LMFDB - Embedded newform 47.2.c.a.21.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [47,2,Mod(2,47)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("47.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(47, base_ring=CyclotomicField(46)) chi = DirichletCharacter(H, H._module([18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	47.c (of order $23$, degree $22$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.375296889500$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$3$ over $\Q(\zeta_{23})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

Embedding invariants

Embedding label			21.1
Character	$\chi$	$=$	47.21
Dual form			47.2.c.a.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.910119 - 1.75645i) q^{2} +(0.226030 - 0.635987i) q^{3} +(-1.10344 + 1.56321i) q^{4} +(-0.813179 - 0.353213i) q^{5} +(-1.32279 + 0.181814i) q^{6} +(0.694533 + 0.422355i) q^{7} +(-0.169663 - 0.0233196i) q^{8} +(1.97374 + 1.60576i) q^{9} +(0.119688 + 1.74977i) q^{10} +(3.86254 - 1.08223i) q^{11} +(0.744774 + 1.05510i) q^{12} +(0.613996 + 2.95471i) q^{13} +(0.109737 - 1.60431i) q^{14} +(-0.408442 + 0.437334i) q^{15} +(1.39499 + 3.92513i) q^{16} +(-6.79109 - 1.90277i) q^{17} +(1.02409 - 4.92821i) q^{18} +(-1.96591 + 0.853916i) q^{19} +(1.44944 - 0.881424i) q^{20} +(0.425597 - 0.346249i) q^{21} +(-5.41626 - 5.79940i) q^{22} +(-0.359215 + 0.693253i) q^{23} +(-0.0531798 + 0.102632i) q^{24} +(-2.87627 - 3.07973i) q^{25} +(4.63099 - 3.76759i) q^{26} +(3.19746 - 1.94442i) q^{27} +(-1.42660 + 0.619662i) q^{28} +(-1.90811 + 9.18234i) q^{29} +(1.13989 + 0.319381i) q^{30} +(-1.95469 - 5.49997i) q^{31} +(5.39089 - 5.77224i) q^{32} +(0.184763 - 2.70114i) q^{33} +(2.83857 + 13.6599i) q^{34} +(-0.415598 - 0.588768i) q^{35} +(-4.68805 + 1.31353i) q^{36} +(0.359568 + 5.25669i) q^{37} +(3.28907 + 2.67586i) q^{38} +(2.01794 + 0.277359i) q^{39} +(0.129729 + 0.0788902i) q^{40} +(0.948271 - 0.130337i) q^{41} +(-0.995513 - 0.432412i) q^{42} +(2.47236 - 3.50254i) q^{43} +(-2.57031 + 7.23215i) q^{44} +(-1.03783 - 2.00292i) q^{45} +1.54459 q^{46} +(6.45396 - 2.31222i) q^{47} +2.81164 q^{48} +(-2.91646 - 5.62852i) q^{49} +(-2.79164 + 7.85493i) q^{50} +(-2.74513 + 3.88896i) q^{51} +(-5.29635 - 2.30053i) q^{52} +(-8.92430 + 1.22662i) q^{53} +(-6.32534 - 3.84652i) q^{54} +(-3.52320 - 0.484252i) q^{55} +(-0.107987 - 0.0878542i) q^{56} +(0.0987247 + 1.44330i) q^{57} +(17.8649 - 5.00551i) q^{58} +(2.44580 + 3.46491i) q^{59} +(-0.232957 - 1.12105i) q^{60} +(0.282947 - 4.13654i) q^{61} +(-7.88142 + 8.43894i) q^{62} +(0.692630 + 1.94887i) q^{63} +(-7.02264 - 1.96765i) q^{64} +(0.544355 - 2.61958i) q^{65} +(-4.91257 + 2.13383i) q^{66} +(10.2126 - 6.21044i) q^{67} +(10.4680 - 8.51633i) q^{68} +(0.359707 + 0.385152i) q^{69} +(-0.655898 + 1.26583i) q^{70} +(1.32772 - 2.56239i) q^{71} +(-0.297425 - 0.318465i) q^{72} +(4.32036 - 3.51487i) q^{73} +(8.90586 - 5.41578i) q^{74} +(-2.60879 + 1.13316i) q^{75} +(0.834406 - 4.01538i) q^{76} +(3.13975 + 0.879716i) q^{77} +(-1.34940 - 3.79684i) q^{78} +(-5.50650 + 5.89603i) q^{79} +(0.252031 - 3.68456i) q^{80} +(1.03914 + 5.00060i) q^{81} +(-1.09197 - 1.54697i) q^{82} +(-16.0272 + 4.49061i) q^{83} +(0.0716416 + 1.04736i) q^{84} +(4.85028 + 3.94600i) q^{85} +(-8.40217 - 1.15485i) q^{86} +(5.40855 + 3.28901i) q^{87} +(-0.680567 + 0.0935418i) q^{88} +(-1.03554 - 0.449797i) q^{89} +(-2.57348 + 3.64579i) q^{90} +(-0.821496 + 2.31147i) q^{91} +(-0.687332 - 1.32649i) q^{92} -3.93972 q^{93} +(-9.93517 - 9.23166i) q^{94} +1.90025 q^{95} +(-2.45256 - 4.73323i) q^{96} +(-2.38226 + 6.70305i) q^{97} +(-7.23188 + 10.2452i) q^{98} +(9.36147 + 4.06626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 21 q^{2} - 19 q^{3} - 19 q^{4} - 15 q^{5} - 3 q^{6} - 19 q^{7} - 5 q^{8} - 12 q^{9} + 3 q^{10} - 5 q^{11} + 16 q^{12} - 17 q^{13} + 6 q^{14} + 3 q^{15} + 3 q^{16} - 11 q^{17} - 3 q^{19} + 19 q^{20}+ \cdots - 101 q^{99}+O(q^{100}) $ 66 * q - 21 * q^2 - 19 * q^3 - 19 * q^4 - 15 * q^5 - 3 * q^6 - 19 * q^7 - 5 * q^8 - 12 * q^9 + 3 * q^10 - 5 * q^11 + 16 * q^12 - 17 * q^13 + 6 * q^14 + 3 * q^15 + 3 * q^16 - 11 * q^17 - 3 * q^19 + 19 * q^20 + 5 * q^21 + 9 * q^22 + 7 * q^23 + 50 * q^24 - 8 * q^25 + 3 * q^26 + 29 * q^27 + 17 * q^28 + 17 * q^29 + 39 * q^30 + 17 * q^31 + 30 * q^32 + 13 * q^33 + 41 * q^34 + 22 * q^35 - 35 * q^36 - 18 * q^37 - 7 * q^38 - 18 * q^39 - 57 * q^40 - 56 * q^41 - 50 * q^42 - 4 * q^43 - q^44 - 26 * q^45 - 84 * q^46 - 26 * q^47 - 158 * q^48 - 14 * q^49 - 37 * q^50 - 58 * q^51 - 21 * q^52 + 14 * q^53 - 36 * q^54 - 4 * q^55 - 43 * q^56 - 22 * q^57 + 29 * q^58 + 10 * q^59 + 7 * q^60 + 22 * q^61 + 89 * q^62 + 65 * q^63 + 135 * q^64 + 45 * q^65 + 89 * q^66 + 35 * q^67 + 60 * q^68 + 79 * q^69 + 151 * q^70 + 61 * q^71 + 145 * q^72 + 29 * q^73 + 73 * q^74 + 77 * q^75 + 95 * q^76 + 37 * q^77 + 35 * q^78 - 55 * q^79 + 14 * q^80 - 44 * q^81 - 84 * q^82 - 5 * q^83 - 56 * q^84 - 97 * q^85 - 113 * q^86 + 17 * q^87 - 121 * q^88 - 19 * q^89 - 127 * q^90 - 119 * q^91 - 76 * q^92 - 28 * q^93 - 159 * q^94 - 126 * q^95 - 119 * q^96 - 47 * q^97 - 44 * q^98 - 101 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/47\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{3}{23}\right)$

Coefficient data

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

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

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

$2$	−0.910119	−	1.75645i	−0.643551	−	1.24200i	−0.956363	−	0.292182i	$-0.905619\pi$
$2$	−0.910119	−	1.75645i	−0.643551	−	1.24200i	0.312812	−	0.949815i	$-0.398729\pi$
$3$	0.226030	−	0.635987i	0.130498	−	0.367187i	−0.858953	−	0.512055i	$-0.828884\pi$
$3$	0.226030	−	0.635987i	0.130498	−	0.367187i	0.989451	+	0.144868i	$0.0462757\pi$
$4$	−1.10344	+	1.56321i	−0.551718	+	0.781607i
$5$	−0.813179	−	0.353213i	−0.363665	−	0.157962i	0.208662	−	0.977988i	$-0.433089\pi$
$5$	−0.813179	−	0.353213i	−0.363665	−	0.157962i	−0.572326	+	0.820026i	$0.693959\pi$
$6$	−1.32279	+	0.181814i	−0.540028	+	0.0742251i
$7$	0.694533	+	0.422355i	0.262509	+	0.159635i	0.644671	−	0.764460i	$-0.276994\pi$
$7$	0.694533	+	0.422355i	0.262509	+	0.159635i	−0.382162	+	0.924095i	$0.624820\pi$
$8$	−0.169663	−	0.0233196i	−0.0599849	−	0.00824473i
$9$	1.97374	+	1.60576i	0.657915	+	0.535253i
$10$	0.119688	+	1.74977i	0.0378486	+	0.553327i
$11$	3.86254	−	1.08223i	1.16460	−	0.326306i	0.367424	−	0.930053i	$-0.380240\pi$
$11$	3.86254	−	1.08223i	1.16460	−	0.326306i	0.797175	+	0.603748i	$0.206327\pi$
$12$	0.744774	+	1.05510i	0.214998	+	0.304582i
$13$	0.613996	+	2.95471i	0.170292	+	0.819489i	0.974367	+	0.224962i	$0.0722259\pi$
$13$	0.613996	+	2.95471i	0.170292	+	0.819489i	−0.804076	+	0.594527i	$0.797339\pi$
$14$	0.109737	−	1.60431i	0.0293286	−	0.428769i
$15$	−0.408442	+	0.437334i	−0.105459	+	0.112919i
$16$	1.39499	+	3.92513i	0.348748	+	0.981282i
$17$	−6.79109	−	1.90277i	−1.64708	−	0.461490i	−0.683730	−	0.729735i	$-0.739643\pi$
$17$	−6.79109	−	1.90277i	−1.64708	−	0.461490i	−0.963351	+	0.268245i	$0.913556\pi$
$18$	1.02409	−	4.92821i	0.241381	−	1.16159i
$19$	−1.96591	+	0.853916i	−0.451011	+	0.195902i	−0.611678	−	0.791107i	$-0.709505\pi$
$19$	−1.96591	+	0.853916i	−0.451011	+	0.195902i	0.160667	+	0.987009i	$0.448636\pi$
$20$	1.44944	−	0.881424i	0.324105	−	0.197092i
$21$	0.425597	−	0.346249i	0.0928729	−	0.0755577i
$22$	−5.41626	−	5.79940i	−1.15475	−	1.23644i
$23$	−0.359215	+	0.693253i	−0.0749015	+	0.144553i	−0.922389	−	0.386262i	$-0.873766\pi$
$23$	−0.359215	+	0.693253i	−0.0749015	+	0.144553i	0.847488	+	0.530815i	$0.178114\pi$
$24$	−0.0531798	+	0.102632i	−0.0108553	+	0.0209498i
$25$	−2.87627	−	3.07973i	−0.575253	−	0.615946i
$26$	4.63099	−	3.76759i	0.908212	−	0.738885i
$27$	3.19746	−	1.94442i	0.615351	−	0.374203i
$28$	−1.42660	+	0.619662i	−0.269603	+	0.117105i
$29$	−1.90811	+	9.18234i	−0.354327	+	1.70512i	0.304240	+	0.952595i	$0.401597\pi$
$29$	−1.90811	+	9.18234i	−0.354327	+	1.70512i	−0.658568	+	0.752522i	$0.728837\pi$
$30$	1.13989	+	0.319381i	0.208114	+	0.0583107i
$31$	−1.95469	−	5.49997i	−0.351073	−	0.987823i	−0.977974	−	0.208725i	$-0.933069\pi$
$31$	−1.95469	−	5.49997i	−0.351073	−	0.987823i	0.626902	−	0.779098i	$-0.284323\pi$
$32$	5.39089	−	5.77224i	0.952984	−	1.02040i
$33$	0.184763	−	2.70114i	0.0321631	−	0.470208i
$34$	2.83857	+	13.6599i	0.486811	+	2.34266i
$35$	−0.415598	−	0.588768i	−0.0702489	−	0.0995200i
$36$	−4.68805	+	1.31353i	−0.781341	+	0.218922i
$37$	0.359568	+	5.25669i	0.0591126	+	0.864195i	0.928797	+	0.370588i	$0.120844\pi$
$37$	0.359568	+	5.25669i	0.0591126	+	0.864195i	−0.869685	+	0.493607i	$0.835678\pi$
$38$	3.28907	+	2.67586i	0.533558	+	0.434082i
$39$	2.01794	+	0.277359i	0.323129	+	0.0444130i
$40$	0.129729	+	0.0788902i	0.0205120	+	0.0124736i
$41$	0.948271	−	0.130337i	0.148095	−	0.0203552i	−0.0617382	−	0.998092i	$-0.519664\pi$
$41$	0.948271	−	0.130337i	0.148095	−	0.0203552i	0.209833	+	0.977737i	$0.432708\pi$
$42$	−0.995513	−	0.432412i	−0.153611	−	0.0667227i
$43$	2.47236	−	3.50254i	0.377031	−	0.534132i	−0.583569	−	0.812063i	$-0.698344\pi$
$43$	2.47236	−	3.50254i	0.377031	−	0.534132i	0.960601	+	0.277931i	$0.0896488\pi$
$44$	−2.57031	+	7.23215i	−0.387488	+	1.09029i
$45$	−1.03783	−	2.00292i	−0.154711	−	0.298578i
$46$	1.54459			0.227738
$47$	6.45396	−	2.31222i	0.941407	−	0.337272i
$47$	6.45396	−	2.31222i	0.941407	−	0.337272i
$48$	2.81164			0.405825
$49$	−2.91646	−	5.62852i	−0.416638	−	0.804074i
$50$	−2.79164	+	7.85493i	−0.394798	+	1.11086i
$51$	−2.74513	+	3.88896i	−0.384395	+	0.544563i
$52$	−5.29635	−	2.30053i	−0.734472	−	0.319026i
$53$	−8.92430	+	1.22662i	−1.22585	+	0.168489i	−0.719901	−	0.694077i	$-0.755813\pi$
$53$	−8.92430	+	1.22662i	−1.22585	+	0.168489i	−0.505946	+	0.862565i	$0.668856\pi$
$54$	−6.32534	−	3.84652i	−0.860769	−	0.523445i
$55$	−3.52320	−	0.484252i	−0.475068	−	0.0652965i
$56$	−0.107987	−	0.0878542i	−0.0144304	−	0.0117400i
$57$	0.0987247	+	1.44330i	0.0130764	+	0.191170i
$58$	17.8649	−	5.00551i	2.34578	−	0.657256i
$59$	2.44580	+	3.46491i	0.318417	+	0.451093i	0.944427	−	0.328721i	$-0.106618\pi$
$59$	2.44580	+	3.46491i	0.318417	+	0.451093i	−0.626010	+	0.779815i	$0.715313\pi$
$60$	−0.232957	−	1.12105i	−0.0300747	−	0.144727i
$61$	0.282947	−	4.13654i	0.0362277	−	0.529630i	−0.943768	−	0.330610i	$-0.892746\pi$
$61$	0.282947	−	4.13654i	0.0362277	−	0.529630i	0.979995	−	0.199021i	$-0.0637760\pi$
$62$	−7.88142	+	8.43894i	−1.00094	+	1.07175i
$63$	0.692630	+	1.94887i	0.0872632	+	0.245535i
$64$	−7.02264	−	1.96765i	−0.877831	−	0.245957i
$65$	0.544355	−	2.61958i	0.0675189	−	0.324919i
$66$	−4.91257	+	2.13383i	−0.604696	+	0.262657i
$67$	10.2126	−	6.21044i	1.24767	−	0.758726i	0.268800	−	0.963196i	$-0.413373\pi$
$67$	10.2126	−	6.21044i	1.24767	−	0.758726i	0.978873	+	0.204470i	$0.0655470\pi$
$68$	10.4680	−	8.51633i	1.26943	−	1.03276i
$69$	0.359707	+	0.385152i	0.0433036	+	0.0463668i
$70$	−0.655898	+	1.26583i	−0.0783948	+	0.151295i
$71$	1.32772	−	2.56239i	0.157572	−	0.304100i	−0.795983	−	0.605319i	$-0.793046\pi$
$71$	1.32772	−	2.56239i	0.157572	−	0.304100i	0.953555	+	0.301219i	$0.0973935\pi$
$72$	−0.297425	−	0.318465i	−0.0350519	−	0.0375314i
$73$	4.32036	−	3.51487i	0.505660	−	0.411385i	−0.343796	−	0.939044i	$-0.611713\pi$
$73$	4.32036	−	3.51487i	0.505660	−	0.411385i	0.849456	+	0.527659i	$0.176930\pi$
$74$	8.90586	−	5.41578i	1.03529	−	0.629571i
$75$	−2.60879	+	1.13316i	−0.301237	+	0.130846i
$76$	0.834406	−	4.01538i	0.0957130	−	0.460596i
$77$	3.13975	+	0.879716i	0.357808	+	0.100253i
$78$	−1.34940	−	3.79684i	−0.152789	−	0.429907i
$79$	−5.50650	+	5.89603i	−0.619530	+	0.663355i	−0.961003	−	0.276537i	$-0.910813\pi$
$79$	−5.50650	+	5.89603i	−0.619530	+	0.663355i	0.341473	+	0.939891i	$0.389074\pi$
$80$	0.252031	−	3.68456i	0.0281779	−	0.411946i
$81$	1.03914	+	5.00060i	0.115460	+	0.555622i
$82$	−1.09197	−	1.54697i	−0.120588	−	0.170834i
$83$	−16.0272	+	4.49061i	−1.75921	+	0.492909i	−0.989382	−	0.145337i	$-0.953573\pi$
$83$	−16.0272	+	4.49061i	−1.75921	+	0.492909i	−0.769832	+	0.638246i	$0.779660\pi$
$84$	0.0716416	+	1.04736i	0.00781674	+	0.114277i
$85$	4.85028	+	3.94600i	0.526087	+	0.428004i
$86$	−8.40217	−	1.15485i	−0.906029	−	0.124531i
$87$	5.40855	+	3.28901i	0.579858	+	0.352619i
$88$	−0.680567	+	0.0935418i	−0.0725487	+	0.00997159i
$89$	−1.03554	−	0.449797i	−0.109767	−	0.0476784i	0.342804	−	0.939407i	$-0.388623\pi$
$89$	−1.03554	−	0.449797i	−0.109767	−	0.0476784i	−0.452571	+	0.891729i	$0.649493\pi$
$90$	−2.57348	+	3.64579i	−0.271269	+	0.384300i
$91$	−0.821496	+	2.31147i	−0.0861162	+	0.242308i
$92$	−0.687332	−	1.32649i	−0.0716593	−	0.138296i
$93$	−3.93972			−0.408530
$94$	−9.93517	−	9.23166i	−1.02473	−	0.952173i
$95$	1.90025			0.194962
$96$	−2.45256	−	4.73323i	−0.250314	−	0.483084i
$97$	−2.38226	+	6.70305i	−0.241882	+	0.680591i	0.757725	+	0.652574i	$0.226311\pi$
$97$	−2.38226	+	6.70305i	−0.241882	+	0.680591i	−0.999607	+	0.0280177i	$0.991081\pi$
$98$	−7.23188	+	10.2452i	−0.730530	+	1.03493i
$99$	9.36147	+	4.06626i	0.940864	+	0.408675i
$100$	7.98805	−	1.09793i	0.798805	−	0.109793i
$101$	3.05562	+	1.85816i	0.304046	+	0.184894i	0.663316	−	0.748339i	$-0.269148\pi$
$101$	3.05562	+	1.85816i	0.304046	+	0.184894i	−0.359271	+	0.933233i	$0.616975\pi$
$102$	9.32915	+	1.28226i	0.923723	+	0.126963i
$103$	−9.00146	−	7.32323i	−0.886941	−	0.721580i	0.0743160	−	0.997235i	$-0.476323\pi$
$103$	−9.00146	−	7.32323i	−0.886941	−	0.721580i	−0.961257	+	0.275655i	$0.911105\pi$
$104$	−0.0352696	−	0.515623i	−0.00345847	−	0.0505610i
$105$	−0.468386	+	0.131236i	−0.0457098	+	0.0128073i
$106$	10.2767	+	14.5587i	0.998157	+	1.41407i
$107$	0.703048	+	3.38325i	0.0679662	+	0.327071i	0.999313	−	0.0370622i	$-0.0118000\pi$
$107$	0.703048	+	3.38325i	0.0679662	+	0.327071i	−0.931347	+	0.364133i	$0.881365\pi$
$108$	−0.488653	+	7.14385i	−0.0470207	+	0.687418i
$109$	4.20578	−	4.50329i	0.402841	−	0.431337i	−0.496869	−	0.867825i	$-0.665517\pi$
$109$	4.20578	−	4.50329i	0.402841	−	0.431337i	0.899710	+	0.436488i	$0.143778\pi$
$110$	2.35596	+	6.62904i	0.224632	+	0.632054i
$111$	3.42446	+	0.959489i	0.325035	+	0.0910706i
$112$	−0.688930	+	3.31531i	−0.0650977	+	0.313268i
$113$	14.4565	−	6.27936i	1.35996	−	0.590712i	0.412606	−	0.910910i	$-0.364619\pi$
$113$	14.4565	−	6.27936i	1.35996	−	0.590712i	0.947351	+	0.320197i	$0.103749\pi$
$114$	2.44524	−	1.48698i	0.229018	−	0.139269i
$115$	0.536972	−	0.436859i	0.0500729	−	0.0407373i
$116$	−12.2485	−	13.1149i	−1.13724	−	1.21769i
$117$	−3.53269	+	6.81777i	−0.326597	+	0.630303i
$118$	3.85997	−	7.44941i	0.355339	−	0.685774i
$119$	−3.91299	−	4.18979i	−0.358703	−	0.384077i
$120$	0.0794958	−	0.0646747i	0.00725694	−	0.00590396i
$121$	4.34938	−	2.64491i	0.395398	−	0.240447i
$122$	−7.52314	+	3.26776i	−0.681113	+	0.295849i
$123$	0.131445	−	0.632548i	0.0118520	−	0.0570349i
$124$	10.7545	+	3.01327i	0.965783	+	0.270600i
$125$	2.73560	+	7.69724i	0.244680	+	0.688462i
$126$	2.79272	−	2.99028i	0.248796	−	0.266395i
$127$	−0.974714	+	14.2498i	−0.0864919	+	1.26447i	0.728521	+	0.685024i	$0.240208\pi$
$127$	−0.974714	+	14.2498i	−0.0864919	+	1.26447i	−0.815013	+	0.579443i	$0.803270\pi$
$128$	−0.278487	−	1.34015i	−0.0246150	−	0.118454i
$129$	−1.66874	−	2.36407i	−0.146924	−	0.208144i
$130$	−5.09659	+	1.42800i	−0.447000	+	0.125244i
$131$	−0.797167	−	11.6542i	−0.0696488	−	1.01823i	−0.892813	−	0.450427i	$-0.851272\pi$
$131$	−0.797167	−	11.6542i	−0.0696488	−	1.01823i	0.823165	−	0.567803i	$-0.192206\pi$
$132$	4.01859	+	3.26936i	0.349773	+	0.284562i
$133$	−1.72605	−	0.237240i	−0.149667	−	0.0205713i
$134$	−20.2030	−	12.2857i	−1.74528	−	1.06133i
$135$	−3.28690	+	0.451774i	−0.282891	+	0.0388825i
$136$	1.10782	+	0.481196i	0.0949951	+	0.0412622i
$137$	8.26358	−	11.7068i	0.706005	−	1.00018i	−0.293023	−	0.956105i	$-0.594661\pi$
$137$	8.26358	−	11.7068i	0.706005	−	1.00018i	0.999028	−	0.0440763i	$-0.0140345\pi$
$138$	0.349124	−	0.982340i	0.0297194	−	0.0836223i
$139$	−10.1244	−	19.5391i	−0.858738	−	1.65729i	−0.748256	−	0.663411i	$-0.769108\pi$
$139$	−10.1244	−	19.5391i	−0.858738	−	1.65729i	−0.110482	−	0.993878i	$-0.535240\pi$
$140$	1.37896			0.116543
$141$	−0.0117548	−	4.62726i	−0.000989932	−	0.389686i
$142$	−5.70910			−0.479097
$143$	5.56927	+	10.7482i	0.465726	+	0.898810i
$144$	−3.54946	+	9.98722i	−0.295788	+	0.832268i
$145$	4.79496	−	6.79291i	0.398200	−	0.564120i
$146$	−10.1057	−	4.38954i	−0.836357	−	0.363281i
$147$	−4.23887	+	0.582619i	−0.349616	+	0.0480536i
$148$	−8.61410	−	5.23835i	−0.708074	−	0.430590i
$149$	1.68086	+	0.231029i	0.137701	+	0.0189266i	0.204688	−	0.978827i	$-0.434382\pi$
$149$	1.68086	+	0.231029i	0.137701	+	0.0189266i	−0.0669867	+	0.997754i	$0.521339\pi$
$150$	4.36464	+	3.55090i	0.356371	+	0.289929i
$151$	−0.611849	−	8.94492i	−0.0497916	−	0.727927i	−0.953806	−	0.300425i	$-0.902872\pi$
$151$	−0.611849	−	8.94492i	−0.0497916	−	0.727927i	0.904014	−	0.427503i	$-0.140607\pi$
$152$	0.353455	−	0.0990335i	0.0286690	−	0.00803268i
$153$	−10.3485	−	14.6604i	−0.836624	−	1.18523i
$154$	−1.31237	−	6.31546i	−0.105754	−	0.508914i
$155$	−0.353151	+	5.16288i	−0.0283657	+	0.414692i
$156$	−2.66024	+	2.84842i	−0.212990	+	0.228056i
$157$	2.55167	+	7.17970i	0.203645	+	0.573003i	0.999471	−	0.0325230i	$-0.0103542\pi$
$157$	2.55167	+	7.17970i	0.203645	+	0.573003i	−0.795826	+	0.605526i	$0.792963\pi$
$158$	15.3676	+	4.30581i	1.22258	+	0.342552i
$159$	−1.23704	+	5.95299i	−0.0981040	+	0.472103i
$160$	−6.42259	+	2.78973i	−0.507750	+	0.220547i
$161$	−0.542286	+	0.329771i	−0.0427381	+	0.0259896i
$162$	7.83756	−	6.37633i	0.615777	−	0.500972i
$163$	5.13501	+	5.49825i	0.402205	+	0.430656i	0.899497	−	0.436927i	$-0.143933\pi$
$163$	5.13501	+	5.49825i	0.402205	+	0.430656i	−0.497292	+	0.867583i	$0.665672\pi$
$164$	−0.842613	+	1.62617i	−0.0657970	+	0.126983i
$165$	−1.10432	+	2.13125i	−0.0859716	+	0.165918i
$166$	22.4742	+	24.0640i	1.74434	+	1.86773i
$167$	−3.03905	+	2.47245i	−0.235168	+	0.191324i	−0.741380	−	0.671086i	$-0.765828\pi$
$167$	−3.03905	+	2.47245i	−0.235168	+	0.191324i	0.506211	+	0.862409i	$0.331046\pi$
$168$	−0.0802824	+	0.0488208i	−0.00619393	+	0.00376661i
$169$	3.57042	−	1.55085i	0.274648	−	0.119296i
$170$	2.51661	−	12.1106i	0.193015	−	0.928841i
$171$	−5.25139	−	1.47137i	−0.401584	−	0.112519i
$172$	2.74712	+	7.72966i	0.209466	+	0.589381i
$173$	−10.4514	+	11.1907i	−0.794604	+	0.850813i	−0.991567	−	0.129598i	$-0.958631\pi$
$173$	−10.4514	+	11.1907i	−0.794604	+	0.850813i	0.196963	+	0.980411i	$0.436892\pi$
$174$	0.854561	−	12.4932i	0.0647841	−	0.947110i
$175$	−0.696923	−	3.35378i	−0.0526824	−	0.253522i
$176$	9.63611	+	13.6513i	0.726349	+	1.02900i
$177$	2.75646	−	0.772325i	0.207189	−	0.0580515i
$178$	0.152415	+	2.22823i	0.0114240	+	0.167013i
$179$	13.4122	+	10.9116i	1.00247	+	0.815573i	0.982882	−	0.184235i	$-0.0589809\pi$
$179$	13.4122	+	10.9116i	1.00247	+	0.815573i	0.0195914	+	0.999808i	$0.493763\pi$
$180$	4.27618	+	0.587747i	0.318727	+	0.0438081i
$181$	11.5257	+	7.00894i	0.856700	+	0.520971i	0.877922	−	0.478804i	$-0.158930\pi$
$181$	11.5257	+	7.00894i	0.856700	+	0.520971i	−0.0212219	+	0.999775i	$0.506756\pi$
$182$	4.80764	−	0.660794i	0.356366	−	0.0489813i
$183$	−2.56683	−	1.11493i	−0.189746	−	0.0824182i
$184$	0.0771118	−	0.109243i	0.00568476	−	0.00805347i
$185$	1.56434	−	4.40163i	0.115013	−	0.323615i
$186$	3.58562	+	6.91993i	0.262910	+	0.507394i
$187$	−28.2901			−2.06878
$188$	−3.50704	+	12.6403i	−0.255777	+	0.921890i
$189$	3.04198			0.221271
$190$	−1.72945	−	3.33770i	−0.125468	−	0.242142i
$191$	3.35548	−	9.44140i	0.242794	−	0.683156i	−0.756772	−	0.653679i	$-0.773225\pi$
$191$	3.35548	−	9.44140i	0.242794	−	0.683156i	0.999565	−	0.0294767i	$-0.00938410\pi$
$192$	−2.83873	+	4.02156i	−0.204868	+	0.290231i
$193$	−10.0673	−	4.37286i	−0.724663	−	0.314766i	0.00366590	−	0.999993i	$-0.498833\pi$
$193$	−10.0673	−	4.37286i	−0.724663	−	0.314766i	−0.728329	+	0.685228i	$0.759703\pi$
$194$	13.9417	−	1.91624i	1.00096	−	0.137578i
$195$	−1.54298	−	0.938305i	−0.110495	−	0.0671934i
$196$	12.0167	+	1.65166i	0.858336	+	0.117976i
$197$	5.15620	+	4.19488i	0.367364	+	0.298873i	0.796822	−	0.604214i	$-0.206513\pi$
$197$	5.15620	+	4.19488i	0.367364	+	0.298873i	−0.429458	+	0.903087i	$0.641295\pi$
$198$	−1.37787	−	20.1437i	−0.0979209	−	1.43155i
$199$	−23.7700	+	6.66004i	−1.68501	+	0.472118i	−0.973144	−	0.230196i	$-0.926063\pi$
$199$	−23.7700	+	6.66004i	−1.68501	+	0.472118i	−0.711867	+	0.702314i	$0.752150\pi$
$200$	0.416177	+	0.589589i	0.0294282	+	0.0416902i
$201$	−1.64140	−	7.89885i	−0.115775	−	0.557142i
$202$	0.482794	−	7.05819i	0.0339692	−	0.496613i
$203$	−5.20345	+	5.57154i	−0.365211	+	0.391045i
$204$	−3.05020	−	8.58244i	−0.213557	−	0.600891i
$205$	−0.817151	−	0.228955i	−0.0570723	−	0.0159909i
$206$	−4.67049	+	22.4756i	−0.325408	+	1.56595i
$207$	−1.82220	+	0.791492i	−0.126651	+	0.0550125i
$208$	−10.7411	+	6.53181i	−0.744761	+	0.452899i
$209$	−6.66928	+	5.42586i	−0.461324	+	0.375315i
$210$	0.656796	+	0.703257i	0.0453232	+	0.0485293i
$211$	−10.1601	+	19.6081i	−0.699451	+	1.34988i	0.227161	+	0.973857i	$0.427056\pi$
$211$	−10.1601	+	19.6081i	−0.699451	+	1.34988i	−0.926611	+	0.376021i	$0.877292\pi$
$212$	7.92994	−	15.3041i	0.544630	−	1.05109i
$213$	−1.32954	−	1.42359i	−0.0910987	−	0.0975429i
$214$	5.30265	−	4.31403i	0.362482	−	0.294901i
$215$	−3.24761	+	1.97492i	−0.221485	+	0.134688i
$216$	−0.587833	+	0.255332i	−0.0399970	+	0.0173731i
$217$	0.965342	−	4.64548i	0.0655317	−	0.315356i
$218$	−11.7376	−	3.28871i	−0.794968	−	0.222740i
$219$	−1.25888	−	3.54216i	−0.0850675	−	0.239357i
$220$	4.64461	−	4.97317i	0.313140	−	0.335291i
$221$	1.45245	−	21.2340i	0.0977020	−	1.42835i
$222$	−1.43137	−	6.88814i	−0.0960674	−	0.462301i
$223$	8.43389	+	11.9481i	0.564775	+	0.800104i	0.994706	−	0.102757i	$-0.0327665\pi$
$223$	8.43389	+	11.9481i	0.564775	+	0.800104i	−0.429931	+	0.902862i	$0.641462\pi$
$224$	6.18209	−	1.73214i	0.413058	−	0.115733i
$225$	−0.731708	−	10.6972i	−0.0487805	−	0.713146i
$226$	−24.1865	−	19.6772i	−1.60886	−	1.30891i
$227$	21.5207	+	2.95796i	1.42838	+	0.196326i	0.808559	−	0.588416i	$-0.200248\pi$
$227$	21.5207	+	2.95796i	1.42838	+	0.196326i	0.619822	+	0.784742i	$0.287205\pi$
$228$	−2.36513	−	1.43827i	−0.156635	−	0.0952516i
$229$	18.9621	−	2.60628i	1.25305	−	0.172228i	0.521046	−	0.853529i	$-0.325542\pi$
$229$	18.9621	−	2.60628i	1.25305	−	0.172228i	0.732003	+	0.681301i	$0.238586\pi$
$230$	−1.25603	−	0.545571i	−0.0828201	−	0.0359739i
$231$	1.26916	−	1.79800i	0.0835049	−	0.118299i
$232$	0.537864	−	1.51341i	0.0353125	−	0.0993599i
$233$	−0.873294	−	1.68538i	−0.0572114	−	0.110413i	0.857562	−	0.514381i	$-0.171978\pi$
$233$	−0.873294	−	1.68538i	−0.0572114	−	0.110413i	−0.914773	+	0.403968i	$0.867631\pi$
$234$	15.1902			0.993017
$235$	−6.06493	−	0.399376i	−0.395633	−	0.0260524i
$236$	−8.11519			−0.528254
$237$	2.50516	+	4.83474i	0.162728	+	0.314050i
$238$	−3.79787	+	10.6862i	−0.246179	+	0.692682i
$239$	13.2582	−	18.7826i	0.857604	−	1.21495i	−0.117471	−	0.993076i	$-0.537479\pi$
$239$	13.2582	−	18.7826i	0.857604	−	1.21495i	0.975076	−	0.221872i	$-0.0712168\pi$
$240$	−2.28636	−	0.993108i	−0.147584	−	0.0641048i
$241$	−8.70544	+	1.19654i	−0.560767	+	0.0770756i	−0.410983	−	0.911643i	$-0.634814\pi$
$241$	−8.70544	+	1.19654i	−0.560767	+	0.0770756i	−0.149784	+	0.988719i	$0.547858\pi$
$242$	−8.60411	−	5.23227i	−0.553093	−	0.336343i
$243$	14.5374	+	1.99812i	0.932575	+	0.128179i
$244$	6.15409	+	5.00672i	0.393975	+	0.320522i
$245$	0.383538	+	5.60712i	0.0245033	+	0.358226i
$246$	−1.23067	+	0.344817i	−0.0784646	+	0.0219847i
$247$	−3.73014	−	5.28440i	−0.237343	−	0.336238i
$248$	0.203381	+	0.978723i	0.0129147	+	0.0621490i
$249$	−0.766655	+	11.2081i	−0.0485848	+	0.710285i
$250$	11.0301	−	11.8103i	0.697604	−	0.746952i
$251$	−0.121681	−	0.342377i	−0.00768043	−	0.0216107i	0.938359	−	0.345663i	$-0.112346\pi$
$251$	−0.121681	−	0.342377i	−0.00768043	−	0.0216107i	−0.946039	+	0.324052i	$0.894955\pi$
$252$	−3.81078	−	1.06773i	−0.240057	−	0.0672607i
$253$	−0.637220	+	3.06647i	−0.0400617	+	0.192787i
$254$	25.9162	−	11.2570i	1.62613	−	0.706326i
$255$	3.60591	−	2.19280i	0.225811	−	0.137319i
$256$	−13.4151	+	10.9140i	−0.838445	+	0.682126i
$257$	5.73538	+	6.14110i	0.357763	+	0.383071i	0.884173	−	0.467160i	$-0.154723\pi$
$257$	5.73538	+	6.14110i	0.357763	+	0.383071i	−0.526409	+	0.850231i	$0.676462\pi$
$258$	−2.63361	+	5.08264i	−0.163961	+	0.316431i
$259$	−1.97046	+	3.80281i	−0.122438	+	0.236295i
$260$	3.49430	+	3.74148i	0.216707	+	0.232037i
$261$	−18.5108	+	15.0596i	−1.14579	+	0.932167i
$262$	−19.7444	+	12.0069i	−1.21982	+	0.741786i
$263$	9.26702	−	4.02524i	0.571429	−	0.248207i	−0.0928640	−	0.995679i	$-0.529602\pi$
$263$	9.26702	−	4.02524i	0.571429	−	0.248207i	0.664293	+	0.747472i	$0.268733\pi$
$264$	−0.0943370	+	0.453975i	−0.00580604	+	0.0279402i
$265$	7.69031	+	2.15472i	0.472412	+	0.132364i
$266$	1.15421	+	3.24763i	0.0707690	+	0.199125i
$267$	−0.520127	+	0.556920i	−0.0318312	+	0.0340829i
$268$	−1.56075	+	22.8174i	−0.0953380	+	1.39379i
$269$	−2.26450	−	10.8974i	−0.138069	−	0.664424i	−0.990034	−	0.140826i	$-0.955024\pi$
$269$	−2.26450	−	10.8974i	−0.138069	−	0.664424i	0.851966	−	0.523598i	$-0.175411\pi$
$270$	3.78499	+	5.36210i	0.230347	+	0.326327i
$271$	25.8641	−	7.24678i	1.57113	−	0.440211i	0.629540	−	0.776968i	$-0.283243\pi$
$271$	25.8641	−	7.24678i	1.57113	−	0.440211i	0.941592	+	0.336757i	$0.109330\pi$
$272$	−2.00487	−	29.3102i	−0.121563	−	1.77719i
$273$	1.28438	+	1.04492i	0.0777343	+	0.0632415i
$274$	−28.0833	−	3.85996i	−1.69657	−	0.233189i
$275$	−14.4427	−	8.78279i	−0.870926	−	0.529622i
$276$	−0.998988	+	0.137308i	−0.0601320	+	0.00826495i
$277$	−0.744526	−	0.323393i	−0.0447342	−	0.0194308i	0.375915	−	0.926654i	$-0.377328\pi$
$277$	−0.744526	−	0.323393i	−0.0447342	−	0.0194308i	−0.420650	+	0.907223i	$0.638198\pi$
$278$	−25.1051	+	35.5659i	−1.50571	+	2.13310i
$279$	4.97357	−	13.9943i	0.297760	−	0.837816i
$280$	0.0567817	+	0.109584i	0.00339336	+	0.00654888i
$281$	−18.7418			−1.11804			−0.559021	−	0.829153i	$-0.688823\pi$
$281$	−18.7418			−1.11804			−0.559021	+	0.829153i	$0.688823\pi$
$282$	−8.11686	+	4.23201i	−0.483352	+	0.252012i
$283$	6.53621			0.388537			0.194269	−	0.980948i	$-0.437767\pi$
$283$	6.53621			0.388537			0.194269	+	0.980948i	$0.437767\pi$
$284$	2.54051	+	4.90295i	0.150751	+	0.290937i
$285$	0.429513	−	1.20854i	0.0254422	−	0.0715874i
$286$	13.8100	−	19.5643i	0.816601	−	1.15686i
$287$	0.713654	+	0.309984i	0.0421257	+	0.0182978i
$288$	19.9091	−	2.73644i	1.17315	−	0.161246i
$289$	27.9732	+	17.0109i	1.64548	+	1.00064i
$290$	−16.2954	−	2.23975i	−0.956898	−	0.131523i
$291$	3.72459	+	3.03018i	0.218339	+	0.177632i
$292$	0.727255	+	10.6321i	0.0425594	+	0.622196i
$293$	−7.90859	+	2.21588i	−0.462025	+	0.129453i	−0.492930	−	0.870069i	$-0.664074\pi$
$293$	−7.90859	+	2.21588i	−0.462025	+	0.129453i	0.0309051	+	0.999522i	$0.490161\pi$
$294$	4.88121	+	6.91511i	0.284678	+	0.403297i
$295$	−0.765022	−	3.68149i	−0.0445413	−	0.214344i
$296$	0.0615788	−	0.900251i	0.00357920	−	0.0523260i
$297$	10.2460	−	10.9708i	0.594533	−	0.636590i
$298$	−1.12399	−	3.16261i	−0.0651111	−	0.183205i
$299$	−2.26892	−	0.635721i	−0.131215	−	0.0367647i
$300$	1.10727	−	5.32846i	0.0639281	−	0.307639i
$301$	3.19645	−	1.38841i	0.184240	−	0.0800269i
$302$	−15.1544	+	9.21562i	−0.872040	+	0.530299i
$303$	1.87243	−	1.52333i	0.107568	−	0.0875132i
$304$	−6.09416	−	6.52525i	−0.349524	−	0.374249i
$305$	−1.69117	+	3.26381i	−0.0968361	+	0.186885i
$306$	−16.3320	+	31.5193i	−0.933638	+	1.80184i
$307$	6.71213	+	7.18694i	0.383081	+	0.410180i	0.893010	−	0.450037i	$-0.148589\pi$
$307$	6.71213	+	7.18694i	0.383081	+	0.410180i	−0.509929	+	0.860217i	$0.670328\pi$
$308$	−4.83970	+	3.93739i	−0.275767	+	0.224353i
$309$	−6.69208	+	4.06954i	−0.380699	+	0.231508i
$310$	9.38974	−	4.07854i	0.533302	−	0.231646i
$311$	−2.99103	+	14.3936i	−0.169606	+	0.816189i	0.805177	+	0.593034i	$0.202070\pi$
$311$	−2.99103	+	14.3936i	−0.169606	+	0.816189i	−0.974783	+	0.223154i	$0.928365\pi$
$312$	−0.335901	−	0.0941151i	−0.0190167	−	0.00532822i
$313$	−1.16731	−	3.28450i	−0.0659804	−	0.185651i	0.904687	−	0.426076i	$-0.140104\pi$
$313$	−1.16731	−	3.28450i	−0.0659804	−	0.185651i	−0.970668	+	0.240425i	$0.922713\pi$
$314$	10.2885	−	11.0163i	0.580611	−	0.621683i
$315$	0.125136	−	1.82943i	0.00705064	−	0.103077i
$316$	−3.14067	−	15.1137i	−0.176676	−	0.850214i
$317$	−0.165874	−	0.234989i	−0.00931639	−	0.0131983i	0.812285	−	0.583261i	$-0.198223\pi$
$317$	−0.165874	−	0.234989i	−0.00931639	−	0.0131983i	−0.821601	+	0.570062i	$0.806919\pi$
$318$	11.5820	−	3.24512i	0.649485	−	0.181977i
$319$	2.56727	+	37.5322i	0.143740	+	2.10140i
$320$	5.01566	+	4.08055i	0.280384	+	0.228109i
$321$	2.31061	+	0.317586i	0.128966	+	0.0177259i
$322$	1.07277	+	0.652366i	0.0597832	+	0.0363549i
$323$	14.9755	−	2.05833i	0.833258	−	0.114529i
$324$	−8.96363	−	3.89345i	−0.497979	−	0.216303i
$325$	7.33369	−	10.3895i	0.406800	−	0.576304i
$326$	4.98393	−	14.0234i	0.276035	−	0.776687i
$327$	−1.91340	−	3.69270i	−0.105811	−	0.204207i
$328$	−0.163926			−0.00905129
$329$	5.45907	+	1.11995i	0.300968	+	0.0617448i
$330$	4.74850			0.261396
$331$	−3.22978	−	6.23319i	−0.177525	−	0.342607i	0.782441	−	0.622725i	$-0.213974\pi$
$331$	−3.22978	−	6.23319i	−0.177525	−	0.342607i	−0.959966	+	0.280118i	$0.909627\pi$
$332$	10.6652	−	30.0091i	0.585330	−	1.64696i
$333$	−7.73129	+	10.9527i	−0.423672	+	0.600207i
$334$	7.10862	+	3.08771i	0.388966	+	0.168952i
$335$	−10.4983	+	1.44296i	−0.573584	+	0.0788373i
$336$	1.95278	+	1.18751i	0.106533	+	0.0647839i
$337$	3.80902	+	0.523537i	0.207490	+	0.0285189i	0.239163	−	0.970979i	$-0.423127\pi$
$337$	3.80902	+	0.523537i	0.207490	+	0.0285189i	−0.0316728	+	0.999498i	$0.510083\pi$
$338$	−5.97350	−	4.85980i	−0.324915	−	0.264338i
$339$	−0.725982	−	10.6135i	−0.0394299	−	0.576445i
$340$	−11.5204	+	3.22787i	−0.624783	+	0.175056i
$341$	−13.5023	−	19.1284i	−0.731191	−	1.03586i
$342$	2.19500	+	10.5629i	0.118692	+	0.571177i
$343$	0.739958	−	10.8178i	0.0399540	−	0.584107i
$344$	−0.501146	+	0.536596i	−0.0270200	+	0.0289313i
$345$	−0.156465	−	0.440250i	−0.00842379	−	0.0237023i
$346$	29.1679	+	8.17246i	1.56807	+	0.439354i
$347$	0.692078	−	3.33046i	0.0371527	−	0.178789i	−0.956418	−	0.292000i	$-0.905679\pi$
$347$	0.692078	−	3.33046i	0.0371527	−	0.178789i	0.993571	+	0.113212i	$0.0361139\pi$
$348$	−11.1094	+	4.82551i	−0.595528	+	0.258674i
$349$	5.41499	−	3.29293i	0.289858	−	0.176266i	−0.367126	−	0.930171i	$-0.619658\pi$
$349$	5.41499	−	3.29293i	0.289858	−	0.176266i	0.656983	+	0.753905i	$0.271832\pi$
$350$	−5.25646	+	4.27645i	−0.280970	+	0.228586i
$351$	7.70842	+	8.25370i	0.411445	+	0.440550i
$352$	14.5756	−	28.1297i	0.776884	−	1.49932i
$353$	−4.49741	+	8.67960i	−0.239373	+	0.461969i	−0.977000	−	0.213240i	$-0.931598\pi$
$353$	−4.49741	+	8.67960i	−0.239373	+	0.461969i	0.737627	+	0.675208i	$0.235946\pi$
$354$	−3.86526	−	4.13868i	−0.205436	−	0.219968i
$355$	−1.98475	+	1.61471i	−0.105340	+	0.0857000i
$356$	1.84578	−	1.12244i	0.0978260	−	0.0594893i
$357$	−3.54910	+	1.54159i	−0.187838	+	0.0815897i
$358$	6.95903	−	33.4887i	0.367796	−	1.76993i
$359$	−19.4420	−	5.44739i	−1.02611	−	0.287502i	−0.284744	−	0.958604i	$-0.591908\pi$
$359$	−19.4420	−	5.44739i	−1.02611	−	0.287502i	−0.741366	+	0.671101i	$0.765822\pi$
$360$	0.129374	+	0.364023i	0.00681861	+	0.0191857i
$361$	−9.83287	+	10.5284i	−0.517520	+	0.554128i
$362$	1.82108	−	26.6233i	0.0957141	−	1.39929i
$363$	−0.699042	−	3.36398i	−0.0366902	−	0.176563i
$364$	−2.70685	−	3.83473i	−0.141878	−	0.200995i
$365$	−4.75473	+	1.33221i	−0.248874	+	0.0697312i
$366$	0.377799	+	5.52323i	0.0197479	+	0.288704i
$367$	−26.7314	−	21.7476i	−1.39537	−	1.13522i	−0.973533	−	0.228545i	$-0.926603\pi$
$367$	−26.7314	−	21.7476i	−1.39537	−	1.13522i	−0.421836	−	0.906672i	$-0.638614\pi$
$368$	−3.22221	−	0.442882i	−0.167969	−	0.0230868i
$369$	2.08093	+	1.26544i	0.108329	+	0.0658764i
$370$	−9.15498	+	1.25832i	−0.475945	+	0.0654171i
$371$	−6.71629	−	2.91730i	−0.348692	−	0.151458i
$372$	4.34724	−	6.15863i	0.225394	−	0.319310i
$373$	−8.60100	+	24.2009i	−0.445343	+	1.25307i	0.481109	+	0.876661i	$0.340234\pi$
$373$	−8.60100	+	24.2009i	−0.445343	+	1.25307i	−0.926452	+	0.376414i	$0.877157\pi$
$374$	25.7473	+	49.6901i	1.33136	+	2.56941i
$375$	5.51367			0.284725
$376$	−1.14892	+	0.241794i	−0.0592509	+	0.0124696i
$377$	−28.3027			−1.45766
$378$	−2.76856	−	5.34308i	−0.142399	−	0.274818i
$379$	3.66292	−	10.3065i	0.188152	−	0.529408i	−0.810240	−	0.586098i	$-0.800663\pi$
$379$	3.66292	−	10.3065i	0.188152	−	0.529408i	0.998392	+	0.0566897i	$0.0180546\pi$
$380$	−2.09681	+	2.97050i	−0.107564	+	0.152383i
$381$	8.84238	+	3.84079i	0.453009	+	0.196769i
$382$	−19.6372	+	2.69907i	−1.00473	+	0.138097i
$383$	5.95079	+	3.61876i	0.304071	+	0.184910i	0.663328	−	0.748329i	$-0.269144\pi$
$383$	5.95079	+	3.61876i	0.304071	+	0.184910i	−0.359256	+	0.933239i	$0.616970\pi$
$384$	−0.915264	−	0.125800i	−0.0467069	−	0.00641971i
$385$	−2.24245	−	1.82437i	−0.114286	−	0.0929784i
$386$	1.48176	+	21.6626i	0.0754197	+	1.10260i
$387$	10.5040	−	2.94309i	0.533950	−	0.149606i
$388$	−7.84962	−	11.1204i	−0.398504	−	0.564552i
$389$	−1.17421	−	5.65063i	−0.0595350	−	0.286498i	0.938781	−	0.344516i	$-0.111957\pi$
$389$	−1.17421	−	5.65063i	−0.0595350	−	0.286498i	−0.998316	+	0.0580174i	$0.981522\pi$
$390$	−0.243793	+	3.56413i	−0.0123449	+	0.180477i
$391$	3.75856	−	4.02444i	0.190079	−	0.203525i
$392$	0.363561	+	1.02296i	0.0183626	+	0.0516673i
$393$	−7.59208	−	2.12720i	−0.382970	−	0.107303i
$394$	2.67534	−	12.8744i	0.134782	−	0.648605i
$395$	6.56033	−	2.84955i	0.330086	−	0.143377i
$396$	−16.6862	+	10.1471i	−0.838515	+	0.509912i
$397$	−17.8262	+	14.5027i	−0.894673	+	0.727870i	−0.962917	−	0.269798i	$-0.913043\pi$
$397$	−17.8262	+	14.5027i	−0.894673	+	0.727870i	0.0682441	+	0.997669i	$0.478260\pi$
$398$	33.3316	+	35.6894i	1.67076	+	1.78895i
$399$	−0.541019	+	1.04412i	−0.0270848	+	0.0522713i
$400$	8.07596	−	15.5859i	0.403798	−	0.779295i
$401$	−18.0314	−	19.3069i	−0.900445	−	0.964141i	0.0990764	−	0.995080i	$-0.468411\pi$
$401$	−18.0314	−	19.3069i	−0.900445	−	0.964141i	−0.999521	+	0.0309388i	$0.990150\pi$
$402$	−12.3801	+	10.0719i	−0.617461	+	0.502342i
$403$	15.0506	−	9.15250i	0.749726	−	0.455919i
$404$	−6.27639	+	2.72622i	−0.312262	+	0.135635i
$405$	0.921275	−	4.43342i	0.0457785	−	0.220298i
$406$	14.5219	+	4.06884i	0.720709	+	0.201933i
$407$	7.07781	+	19.9151i	0.350834	+	0.987152i
$408$	0.556435	−	0.595796i	0.0275476	−	0.0294963i
$409$	−1.86583	+	27.2774i	−0.0922592	+	1.34878i	0.689084	+	0.724681i	$0.258013\pi$
$409$	−1.86583	+	27.2774i	−0.0922592	+	1.34878i	−0.781344	+	0.624101i	$0.785465\pi$
$410$	0.341556	+	1.64366i	0.0168683	+	0.0811746i
$411$	−5.57757	−	7.90162i	−0.275121	−	0.389758i
$412$	21.3803	−	5.99049i	1.05333	−	0.295130i
$413$	0.235268	+	3.43950i	0.0115768	+	0.169247i
$414$	3.04863	+	2.48024i	0.149832	+	0.121897i
$415$	14.6191	+	2.00935i	0.717625	+	0.0986353i
$416$	20.3653	+	12.3844i	0.998490	+	0.607195i
$417$	−14.7150	+	2.02254i	−0.720599	+	0.0990440i
$418$	15.6001	+	6.77607i	0.763025	+	0.331428i
$419$	3.94348	−	5.58664i	0.192652	−	0.272925i	−0.709166	−	0.705041i	$-0.750929\pi$
$419$	3.94348	−	5.58664i	0.192652	−	0.272925i	0.901818	+	0.432116i	$0.142233\pi$
$420$	0.311685	−	0.876999i	0.0152087	−	0.0427931i
$421$	−5.43105	−	10.4815i	−0.264693	−	0.510835i	0.718007	−	0.696035i	$-0.245054\pi$
$421$	−5.43105	−	10.4815i	−0.264693	−	0.510835i	−0.982701	+	0.185201i	$0.940707\pi$
$422$	43.6876			2.12668
$423$	16.4513	+	5.79978i	0.799892	+	0.281995i
$424$	1.54273			0.0749214
$425$	13.6729	+	26.3876i	0.663235	+	1.27999i
$426$	−1.29043	+	3.63091i	−0.0625213	+	0.175918i
$427$	1.94361	−	2.75346i	0.0940577	−	0.133249i
$428$	−6.06451	−	2.63419i	−0.293139	−	0.127328i
$429$	8.09454	−	1.11257i	0.390808	−	0.0537153i
$430$	6.42456	+	3.90686i	0.309820	+	0.188405i
$431$	−8.93784	−	1.22848i	−0.430521	−	0.0591737i	−0.0823470	−	0.996604i	$-0.526242\pi$
$431$	−8.93784	−	1.22848i	−0.430521	−	0.0591737i	−0.348174	+	0.937430i	$0.613198\pi$
$432$	12.0925	+	9.83799i	0.581801	+	0.473330i
$433$	−0.0766035	−	1.11990i	−0.00368133	−	0.0538192i	0.995465	−	0.0951272i	$-0.0303258\pi$
$433$	−0.0766035	−	1.11990i	−0.00368133	−	0.0538192i	−0.999146	+	0.0413080i	$0.986848\pi$
$434$	−9.03813	+	2.53237i	−0.433844	+	0.121557i
$435$	−3.23640	−	4.58493i	−0.155173	−	0.219831i
$436$	2.39879	+	11.5436i	0.114881	+	0.552840i
$437$	0.114205	−	1.66961i	0.00546315	−	0.0798685i
$438$	−5.07589	+	5.43495i	−0.242535	+	0.259692i
$439$	−10.7554	−	30.2627i	−0.513326	−	1.44436i	−0.861900	−	0.507079i	$-0.830725\pi$
$439$	−10.7554	−	30.2627i	−0.513326	−	1.44436i	0.348574	−	0.937281i	$-0.386666\pi$
$440$	0.586463	+	0.164319i	0.0279585	+	0.00783361i
$441$	3.28170	−	15.7924i	0.156271	−	0.752019i
$442$	−38.6183	+	16.7743i	−1.83689	+	0.797873i
$443$	−3.95869	+	2.40733i	−0.188083	+	0.114376i	−0.610469	−	0.792040i	$-0.709019\pi$
$443$	−3.95869	+	2.40733i	−0.188083	+	0.114376i	0.422386	+	0.906416i	$0.361193\pi$
$444$	−5.27856	+	4.29443i	−0.250509	+	0.203805i
$445$	0.683201	+	0.731530i	0.0323869	+	0.0346779i
$446$	13.3104	−	25.6879i	0.630265	−	1.21636i
$447$	0.526855	−	1.01678i	0.0249194	−	0.0480923i
$448$	−4.04641	−	4.33265i	−0.191175	−	0.204698i
$449$	5.81751	−	4.73290i	0.274545	−	0.223359i	−0.483855	−	0.875148i	$-0.660764\pi$
$449$	5.81751	−	4.73290i	0.274545	−	0.223359i	0.758400	+	0.651789i	$0.225981\pi$
$450$	−18.1231	+	11.0209i	−0.854332	+	0.519531i
$451$	3.52168	−	1.52968i	0.165830	−	0.0720299i
$452$	−6.13589	+	29.5275i	−0.288608	+	1.38886i
$453$	−5.82715	−	1.63269i	−0.273783	−	0.0767105i
$454$	−14.3909	−	40.4922i	−0.675399	−	1.90039i
$455$	1.48447	−	1.58947i	0.0695928	−	0.0745157i
$456$	0.0169074	−	0.247177i	0.000791761	−	0.0115751i
$457$	2.56955	+	12.3653i	0.120198	+	0.578427i	0.995493	+	0.0948362i	$0.0302327\pi$
$457$	2.56955	+	12.3653i	0.120198	+	0.578427i	−0.875294	+	0.483590i	$0.839332\pi$
$458$	−21.8355	−	30.9339i	−1.02031	−	1.44545i
$459$	−25.4140	+	7.12067i	−1.18622	+	0.332364i
$460$	0.0903896	+	1.32145i	0.00421444	+	0.0616129i
$461$	17.5372	+	14.2675i	0.816787	+	0.664505i	0.944938	−	0.327249i	$-0.106122\pi$
$461$	17.5372	+	14.2675i	0.816787	+	0.664505i	−0.128151	+	0.991755i	$0.540904\pi$
$462$	−4.31318	−	0.592833i	−0.200667	−	0.0275811i
$463$	21.7294	+	13.2140i	1.00985	+	0.614105i	0.924076	−	0.382209i	$-0.124837\pi$
$463$	21.7294	+	13.2140i	1.00985	+	0.614105i	0.0857770	+	0.996314i	$0.472663\pi$
$464$	−38.7036	+	5.31969i	−1.79677	+	0.246960i
$465$	3.20370	+	1.39156i	0.148568	+	0.0645322i
$466$	−2.16548	+	3.06779i	−0.100314	+	0.142113i
$467$	0.660964	−	1.85977i	0.0305858	−	0.0860601i	−0.925985	−	0.377560i	$-0.876763\pi$
$467$	0.660964	−	1.85977i	0.0305858	−	0.0860601i	0.956571	+	0.291500i	$0.0941544\pi$
$468$	−6.75954	−	13.0453i	−0.312460	−	0.603021i
$469$	9.71603			0.448644
$470$	4.81832	+	11.0162i	0.222253	+	0.508141i
$471$	5.14295			0.236974
$472$	−0.334162	−	0.644903i	−0.0153810	−	0.0296840i
$473$	5.75903	−	16.2044i	0.264801	−	0.745077i
$474$	6.21198	−	8.80037i	0.285326	−	0.404214i
$475$	8.28431	+	3.59839i	0.380110	+	0.165105i
$476$	10.8673	−	1.49367i	0.498101	−	0.0684624i
$477$	−19.5839	−	11.9093i	−0.896687	−	0.545287i
$478$	−45.0573	−	6.19299i	−2.06087	−	0.283261i
$479$	−16.6611	−	13.5548i	−0.761264	−	0.619335i	0.169257	−	0.985572i	$-0.445863\pi$
$479$	−16.6611	−	13.5548i	−0.761264	−	0.619335i	−0.930521	+	0.366237i	$0.880646\pi$
$480$	0.322531	+	4.71524i	0.0147215	+	0.215220i
$481$	−15.3112	+	4.29001i	−0.698132	+	0.195607i
$482$	10.0246	+	14.2017i	0.456610	+	0.646869i
$483$	0.0871574	+	0.419424i	0.00396580	+	0.0190845i
$484$	−0.664695	+	9.71750i	−0.0302134	+	0.441705i
$485$	4.30481	−	4.60933i	0.195471	−	0.209299i
$486$	−9.72116	−	27.3527i	−0.440961	−	1.24075i
$487$	−11.5329	−	3.23138i	−0.522607	−	0.146428i	−0.00163063	−	0.999999i	$-0.500519\pi$
$487$	−11.5329	−	3.23138i	−0.522607	−	0.146428i	−0.520977	+	0.853571i	$0.674432\pi$
$488$	−0.144468	+	0.695220i	−0.00653977	+	0.0314711i
$489$	4.65748	−	2.02303i	0.210619	−	0.0914846i
$490$	9.49956	−	5.77681i	0.429147	−	0.260970i
$491$	21.1840	−	17.2345i	0.956020	−	0.777780i	−0.0190178	−	0.999819i	$-0.506054\pi$
$491$	21.1840	−	17.2345i	0.956020	−	0.777780i	0.975038	+	0.222039i	$0.0712713\pi$
$492$	0.843767	+	0.903453i	0.0380399	+	0.0407308i
$493$	30.4301	−	58.7273i	1.37050	−	2.64495i
$494$	−5.88691	+	11.3612i	−0.264865	+	0.511166i
$495$	−6.17629	−	6.61320i	−0.277604	−	0.297241i
$496$	18.8613	−	15.3448i	0.846897	−	0.689002i
$497$	2.00439	−	1.21890i	0.0899091	−	0.0546749i
$498$	20.3842	−	8.85411i	0.913438	−	0.396762i
$499$	−7.56203	+	36.3905i	−0.338523	+	1.62906i	0.374011	+	0.927424i	$0.377982\pi$
$499$	−7.56203	+	36.3905i	−0.338523	+	1.62906i	−0.712534	+	0.701638i	$0.752452\pi$
$500$	−15.0510	−	4.21709i	−0.673101	−	0.188594i
$501$	0.885529	+	2.49164i	0.0395625	+	0.111318i
$502$	−0.490624	+	0.525330i	−0.0218976	+	0.0234466i
$503$	−0.882089	+	12.8957i	−0.0393304	+	0.574990i	0.935683	+	0.352843i	$0.114785\pi$
$503$	−0.882089	+	12.8957i	−0.0393304	+	0.574990i	−0.975013	+	0.222148i	$0.928693\pi$
$504$	−0.0720666	−	0.346803i	−0.00321010	−	0.0154479i
$505$	−1.82844	−	2.59031i	−0.0813644	−	0.115267i
$506$	5.96605	−	1.67161i	0.265223	−	0.0743121i
$507$	−0.179300	−	2.62128i	−0.00796301	−	0.116415i
$508$	−21.2000	−	17.2475i	−0.940597	−	0.765232i
$509$	−25.0982	−	3.44967i	−1.11246	−	0.152904i	−0.443551	−	0.896249i	$-0.646281\pi$
$509$	−25.0982	−	3.44967i	−1.11246	−	0.152904i	−0.668908	+	0.743345i	$0.733238\pi$
$510$	−7.13335	−	4.33789i	−0.315870	−	0.192085i
$511$	4.48516	−	0.616471i	0.198412	−	0.0272711i
$512$	28.8683	+	12.5393i	1.27581	+	0.554163i
$513$	−4.62555	+	6.55292i	−0.204223	+	0.289318i
$514$	5.56664	−	15.6630i	0.245534	−	0.690867i
$515$	4.73314	+	9.13454i	0.208567	+	0.402516i
$516$	5.53689			0.243748
$517$	22.4263	−	15.9157i	0.986309	−	0.699973i
$518$	8.47280			0.372273
$519$	4.75481	+	9.17637i	0.208713	+	0.402798i
$520$	−0.153444	+	0.431751i	−0.00672898	+	0.0189335i
$521$	−21.1522	+	29.9658i	−0.926694	+	1.31283i	0.0230293	+	0.999735i	$0.492669\pi$
$521$	−21.1522	+	29.9658i	−0.926694	+	1.31283i	−0.949723	+	0.313091i	$0.898635\pi$
$522$	43.2984	+	18.8072i	1.89512	+	0.823167i
$523$	10.2506	−	1.40891i	0.448226	−	0.0616073i	0.0914765	−	0.995807i	$-0.470841\pi$
$523$	10.2506	−	1.40891i	0.448226	−	0.0616073i	0.356750	+	0.934200i	$0.383885\pi$
$524$	19.0976	+	11.6135i	0.834282	+	0.507338i
$525$	−2.29048	−	0.314820i	−0.0999649	−	0.0137399i
$526$	−15.5042	−	12.6136i	−0.676016	−	0.549980i
$527$	2.80927	+	41.0701i	0.122374	+	1.78904i
$528$	10.8601	−	3.04285i	0.472624	−	0.132423i
$529$	12.9121	+	18.2923i	0.561395	+	0.795315i
$530$	−3.21443	−	15.4687i	−0.139626	−	0.671917i
$531$	−0.736430	+	10.7662i	−0.0319584	+	0.467215i
$532$	2.27544	−	2.43640i	0.0986528	−	0.105631i
$533$	0.967343	+	2.72184i	0.0419003	+	0.117896i
$534$	1.45158	+	0.406713i	0.0628159	+	0.0176002i
$535$	0.623306	−	2.99951i	0.0269479	−	0.129680i
$536$	−1.87753	+	0.815527i	−0.0810970	+	0.0352254i
$537$	9.97120	−	6.06362i	0.430289	−	0.261664i
$538$	−17.0797	+	13.8954i	−0.736358	+	0.599072i
$539$	−17.3563	−	18.5841i	−0.747590	−	0.800473i
$540$	2.92067	−	5.63663i	0.125686	−	0.242562i
$541$	0.553753	−	1.06869i	0.0238077	−	0.0459467i	−0.875684	−	0.482884i	$-0.839589\pi$
$541$	0.553753	−	1.06869i	0.0238077	−	0.0459467i	0.899492	+	0.436938i	$0.143937\pi$
$542$	−36.2680	−	38.8335i	−1.55784	−	1.66804i
$543$	7.06275	−	5.74597i	0.303092	−	0.246583i
$544$	−47.5933	+	28.9421i	−2.04055	+	1.24088i
$545$	−5.01067	+	2.17644i	−0.214634	+	0.0932286i
$546$	0.666412	−	3.20695i	0.0285198	−	0.137245i
$547$	20.7378	+	5.81046i	0.886684	+	0.248437i	0.682842	−	0.730567i	$-0.260744\pi$
$547$	20.7378	+	5.81046i	0.886684	+	0.248437i	0.203842	+	0.979004i	$0.434657\pi$
$548$	9.18194	+	25.8355i	0.392233	+	1.10364i
$549$	7.20076	−	7.71013i	0.307321	−	0.329060i
$550$	−2.28197	+	33.3612i	−0.0973035	+	1.42253i
$551$	−4.08976	−	19.6810i	−0.174230	−	0.838440i
$552$	−0.0520473	−	0.0737342i	−0.00221528	−	0.00313833i
$553$	−6.31466	+	1.76929i	−0.268527	+	0.0752377i
$554$	0.109583	+	1.60205i	0.00465574	+	0.0680645i
$555$	−2.44579	−	1.98980i	−0.103818	−	0.0844623i
$556$	41.7155	+	5.73366i	1.76913	+	0.243161i
$557$	8.74826	+	5.31993i	0.370676	+	0.225413i	0.692551	−	0.721369i	$-0.256487\pi$
$557$	8.74826	+	5.31993i	0.370676	+	0.225413i	−0.321875	+	0.946782i	$0.604313\pi$
$558$	−29.1068	+	4.00064i	−1.23219	+	0.169361i
$559$	11.8670	+	5.15457i	0.501921	+	0.218015i
$560$	1.73124	−	2.45260i	0.0731580	−	0.103641i
$561$	−6.39440	+	17.9921i	−0.269972	+	0.759628i
$562$	17.0573	+	32.9190i	0.719517	+	1.38860i
$563$	22.8402			0.962598			0.481299	−	0.876556i	$-0.340165\pi$
$563$	22.8402			0.962598			0.481299	+	0.876556i	$0.340165\pi$
$564$	7.24638	+	5.08752i	0.305127	+	0.214223i
$565$	−13.9737			−0.587878
$566$	−5.94872	−	11.4805i	−0.250043	−	0.482562i
$567$	−1.39031	+	3.91197i	−0.0583877	+	0.164287i
$568$	−0.285020	+	0.403781i	−0.0119592	+	0.0169423i
$569$	21.2038	+	9.21009i	0.888908	+	0.386107i	0.792956	−	0.609279i	$-0.208541\pi$
$569$	21.2038	+	9.21009i	0.888908	+	0.386107i	0.0959518	+	0.995386i	$0.469411\pi$
$570$	−2.51364	+	0.345492i	−0.105285	+	0.0144711i
$571$	−17.3435	−	10.5468i	−0.725804	−	0.441371i	0.107487	−	0.994207i	$-0.465720\pi$
$571$	−17.3435	−	10.5468i	−0.725804	−	0.441371i	−0.833290	+	0.552836i	$0.813546\pi$
$572$	−22.9471	−	3.15400i	−0.959466	−	0.131876i
$573$	−5.24617	−	4.26808i	−0.219162	−	0.178301i
$574$	−0.105039	−	1.53562i	−0.00438425	−	0.0640955i
$575$	3.16823	−	0.887696i	0.132124	−	0.0370195i
$576$	−10.7013	−	15.1603i	−0.445889	−	0.631680i
$577$	2.40739	+	11.5850i	0.100221	+	0.482290i	0.999033	+	0.0439566i	$0.0139963\pi$
$577$	2.40739	+	11.5850i	0.100221	+	0.482290i	−0.898812	+	0.438333i	$0.855569\pi$
$578$	4.41981	−	64.6154i	0.183840	−	2.68765i
$579$	−5.05660	+	5.41430i	−0.210145	+	0.225011i
$580$	5.32784	+	14.9911i	0.221226	+	0.622471i
$581$	−13.0281	−	3.65029i	−0.540495	−	0.151440i
$582$	1.93253	−	9.29987i	0.0801061	−	0.385492i
$583$	−33.1430	+	14.3960i	−1.37264	+	0.596222i
$584$	−0.814970	+	0.495595i	−0.0337237	+	0.0205078i
$585$	5.28083	−	4.29628i	0.218336	−	0.177629i
$586$	11.0898	+	11.8743i	0.458117	+	0.490524i
$587$	−9.35981	+	18.0636i	−0.386321	+	0.745565i	−0.998997	−	0.0447684i	$-0.985745\pi$
$587$	−9.35981	+	18.0636i	−0.386321	+	0.745565i	0.612677	+	0.790334i	$0.290093\pi$
$588$	3.76657	−	7.26914i	0.155331	−	0.299774i
$589$	8.53926	+	9.14331i	0.351854	+	0.376744i
$590$	−5.77008	+	4.69431i	−0.237551	+	0.193262i
$591$	3.83334	−	2.33111i	0.157683	−	0.0958889i
$592$	−20.1316	+	8.74438i	−0.827403	+	0.359392i
$593$	4.49141	−	21.6139i	0.184440	−	0.887575i	−0.780510	−	0.625143i	$-0.785041\pi$
$593$	4.49141	−	21.6139i	0.184440	−	0.887575i	0.964950	−	0.262432i	$-0.0845246\pi$
$594$	−28.5947	−	8.01186i	−1.17326	−	0.328731i
$595$	1.70207	+	4.78917i	0.0697781	+	0.196337i
$596$	−2.21587	+	2.37262i	−0.0907656	+	0.0971862i
$597$	−1.13703	+	16.6228i	−0.0465355	+	0.680325i
$598$	0.948373	+	4.56382i	0.0387819	+	0.186629i
$599$	−23.7216	−	33.6058i	−0.969238	−	1.37310i	−0.927440	−	0.373971i	$-0.877996\pi$
$599$	−23.7216	−	33.6058i	−0.969238	−	1.37310i	−0.0417974	−	0.999126i	$-0.513308\pi$
$600$	0.469039	−	0.131419i	0.0191484	−	0.00536514i
$601$	1.66550	+	24.3487i	0.0679370	+	0.993204i	0.899260	+	0.437415i	$0.144106\pi$
$601$	1.66550	+	24.3487i	0.0679370	+	0.993204i	−0.831323	+	0.555790i	$0.812416\pi$
$602$	−5.34783	−	4.35078i	−0.217961	−	0.177325i
$603$	30.1296	+	4.14122i	1.22697	+	0.168644i
$604$	14.6580	+	8.91371i	0.596424	+	0.362694i
$605$	−4.47104	+	0.614530i	−0.181774	+	0.0249842i
$606$	−4.37979	−	1.90241i	−0.177917	−	0.0772802i
$607$	4.35349	−	6.16749i	0.176703	−	0.250331i	−0.718974	−	0.695037i	$-0.755388\pi$
$607$	4.35349	−	6.16749i	0.176703	−	0.250331i	0.895676	+	0.444707i	$0.146692\pi$
$608$	−5.66901	+	15.9511i	−0.229909	+	0.646902i
$609$	2.36729	+	4.56866i	0.0959274	+	0.185131i
$610$	7.27188			0.294430
$611$	10.7947	+	17.6499i	0.436705	+	0.714039i
$612$	34.3363			1.38796
$613$	−13.5675	−	26.1840i	−0.547985	−	1.05756i	−0.987246	−	0.159203i	$-0.949108\pi$
$613$	−13.5675	−	26.1840i	−0.547985	−	1.05756i	0.439261	−	0.898359i	$-0.355240\pi$
$614$	6.51465	−	18.3305i	0.262910	−	0.739758i
$615$	−0.330313	+	0.467946i	−0.0133195	+	0.0188694i
$616$	−0.512184	−	0.222473i	−0.0206365	−	0.00896369i
$617$	−9.50247	+	1.30608i	−0.382555	+	0.0525810i	−0.324882	−	0.945755i	$-0.605325\pi$
$617$	−9.50247	+	1.30608i	−0.382555	+	0.0525810i	−0.0576730	+	0.998336i	$0.518368\pi$
$618$	13.2385	+	8.05053i	0.532532	+	0.323840i
$619$	−28.2895	−	3.88830i	−1.13705	−	0.156284i	−0.457012	−	0.889460i	$-0.651081\pi$
$619$	−28.2895	−	3.88830i	−1.13705	−	0.156284i	−0.680039	+	0.733176i	$0.738037\pi$
$620$	−7.68101	−	6.24896i	−0.308477	−	0.250964i
$621$	0.199399	+	2.91511i	0.00800161	+	0.116979i
$622$	28.0039	−	7.84633i	1.12285	−	0.314609i
$623$	−0.529240	−	0.749762i	−0.0212036	−	0.0300386i
$624$	1.72633	+	8.30758i	0.0691087	+	0.332569i
$625$	−0.943624	+	13.7953i	−0.0377450	+	0.551812i
$626$	−4.70667	+	5.03961i	−0.188116	+	0.201423i
$627$	1.94332	+	5.46798i	0.0776087	+	0.218370i
$628$	−14.0390	−	3.93355i	−0.560218	−	0.156966i
$629$	7.56044	−	36.3828i	0.301454	−	1.45068i
$630$	−3.32719	+	1.44520i	−0.132558	+	0.0575782i
$631$	−16.1383	+	9.81389i	−0.642454	+	0.390685i	−0.802692	−	0.596394i	$-0.796600\pi$
$631$	−16.1383	+	9.81389i	−0.642454	+	0.390685i	0.160238	+	0.987078i	$0.448774\pi$
$632$	1.07174	−	0.871927i	0.0426316	−	0.0346834i
$633$	10.1740	+	10.8937i	0.404381	+	0.432986i
$634$	−0.261782	+	0.505217i	−0.0103967	+	0.0200647i
$635$	5.82584	−	11.2434i	0.231192	−	0.446179i
$636$	−7.94079	−	8.50251i	−0.314873	−	0.337146i
$637$	14.8399	−	12.0732i	0.587980	−	0.478357i
$638$	63.5868	−	38.6680i	2.51743	−	1.53088i
$639$	6.73517	−	2.92550i	0.266439	−	0.115731i
$640$	−0.246900	+	1.18815i	−0.00975958	+	0.0469657i
$641$	5.41579	+	1.51743i	0.213911	+	0.0599351i	0.375083	−	0.926991i	$-0.377614\pi$
$641$	5.41579	+	1.51743i	0.213911	+	0.0599351i	−0.161172	+	0.986926i	$0.551527\pi$
$642$	−1.54511	−	4.34751i	−0.0609805	−	0.171583i
$643$	−20.4024	+	21.8457i	−0.804593	+	0.861509i	−0.992696	−	0.120641i	$-0.961505\pi$
$643$	−20.4024	+	21.8457i	−0.804593	+	0.861509i	0.188103	+	0.982149i	$0.439766\pi$
$644$	0.0828750	−	1.21159i	0.00326573	−	0.0477433i
$645$	0.521964	+	2.51183i	0.0205523	+	0.0989032i
$646$	−17.2448	−	24.4304i	−0.678489	−	0.961199i
$647$	32.8734	−	9.21069i	1.29239	−	0.362109i	0.446169	−	0.894949i	$-0.352788\pi$
$647$	32.8734	−	9.21069i	1.29239	−	0.362109i	0.846217	+	0.532839i	$0.178875\pi$
$648$	−0.0596908	−	0.872648i	−0.00234488	−	0.0342809i
$649$	13.1969	+	10.7364i	0.518022	+	0.421442i
$650$	−24.9231	−	3.42560i	−0.977565	−	0.134363i
$651$	−2.73627	−	1.66396i	−0.107243	−	0.0652158i
$652$	−14.2611	+	1.96014i	−0.558508	+	0.0767652i
$653$	−1.97586	−	0.858239i	−0.0773215	−	0.0335855i	0.359386	−	0.933189i	$-0.382986\pi$
$653$	−1.97586	−	0.858239i	−0.0773215	−	0.0335855i	−0.436708	+	0.899603i	$0.643856\pi$
$654$	−4.74461	+	6.72158i	−0.185529	+	0.262835i
$655$	−3.46817	+	9.75849i	−0.135513	+	0.381296i
$656$	1.83442	+	3.54027i	0.0716220	+	0.138224i
$657$	14.1713			0.552876
$658$	−3.00127	−	10.6079i	−0.117002	−	0.413538i
$659$	9.04882			0.352492			0.176246	−	0.984346i	$-0.443605\pi$
$659$	9.04882			0.352492			0.176246	+	0.984346i	$0.443605\pi$
$660$	−2.11305	−	4.07800i	−0.0822502	−	0.158736i
$661$	14.7598	−	41.5302i	0.574092	−	1.61534i	−0.198264	−	0.980149i	$-0.563530\pi$
$661$	14.7598	−	41.5302i	0.574092	−	1.61534i	0.772356	−	0.635190i	$-0.219078\pi$
$662$	−8.00880	+	11.3459i	−0.311271	+	0.440970i
$663$	−13.1762	−	5.72325i	−0.511723	−	0.222273i
$664$	2.82394	−	0.388142i	0.109590	−	0.0150628i
$665$	1.31979	+	0.802581i	0.0511792	+	0.0311228i
$666$	26.2743	+	3.61132i	1.01811	+	0.139936i
$667$	−5.68026	−	4.62124i	−0.219941	−	0.178935i
$668$	−0.511568	−	7.47887i	−0.0197932	−	0.289366i
$669$	9.50515	−	2.66322i	0.367490	−	0.102966i
$670$	12.0892	+	17.1265i	0.467046	+	0.661654i
$671$	−3.38381	−	16.2838i	−0.130630	−	0.628628i
$672$	0.295718	−	4.32324i	0.0114076	−	0.166773i
$673$	−13.6092	+	14.5719i	−0.524597	+	0.561707i	−0.937015	−	0.349288i	$-0.886423\pi$
$673$	−13.6092	+	14.5719i	−0.524597	+	0.561707i	0.412418	+	0.910995i	$0.364684\pi$
$674$	−2.54709	−	7.16683i	−0.0981103	−	0.276056i
$675$	−15.1850	−	4.25464i	−0.584472	−	0.163761i
$676$	−1.51542	+	7.29260i	−0.0582854	+	0.280485i
$677$	3.92823	−	1.70627i	0.150974	−	0.0655774i	−0.321562	−	0.946888i	$-0.604208\pi$
$677$	3.92823	−	1.70627i	0.150974	−	0.0655774i	0.472537	+	0.881311i	$0.343338\pi$
$678$	−17.9813	+	10.9347i	−0.690568	+	0.419944i
$679$	−4.48563	+	3.64933i	−0.172143	+	0.140048i
$680$	−0.730894	−	0.782596i	−0.0280285	−	0.0300112i
$681$	6.74555	−	13.0183i	0.258490	−	0.498863i
$682$	−21.3094	+	41.1253i	−0.815979	+	1.57477i
$683$	−6.69445	−	7.16800i	−0.256156	−	0.274276i	0.589776	−	0.807567i	$-0.299216\pi$
$683$	−6.69445	−	7.16800i	−0.256156	−	0.274276i	−0.845932	+	0.533291i	$0.820955\pi$
$684$	8.09465	−	6.58548i	0.309507	−	0.251802i
$685$	−10.8548	+	6.60094i	−0.414740	+	0.252209i
$686$	−19.6744	+	8.54579i	−0.751171	+	0.326280i
$687$	2.62843	−	12.6487i	0.100281	−	0.482579i
$688$	17.1968	+	4.81832i	0.655623	+	0.183697i
$689$	−9.10378	−	25.6156i	−0.346826	−	0.975876i
$690$	−0.630876	+	0.675503i	−0.0240170	+	0.0257160i
$691$	0.669638	−	9.78976i	0.0254742	−	0.372420i	−0.967400	−	0.253253i	$-0.918499\pi$
$691$	0.669638	−	9.78976i	0.0254742	−	0.372420i	0.992874	−	0.119167i	$-0.0380223\pi$
$692$	−5.96101	−	28.6860i	−0.226604	−	1.09048i
$693$	4.78445	+	6.77802i	0.181746	+	0.257476i
$694$	−6.47966	+	1.81552i	−0.245965	+	0.0689160i
$695$	1.33143	+	19.4649i	0.0505042	+	0.738345i
$696$	−0.840932	−	0.684149i	−0.0318755	−	0.0259326i
$697$	−6.68780	−	0.919216i	−0.253318	−	0.0348178i
$698$	−10.7121	−	6.51419i	−0.405460	−	0.246566i
$699$	−1.26927	+	0.174457i	−0.0480082	+	0.00659858i
$700$	6.01168	+	2.61124i	0.227220	+	0.0986957i
$701$	−15.7348	+	22.2912i	−0.594296	+	0.841926i	−0.997312	−	0.0732670i	$-0.976657\pi$
$701$	−15.7348	+	22.2912i	−0.594296	+	0.841926i	0.403016	+	0.915193i	$0.367962\pi$
$702$	7.48163	−	21.0513i	0.282376	−	0.794530i
$703$	−5.19565	−	10.0272i	−0.195958	−	0.378181i
$704$	−29.2547			−1.10258
$705$	−1.62485	+	3.76695i	−0.0611955	+	0.141871i
$706$	19.3384			0.727812
$707$	1.33743	+	2.58111i	0.0502990	+	0.0970728i
$708$	−1.83427	+	5.16115i	−0.0689363	+	0.193968i
$709$	1.80274	−	2.55390i	0.0677032	−	0.0959136i	−0.781710	−	0.623643i	$-0.785652\pi$
$709$	1.80274	−	2.55390i	0.0677032	−	0.0959136i	0.849413	+	0.527729i	$0.176956\pi$
$710$	4.64252	+	2.01653i	0.174231	+	0.0756790i
$711$	−20.3360	+	2.79512i	−0.762661	+	0.104825i
$712$	0.165203	+	0.100462i	0.00619124	+	0.00376498i
$713$	4.51502	+	0.620576i	0.169089	+	0.0232407i
$714$	5.93783	+	4.83078i	0.222218	+	0.180788i
$715$	−0.732403	−	10.7074i	−0.0273903	−	0.400432i
$716$	−31.8567	+	8.92583i	−1.19054	+	0.333574i
$717$	−8.94876	−	12.6775i	−0.334197	−	0.473450i
$718$	8.12645	+	39.1066i	0.303277	+	1.45945i
$719$	−3.08942	+	45.1657i	−0.115216	+	1.68439i	0.477225	+	0.878781i	$0.341643\pi$
$719$	−3.08942	+	45.1657i	−0.115216	+	1.68439i	−0.592441	+	0.805614i	$0.701836\pi$
$720$	6.41396	−	6.86768i	0.239034	−	0.255943i
$721$	−3.15881	−	8.88804i	−0.117640	−	0.331008i
$722$	27.4417	+	7.68882i	1.02128	+	0.286148i
$723$	−1.20671	+	5.80700i	−0.0448780	+	0.215965i
$724$	−23.6744	+	10.2832i	−0.879852	+	0.382173i
$725$	33.7673	−	20.5344i	1.25409	−	0.762627i
$726$	−5.27244	+	4.28945i	−0.195679	+	0.159196i
$727$	−15.7619	−	16.8769i	−0.584577	−	0.625929i	0.368147	−	0.929768i	$-0.379992\pi$
$727$	−15.7619	−	16.8769i	−0.584577	−	0.625929i	−0.952723	+	0.303839i	$0.901732\pi$
$728$	0.193280	−	0.373013i	0.00716343	−	0.0138248i
$729$	−2.49258	+	4.81047i	−0.0923179	+	0.178165i
$730$	6.66733	+	7.13896i	0.246769	+	0.264225i
$731$	−23.4546	+	19.0817i	−0.867498	+	0.705762i
$732$	4.57521	−	2.78225i	0.169105	−	0.102835i
$733$	38.2175	−	16.6002i	1.41160	−	0.613143i	0.451363	−	0.892341i	$-0.350938\pi$
$733$	38.2175	−	16.6002i	1.41160	−	0.613143i	0.960234	+	0.279198i	$0.0900685\pi$
$734$	−13.8698	+	66.7453i	−0.511945	+	2.46362i
$735$	3.65275	+	1.02345i	0.134734	+	0.0377506i
$736$	2.06513	+	5.81073i	0.0761218	+	0.214186i
$737$	32.7256	−	35.0405i	1.20546	−	1.29074i
$738$	0.328791	−	4.80676i	0.0121030	−	0.176939i
$739$	3.85297	+	18.5415i	0.141734	+	0.682060i	0.988638	+	0.150315i	$0.0480288\pi$
$739$	3.85297	+	18.5415i	0.141734	+	0.682060i	−0.846904	+	0.531745i	$0.821536\pi$
$740$	5.15455	+	7.30233i	0.189485	+	0.268439i
$741$	−4.20393	+	1.17789i	−0.154435	+	0.0432707i
$742$	0.988537	+	14.4519i	0.0362903	+	0.530546i
$743$	−13.9709	−	11.3662i	−0.512543	−	0.416985i	0.339382	−	0.940649i	$-0.389782\pi$
$743$	−13.9709	−	11.3662i	−0.512543	−	0.416985i	−0.851925	+	0.523664i	$0.824565\pi$
$744$	0.668425	+	0.0918729i	0.0245056	+	0.00336822i
$745$	−1.28524	−	0.781570i	−0.0470874	−	0.0286345i
$746$	50.3356	−	6.91847i	1.84292	−	0.253303i
$747$	−38.8445	−	16.8725i	−1.42124	−	0.617334i
$748$	31.2163	−	44.2235i	1.14138	−	1.61697i
$749$	−0.940643	+	2.64672i	−0.0343703	+	0.0967089i
$750$	−5.01809	−	9.68448i	−0.183235	−	0.353627i
$751$	30.8610			1.12613			0.563067	−	0.826411i	$-0.309621\pi$
$751$	30.8610			1.12613			0.563067	+	0.826411i	$0.309621\pi$
$752$	18.0790	+	22.1071i	0.659272	+	0.806163i
$753$	−0.245251			−0.00893744
$754$	25.7588	+	49.7123i	0.938081	+	1.81041i
$755$	−2.66192	+	7.48993i	−0.0968773	+	0.272587i
$756$	−3.35663	+	4.75526i	−0.122079	+	0.172947i
$757$	−43.8118	−	19.0301i	−1.59237	−	0.691662i	−0.598385	−	0.801209i	$-0.704191\pi$
$757$	−43.8118	−	19.0301i	−1.59237	−	0.691662i	−0.993982	+	0.109546i	$0.965060\pi$
$758$	−21.4365	+	2.94638i	−0.778609	+	0.107017i
$759$	1.80621	+	1.09838i	0.0655611	+	0.0398686i
$760$	−0.322402	−	0.0443132i	−0.0116948	−	0.00160741i
$761$	35.0467	+	28.5126i	1.27044	+	1.03358i	0.997436	+	0.0715699i	$0.0228009\pi$
$761$	35.0467	+	28.5126i	1.27044	+	1.03358i	0.273007	+	0.962012i	$0.411982\pi$
$762$	−1.30147	−	19.0268i	−0.0471471	−	0.689267i
$763$	4.82304	−	1.35135i	0.174606	−	0.0489222i
$764$	11.0564	+	15.6633i	0.400006	+	0.566679i
$765$	3.23689	+	15.5768i	0.117030	+	0.563180i
$766$	0.940236	−	13.7458i	0.0339721	−	0.496654i
$767$	−8.73611	+	9.35409i	−0.315443	+	0.337757i
$768$	3.90895	+	10.9987i	0.141052	+	0.396882i
$769$	−3.61218	−	1.01209i	−0.130259	−	0.0364968i	0.204050	−	0.978961i	$-0.434590\pi$
$769$	−3.61218	−	1.01209i	−0.130259	−	0.0364968i	−0.334308	+	0.942464i	$0.608503\pi$
$770$	−1.16351	+	5.59914i	−0.0419302	+	0.201779i
$771$	5.20202	−	2.25956i	0.187346	−	0.0813760i
$772$	17.9444	−	10.9122i	0.645833	−	0.392740i
$773$	1.20080	−	0.976924i	0.0431898	−	0.0351375i	−0.609248	−	0.792979i	$-0.708529\pi$
$773$	1.20080	−	0.976924i	0.0431898	−	0.0351375i	0.652438	+	0.757842i	$0.273746\pi$
$774$	−14.7293	−	15.7712i	−0.529434	−	0.566886i
$775$	−11.3162	+	21.8393i	−0.406490	+	0.784490i
$776$	0.560494	−	1.08170i	0.0201206	−	0.0388309i
$777$	1.97316	+	2.11273i	0.0707866	+	0.0757939i
$778$	−8.85637	+	7.20519i	−0.317516	+	0.258319i
$779$	−1.75292	+	1.06597i	−0.0628049	+	0.0381925i
$780$	3.16935	−	1.37664i	0.113481	−	0.0492917i
$781$	2.35528	−	11.3342i	0.0842787	−	0.405571i
$782$	−10.4895	−	2.93901i	−0.375102	−	0.105099i
$783$	11.7532	+	33.0703i	0.420025	+	1.18184i
$784$	18.0242	−	19.2992i	0.643722	−	0.689258i
$785$	0.461006	−	6.73966i	0.0164540	−	0.240549i
$786$	3.17337	+	15.2711i	0.113190	+	0.544702i
$787$	−13.1549	−	18.6363i	−0.468922	−	0.664312i	0.511938	−	0.859022i	$-0.328928\pi$
$787$	−13.1549	−	18.6363i	−0.468922	−	0.664312i	−0.980861	+	0.194710i	$0.937623\pi$
$788$	−12.2470	+	3.43146i	−0.436283	+	0.122241i
$789$	−0.465374	−	6.80353i	−0.0165678	−	0.242212i
$790$	−10.9758	−	8.92945i	−0.390500	−	0.317696i
$791$	12.6927	+	1.74457i	0.451299	+	0.0620296i
$792$	−1.49347	−	0.908200i	−0.0530682	−	0.0322715i
$793$	12.3960	−	1.70379i	0.440196	−	0.0605035i
$794$	41.6973	+	18.1117i	1.47978	+	0.642759i
$795$	3.10861	−	4.40390i	0.110251	−	0.156190i
$796$	15.8176	−	44.5065i	0.560641	−	1.57749i
$797$	6.43718	+	12.4232i	0.228017	+	0.440052i	0.974199	−	0.225689i	$-0.0724634\pi$
$797$	6.43718	+	12.4232i	0.228017	+	0.440052i	−0.746183	+	0.665741i	$0.768116\pi$
$798$	2.32633			0.0823513
$799$	−48.2291	+	3.42207i	−1.70622	+	0.121064i
$800$	−33.2826			−1.17672
$801$	−1.32162	−	2.55061i	−0.0466971	−	0.0901212i
$802$	−17.5009	+	49.2428i	−0.617978	+	1.73882i
$803$	12.8837	−	18.2520i	0.454654	−	0.644099i
$804$	14.1588	+	6.15002i	0.499341	+	0.216895i
$805$	0.557455	−	0.0766204i	0.0196477	−	0.00270051i
$806$	−29.7738	−	18.1058i	−1.04874	−	0.637751i
$807$	−7.44242	−	1.02294i	−0.261986	−	0.0360091i
$808$	−0.475094	−	0.386517i	−0.0167137	−	0.0135976i
$809$	1.17371	+	17.1590i	0.0412653	+	0.603278i	0.971609	+	0.236590i	$0.0760299\pi$
$809$	1.17371	+	17.1590i	0.0412653	+	0.603278i	−0.930344	+	0.366688i	$0.880492\pi$
$810$	−8.62554	+	2.41676i	−0.303071	+	0.0849164i
$811$	6.10866	+	8.65400i	0.214504	+	0.303883i	0.909968	−	0.414678i	$-0.136106\pi$
$811$	6.10866	+	8.65400i	0.214504	+	0.303883i	−0.695464	+	0.718561i	$0.744801\pi$
$812$	−2.96782	−	14.2819i	−0.104150	−	0.501198i
$813$	1.23720	−	18.0872i	0.0433905	−	0.634346i
$814$	28.5381	−	30.5569i	1.00026	−	1.07102i
$815$	−2.23362	−	6.28482i	−0.0782405	−	0.220148i
$816$	−19.0941	−	5.34991i	−0.668426	−	0.187284i
$817$	−1.86957	+	8.99687i	−0.0654080	+	0.314761i
$818$	49.6095	−	21.5485i	1.73456	−	0.753424i
$819$	−5.33309	+	3.24312i	−0.186353	+	0.113324i
$820$	1.25958	−	1.02474i	0.0439864	−	0.0357856i
$821$	0.237483	+	0.254282i	0.00828821	+	0.00887451i	0.734967	−	0.678103i	$-0.237198\pi$
$821$	0.237483	+	0.254282i	0.00828821	+	0.00887451i	−0.726678	+	0.686978i	$0.758937\pi$
$822$	−8.80254	+	16.9881i	−0.307024	+	0.592529i
$823$	13.5778	−	26.2039i	0.473291	−	0.913411i	−0.524774	−	0.851241i	$-0.675850\pi$
$823$	13.5778	−	26.2039i	0.473291	−	0.913411i	0.998066	−	0.0621694i	$-0.0198019\pi$
$824$	1.35644	+	1.45239i	0.0472538	+	0.0505965i
$825$	−8.85021	+	7.20018i	−0.308125	+	0.250678i
$826$	5.82718	−	3.54358i	0.202753	−	0.123297i
$827$	−22.8275	+	9.91536i	−0.793788	+	0.344791i	−0.756064	−	0.654497i	$-0.772880\pi$
$827$	−22.8275	+	9.91536i	−0.793788	+	0.344791i	−0.0377239	+	0.999288i	$0.512011\pi$
$828$	0.773408	−	3.72184i	0.0268778	−	0.129343i
$829$	−23.2201	−	6.50596i	−0.806467	−	0.225962i	−0.158232	−	0.987402i	$-0.550579\pi$
$829$	−23.2201	−	6.50596i	−0.806467	−	0.225962i	−0.648235	+	0.761440i	$0.724493\pi$
$830$	−9.77581	−	27.5065i	−0.339323	−	0.954765i
$831$	−0.373959	+	0.400412i	−0.0129725	+	0.0138901i
$832$	1.50197	−	21.9580i	0.0520714	−	0.761257i
$833$	9.09616	+	43.7731i	0.315163	+	1.51665i
$834$	16.9449	+	24.0055i	0.586754	+	0.831242i
$835$	3.34459	−	0.937110i	0.115744	−	0.0324300i
$836$	−1.12265	−	16.4126i	−0.0388278	−	0.567642i
$837$	−16.9443	−	13.7852i	−0.585680	−	0.476486i
$838$	−13.4017	−	1.84202i	−0.462953	−	0.0636315i
$839$	−33.6658	−	20.4726i	−1.16227	−	0.706793i	−0.200244	−	0.979746i	$-0.564174\pi$
$839$	−33.6658	−	20.4726i	−1.16227	−	0.706793i	−0.962027	+	0.272953i	$0.912000\pi$
$840$	0.0825282	−	0.0113432i	0.00284749	−	0.000391379i
$841$	−54.0753	−	23.4882i	−1.86466	−	0.809938i
$842$	−13.4672	+	19.0787i	−0.464112	+	0.657496i
$843$	−4.23620	+	11.9195i	−0.145903	+	0.410531i
$844$	−19.4406	−	37.5187i	−0.669175	−	1.29145i
$845$	−3.45117			−0.118724
$846$	−4.78565	−	34.1744i	−0.164534	−	1.17494i
$847$	4.13788			0.142179
$848$	−17.2639	−	33.3179i	−0.592846	−	1.14414i
$849$	1.47738	−	4.15694i	0.0507034	−	0.142666i
$850$	33.9045	−	48.0317i	1.16291	−	1.64747i
$851$	−3.77338	−	1.63901i	−0.129350	−	0.0561846i
$852$	3.69244	−	0.507515i	0.126501	−	0.0173872i
$853$	24.0075	+	14.5993i	0.822000	+	0.499869i	0.866522	−	0.499139i	$-0.166350\pi$
$853$	24.0075	+	14.5993i	0.822000	+	0.499869i	−0.0445217	+	0.999008i	$0.514176\pi$
$854$	−6.60523	−	0.907868i	−0.226026	−	0.0310666i
$855$	3.75061	+	3.05135i	0.128268	+	0.104354i
$856$	−0.0403849	−	0.590407i	−0.00138033	−	0.0201797i
$857$	−3.80159	+	1.06516i	−0.129860	+	0.0363850i	−0.334113	−	0.942533i	$-0.608437\pi$
$857$	−3.80159	+	1.06516i	−0.129860	+	0.0363850i	0.204253	+	0.978918i	$0.434524\pi$
$858$	−9.32116	−	13.2051i	−0.318219	−	0.450814i
$859$	−3.50863	−	16.8845i	−0.119713	−	0.576091i	−0.995611	−	0.0935934i	$-0.970165\pi$
$859$	−3.50863	−	16.8845i	−0.119713	−	0.576091i	0.875898	−	0.482497i	$-0.160270\pi$
$860$	0.496318	−	7.25591i	0.0169243	−	0.247425i
$861$	0.358453	−	0.383809i	0.0122160	−	0.0130802i
$862$	5.97674	+	16.8169i	0.203568	+	0.572787i
$863$	17.8769	+	5.00888i	0.608538	+	0.170504i	0.560242	−	0.828329i	$-0.310708\pi$
$863$	17.8769	+	5.00888i	0.608538	+	0.170504i	0.0482957	+	0.998833i	$0.484621\pi$
$864$	6.01352	−	28.9386i	0.204584	−	0.984513i
$865$	12.4515	−	5.40847i	0.423365	−	0.183893i
$866$	−1.89734	+	1.15380i	−0.0644741	+	0.0392076i
$867$	17.1415	−	13.9456i	0.582155	−	0.473618i
$868$	6.19669	+	6.63503i	0.210329	+	0.225208i
$869$	−14.8882	+	28.7330i	−0.505048	+	0.974699i
$870$	−5.10769	+	9.85740i	−0.173167	+	0.334197i
$871$	24.6206	+	26.3622i	0.834237	+	0.893249i
$872$	−0.818580	+	0.665964i	−0.0277206	+	0.0225524i
$873$	−15.4655	+	9.40476i	−0.523427	+	0.318303i
$874$	−3.03653	+	1.31895i	−0.102712	+	0.0446142i
$875$	−1.35100	+	6.50138i	−0.0456722	+	0.219787i
$876$	6.92625	+	1.94064i	0.234016	+	0.0655683i
$877$	−13.4651	−	37.8870i	−0.454682	−	1.27935i	−0.919200	−	0.393790i	$-0.871164\pi$
$877$	−13.4651	−	37.8870i	−0.454682	−	1.27935i	0.464518	−	0.885564i	$-0.346228\pi$
$878$	−43.3662	+	46.4339i	−1.46354	+	1.56707i
$879$	−0.378304	+	5.53061i	−0.0127599	+	0.186543i
$880$	−3.01407	−	14.5045i	−0.101604	−	0.488947i
$881$	27.3630	+	38.7645i	0.921882	+	1.30601i	0.951884	+	0.306459i	$0.0991443\pi$
$881$	27.3630	+	38.7645i	0.921882	+	1.30601i	−0.0300020	+	0.999550i	$0.509551\pi$
$882$	−30.7253	+	8.60882i	−1.03457	+	0.289874i
$883$	0.0625882	+	0.915008i	0.00210626	+	0.0307925i	0.998603	−	0.0528381i	$-0.0168267\pi$
$883$	0.0625882	+	0.915008i	0.00210626	+	0.0307925i	−0.996497	+	0.0836305i	$0.973348\pi$
$884$	31.5906	+	25.7009i	1.06251	+	0.864413i
$885$	−2.51429	−	0.345582i	−0.0845171	−	0.0116166i
$886$	7.83123	+	4.76228i	0.263095	+	0.159992i
$887$	35.9393	−	4.93975i	1.20672	−	0.165861i	0.495363	−	0.868686i	$-0.335035\pi$
$887$	35.9393	−	4.93975i	1.20672	−	0.165861i	0.711362	+	0.702826i	$0.248079\pi$
$888$	−0.558629	−	0.242647i	−0.0187464	−	0.00814269i
$889$	−6.69545	+	9.48529i	−0.224558	+	0.318127i
$890$	0.663101	−	1.86579i	0.0222272	−	0.0625413i
$891$	9.42552	+	18.1904i	0.315767	+	0.609402i
$892$	−27.9837			−0.936964
$893$	−10.7135	+	10.0568i	−0.358513	+	0.336537i
$894$	−2.26543			−0.0757674
$895$	−7.05237	−	13.6105i	−0.235735	−	0.454947i
$896$	0.372601	−	1.04840i	0.0124477	−	0.0350246i
$897$	−0.917154	+	1.29931i	−0.0306229	+	0.0433827i
$898$	−13.6077	−	5.91067i	−0.454096	−	0.197242i
$899$	54.2323	−	7.45406i	1.80875	−	0.248607i
$900$	17.5294	+	10.6599i	0.584313	+	0.355329i
$901$	62.9397	+	8.65086i	2.09682	+	0.288202i
$902$	−5.89196	−	4.79346i	−0.196181	−	0.159605i
$903$	−0.160520	−	2.34672i	−0.00534178	−	0.0780940i
$904$	−2.59917	+	0.728253i	−0.0864471	+	0.0242213i
$905$	−6.89682	−	9.77056i	−0.229258	−	0.324784i
$906$	2.43566	+	11.7210i	0.0809193	+	0.389405i
$907$	0.631798	−	9.23656i	0.0209785	−	0.306695i	−0.975324	−	0.220779i	$-0.929140\pi$
$907$	0.631798	−	9.23656i	0.0209785	−	0.306695i	0.996302	−	0.0859160i	$-0.0273817\pi$
$908$	−28.3707	+	30.3776i	−0.941514	+	1.00812i
$909$	3.04725	+	8.57413i	0.101071	+	0.284386i
$910$	−4.14287	−	1.16078i	−0.137335	−	0.0384794i
$911$	−8.82768	+	42.4811i	−0.292474	+	1.40746i	0.534475	+	0.845185i	$0.320510\pi$
$911$	−8.82768	+	42.4811i	−0.292474	+	1.40746i	−0.826949	+	0.562278i	$0.809925\pi$
$912$	−5.52743	+	2.40090i	−0.183032	+	0.0795018i
$913$	−57.0459	+	34.6904i	−1.88794	+	1.14808i
$914$	19.3805	−	15.7672i	0.641050	−	0.521533i
$915$	1.69348	+	1.81328i	0.0559849	+	0.0599451i
$916$	−16.8493	+	32.5176i	−0.556716	+	1.07441i
$917$	4.36854	−	8.43089i	0.144262	−	0.278413i
$918$	35.6369	+	38.1578i	1.17619	+	1.25939i
$919$	29.2187	−	23.7712i	0.963836	−	0.784139i	−0.0126057	−	0.999921i	$-0.504013\pi$
$919$	29.2187	−	23.7712i	0.963836	−	0.784139i	0.976442	+	0.215782i	$0.0692300\pi$
$920$	−0.101292	+	0.0615968i	−0.00333949	+	0.00203079i
$921$	6.08794	−	2.64436i	0.200604	−	0.0871348i
$922$	9.09931	−	43.7883i	0.299670	−	1.44209i
$923$	8.38635	+	2.34974i	0.276040	+	0.0773428i
$924$	1.41021	+	3.96795i	0.0463925	+	0.130536i
$925$	15.1550	−	16.2270i	0.498293	−	0.533541i
$926$	3.43329	−	50.1929i	0.112825	−	1.64944i
$927$	−6.00723	−	28.9084i	−0.197303	−	0.949476i
$928$	42.7162	+	60.5151i	1.40223	+	1.98650i
$929$	37.8096	−	10.5937i	1.24049	−	0.347570i	0.413875	−	0.910334i	$-0.364175\pi$
$929$	37.8096	−	10.5937i	1.24049	−	0.347570i	0.826617	+	0.562764i	$0.190262\pi$
$930$	−0.471537	−	6.89362i	−0.0154623	−	0.226051i
$931$	10.5398	+	8.57475i	0.345428	+	0.281026i
$932$	3.59824	+	0.494566i	0.117864	+	0.0162000i
$933$	8.47811	+	5.15565i	0.277561	+	0.168788i
$934$	−3.86815	+	0.531666i	−0.126570	+	0.0173966i
$935$	23.0049	+	9.99244i	0.752341	+	0.326788i
$936$	0.758354	−	1.07434i	0.0247876	−	0.0351160i
$937$	−3.70570	+	10.4269i	−0.121060	+	0.340630i	−0.987271	−	0.159049i	$-0.949157\pi$
$937$	−3.70570	+	10.4269i	−0.121060	+	0.340630i	0.866211	+	0.499679i	$0.166549\pi$
$938$	−8.84274	−	17.0657i	−0.288726	−	0.557215i
$939$	−2.35275			−0.0767790
$940$	7.31658	−	9.04010i	0.238641	−	0.294856i
$941$	−19.9463			−0.650231			−0.325116	−	0.945674i	$-0.605403\pi$
$941$	−19.9463			−0.650231			−0.325116	+	0.945674i	$0.605403\pi$
$942$	−4.68069	−	9.03332i	−0.152505	−	0.294322i
$943$	−0.250277	+	0.704211i	−0.00815013	+	0.0229323i
$944$	−10.1884	+	14.4336i	−0.331603	+	0.469774i
$945$	−2.47367	−	1.07447i	−0.0804685	−	0.0349524i
$946$	−33.7035	+	4.63244i	−1.09580	+	0.150614i
$947$	−46.2976	−	28.1542i	−1.50447	−	0.914888i	−0.998634	−	0.0522585i	$-0.983358\pi$
$947$	−46.2976	−	28.1542i	−1.50447	−	0.914888i	−0.505836	−	0.862630i	$-0.668816\pi$
$948$	−10.3220	−	1.41873i	−0.335244	−	0.0460782i
$949$	13.0381	+	10.6073i	0.423235	+	0.344328i
$950$	−1.21933	−	17.8259i	−0.0395602	−	0.578350i
$951$	−0.186942	+	0.0523788i	−0.00606203	+	0.00169850i
$952$	0.566185	+	0.802101i	0.0183502	+	0.0259962i
$953$	−7.69318	−	37.0216i	−0.249207	−	1.19925i	−0.898591	−	0.438788i	$-0.855408\pi$
$953$	−7.69318	−	37.0216i	−0.249207	−	1.19925i	0.649384	−	0.760461i	$-0.275027\pi$
$954$	−3.09430	+	45.2370i	−0.100182	+	1.46460i
$955$	−6.06343	+	6.49235i	−0.196208	+	0.210087i
$956$	14.7317	+	41.4509i	0.476456	+	1.34062i
$957$	24.4502	+	6.85064i	0.790364	+	0.221450i
$958$	−8.64475	+	41.6008i	−0.279299	+	1.34406i
$959$	10.6838	−	4.64062i	0.344997	−	0.149853i
$960$	3.72886	−	2.26757i	0.120348	−	0.0731855i
$961$	−2.38179	+	1.93773i	−0.0768320	+	0.0625074i
$962$	21.4702	+	22.9890i	0.692228	+	0.741195i
$963$	−4.04505	+	7.80660i	−0.130350	+	0.251564i
$964$	7.73546	−	14.9288i	0.249143	−	0.480823i
$965$	6.64199	+	7.11184i	0.213813	+	0.228938i
$966$	0.657374	−	0.534814i	0.0211507	−	0.0172073i
$967$	13.2375	−	8.04992i	0.425691	−	0.258868i	−0.290359	−	0.956918i	$-0.593775\pi$
$967$	13.2375	−	8.04992i	0.425691	−	0.258868i	0.716049	+	0.698050i	$0.245949\pi$
$968$	−0.799606	+	0.347318i	−0.0257003	+	0.0111632i
$969$	2.07583	−	9.98946i	0.0666854	−	0.320908i
$970$	−12.0139	−	3.36615i	−0.385744	−	0.108081i
$971$	7.04267	+	19.8162i	0.226010	+	0.635932i	0.999996	+	0.00272903i	$0.000868679\pi$
$971$	7.04267	+	19.8162i	0.226010	+	0.635932i	−0.773986	+	0.633203i	$0.781740\pi$
$972$	−19.1646	+	20.5203i	−0.614705	+	0.658188i
$973$	1.22075	−	17.8467i	0.0391353	−	0.572138i
$974$	4.82059	+	23.1979i	0.154462	+	0.743310i
$975$	−4.94994	−	7.01246i	−0.158525	−	0.224578i
$976$	16.6312	−	4.65983i	0.532351	−	0.149158i
$977$	−2.87424	−	42.0199i	−0.0919552	−	1.34434i	−0.783224	−	0.621739i	$-0.786426\pi$
$977$	−2.87424	−	42.0199i	−0.0919552	−	1.34434i	0.691269	−	0.722597i	$-0.257052\pi$
$978$	−7.79221	−	6.33943i	−0.249167	−	0.202713i
$979$	−4.48658	−	0.616667i	−0.143392	−	0.0197088i
$980$	−9.18834	−	5.58756i	−0.293511	−	0.178488i
$981$	15.5323	−	2.13487i	0.495909	−	0.0681612i
$982$	−49.5514	−	21.5232i	−1.58125	−	0.686833i
$983$	−10.2243	+	14.4845i	−0.326104	+	0.461984i	−0.946686	−	0.322158i	$-0.895592\pi$
$983$	−10.2243	+	14.4845i	−0.326104	+	0.461984i	0.620582	+	0.784141i	$0.286896\pi$
$984$	−0.0370521	+	0.104255i	−0.00118118	+	0.00332352i
$985$	−2.71122	−	5.23243i	−0.0863868	−	0.166719i
$986$	−130.847			−4.16700
$987$	1.94618	−	3.21875i	0.0619477	−	0.102454i
$988$	12.3766			0.393753
$989$	1.54004	+	2.97214i	0.0489703	+	0.0945084i
$990$	−5.99458	+	16.8671i	−0.190520	+	0.536073i
$991$	−17.3923	+	24.6393i	−0.552486	+	0.782694i	−0.993381	−	0.114864i	$-0.963357\pi$
$991$	−17.3923	+	24.6393i	−0.552486	+	0.782694i	0.440895	+	0.897559i	$0.354661\pi$
$992$	−42.2846	−	18.3668i	−1.34254	−	0.583147i
$993$	−4.69425	+	0.645210i	−0.148968	+	0.0204751i
$994$	−3.96516	−	2.41127i	−0.125767	−	0.0764807i
$995$	21.6817	+	2.98008i	0.687356	+	0.0944748i
$996$	−16.6747	−	13.5659i	−0.528358	−	0.429851i
$997$	1.50923	+	22.0642i	0.0477979	+	0.698781i	0.958388	+	0.285469i	$0.0921495\pi$
$997$	1.50923	+	22.0642i	0.0477979	+	0.698781i	−0.910590	+	0.413311i	$0.864372\pi$
$998$	70.8004	−	19.8373i	2.24115	−	0.627940i
$999$	11.3709	+	16.1089i	0.359760	+	0.509663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.2.c.a.21.1	yes	66
3.2	odd	2		423.2.i.a.397.3		66
4.3	odd	2		752.2.m.c.209.1		66
47.3	even	23		2209.2.a.l.1.5		33
47.9	even	23	inner	47.2.c.a.9.1	✓	66
47.44	odd	46		2209.2.a.m.1.5		33
141.56	odd	46		423.2.i.a.244.3		66
188.103	odd	46		752.2.m.c.385.1		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.2.c.a.9.1	✓	66	47.9	even	23	inner
47.2.c.a.21.1	yes	66	1.1	even	1	trivial
423.2.i.a.244.3		66	141.56	odd	46
423.2.i.a.397.3		66	3.2	odd	2
752.2.m.c.209.1		66	4.3	odd	2
752.2.m.c.385.1		66	188.103	odd	46
2209.2.a.l.1.5		33	47.3	even	23
2209.2.a.m.1.5		33	47.44	odd	46

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:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	47.c (of order \(23\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.910119 - 1.75645i) q^{2} +(0.226030 - 0.635987i) q^{3} +(-1.10344 + 1.56321i) q^{4} +(-0.813179 - 0.353213i) q^{5} +(-1.32279 + 0.181814i) q^{6} +(0.694533 + 0.422355i) q^{7} +(-0.169663 - 0.0233196i) q^{8} +(1.97374 + 1.60576i) q^{9} +(0.119688 + 1.74977i) q^{10} +(3.86254 - 1.08223i) q^{11} +(0.744774 + 1.05510i) q^{12} +(0.613996 + 2.95471i) q^{13} +(0.109737 - 1.60431i) q^{14} +(-0.408442 + 0.437334i) q^{15} +(1.39499 + 3.92513i) q^{16} +(-6.79109 - 1.90277i) q^{17} +(1.02409 - 4.92821i) q^{18} +(-1.96591 + 0.853916i) q^{19} +(1.44944 - 0.881424i) q^{20} +(0.425597 - 0.346249i) q^{21} +(-5.41626 - 5.79940i) q^{22} +(-0.359215 + 0.693253i) q^{23} +(-0.0531798 + 0.102632i) q^{24} +(-2.87627 - 3.07973i) q^{25} +(4.63099 - 3.76759i) q^{26} +(3.19746 - 1.94442i) q^{27} +(-1.42660 + 0.619662i) q^{28} +(-1.90811 + 9.18234i) q^{29} +(1.13989 + 0.319381i) q^{30} +(-1.95469 - 5.49997i) q^{31} +(5.39089 - 5.77224i) q^{32} +(0.184763 - 2.70114i) q^{33} +(2.83857 + 13.6599i) q^{34} +(-0.415598 - 0.588768i) q^{35} +(-4.68805 + 1.31353i) q^{36} +(0.359568 + 5.25669i) q^{37} +(3.28907 + 2.67586i) q^{38} +(2.01794 + 0.277359i) q^{39} +(0.129729 + 0.0788902i) q^{40} +(0.948271 - 0.130337i) q^{41} +(-0.995513 - 0.432412i) q^{42} +(2.47236 - 3.50254i) q^{43} +(-2.57031 + 7.23215i) q^{44} +(-1.03783 - 2.00292i) q^{45} +1.54459 q^{46} +(6.45396 - 2.31222i) q^{47} +2.81164 q^{48} +(-2.91646 - 5.62852i) q^{49} +(-2.79164 + 7.85493i) q^{50} +(-2.74513 + 3.88896i) q^{51} +(-5.29635 - 2.30053i) q^{52} +(-8.92430 + 1.22662i) q^{53} +(-6.32534 - 3.84652i) q^{54} +(-3.52320 - 0.484252i) q^{55} +(-0.107987 - 0.0878542i) q^{56} +(0.0987247 + 1.44330i) q^{57} +(17.8649 - 5.00551i) q^{58} +(2.44580 + 3.46491i) q^{59} +(-0.232957 - 1.12105i) q^{60} +(0.282947 - 4.13654i) q^{61} +(-7.88142 + 8.43894i) q^{62} +(0.692630 + 1.94887i) q^{63} +(-7.02264 - 1.96765i) q^{64} +(0.544355 - 2.61958i) q^{65} +(-4.91257 + 2.13383i) q^{66} +(10.2126 - 6.21044i) q^{67} +(10.4680 - 8.51633i) q^{68} +(0.359707 + 0.385152i) q^{69} +(-0.655898 + 1.26583i) q^{70} +(1.32772 - 2.56239i) q^{71} +(-0.297425 - 0.318465i) q^{72} +(4.32036 - 3.51487i) q^{73} +(8.90586 - 5.41578i) q^{74} +(-2.60879 + 1.13316i) q^{75} +(0.834406 - 4.01538i) q^{76} +(3.13975 + 0.879716i) q^{77} +(-1.34940 - 3.79684i) q^{78} +(-5.50650 + 5.89603i) q^{79} +(0.252031 - 3.68456i) q^{80} +(1.03914 + 5.00060i) q^{81} +(-1.09197 - 1.54697i) q^{82} +(-16.0272 + 4.49061i) q^{83} +(0.0716416 + 1.04736i) q^{84} +(4.85028 + 3.94600i) q^{85} +(-8.40217 - 1.15485i) q^{86} +(5.40855 + 3.28901i) q^{87} +(-0.680567 + 0.0935418i) q^{88} +(-1.03554 - 0.449797i) q^{89} +(-2.57348 + 3.64579i) q^{90} +(-0.821496 + 2.31147i) q^{91} +(-0.687332 - 1.32649i) q^{92} -3.93972 q^{93} +(-9.93517 - 9.23166i) q^{94} +1.90025 q^{95} +(-2.45256 - 4.73323i) q^{96} +(-2.38226 + 6.70305i) q^{97} +(-7.23188 + 10.2452i) q^{98} +(9.36147 + 4.06626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 21 q^{2} - 19 q^{3} - 19 q^{4} - 15 q^{5} - 3 q^{6} - 19 q^{7} - 5 q^{8} - 12 q^{9} + 3 q^{10} - 5 q^{11} + 16 q^{12} - 17 q^{13} + 6 q^{14} + 3 q^{15} + 3 q^{16} - 11 q^{17} - 3 q^{19} + 19 q^{20}+ \cdots - 101 q^{99}+O(q^{100}) \) 66 * q - 21 * q^2 - 19 * q^3 - 19 * q^4 - 15 * q^5 - 3 * q^6 - 19 * q^7 - 5 * q^8 - 12 * q^9 + 3 * q^10 - 5 * q^11 + 16 * q^12 - 17 * q^13 + 6 * q^14 + 3 * q^15 + 3 * q^16 - 11 * q^17 - 3 * q^19 + 19 * q^20 + 5 * q^21 + 9 * q^22 + 7 * q^23 + 50 * q^24 - 8 * q^25 + 3 * q^26 + 29 * q^27 + 17 * q^28 + 17 * q^29 + 39 * q^30 + 17 * q^31 + 30 * q^32 + 13 * q^33 + 41 * q^34 + 22 * q^35 - 35 * q^36 - 18 * q^37 - 7 * q^38 - 18 * q^39 - 57 * q^40 - 56 * q^41 - 50 * q^42 - 4 * q^43 - q^44 - 26 * q^45 - 84 * q^46 - 26 * q^47 - 158 * q^48 - 14 * q^49 - 37 * q^50 - 58 * q^51 - 21 * q^52 + 14 * q^53 - 36 * q^54 - 4 * q^55 - 43 * q^56 - 22 * q^57 + 29 * q^58 + 10 * q^59 + 7 * q^60 + 22 * q^61 + 89 * q^62 + 65 * q^63 + 135 * q^64 + 45 * q^65 + 89 * q^66 + 35 * q^67 + 60 * q^68 + 79 * q^69 + 151 * q^70 + 61 * q^71 + 145 * q^72 + 29 * q^73 + 73 * q^74 + 77 * q^75 + 95 * q^76 + 37 * q^77 + 35 * q^78 - 55 * q^79 + 14 * q^80 - 44 * q^81 - 84 * q^82 - 5 * q^83 - 56 * q^84 - 97 * q^85 - 113 * q^86 + 17 * q^87 - 121 * q^88 - 19 * q^89 - 127 * q^90 - 119 * q^91 - 76 * q^92 - 28 * q^93 - 159 * q^94 - 126 * q^95 - 119 * q^96 - 47 * q^97 - 44 * q^98 - 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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