.88415 - 4.76673i) q^{52} +(-3.05367 + 2.21862i) q^{53} +(2.88944 + 6.76539i) q^{54} +(-5.93126 - 4.59048i) q^{55} +(-10.0458 - 8.02494i) q^{56} +(0.291581 + 0.572260i) q^{57} +(-4.19850 + 1.05669i) q^{58} +(-0.610546 - 1.87907i) q^{59} +(-7.73710 - 0.0653770i) q^{60} +(-3.93490 - 1.27853i) q^{61} +(-1.19848 + 5.24414i) q^{62} +(-0.00933968 + 0.0287446i) q^{63} +(-6.01578 - 5.27355i) q^{64} +(-10.7576 - 5.89888i) q^{65} +(6.95019 - 4.36440i) q^{66} +(5.83060 + 8.02513i) q^{67} +(11.4764 - 2.07606i) q^{68} +(-2.18739 + 4.29300i) q^{69} +(-10.7479 - 9.54614i) q^{70} +(-0.960600 - 6.06499i) q^{71} +(-0.00662240 + 0.0176007i) q^{72} +(-1.33173 + 1.33173i) q^{73} +(1.08224 + 4.30003i) q^{74} +(-8.63474 - 0.524488i) q^{75} +(-0.213922 + 0.710958i) q^{76} +(15.0598 + 2.38524i) q^{77} +(10.1123 - 8.82993i) q^{78} +(5.38411 - 5.38411i) q^{79} +(-6.40895 - 6.23902i) q^{80} -8.98001 q^{81} +(0.0992377 + 9.05484i) q^{82} +(6.44284 - 6.44284i) q^{83} +(13.8557 - 7.44614i) q^{84} +(12.9346 - 1.64825i) q^{85} +(-0.225391 + 3.32921i) q^{86} +(0.828567 - 5.23137i) q^{87} +(9.29262 + 1.91075i) q^{88} +(-4.00873 + 2.04255i) q^{89} +(-0.00842106 + 0.0192649i) q^{90} +24.9419 q^{91} +(-5.25816 + 1.83663i) q^{92} +(-5.32416 - 3.86823i) q^{93} +(5.31281 - 4.63906i) q^{94} +(-0.280333 + 0.781308i) q^{95} +(8.82376 - 4.23420i) q^{96} +(11.9882 - 8.70996i) q^{97} +(18.8390 + 4.30538i) q^{98} +(-0.00348862 - 0.0220263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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