LMFDB - Embedded newform 164.5.d.f.163.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [164,5,Mod(163,164)] 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("164.163"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(164, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	164.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,6,0,-162,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$16.9526739458$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.39
Character	$\chi$	$=$	164.163
Dual form			164.5.d.f.163.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.537197 + 3.96376i) q^{2} -11.6711 q^{3} +(-15.4228 + 4.25865i) q^{4} -0.283823 q^{5} +(-6.26970 - 46.2616i) q^{6} +88.0916 q^{7} +(-25.1654 - 58.8447i) q^{8} +55.2152 q^{9} +(-0.152469 - 1.12501i) q^{10} +91.8123 q^{11} +(180.002 - 49.7032i) q^{12} +185.258i q^{13} +(47.3226 + 349.174i) q^{14} +3.31253 q^{15} +(219.728 - 131.361i) q^{16} -98.4681i q^{17} +(29.6615 + 218.860i) q^{18} -9.27529 q^{19} +(4.37735 - 1.20870i) q^{20} -1028.13 q^{21} +(49.3213 + 363.922i) q^{22} -120.338i q^{23} +(293.708 + 686.784i) q^{24} -624.919 q^{25} +(-734.320 + 99.5203i) q^{26} +300.938 q^{27} +(-1358.62 + 375.151i) q^{28} -136.920i q^{29} +(1.77948 + 13.1301i) q^{30} +1330.53i q^{31} +(638.721 + 800.382i) q^{32} -1071.55 q^{33} +(390.304 - 52.8968i) q^{34} -25.0024 q^{35} +(-851.575 + 235.142i) q^{36} -1313.01 q^{37} +(-4.98266 - 36.7651i) q^{38} -2162.17i q^{39} +(7.14251 + 16.7015i) q^{40} +(979.684 + 1366.01i) q^{41} +(-552.308 - 4075.26i) q^{42} +2593.95i q^{43} +(-1416.01 + 390.996i) q^{44} -15.6713 q^{45} +(476.990 - 64.6451i) q^{46} +1262.49 q^{47} +(-2564.47 + 1533.13i) q^{48} +5359.13 q^{49} +(-335.705 - 2477.03i) q^{50} +1149.23i q^{51} +(-788.950 - 2857.21i) q^{52} +3827.50i q^{53} +(161.663 + 1192.85i) q^{54} -26.0584 q^{55} +(-2216.86 - 5183.73i) q^{56} +108.253 q^{57} +(542.720 - 73.5532i) q^{58} -1921.58i q^{59} +(-51.0886 + 14.1069i) q^{60} -1743.27 q^{61} +(-5273.91 + 714.758i) q^{62} +4864.00 q^{63} +(-2829.41 + 2961.70i) q^{64} -52.5805i q^{65} +(-575.635 - 4247.38i) q^{66} -5360.12 q^{67} +(419.341 + 1518.66i) q^{68} +1404.48i q^{69} +(-13.4312 - 99.1036i) q^{70} +4274.63 q^{71} +(-1389.51 - 3249.12i) q^{72} +105.236 q^{73} +(-705.343 - 5204.44i) q^{74} +7293.51 q^{75} +(143.051 - 39.5002i) q^{76} +8087.89 q^{77} +(8570.34 - 1161.51i) q^{78} +6153.05 q^{79} +(-62.3638 + 37.2832i) q^{80} -7984.71 q^{81} +(-4888.25 + 4617.05i) q^{82} +12363.0i q^{83} +(15856.7 - 4378.44i) q^{84} +27.9475i q^{85} +(-10281.8 + 1393.46i) q^{86} +1598.01i q^{87} +(-2310.49 - 5402.67i) q^{88} +7494.74i q^{89} +(-8.41860 - 62.1174i) q^{90} +16319.7i q^{91} +(512.476 + 1855.95i) q^{92} -15528.8i q^{93} +(678.206 + 5004.21i) q^{94} +2.63254 q^{95} +(-7454.59 - 9341.37i) q^{96} -15047.2i q^{97} +(2878.91 + 21242.3i) q^{98} +5069.43 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40}+ \cdots + 2902 q^{98}+O(q^{100}) $ 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$-1$

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 $

$2$	0.537197	+	3.96376i	0.134299	+	0.990941i
$2$	0.537197	+	3.96376i	0.134299	+	0.990941i
$3$	−11.6711			−1.29679			−0.648396	−	0.761303i	$-0.724560\pi$
$3$	−11.6711			−1.29679			−0.648396	+	0.761303i	$0.724560\pi$
$4$	−15.4228	+	4.25865i	−0.963927	+	0.266165i
$5$	−0.283823			−0.0113529			−0.00567645	−	0.999984i	$-0.501807\pi$
$5$	−0.283823			−0.0113529			−0.00567645	+	0.999984i	$0.501807\pi$
$6$	−6.26970	−	46.2616i	−0.174158	−	1.28504i
$7$	88.0916			1.79779			0.898894	−	0.438166i	$-0.144372\pi$
$7$	88.0916			1.79779			0.898894	+	0.438166i	$0.144372\pi$
$8$	−25.1654	−	58.8447i	−0.393209	−	0.919449i
$9$	55.2152			0.681669
$10$	−0.152469	−	1.12501i	−0.00152469	−	0.0112501i
$11$	91.8123			0.758779			0.379390	−	0.925237i	$-0.376134\pi$
$11$	91.8123			0.758779			0.379390	+	0.925237i	$0.376134\pi$
$12$	180.002	−	49.7032i	1.25001	−	0.345161i
$13$			185.258i			1.09620i	0.836412	+	0.548102i	$0.184649\pi$
$13$			185.258i			1.09620i	−0.836412	+	0.548102i	$0.815351\pi$
$14$	47.3226	+	349.174i	0.241442	+	1.78150i
$15$	3.31253			0.0147224
$16$	219.728	−	131.361i	0.858312	−	0.513128i
$17$		−	98.4681i		−	0.340720i	−0.985382	−	0.170360i	$-0.945507\pi$
$17$		−	98.4681i		−	0.340720i	0.985382	−	0.170360i	$-0.0544931\pi$
$18$	29.6615	+	218.860i	0.0915477	+	0.675494i
$19$	−9.27529			−0.0256933			−0.0128467	−	0.999917i	$-0.504089\pi$
$19$	−9.27529			−0.0256933			−0.0128467	+	0.999917i	$0.504089\pi$
$20$	4.37735	−	1.20870i	0.0109434	−	0.00302175i
$21$	−1028.13			−2.33136
$22$	49.3213	+	363.922i	0.101904	+	0.751905i
$23$		−	120.338i		−	0.227482i	−0.993510	−	0.113741i	$-0.963717\pi$
$23$		−	120.338i		−	0.227482i	0.993510	−	0.113741i	$-0.0362833\pi$
$24$	293.708	+	686.784i	0.509910	+	1.19233i
$25$	−624.919			−0.999871
$26$	−734.320	+	99.5203i	−1.08627	+	0.147219i
$27$	300.938			0.412809
$28$	−1358.62	+	375.151i	−1.73294	+	0.478509i
$29$		−	136.920i		−	0.162807i	−0.996681	−	0.0814033i	$-0.974060\pi$
$29$		−	136.920i		−	0.162807i	0.996681	−	0.0814033i	$-0.0259402\pi$
$30$	1.77948	+	13.1301i	0.00197720	+	0.0145890i
$31$			1330.53i			1.38453i	0.721644	+	0.692264i	$0.243387\pi$
$31$			1330.53i			1.38453i	−0.721644	+	0.692264i	$0.756613\pi$
$32$	638.721	+	800.382i	0.623750	+	0.781624i
$33$	−1071.55			−0.983979
$34$	390.304	−	52.8968i	0.337633	−	0.0457585i
$35$	−25.0024			−0.0204101
$36$	−851.575	+	235.142i	−0.657080	+	0.181437i
$37$	−1313.01			−0.959098			−0.479549	−	0.877515i	$-0.659200\pi$
$37$	−1313.01			−0.959098			−0.479549	+	0.877515i	$0.659200\pi$
$38$	−4.98266	−	36.7651i	−0.00345060	−	0.0254606i
$39$		−	2162.17i		−	1.42155i
$40$	7.14251	+	16.7015i	0.00446407	+	0.0104384i
$41$	979.684	+	1366.01i	0.582798	+	0.812617i
$41$	979.684	+	1366.01i	0.582798	+	0.812617i
$42$	−552.308	−	4075.26i	−0.313100	−	2.31024i
$43$			2593.95i			1.40289i	0.712722	+	0.701447i	$0.247462\pi$
$43$			2593.95i			1.40289i	−0.712722	+	0.701447i	$0.752538\pi$
$44$	−1416.01	+	390.996i	−0.731408	+	0.201961i
$45$	−15.6713			−0.00773893
$46$	476.990	−	64.6451i	0.225421	−	0.0305506i
$47$	1262.49			0.571521			0.285760	−	0.958301i	$-0.407754\pi$
$47$	1262.49			0.571521			0.285760	+	0.958301i	$0.407754\pi$
$48$	−2564.47	+	1533.13i	−1.11305	+	0.665421i
$49$	5359.13			2.23204
$50$	−335.705	−	2477.03i	−0.134282	−	0.990813i
$51$			1149.23i			0.441843i
$52$	−788.950	−	2857.21i	−0.291771	−	1.05666i
$53$			3827.50i			1.36258i	0.732012	+	0.681292i	$0.238582\pi$
$53$			3827.50i			1.36258i	−0.732012	+	0.681292i	$0.761418\pi$
$54$	161.663	+	1192.85i	0.0554400	+	0.409069i
$55$	−26.0584			−0.00861435
$56$	−2216.86	−	5183.73i	−0.706907	−	1.65297i
$57$	108.253			0.0333189
$58$	542.720	−	73.5532i	0.161332	−	0.0218648i
$59$		−	1921.58i		−	0.552021i	−0.961155	−	0.276010i	$-0.910988\pi$
$59$		−	1921.58i		−	0.552021i	0.961155	−	0.276010i	$-0.0890124\pi$
$60$	−51.0886	+	14.1069i	−0.0141913	+	0.00391858i
$61$	−1743.27			−0.468495			−0.234247	−	0.972177i	$-0.575263\pi$
$61$	−1743.27			−0.468495			−0.234247	+	0.972177i	$0.575263\pi$
$62$	−5273.91	+	714.758i	−1.37199	+	0.185941i
$63$	4864.00			1.22550
$64$	−2829.41	+	2961.70i	−0.690773	+	0.723071i
$65$		−	52.5805i		−	0.0124451i
$66$	−575.635	−	4247.38i	−0.132148	−	0.975065i
$67$	−5360.12			−1.19406			−0.597029	−	0.802220i	$-0.703652\pi$
$67$	−5360.12			−1.19406			−0.597029	+	0.802220i	$0.703652\pi$
$68$	419.341	+	1518.66i	0.0906879	+	0.328429i
$69$			1404.48i			0.294996i
$70$	−13.4312	−	99.1036i	−0.00274107	−	0.0202252i
$71$	4274.63			0.847974			0.423987	−	0.905668i	$-0.360630\pi$
$71$	4274.63			0.847974			0.423987	+	0.905668i	$0.360630\pi$
$72$	−1389.51	−	3249.12i	−0.268038	−	0.626760i
$73$	105.236			0.0197477			0.00987385	−	0.999951i	$-0.496857\pi$
$73$	105.236			0.0197477			0.00987385	+	0.999951i	$0.496857\pi$
$74$	−705.343	−	5204.44i	−0.128806	−	0.950410i
$75$	7293.51			1.29662
$76$	143.051	−	39.5002i	0.0247665	−	0.00683868i
$77$	8087.89			1.36412
$78$	8570.34	−	1161.51i	1.40867	−	0.190913i
$79$	6153.05			0.985908			0.492954	−	0.870055i	$-0.335917\pi$
$79$	6153.05			0.985908			0.492954	+	0.870055i	$0.335917\pi$
$80$	−62.3638	+	37.2832i	−0.00974434	+	0.00582550i
$81$	−7984.71			−1.21700
$82$	−4888.25	+	4617.05i	−0.726986	+	0.686652i
$83$			12363.0i			1.79461i	0.441415	+	0.897303i	$0.354477\pi$
$83$			12363.0i			1.79461i	−0.441415	+	0.897303i	$0.645523\pi$
$84$	15856.7	−	4378.44i	2.24726	−	0.620527i
$85$			27.9475i			0.00386816i
$86$	−10281.8	+	1393.46i	−1.39018	+	0.188408i
$87$			1598.01i			0.211126i
$88$	−2310.49	−	5402.67i	−0.298359	−	0.697659i
$89$			7494.74i			0.946186i	0.881012	+	0.473093i	$0.156863\pi$
$89$			7494.74i			0.946186i	−0.881012	+	0.473093i	$0.843137\pi$
$90$	−8.41860	−	62.1174i	−0.00103933	−	0.00766882i
$91$			16319.7i			1.97074i
$92$	512.476	+	1855.95i	0.0605477	+	0.219276i
$93$		−	15528.8i		−	1.79545i
$94$	678.206	+	5004.21i	0.0767549	+	0.566343i
$95$	2.63254			0.000291694
$96$	−7454.59	−	9341.37i	−0.808875	−	1.01360i
$97$		−	15047.2i		−	1.59924i	−0.600507	−	0.799620i	$-0.705034\pi$
$97$		−	15047.2i		−	1.59924i	0.600507	−	0.799620i	$-0.294966\pi$
$98$	2878.91	+	21242.3i	0.299762	+	2.21182i
$99$	5069.43			0.517236
$100$	9638.03	−	2661.31i	0.963803	−	0.266131i
$101$		−	3321.58i		−	0.325613i	−0.986658	−	0.162807i	$-0.947945\pi$
$101$		−	3321.58i		−	0.325613i	0.986658	−	0.162807i	$-0.0520547\pi$
$102$	−4555.29	+	617.365i	−0.437840	+	0.0593392i
$103$		−	10434.1i		−	0.983515i	−0.870732	−	0.491757i	$-0.836355\pi$
$103$		−	10434.1i		−	0.983515i	0.870732	−	0.491757i	$-0.163645\pi$
$104$	10901.5	−	4662.10i	1.00790	−	0.431037i
$105$	291.806			0.0264677
$106$	−15171.3	+	2056.12i	−1.35024	+	0.182994i
$107$			14089.4i			1.23062i	0.788284	+	0.615312i	$0.210970\pi$
$107$			14089.4i			1.23062i	−0.788284	+	0.615312i	$0.789030\pi$
$108$	−4641.31	+	1281.59i	−0.397918	+	0.109875i
$109$			6676.06i			0.561911i	0.959721	+	0.280955i	$0.0906513\pi$
$109$			6676.06i			0.561911i	−0.959721	+	0.280955i	$0.909349\pi$
$110$	−13.9985	−	103.289i	−0.00115690	−	0.00853631i
$111$	15324.3			1.24375
$112$	19356.2	−	11571.8i	1.54306	−	0.922496i
$113$	7660.91			0.599962			0.299981	−	0.953945i	$-0.403020\pi$
$113$	7660.91			0.599962			0.299981	+	0.953945i	$0.403020\pi$
$114$	58.1533	+	429.090i	0.00447471	+	0.0330171i
$115$			34.1546i			0.00258258i
$116$	583.095	+	2111.70i	0.0433335	+	0.156934i
$117$			10229.1i			0.747248i
$118$	7616.71	−	1032.27i	0.547020	−	0.0741361i
$119$		−	8674.22i		−	0.612543i
$120$	−83.3611	−	194.925i	−0.00578896	−	0.0135365i
$121$	−6211.50			−0.424254
$122$	−936.480	−	6909.91i	−0.0629186	−	0.464251i
$123$	−11434.0	−	15942.9i	−0.755768	−	1.05379i
$124$	−5666.26	−	20520.6i	−0.368514	−	1.33458i
$125$	354.756			0.0227044
$126$	2612.93	+	19279.7i	0.164583	+	1.21439i
$127$		−	23909.3i		−	1.48238i	−0.671296	−	0.741189i	$-0.734262\pi$
$127$		−	23909.3i		−	1.48238i	0.671296	−	0.741189i	$-0.265738\pi$
$128$	−13259.4	−	9624.08i	−0.809291	−	0.587407i
$129$		−	30274.3i		−	1.81926i
$130$	208.417	−	28.2461i	0.0123324	−	0.00167137i
$131$			19433.2i			1.13240i	0.824267	+	0.566201i	$0.191588\pi$
$131$			19433.2i			1.13240i	−0.824267	+	0.566201i	$0.808412\pi$
$132$	16526.4	−	4563.37i	0.948484	−	0.261901i
$133$	−817.076			−0.0461912
$134$	−2879.44	−	21246.3i	−0.160361	−	1.18324i
$135$	−85.4129			−0.00468658
$136$	−5794.33	+	2477.99i	−0.313275	+	0.133974i
$137$			13314.3i			0.709375i	0.934985	+	0.354687i	$0.115413\pi$
$137$			13314.3i			0.709375i	−0.934985	+	0.354687i	$0.884587\pi$
$138$	−5567.02	+	754.482i	−0.292324	+	0.0396178i
$139$		−	29105.8i		−	1.50643i	−0.657772	−	0.753217i	$-0.728501\pi$
$139$		−	29105.8i		−	1.50643i	0.657772	−	0.753217i	$-0.271499\pi$
$140$	385.608	−	106.476i	0.0196739	−	0.00543247i
$141$	−14734.7			−0.741144
$142$	2296.32	+	16943.6i	0.113882	+	0.840292i
$143$			17009.0i			0.831776i
$144$	12132.3	−	7253.12i	0.585085	−	0.349784i
$145$			38.8611i			0.00184833i
$146$	56.5322	+	417.129i	0.00265210	+	0.0195688i
$147$	−62547.1			−2.89450
$148$	20250.3	−	5591.63i	0.924501	−	0.255279i
$149$			14318.6i			0.644954i	0.946577	+	0.322477i	$0.104515\pi$
$149$			14318.6i			0.644954i	−0.946577	+	0.322477i	$0.895485\pi$
$150$	3918.06	+	28909.8i	0.174136	+	1.28488i
$151$	13902.8			0.609745			0.304872	−	0.952393i	$-0.401386\pi$
$151$	13902.8			0.609745			0.304872	+	0.952393i	$0.401386\pi$
$152$	233.416	+	545.802i	0.0101029	+	0.0236237i
$153$		−	5436.94i		−	0.232258i
$154$	4344.80	+	32058.5i	0.183201	+	1.35177i
$155$		−	377.635i		−	0.0157184i
$156$	9207.93	+	33346.9i	0.378367	+	1.37027i
$157$			3348.74i			0.135857i	0.997690	+	0.0679286i	$0.0216390\pi$
$157$			3348.74i			0.135857i	−0.997690	+	0.0679286i	$0.978361\pi$
$158$	3305.40	+	24389.2i	0.132407	+	0.976976i
$159$		−	44671.2i		−	1.76699i
$160$	−181.283	−	227.167i	−0.00708138	−	0.00887370i
$161$		−	10600.7i		−	0.408964i
$162$	−4289.37	−	31649.5i	−0.163442	−	1.20597i
$163$			36435.5i			1.37135i	0.727907	+	0.685676i	$0.240493\pi$
$163$			36435.5i			1.37135i	−0.727907	+	0.685676i	$0.759507\pi$
$164$	−20926.9	−	16895.6i	−0.778066	−	0.628183i
$165$	304.131			0.0111710
$166$	−49004.2	+	6641.40i	−1.77835	+	0.241015i
$167$	29283.2			1.04999			0.524995	−	0.851105i	$-0.324067\pi$
$167$	29283.2			1.04999			0.524995	+	0.851105i	$0.324067\pi$
$168$	25873.2	+	60500.0i	0.916711	+	2.14356i
$169$	−5759.66			−0.201662
$170$	−110.777	+	15.0133i	−0.00383312	+	0.000519492i
$171$	−512.137			−0.0175144
$172$	−11046.7	−	40006.1i	−0.373402	−	1.35229i
$173$	−28645.5			−0.957116			−0.478558	−	0.878056i	$-0.658840\pi$
$173$	−28645.5			−0.957116			−0.478558	+	0.878056i	$0.658840\pi$
$174$	−6334.15	+	858.449i	−0.209214	+	0.0283541i
$175$	−55050.2			−1.79756
$176$	20173.7	−	12060.5i	0.651269	−	0.389351i
$177$			22427.1i			0.715856i
$178$	−29707.4	+	4026.15i	−0.937614	+	0.127072i
$179$	−1822.31			−0.0568744			−0.0284372	−	0.999596i	$-0.509053\pi$
$179$	−1822.31			−0.0568744			−0.0284372	+	0.999596i	$0.509053\pi$
$180$	241.696	−	66.7387i	0.00745977	−	0.00205984i
$181$			17439.2i			0.532317i	0.963929	+	0.266158i	$0.0857544\pi$
$181$			17439.2i			0.532317i	−0.963929	+	0.266158i	$0.914246\pi$
$182$	−64687.5	+	8766.91i	−1.95289	+	0.264669i
$183$	20345.9			0.607540
$184$	−7081.24	+	3028.34i	−0.209158	+	0.0894478i
$185$	372.661			0.0108886
$186$	61552.5	−	8342.03i	1.77918	−	0.241127i
$187$		−	9040.58i		−	0.258531i
$188$	−19471.2	+	5376.50i	−0.550905	+	0.152119i
$189$	26510.1			0.742143
$190$	1.41419	+	10.4348i	3.91743e−5	+	0.000289052i
$191$	−41190.1			−1.12908			−0.564541	−	0.825405i	$-0.690947\pi$
$191$	−41190.1			−1.12908			−0.564541	+	0.825405i	$0.690947\pi$
$192$	33022.4	−	34566.4i	0.895789	−	0.937673i
$193$			52114.7i			1.39909i	0.714589	+	0.699545i	$0.246614\pi$
$193$			52114.7i			1.39909i	−0.714589	+	0.699545i	$0.753386\pi$
$194$	59643.7	−	8083.34i	1.58475	−	0.214777i
$195$			613.674i			0.0161387i
$196$	−82653.1	+	22822.7i	−2.15153	+	0.594093i
$197$	60362.6			1.55538			0.777689	−	0.628650i	$-0.216392\pi$
$197$	60362.6			1.55538			0.777689	+	0.628650i	$0.216392\pi$
$198$	2723.29	+	20094.0i	0.0694645	+	0.512551i
$199$	−35549.3			−0.897687			−0.448844	−	0.893610i	$-0.648164\pi$
$199$	−35549.3			−0.897687			−0.448844	+	0.893610i	$0.648164\pi$
$200$	15726.3	+	36773.2i	0.393158	+	0.919331i
$201$	62558.7			1.54844
$202$	13166.0	−	1784.35i	0.322664	−	0.0437297i
$203$		−	12061.5i		−	0.292692i
$204$	−4894.18	−	17724.4i	−0.117603	−	0.425905i
$205$	−278.057	−	387.704i	−0.00661646	−	0.00922557i
$206$	41358.3	−	5605.17i	0.974605	−	0.132085i
$207$		−	6644.47i		−	0.155067i
$208$	24335.7	+	40706.4i	0.562493	+	0.940884i
$209$	−851.586			−0.0194956
$210$	156.758	+	1156.65i	0.00355459	+	0.0262279i
$211$	−40151.0			−0.901843			−0.450921	−	0.892564i	$-0.648905\pi$
$211$	−40151.0			−0.901843			−0.450921	+	0.892564i	$0.648905\pi$
$212$	−16300.0	−	59030.9i	−0.362673	−	1.31343i
$213$	−49889.8			−1.09965
$214$	−55847.1	+	7568.80i	−1.21948	+	0.165272i
$215$		−	736.222i		−	0.0159269i
$216$	−7573.21	−	17708.6i	−0.162320	−	0.379557i
$217$			117209.i			2.48909i
$218$	−26462.3	+	3586.36i	−0.556820	+	0.0754643i
$219$	−1228.22			−0.0256087
$220$	401.895	−	110.974i	0.00830361	−	0.00229284i
$221$	18242.0			0.373499
$222$	8232.15	+	60741.7i	0.167035	+	1.23248i
$223$		−	18192.7i		−	0.365837i	−0.983128	−	0.182919i	$-0.941446\pi$
$223$		−	18192.7i		−	0.365837i	0.983128	−	0.182919i	$-0.0585545\pi$
$224$	56265.9	+	70507.0i	1.12137	+	1.40519i
$225$	−34505.1			−0.681581
$226$	4115.42	+	30366.0i	0.0805745	+	0.594526i
$227$	68894.6			1.33701			0.668503	−	0.743710i	$-0.266935\pi$
$227$	68894.6			1.33701			0.668503	+	0.743710i	$0.266935\pi$
$228$	−1669.57	+	461.012i	−0.0321170	+	0.00886834i
$229$		−	60150.2i		−	1.14701i	−0.819203	−	0.573504i	$-0.805584\pi$
$229$		−	60150.2i		−	1.14701i	0.819203	−	0.573504i	$-0.194416\pi$
$230$	−135.381	+	18.3478i	−0.00255918	+	0.000346839i
$231$	−94394.8			−1.76899
$232$	−8057.04	+	3445.65i	−0.149692	+	0.0640170i
$233$		−	59556.7i		−	1.09703i	−0.836141	−	0.548515i	$-0.815193\pi$
$233$		−	59556.7i		−	1.09703i	0.836141	−	0.548515i	$-0.184807\pi$
$234$	−40545.6	+	5495.03i	−0.740479	+	0.100355i
$235$	−358.323			−0.00648843
$236$	8183.35	+	29636.3i	0.146929	+	0.532108i
$237$	−71813.0			−1.27852
$238$	34382.5	−	4659.77i	0.606994	−	0.0822641i
$239$	96486.8			1.68916			0.844582	−	0.535426i	$-0.179849\pi$
$239$	96486.8			1.68916			0.844582	+	0.535426i	$0.179849\pi$
$240$	727.855	−	435.137i	0.0126364	−	0.00755446i
$241$	−10724.2			−0.184643			−0.0923215	−	0.995729i	$-0.529429\pi$
$241$	−10724.2			−0.184643			−0.0923215	+	0.995729i	$0.529429\pi$
$242$	−3336.80	−	24620.9i	−0.0569771	−	0.420411i
$243$	68814.7			1.16538
$244$	26886.2	−	7423.97i	0.451595	−	0.124697i
$245$	−1521.04			−0.0253402
$246$	57051.4	−	53886.2i	0.942749	−	0.890445i
$247$		−	1718.33i		−	0.0281651i
$248$	78294.8	−	33483.3i	1.27300	−	0.544409i
$249$		−	144291.i		−	2.32723i
$250$	190.574	+	1406.17i	0.00304918	+	0.0224987i
$251$		−	94132.8i		−	1.49415i	−0.664741	−	0.747074i	$-0.731458\pi$
$251$		−	94132.8i		−	1.49415i	0.664741	−	0.747074i	$-0.268542\pi$
$252$	−75016.6	+	20714.0i	−1.18129	+	0.326185i
$253$		−	11048.5i		−	0.172608i
$254$	94770.7	−	12844.0i	1.46895	−	0.199082i
$255$		−	326.179i		−	0.00501620i
$256$	31024.7	−	57727.3i	0.473399	−	0.880848i
$257$			19618.0i			0.297022i	0.988911	+	0.148511i	$0.0474481\pi$
$257$			19618.0i			0.297022i	−0.988911	+	0.148511i	$0.952552\pi$
$258$	120000.	−	16263.3i	1.80278	−	0.244326i
$259$	−115665.			−1.72426
$260$	223.922	+	810.941i	0.00331245	+	0.0119962i
$261$		−	7560.08i		−	0.110980i
$262$	−77028.5	+	10439.4i	−1.12214	+	0.152081i
$263$	14085.6			0.203640			0.101820	−	0.994803i	$-0.467533\pi$
$263$	14085.6			0.203640			0.101820	+	0.994803i	$0.467533\pi$
$264$	26966.0	+	63055.3i	0.386909	+	0.904718i
$265$		−	1086.33i		−	0.0154693i
$266$	−438.931	−	3238.69i	−0.00620345	−	0.0457727i
$267$		−	87472.1i		−	1.22701i
$268$	82668.3	−	22826.9i	1.15098	−	0.317817i
$269$	−43104.1			−0.595682			−0.297841	−	0.954616i	$-0.596266\pi$
$269$	−43104.1			−0.595682			−0.297841	+	0.954616i	$0.596266\pi$
$270$	−45.8836	−	338.557i	−0.000629405	−	0.00464412i
$271$		−	72579.6i		−	0.988271i	−0.869385	−	0.494136i	$-0.835485\pi$
$271$		−	72579.6i		−	0.988271i	0.869385	−	0.494136i	$-0.164515\pi$
$272$	−12934.9	−	21636.2i	−0.174833	−	0.292444i
$273$		−	190469.i		−	2.55564i
$274$	−52774.6	+	7152.38i	−0.702948	+	0.0952686i
$275$	−57375.3			−0.758681
$276$	−5981.17	−	21661.0i	−0.0785178	−	0.284355i
$277$	33123.2			0.431691			0.215845	−	0.976428i	$-0.430749\pi$
$277$	33123.2			0.431691			0.215845	+	0.976428i	$0.430749\pi$
$278$	115369.	−	15635.6i	1.49279	−	0.202313i
$279$			73465.6i			0.943790i
$280$	629.195	+	1471.26i	0.00802545	+	0.0187661i
$281$		−	67891.2i		−	0.859807i	−0.902875	−	0.429904i	$-0.858548\pi$
$281$		−	67891.2i		−	0.859807i	0.902875	−	0.429904i	$-0.141452\pi$
$282$	−7915.43	−	58404.8i	−0.0995351	−	0.734430i
$283$			38952.5i			0.486366i	0.969980	+	0.243183i	$0.0781915\pi$
$283$			38952.5i			0.486366i	−0.969980	+	0.243183i	$0.921809\pi$
$284$	−65927.0	+	18204.2i	−0.817385	+	0.225701i
$285$	−30.7247			−0.000378267
$286$	−67419.6	+	9137.19i	−0.824241	+	0.111707i
$287$	86301.9	+	120334.i	1.04775	+	1.46091i
$288$	35267.1	+	44193.3i	0.425192	+	0.532809i
$289$	73825.0			0.883910
$290$	−154.036	+	20.8761i	−0.00183158	+	0.000248229i
$291$			175618.i			2.07388i
$292$	−1623.03	+	448.161i	−0.0190354	+	0.00525616i
$293$		−	96912.0i		−	1.12887i	−0.825479	−	0.564433i	$-0.809095\pi$
$293$		−	96912.0i		−	1.12887i	0.825479	−	0.564433i	$-0.190905\pi$
$294$	−33600.2	−	247922.i	−0.388729	−	2.86827i
$295$			545.389i			0.00626704i
$296$	33042.3	+	77263.5i	0.377126	+	0.881842i
$297$	27629.8			0.313231
$298$	−56755.6	+	7691.93i	−0.639111	+	0.0866169i
$299$	22293.6			0.249366
$300$	−112487.	+	31060.5i	−1.24985	+	0.345117i
$301$			228505.i			2.52211i
$302$	7468.55	+	55107.4i	0.0818884	+	0.604221i
$303$			38766.6i			0.422253i
$304$	−2038.04	+	1218.41i	−0.0220529	+	0.0131840i
$305$	494.780			0.00531878
$306$	21550.7	−	2920.71i	0.230154	−	0.0311922i
$307$			11786.8i			0.125060i	0.998043	+	0.0625299i	$0.0199169\pi$
$307$			11786.8i			0.125060i	−0.998043	+	0.0625299i	$0.980083\pi$
$308$	−124738.	+	34443.5i	−1.31492	+	0.363083i
$309$			121778.i			1.27541i
$310$	1496.86	−	202.865i	0.0155760	−	0.00211097i
$311$	−81525.1			−0.842889			−0.421445	−	0.906854i	$-0.638477\pi$
$311$	−81525.1			−0.842889			−0.421445	+	0.906854i	$0.638477\pi$
$312$	−127233.	+	54411.9i	−1.30704	+	0.558965i
$313$			143714.i			1.46694i	0.679724	+	0.733468i	$0.262100\pi$
$313$			143714.i			1.46694i	−0.679724	+	0.733468i	$0.737900\pi$
$314$	−13273.6	+	1798.94i	−0.134626	+	0.0182455i
$315$	−1380.51			−0.0139130
$316$	−94897.5	+	26203.7i	−0.950344	+	0.262415i
$317$			72857.0i			0.725025i	0.931979	+	0.362513i	$0.118081\pi$
$317$			72857.0i			0.725025i	−0.931979	+	0.362513i	$0.881919\pi$
$318$	177066.	−	23997.3i	1.75098	−	0.237305i
$319$		−	12571.0i		−	0.123534i
$320$	803.050	−	840.598i	0.00784229	−	0.00820896i
$321$		−	164439.i		−	1.59586i
$322$	42018.9	−	5694.69i	0.405259	−	0.0549236i
$323$			913.321i			0.00875424i
$324$	123147.	−	34004.1i	1.17310	−	0.323922i
$325$		−	115772.i		−	1.09606i
$326$	−144422.	+	19573.0i	−1.35893	+	0.184172i
$327$		−	77917.2i		−	0.728682i
$328$	55728.3	−	92025.4i	0.517998	−	0.855382i
$329$	111215.			1.02747
$330$	163.378	+	1205.50i	0.00150026	+	0.0110698i
$331$	180664.			1.64898			0.824491	−	0.565874i	$-0.191461\pi$
$331$	180664.			1.64898			0.824491	+	0.565874i	$0.191461\pi$
$332$	−52649.8	−	190673.i	−0.477662	−	1.72987i
$333$	−72497.9			−0.653788
$334$	15730.9	+	116072.i	0.141013	+	1.04048i
$335$	1521.32			0.0135560
$336$	−225908.	+	135056.i	−2.00103	+	1.19629i
$337$	197260.			1.73691			0.868457	−	0.495764i	$-0.165112\pi$
$337$	197260.			1.73691			0.868457	+	0.495764i	$0.165112\pi$
$338$	−3094.07	−	22829.9i	−0.0270830	−	0.199835i
$339$	−89411.5			−0.778025
$340$	−119.018	−	431.030i	−0.00102957	−	0.00372863i
$341$			122159.i			1.05055i
$342$	−275.119	−	2029.99i	−0.00235217	−	0.0173557i
$343$	260587.			2.21495
$344$	152640.	−	65277.8i	1.28989	−	0.551631i
$345$		−	398.623i		−	0.00334907i
$346$	−15388.3	−	113544.i	−0.128540	−	0.948445i
$347$	192372.			1.59765			0.798826	−	0.601562i	$-0.205455\pi$
$347$	192372.			1.59765			0.798826	+	0.601562i	$0.205455\pi$
$348$	−6805.38	−	24645.9i	−0.0561945	−	0.203510i
$349$	−123583.			−1.01463			−0.507316	−	0.861760i	$-0.669362\pi$
$349$	−123583.			−1.01463			−0.507316	+	0.861760i	$0.669362\pi$
$350$	−29572.8	−	218206.i	−0.241411	−	1.78127i
$351$			55751.2i			0.452522i
$352$	58642.4	+	73484.9i	0.473289	+	0.593080i
$353$	−155844.			−1.25066			−0.625332	−	0.780358i	$-0.715037\pi$
$353$	−155844.			−1.25066			−0.625332	+	0.780358i	$0.715037\pi$
$354$	−88895.6	+	12047.8i	−0.709371	+	0.0961390i
$355$	−1213.24			−0.00962697
$356$	−31917.4	−	115590.i	−0.251842	−	0.912055i
$357$			101238.i			0.794340i
$358$	−978.941	−	7223.21i	−0.00763819	−	0.0563591i
$359$			44309.5i			0.343801i	0.985114	+	0.171901i	$0.0549908\pi$
$359$			44309.5i			0.343801i	−0.985114	+	0.171901i	$0.945009\pi$
$360$	394.375	+	922.175i	0.00304302	+	0.00711555i
$361$	−130235.			−0.999340
$362$	−69125.0	+	9368.31i	−0.527494	+	0.0714898i
$363$	72495.3			0.550169
$364$	−69499.9	−	251696.i	−0.524543	−	1.89965i
$365$	−29.8682			−0.000224194
$366$	10929.8	+	80646.4i	0.0815923	+	0.602037i
$367$		−	253331.i		−	1.88086i	−0.339989	−	0.940429i	$-0.610423\pi$
$367$		−	253331.i		−	1.88086i	0.339989	−	0.940429i	$-0.389577\pi$
$368$	−15807.7	−	26441.6i	−0.116727	−	0.195250i
$369$	54093.4	+	75424.5i	0.397276	+	0.553936i
$370$	200.192	+	1477.14i	0.00146233	+	0.0107899i
$371$			337171.i			2.44964i
$372$	66131.7	+	239498.i	0.477885	+	1.73068i
$373$	43093.6			0.309738			0.154869	−	0.987935i	$-0.450504\pi$
$373$	43093.6			0.309738			0.154869	+	0.987935i	$0.450504\pi$
$374$	35834.7	−	4856.58i	0.256189	−	0.0347206i
$375$	−4140.40			−0.0294428
$376$	−31771.0	−	74290.9i	−0.224727	−	0.525484i
$377$	25365.6			0.178469
$378$	14241.1	+	105080.i	0.0996693	+	0.735420i
$379$			82263.8i			0.572704i	0.958124	+	0.286352i	$0.0924427\pi$
$379$			82263.8i			0.572704i	−0.958124	+	0.286352i	$0.907557\pi$
$380$	−40.6012	+	11.2111i	−0.000281172	+	7.76389e-5i
$381$			279048.i			1.92234i
$382$	−22127.2	−	163268.i	−0.151635	−	1.11885i
$383$	163372.			1.11373			0.556867	−	0.830602i	$-0.312003\pi$
$383$	163372.			1.11373			0.556867	+	0.830602i	$0.312003\pi$
$384$	154752.	+	112324.i	1.04948	+	0.761745i
$385$	−2295.53			−0.0154868
$386$	−206570.	+	27995.9i	−1.38642	+	0.187897i
$387$			143226.i			0.956310i
$388$	64080.9	+	232071.i	0.425662	+	1.54155i
$389$	48751.6			0.322174			0.161087	−	0.986940i	$-0.448500\pi$
$389$	48751.6			0.322174			0.161087	+	0.986940i	$0.448500\pi$
$390$	−2432.46	+	329.664i	−0.0159925	+	0.00216742i
$391$	−11849.4			−0.0775075
$392$	−134865.	−	315357.i	−0.877659	−	2.05225i
$393$		−	226807.i		−	1.46849i
$394$	32426.7	+	239263.i	0.208886	+	1.54129i
$395$	−1746.38			−0.0111929
$396$	−78185.1	+	21588.9i	−0.498578	+	0.137670i
$397$			12961.3i			0.0822371i	0.999154	+	0.0411186i	$0.0130921\pi$
$397$			12961.3i			0.0822371i	−0.999154	+	0.0411186i	$0.986908\pi$
$398$	−19097.0	−	140909.i	−0.120559	−	0.889555i
$399$	9536.19			0.0599003
$400$	−137312.	+	82089.9i	−0.858201	+	0.513062i
$401$	167374.			1.04088			0.520438	−	0.853900i	$-0.325769\pi$
$401$	167374.			1.04088			0.520438	+	0.853900i	$0.325769\pi$
$402$	33606.4	+	247968.i	0.207955	+	1.53442i
$403$	−246492.			−1.51772
$404$	14145.4	+	51228.2i	0.0866670	+	0.313868i
$405$	2266.24			0.0138164
$406$	47809.1	−	6479.42i	0.290040	−	0.0393083i
$407$	−120550.			−0.727744
$408$	67626.4	−	28920.9i	0.406252	−	0.173737i
$409$	−268931.			−1.60766			−0.803830	−	0.594859i	$-0.797208\pi$
$409$	−268931.			−1.60766			−0.803830	+	0.594859i	$0.797208\pi$
$410$	1387.40	−	1310.42i	0.00825340	−	0.00779550i
$411$		−	155392.i		−	0.919912i
$412$	44435.2	+	160924.i	0.261778	+	0.948037i
$413$		−	169276.i		−	0.992417i
$414$	26337.1	−	3569.39i	0.153662	−	0.0208254i
$415$		−	3508.91i		−	0.0203740i
$416$	−148278.	+	118328.i	−0.856818	+	0.683757i
$417$			339698.i			1.95353i
$418$	−457.470	−	3375.48i	−0.00261824	−	0.0193190i
$419$		−	268459.i		−	1.52915i	−0.644536	−	0.764574i	$-0.722950\pi$
$419$		−	268459.i		−	1.52915i	0.644536	−	0.764574i	$-0.277050\pi$
$420$	−4500.48	+	1242.70i	−0.0255129	+	0.00704478i
$421$			92905.9i			0.524178i	0.965044	+	0.262089i	$0.0844115\pi$
$421$			92905.9i			0.524178i	−0.965044	+	0.262089i	$0.915589\pi$
$422$	−21569.0	−	159149.i	−0.121117	−	0.893673i
$423$	69708.6			0.389588
$424$	225228.	−	96320.5i	1.25283	−	0.535780i
$425$			61534.6i			0.340676i
$426$	−26800.7	−	197751.i	−0.147682	−	1.08968i
$427$	−153567.			−0.842255
$428$	−60001.9	−	217299.i	−0.327550	−	1.18623i
$429$		−	198514.i		−	1.07864i
$430$	2918.21	−	395.497i	0.0157826	−	0.00213898i
$431$			299523.i			1.61241i	0.591637	+	0.806205i	$0.298482\pi$
$431$			299523.i			1.61241i	−0.591637	+	0.806205i	$0.701518\pi$
$432$	66124.4	−	39531.4i	0.354319	−	0.211824i
$433$	−187164.			−0.998267			−0.499134	−	0.866525i	$-0.666348\pi$
$433$	−187164.			−0.998267			−0.499134	+	0.866525i	$0.666348\pi$
$434$	−464588.	+	62964.2i	−2.46654	+	0.334283i
$435$		−	453.553i		−	0.00239690i
$436$	−28431.0	−	102964.i	−0.149561	−	0.541641i
$437$			1116.17i			0.00584476i
$438$	−659.795	−	4868.36i	−0.00343923	−	0.0253767i
$439$	−51995.5			−0.269797			−0.134898	−	0.990859i	$-0.543071\pi$
$439$	−51995.5			−0.269797			−0.134898	+	0.990859i	$0.543071\pi$
$440$	655.770	+	1533.40i	0.00338724	+	0.00792046i
$441$	295906.			1.52151
$442$	9799.58	+	72307.1i	0.0501606	+	0.370115i
$443$		−	97151.4i		−	0.495041i	−0.968883	−	0.247521i	$-0.920384\pi$
$443$		−	97151.4i		−	0.495041i	0.968883	−	0.247521i	$-0.0796158\pi$
$444$	−236343.	+	65260.6i	−1.19889	+	0.331043i
$445$		−	2127.18i		−	0.0107420i
$446$	72111.6	−	9773.08i	0.362523	−	0.0491317i
$447$		−	167114.i		−	0.836371i
$448$	−249247.	+	260901.i	−1.24186	+	1.29993i
$449$	−70090.7			−0.347670			−0.173835	−	0.984775i	$-0.555616\pi$
$449$	−70090.7			−0.347670			−0.173835	+	0.984775i	$0.555616\pi$
$450$	−18536.0	−	136770.i	−0.0915359	−	0.675407i
$451$	89947.0	+	125416.i	0.442215	+	0.616597i
$452$	−118153.	+	32625.1i	−0.578319	+	0.159689i
$453$	−162261.			−0.790712
$454$	37010.0	+	273082.i	0.179559	+	1.32489i
$455$		−	4631.90i		−	0.0223736i
$456$	−2724.23	−	6370.13i	−0.0131013	−	0.0306350i
$457$		−	238633.i		−	1.14261i	−0.820738	−	0.571305i	$-0.806437\pi$
$457$		−	238633.i		−	1.14261i	0.820738	−	0.571305i	$-0.193563\pi$
$458$	238421.	−	32312.6i	1.13662	−	0.154042i
$459$		−	29632.8i		−	0.140652i
$460$	−145.452	−	526.761i	−0.000687393	−	0.00248942i
$461$	113261.			0.532940			0.266470	−	0.963843i	$-0.414143\pi$
$461$	113261.			0.532940			0.266470	+	0.963843i	$0.414143\pi$
$462$	−50708.7	−	374159.i	−0.237574	−	1.75296i
$463$	52810.6			0.246354			0.123177	−	0.992385i	$-0.460692\pi$
$463$	52810.6			0.246354			0.123177	+	0.992385i	$0.460692\pi$
$464$	−17986.0	−	30085.2i	−0.0835406	−	0.139739i
$465$			4407.43i			0.0203835i
$466$	236069.	−	31993.7i	1.08709	−	0.147330i
$467$		−	63325.7i		−	0.290366i	−0.989405	−	0.145183i	$-0.953623\pi$
$467$		−	63325.7i		−	0.290366i	0.989405	−	0.145183i	$-0.0463772\pi$
$468$	−43562.0	−	157761.i	−0.198892	−	0.720293i
$469$	−472182.			−2.14666
$470$	−192.490	−	1420.31i	−0.000871391	−	0.00642965i
$471$		−	39083.6i		−	0.176178i
$472$	−113075.	+	48357.4i	−0.507555	+	0.217060i
$473$			238157.i			1.06449i
$474$	−38577.8	−	284650.i	−0.171704	−	1.26694i
$475$	5796.31			0.0256900
$476$	36940.4	+	133781.i	0.163038	+	0.590447i
$477$			211336.i			0.928832i
$478$	51832.5	+	382451.i	0.226854	+	1.67386i
$479$	−418037.			−1.82198			−0.910990	−	0.412428i	$-0.864681\pi$
$479$	−418037.			−1.82198			−0.910990	+	0.412428i	$0.864681\pi$
$480$	2115.78	+	2651.29i	0.00918308	+	0.0115073i
$481$		−	243245.i		−	1.05137i
$482$	−5761.04	−	42508.4i	−0.0247974	−	0.182970i
$483$			123723.i			0.530341i
$484$	95799.0	−	26452.6i	0.408950	−	0.112922i
$485$			4270.75i			0.0181560i
$486$	36967.1	+	272765.i	0.156510	+	1.15482i
$487$			157518.i			0.664159i	0.943251	+	0.332080i	$0.107750\pi$
$487$			157518.i			0.664159i	−0.943251	+	0.332080i	$0.892250\pi$
$488$	43870.0	+	102582.i	0.184216	+	0.430757i
$489$		−	425243.i		−	1.77836i
$490$	−817.101	−	6029.06i	−0.00340317	−	0.0251106i
$491$		−	242531.i		−	1.00602i	−0.864282	−	0.503008i	$-0.832227\pi$
$491$		−	242531.i		−	1.00602i	0.864282	−	0.503008i	$-0.167773\pi$
$492$	244240.	+	197191.i	1.00899	+	0.814622i
$493$	−13482.3			−0.0554715
$494$	6811.04	−	923.080i	0.0279100	−	0.00378256i
$495$	−1438.82			−0.00587214
$496$	174780.	+	292355.i	0.710441	+	1.18836i
$497$	376560.			1.52448
$498$	571934.	−	77512.6i	2.30615	−	0.312546i
$499$	−231613.			−0.930169			−0.465085	−	0.885266i	$-0.653976\pi$
$499$	−231613.			−0.930169			−0.465085	+	0.885266i	$0.653976\pi$
$500$	−5471.34	+	1510.78i	−0.0218853	+	0.00604311i
$501$	−341768.			−1.36162
$502$	373120.	−	50567.9i	1.48061	−	0.200663i
$503$	−135731.			−0.536468			−0.268234	−	0.963354i	$-0.586440\pi$
$503$	−135731.			−0.536468			−0.268234	+	0.963354i	$0.586440\pi$
$504$	−122404.	−	286221.i	−0.481876	−	1.12678i
$505$			942.740i			0.00369666i
$506$	43793.6	−	5935.22i	0.171045	−	0.0231812i
$507$	67221.7			0.261513
$508$	101821.	+	368749.i	0.394558	+	1.42890i
$509$		−	137853.i		−	0.532083i	−0.963962	−	0.266041i	$-0.914284\pi$
$509$		−	137853.i		−	0.532083i	0.963962	−	0.266041i	$-0.0857158\pi$
$510$	1292.90	−	175.222i	0.00497076	−	0.000673673i
$511$	9270.37			0.0355022
$512$	245484.	+	91963.5i	0.936446	+	0.350813i
$513$	−2791.28			−0.0106064
$514$	−77761.2	+	10538.7i	−0.294331	+	0.0398899i
$515$			2961.44i			0.0111658i
$516$	128928.	+	466916.i	0.484225	+	1.75364i
$517$	115912.			0.433658
$518$	−62134.8	−	458468.i	−0.231566	−	1.70864i
$519$	334326.			1.24118
$520$	−3094.09	+	1323.21i	−0.0114426	+	0.00489352i
$521$		−	507650.i		−	1.87020i	−0.354381	−	0.935101i	$-0.615308\pi$
$521$		−	507650.i		−	1.87020i	0.354381	−	0.935101i	$-0.384692\pi$
$522$	29966.4	−	4061.26i	0.109975	−	0.0149046i
$523$		−	366767.i		−	1.34087i	−0.741967	−	0.670436i	$-0.766107\pi$
$523$		−	366767.i		−	1.34087i	0.741967	−	0.670436i	$-0.233893\pi$
$524$	−82759.0	−	299715.i	−0.301406	−	1.09155i
$525$	642498.			2.33106
$526$	7566.74	+	55831.9i	0.0273487	+	0.201795i
$527$	131015.			0.471737
$528$	−235450.	+	140760.i	−0.844561	+	0.504907i
$529$	265360.			0.948252
$530$	4305.96	−	583.574i	0.0153292	−	0.00207752i
$531$		−	106101.i		−	0.376296i
$532$	12601.6	−	3479.64i	0.0445249	−	0.0122945i
$533$	−253065.	+	181495.i	−0.890793	+	0.638865i
$534$	346719.	−	46989.8i	1.21589	−	0.164786i
$535$		−	3998.90i		−	0.0139712i
$536$	134890.	+	315415.i	0.469514	+	1.09787i
$537$	21268.4			0.0737542
$538$	−23155.4	−	170855.i	−0.0799997	−	0.590285i
$539$	492034.			1.69363
$540$	1317.31	−	363.744i	0.00451752	−	0.00124741i
$541$	−525108.			−1.79413			−0.897065	−	0.441899i	$-0.854305\pi$
$541$	−525108.			−1.79413			−0.897065	+	0.441899i	$0.854305\pi$
$542$	287688.	−	38989.6i	0.979318	−	0.132724i
$543$		−	203535.i		−	0.690304i
$544$	78812.2	−	62893.6i	0.266315	−	0.212524i
$545$		−	1894.82i		−	0.00637932i
$546$	754976.	−	102320.i	2.53249	−	0.343221i
$547$	203702.			0.680803			0.340401	−	0.940280i	$-0.389437\pi$
$547$	203702.			0.680803			0.340401	+	0.940280i	$0.389437\pi$
$548$	−56700.7	−	205344.i	−0.188811	−	0.683786i
$549$	−96255.0			−0.319359
$550$	−30821.9	−	227422.i	−0.101890	−	0.751808i
$551$			1269.98i			0.00418304i
$552$	82646.1	−	35344.2i	0.271234	−	0.115995i
$553$	542032.			1.77245
$554$	17793.7	+	131293.i	0.0579758	+	0.427780i
$555$	−4349.37			−0.0141202
$556$	123951.	+	448894.i	0.400961	+	1.45209i
$557$		−	327375.i		−	1.05520i	−0.849493	−	0.527600i	$-0.823092\pi$
$557$		−	327375.i		−	1.05520i	0.849493	−	0.527600i	$-0.176908\pi$
$558$	−291200.	+	39465.5i	−0.935240	+	0.126750i
$559$	−480551.			−1.53786
$560$	−5493.72	+	3284.34i	−0.0175183	+	0.0104730i
$561$			105514.i			0.335261i
$562$	269105.	−	36471.0i	0.852018	−	0.115472i
$563$	402306.			1.26923			0.634613	−	0.772830i	$-0.281159\pi$
$563$	402306.			1.26923			0.634613	+	0.772830i	$0.281159\pi$
$564$	227251.	−	62749.8i	0.714409	−	0.197267i
$565$	−2174.34			−0.00681131
$566$	−154399.	+	20925.2i	−0.481960	+	0.0653186i
$567$	−703386.			−2.18790
$568$	−107573.	−	251540.i	−0.333431	−	0.779669i
$569$	−278769.			−0.861034			−0.430517	−	0.902582i	$-0.641669\pi$
$569$	−278769.			−0.861034			−0.430517	+	0.902582i	$0.641669\pi$
$570$	−16.5052	−	121.785i	−5.08010e−5	−	0.000374840i
$571$	−490581.			−1.50466			−0.752331	−	0.658786i	$-0.771070\pi$
$571$	−490581.			−1.50466			−0.752331	+	0.658786i	$0.771070\pi$
$572$	−72435.3	−	262327.i	−0.221390	−	0.801772i
$573$	480734.			1.46419
$574$	−430614.	+	406724.i	−1.30697	+	1.23446i
$575$			75201.4i			0.227452i
$576$	−156226.	+	163531.i	−0.470879	+	0.492895i
$577$		−	435516.i		−	1.30813i	−0.756436	−	0.654067i	$-0.773061\pi$
$577$		−	435516.i		−	1.30813i	0.756436	−	0.654067i	$-0.226939\pi$
$578$	39658.6	+	292625.i	0.118709	+	0.875902i
$579$		−	608237.i		−	1.81433i
$580$	−165.496	−	599.348i	−0.000491961	−	0.00178165i
$581$			1.08908e6i			3.22632i
$582$	−696109.	+	94341.7i	−2.05509	+	0.278521i
$583$			351411.i			1.03390i
$584$	−2648.29	−	6192.56i	−0.00776498	−	0.0181570i
$585$		−	2903.24i		−	0.00848344i
$586$	384136.	−	52060.9i	1.11864	−	0.151606i
$587$	376666.			1.09315			0.546576	−	0.837410i	$-0.315931\pi$
$587$	376666.			1.09315			0.546576	+	0.837410i	$0.315931\pi$
$588$	964654.	−	266366.i	2.79008	−	0.770415i
$589$		−	12341.1i		−	0.0355731i
$590$	−2161.79	+	292.982i	−0.00621027	+	0.000841660i
$591$	−704500.			−2.01700
$592$	−288504.	+	172478.i	−0.823205	+	0.492140i
$593$		−	326481.i		−	0.928427i	−0.885723	−	0.464214i	$-0.846337\pi$
$593$		−	326481.i		−	0.928427i	0.885723	−	0.464214i	$-0.153663\pi$
$594$	14842.6	+	109518.i	0.0420667	+	0.310393i
$595$			2461.94i			0.00695414i
$596$	−60978.0	−	220834.i	−0.171664	−	0.621689i
$597$	414900.			1.16411
$598$	11976.1	+	88366.4i	0.0334897	+	0.247107i
$599$			436674.i			1.21704i	0.793540	+	0.608518i	$0.208236\pi$
$599$			436674.i			1.21704i	−0.793540	+	0.608518i	$0.791764\pi$
$600$	−183544.	−	429185.i	−0.509845	−	1.19218i
$601$			431142.i			1.19363i	0.802378	+	0.596817i	$0.203568\pi$
$601$			431142.i			1.19363i	−0.802378	+	0.596817i	$0.796432\pi$
$602$	−905741.	+	122752.i	−2.49926	+	0.338717i
$603$	−295960.			−0.813952
$604$	−214421.	+	59207.1i	−0.587750	+	0.162293i
$605$	1762.97			0.00481652
$606$	−153662.	+	20825.3i	−0.418427	+	0.0567083i
$607$			678351.i			1.84110i	0.390627	+	0.920549i	$0.372258\pi$
$607$			678351.i			1.84110i	−0.390627	+	0.920549i	$0.627742\pi$
$608$	−5924.32	−	7423.78i	−0.0160262	−	0.0200825i
$609$			140772.i			0.379560i
$610$	265.794	+	1961.19i	0.000714309	+	0.00527060i
$611$			233887.i			0.626503i
$612$	23154.0	+	83853.0i	0.0618192	+	0.223880i
$613$	−207691.			−0.552709			−0.276355	−	0.961056i	$-0.589126\pi$
$613$	−207691.			−0.552709			−0.276355	+	0.961056i	$0.589126\pi$
$614$	−46719.9	+	6331.82i	−0.123927	+	0.0167954i
$615$	3245.23	+	4524.95i	0.00858017	+	0.0119636i
$616$	−203535.	−	475930.i	−0.536386	−	1.25424i
$617$	136128.			0.357584			0.178792	−	0.983887i	$-0.442781\pi$
$617$	136128.			0.357584			0.178792	+	0.983887i	$0.442781\pi$
$618$	−482698.	+	65418.7i	−1.26386	+	0.171287i
$619$		−	349654.i		−	0.912550i	−0.889839	−	0.456275i	$-0.849183\pi$
$619$		−	349654.i		−	0.912550i	0.889839	−	0.456275i	$-0.150817\pi$
$620$	1608.21	+	5824.21i	0.00418370	+	0.0151514i
$621$		−	36214.2i		−	0.0939064i
$622$	−43795.1	−	323146.i	−0.113199	−	0.835253i
$623$			660224.i			1.70104i
$624$	−284025.	−	475090.i	−0.729436	−	1.22013i
$625$	390474.			0.999613
$626$	−569650.	+	77203.0i	−1.45365	+	0.197009i
$627$	9938.97			0.0252817
$628$	−14261.1	−	51647.1i	−0.0361605	−	0.130956i
$629$			129289.i			0.326784i
$630$	−741.608	−	5472.03i	−0.00186850	−	0.0137869i
$631$		−	642980.i		−	1.61488i	−0.589953	−	0.807438i	$-0.700854\pi$
$631$		−	642980.i		−	1.61488i	0.589953	−	0.807438i	$-0.299146\pi$
$632$	−154844.	−	362075.i	−0.387668	−	0.906492i
$633$	468607.			1.16950
$634$	−288788.	+	39138.6i	−0.718457	+	0.0973704i
$635$			6786.00i			0.0168293i
$636$	190239.	+	688957.i	0.470311	+	1.70325i
$637$			992824.i			2.44677i
$638$	49828.3	−	6753.09i	0.122415	−	0.0165906i
$639$	236025.			0.578037
$640$	3763.33	+	2731.53i	0.00918781	+	0.00666878i
$641$		−	333773.i		−	0.812335i	−0.913799	−	0.406168i	$-0.866865\pi$
$641$		−	333773.i		−	0.812335i	0.913799	−	0.406168i	$-0.133135\pi$
$642$	651799.	−	88336.4i	1.58141	−	0.214323i
$643$	−558445.			−1.35070			−0.675349	−	0.737498i	$-0.736007\pi$
$643$	−558445.			−1.35070			−0.675349	+	0.737498i	$0.736007\pi$
$644$	45144.8	+	163494.i	0.108852	+	0.394211i
$645$			8592.54i			0.0206539i
$646$	−3620.19	+	490.634i	−0.00867493	+	0.00117569i
$647$			69092.9i			0.165053i	0.996589	+	0.0825267i	$0.0262990\pi$
$647$			69092.9i			0.165053i	−0.996589	+	0.0825267i	$0.973701\pi$
$648$	200938.	+	469858.i	0.478534	+	1.11897i
$649$		−	176425.i		−	0.418862i
$650$	458891.	−	62192.2i	1.08613	−	0.147200i
$651$		−	1.36796e6i		−	3.22783i
$652$	−155166.	−	561938.i	−0.365006	−	1.32188i
$653$		−	797489.i		−	1.87024i	−0.354325	−	0.935122i	$-0.615289\pi$
$653$		−	797489.i		−	1.87024i	0.354325	−	0.935122i	$-0.384711\pi$
$654$	308845.	−	41856.9i	0.722080	−	0.0978615i
$655$		−	5515.57i		−	0.0128561i
$656$	394704.	+	171458.i	0.917199	+	0.398428i
$657$	5810.60			0.0134614
$658$	59744.3	+	440829.i	0.137989	+	1.01817i
$659$	90553.6			0.208514			0.104257	−	0.994550i	$-0.466754\pi$
$659$	90553.6			0.208514			0.104257	+	0.994550i	$0.466754\pi$
$660$	−4690.56	+	1295.19i	−0.0107681	+	0.00297334i
$661$	−359808.			−0.823508			−0.411754	−	0.911295i	$-0.635084\pi$
$661$	−359808.			−0.823508			−0.411754	+	0.911295i	$0.635084\pi$
$662$	97052.4	+	716110.i	0.221457	+	1.63404i
$663$	−212905.			−0.484350
$664$	727500.	−	311121.i	1.65005	−	0.705655i
$665$	231.905			0.000524404
$666$	−38945.7	−	287364.i	−0.0878033	−	0.647865i
$667$	−16476.7			−0.0370355
$668$	−451630.	+	124707.i	−1.01211	+	0.279471i
$669$			212329.i			0.474415i
$670$	817.252	+	6030.17i	0.00182057	+	0.0134332i
$671$	−160054.			−0.355484
$672$	−656687.	−	822896.i	−1.45419	−	1.82224i
$673$			8719.05i			0.0192504i	0.999954	+	0.00962519i	$0.00306384\pi$
$673$			8719.05i			0.0192504i	−0.999954	+	0.00962519i	$0.996936\pi$
$674$	105967.	+	781890.i	0.233266	+	1.72118i
$675$	−188062.			−0.412756
$676$	88830.3	−	24528.3i	0.194387	−	0.0536754i
$677$	−353177.			−0.770575			−0.385287	−	0.922797i	$-0.625898\pi$
$677$	−353177.			−0.770575			−0.385287	+	0.922797i	$0.625898\pi$
$678$	−48031.6	−	354406.i	−0.104488	−	0.770977i
$679$		−	1.32554e6i		−	2.87509i
$680$	1644.56	−	703.309i	0.00355658	−	0.00152100i
$681$	−804077.			−1.73382
$682$	−484210.	+	65623.6i	−1.04103	+	0.141088i
$683$	518404.			1.11129			0.555644	−	0.831420i	$-0.312472\pi$
$683$	518404.			1.11129			0.555644	+	0.831420i	$0.312472\pi$
$684$	7898.61	−	2181.01i	0.0168826	−	0.00466172i
$685$		−	3778.89i		−	0.00805347i
$686$	139987.	+	1.03290e6i	0.297467	+	2.19489i
$687$			702021.i			1.48743i
$688$	340744.	+	569963.i	0.719865	+	1.20412i
$689$	−709076.			−1.49367
$690$	1580.05	−	214.139i	0.00331873	−	0.000449777i
$691$	468201.			0.980565			0.490282	−	0.871564i	$-0.336894\pi$
$691$	468201.			0.980565			0.490282	+	0.871564i	$0.336894\pi$
$692$	441795.	−	121991.i	0.922590	−	0.254751i
$693$	446575.			0.929882
$694$	103342.	+	762516.i	0.214564	+	1.58318i
$695$			8260.90i			0.0171024i
$696$	94034.7	−	40214.6i	0.194120	−	0.0830167i
$697$	134508.	−	96467.6i	0.276875	−	0.198571i
$698$	−66388.6	−	489854.i	−0.136264	−	1.00544i
$699$			695094.i			1.42262i
$700$	849030.	−	234439.i	1.73271	−	0.478447i
$701$	−726853.			−1.47914			−0.739572	−	0.673078i	$-0.764972\pi$
$701$	−726853.			−1.47914			−0.739572	+	0.673078i	$0.764972\pi$
$702$	−220985.	+	29949.4i	−0.448423	+	0.0607735i
$703$	12178.5			0.0246424
$704$	−259774.	+	271920.i	−0.524144	+	0.548652i
$705$	4182.04			0.00841414
$706$	−83719.1	−	617729.i	−0.167963	−	1.23933i
$707$		−	292604.i		−	0.585384i
$708$	−95508.9	−	345889.i	−0.190536	−	0.690033i
$709$		−	442762.i		−	0.880800i	−0.897802	−	0.440400i	$-0.854837\pi$
$709$		−	442762.i		−	0.880800i	0.897802	−	0.440400i	$-0.145163\pi$
$710$	−651.749	−	4808.99i	−0.00129290	−	0.00953975i
$711$	339742.			0.672063
$712$	441026.	−	188608.i	0.869970	−	0.372049i
$713$	160113.			0.314955
$714$	−401283.	+	54384.7i	−0.787144	+	0.106679i
$715$		−	4827.54i		−	0.00944308i
$716$	28105.2	−	7760.58i	0.0548228	−	0.0151380i
$717$	−1.12611e6			−2.19050
$718$	−175632.	+	23802.9i	−0.340687	+	0.0461723i
$719$	129677.			0.250845			0.125422	−	0.992103i	$-0.459971\pi$
$719$	129677.			0.250845			0.125422	+	0.992103i	$0.459971\pi$
$720$	−3443.43	+	2058.60i	−0.00664241	+	0.00397106i
$721$		−	919157.i		−	1.76815i
$722$	−69961.9	−	516221.i	−0.134211	−	0.990287i
$723$	125164.			0.239444
$724$	−74267.5	−	268962.i	−0.141684	−	0.513115i
$725$			85564.2i			0.162786i
$726$	38944.3	+	287354.i	0.0738874	+	0.545185i
$727$	249631.			0.472312			0.236156	−	0.971715i	$-0.424112\pi$
$727$	249631.			0.472312			0.236156	+	0.971715i	$0.424112\pi$
$728$	960329.	−	410692.i	1.81200	−	0.774913i
$729$	−156383.			−0.294262
$730$	−16.0451	−	118.391i	−3.01091e−5	−	0.000222163i
$731$	255421.			0.477994
$732$	−313792.	+	86646.1i	−0.585625	+	0.161706i
$733$	478223.			0.890067			0.445033	−	0.895514i	$-0.353192\pi$
$733$	478223.			0.890067			0.445033	+	0.895514i	$0.353192\pi$
$734$	1.00414e6	−	136089.i	1.86382	−	0.252598i
$735$	17752.3			0.0328609
$736$	96316.2	−	76862.2i	0.177805	−	0.141892i
$737$	−492125.			−0.906026
$738$	−269906.	+	254931.i	−0.495564	+	0.468070i
$739$			19146.5i			0.0350590i	0.999846	+	0.0175295i	$0.00558010\pi$
$739$			19146.5i			0.0350590i	−0.999846	+	0.0175295i	$0.994420\pi$
$740$	−5747.49	+	1587.03i	−0.0104958	+	0.00289816i
$741$			20054.8i			0.0365243i
$742$	−1.33646e6	+	181127.i	−2.42745	+	0.328985i
$743$			804197.i			1.45675i	0.685179	+	0.728374i	$0.259724\pi$
$743$			804197.i			1.45675i	−0.685179	+	0.728374i	$0.740276\pi$
$744$	−913789.	+	390788.i	−1.65082	+	0.705985i
$745$		−	4063.95i		−	0.00732210i
$746$	23149.8	+	170813.i	0.0415977	+	0.306932i
$747$			682628.i			1.22333i
$748$	38500.6	+	139431.i	0.0688121	+	0.249205i
$749$			1.24116e6i			2.21240i
$750$	−2224.21	−	16411.6i	−0.00395415	−	0.0291761i
$751$	−114539.			−0.203083			−0.101542	−	0.994831i	$-0.532378\pi$
$751$	−114539.			−0.203083			−0.101542	+	0.994831i	$0.532378\pi$
$752$	277404.	−	165842.i	0.490543	−	0.293264i
$753$			1.09864e6i			1.93760i
$754$	13626.4	+	100543.i	0.0239683	+	0.176852i
$755$	−3945.93			−0.00692238
$756$	−408861.	+	112897.i	−0.715372	+	0.197533i
$757$			189862.i			0.331318i	0.986183	+	0.165659i	$0.0529752\pi$
$757$			189862.i			0.331318i	−0.986183	+	0.165659i	$0.947025\pi$
$758$	−326074.	+	44191.9i	−0.567516	+	0.0769138i
$759$			128948.i			0.223837i
$760$	−66.2488	−	154.911i	−0.000114697	−	0.000268198i
$761$	−499225.			−0.862039			−0.431019	−	0.902343i	$-0.641846\pi$
$761$	−499225.			−0.862039			−0.431019	+	0.902343i	$0.641846\pi$
$762$	−1.10608e6	+	149904.i	−1.90492	+	0.258169i
$763$			588105.i			1.01020i
$764$	635268.	−	175414.i	1.08835	−	0.300523i
$765$			1543.13i			0.00263681i
$766$	87763.2	+	647569.i	0.149574	+	1.10364i
$767$	355990.			0.605127
$768$	−362093.	+	673742.i	−0.613900	+	1.14228i
$769$	217831.			0.368355			0.184177	−	0.982893i	$-0.441038\pi$
$769$	217831.			0.368355			0.184177	+	0.982893i	$0.441038\pi$
$770$	−1233.15	−	9098.93i	−0.00207986	−	0.0153465i
$771$		−	228964.i		−	0.385176i
$772$	−221938.	−	803757.i	−0.372389	−	1.34862i
$773$		−	23677.9i		−	0.0396264i	−0.999804	−	0.0198132i	$-0.993693\pi$
$773$		−	23677.9i		−	0.0396264i	0.999804	−	0.0198132i	$-0.00630715\pi$
$774$	−567712.	+	76940.4i	−0.947646	+	0.128432i
$775$		−	831475.i		−	1.38435i
$776$	−885451.	+	378670.i	−1.47042	+	0.628835i
$777$	1.34994e6			2.23600
$778$	26189.3	+	193240.i	0.0432677	+	0.319255i
$779$	−9086.86	−	12670.1i	−0.0149740	−	0.0208788i
$780$	−2613.42	−	9464.60i	−0.00429556	−	0.0155565i
$781$	392464.			0.643425
$782$	−6365.48	−	46968.3i	−0.0104092	−	0.0768054i
$783$		−	41204.5i		−	0.0672080i
$784$	1.17755e6	−	703980.i	1.91579	−	1.14532i
$785$		−	950.450i		−	0.00154237i
$786$	899009.	−	121840.i	1.45519	−	0.197217i
$787$			849966.i			1.37231i	0.727455	+	0.686155i	$0.240703\pi$
$787$			849966.i			1.37231i	−0.727455	+	0.686155i	$0.759297\pi$
$788$	−930963.	+	257063.i	−1.49927	+	0.413988i
$789$	−164395.			−0.264079
$790$	−938.149	−	6922.22i	−0.00150320	−	0.0110915i
$791$	674862.			1.07860
$792$	−127574.	−	298310.i	−0.203382	−	0.475573i
$793$		−	322955.i		−	0.513566i
$794$	−51375.6	+	6962.78i	−0.0814921	+	0.0110444i
$795$			12678.7i			0.0200605i
$796$	548271.	−	151392.i	0.865305	−	0.238933i
$797$	330393.			0.520133			0.260066	−	0.965591i	$-0.416256\pi$
$797$	330393.			0.520133			0.260066	+	0.965591i	$0.416256\pi$
$798$	5122.82	+	37799.2i	0.00804458	+	0.0593577i
$799$		−	124315.i		−	0.194729i
$800$	−399149.	−	500175.i	−0.623670	−	0.781523i
$801$			413824.i			0.644986i
$802$	89912.8	+	663430.i	0.139789	+	1.03145i
$803$	9661.91			0.0149841
$804$	−964832.	+	266415.i	−1.49259	+	0.412142i
$805$			3008.73i			0.00464293i
$806$	−132415.	−	977036.i	−0.203829	−	1.50398i
$807$	503074.			0.772475
$808$	−195458.	+	83588.9i	−0.299385	+	0.128034i
$809$		−	373647.i		−	0.570906i	−0.958393	−	0.285453i	$-0.907856\pi$
$809$		−	373647.i		−	0.570906i	0.958393	−	0.285453i	$-0.0921440\pi$
$810$	1217.42	+	8982.85i	0.00185554	+	0.0136913i
$811$			266226.i			0.404770i	0.979306	+	0.202385i	$0.0648693\pi$
$811$			266226.i			0.404770i	−0.979306	+	0.202385i	$0.935131\pi$
$812$	51365.8	+	186023.i	0.0779044	+	0.282134i
$813$			847086.i			1.28158i
$814$	−64759.2	−	477832.i	−0.0977355	−	0.721151i
$815$		−	10341.2i		−	0.0155688i
$816$	150964.	+	252519.i	0.226722	+	0.379239i
$817$		−	24059.7i		−	0.0360450i
$818$	−144469.	−	1.06598e6i	−0.215908	−	1.59310i
$819$			901096.i			1.34339i
$820$	5939.52	+	4795.36i	0.00883331	+	0.00713170i
$821$	−1.13571e6			−1.68493			−0.842467	−	0.538748i	$-0.818897\pi$
$821$	−1.13571e6			−1.68493			−0.842467	+	0.538748i	$0.818897\pi$
$822$	615939.	−	83476.4i	0.911578	−	0.123544i
$823$	1.04247e6			1.53910			0.769548	−	0.638589i	$-0.220482\pi$
$823$	1.04247e6			1.53910			0.769548	+	0.638589i	$0.220482\pi$
$824$	−613992.	+	262578.i	−0.904292	+	0.386727i
$825$	669634.			0.983852
$826$	670968.	−	90934.4i	0.983426	−	0.133281i
$827$	80496.1			0.117697			0.0588483	−	0.998267i	$-0.481257\pi$
$827$	80496.1			0.117697			0.0588483	+	0.998267i	$0.481257\pi$
$828$	28296.5	+	102477.i	0.0412735	+	0.149474i
$829$	−320934.			−0.466989			−0.233494	−	0.972358i	$-0.575016\pi$
$829$	−320934.			−0.466989			−0.233494	+	0.972358i	$0.575016\pi$
$830$	13908.5	−	1884.98i	0.0201894	−	0.00273622i
$831$	−386585.			−0.559813
$832$	−548680.	−	524171.i	−0.792633	−	0.757228i
$833$		−	527704.i		−	0.760502i
$834$	−1.34648e6	+	182485.i	−1.93584	+	0.262358i
$835$	−8311.23			−0.0119204
$836$	13133.9	−	3626.60i	0.0187923	−	0.00518905i
$837$			400407.i			0.571545i
$838$	1.06411e6	−	144215.i	1.51529	−	0.205364i
$839$	884020.			1.25585			0.627925	−	0.778274i	$-0.283904\pi$
$839$	884020.			1.25585			0.627925	+	0.778274i	$0.283904\pi$
$840$	−7343.41	−	17171.3i	−0.0104073	−	0.0243357i
$841$	688534.			0.973494
$842$	−368257.	+	49908.8i	−0.519430	+	0.0703968i
$843$			792367.i			1.11499i
$844$	619242.	−	170989.i	0.869311	−	0.240039i
$845$	1634.72			0.00228945
$846$	37447.3	+	276309.i	0.0523215	+	0.386059i
$847$	−547182.			−0.762719
$848$	502784.	+	841008.i	0.699181	+	1.16952i
$849$		−	454620.i		−	0.630715i
$850$	−243909.	+	33056.3i	−0.337590	+	0.0457526i
$851$			158004.i			0.218177i
$852$	769442.	−	212463.i	1.05998	−	0.292688i
$853$	667015.			0.916721			0.458361	−	0.888766i	$-0.348437\pi$
$853$	667015.			0.916721			0.458361	+	0.888766i	$0.348437\pi$
$854$	−82496.1	−	608705.i	−0.113114	−	0.834625i
$855$	145.356			0.000198839
$856$	829088.	−	354566.i	1.13150	−	0.483893i
$857$	94572.6			0.128767			0.0643834	−	0.997925i	$-0.479492\pi$
$857$	94572.6			0.128767			0.0643834	+	0.997925i	$0.479492\pi$
$858$	786863.	−	106641.i	1.06887	−	0.144861i
$859$			464186.i			0.629080i	0.949244	+	0.314540i	$0.101850\pi$
$859$			464186.i			0.629080i	−0.949244	+	0.314540i	$0.898150\pi$
$860$	3135.31	+	11354.6i	0.00423920	+	0.0153524i
$861$	−1.00724e6	−	1.40443e6i	−1.35871	−	1.89450i
$862$	−1.18724e6	+	160903.i	−1.59780	+	0.216546i
$863$			60774.7i			0.0816020i	0.999167	+	0.0408010i	$0.0129910\pi$
$863$			60774.7i			0.0816020i	−0.999167	+	0.0408010i	$0.987009\pi$
$864$	192215.	+	240865.i	0.257490	+	0.322661i
$865$	8130.25			0.0108660
$866$	−100544.	−	741874.i	−0.134067	−	0.989224i
$867$	−861621.			−1.14625
$868$	−499151.	−	1.80769e6i	−0.662509	−	2.39930i
$869$	564926.			0.748086
$870$	1797.78	−	243.647i	0.00237518	−	0.000321902i
$871$		−	993008.i		−	1.30893i
$872$	392851.	−	168006.i	0.516649	−	0.220948i
$873$		−	830837.i		−	1.09015i
$874$	−4424.23	+	599.603i	−0.00579181	+	0.000784947i
$875$	31251.0			0.0408176
$876$	18942.6	−	5230.54i	0.0246849	−	0.00681614i
$877$	−505825.			−0.657660			−0.328830	−	0.944389i	$-0.606654\pi$
$877$	−505825.			−0.657660			−0.328830	+	0.944389i	$0.606654\pi$
$878$	−27931.8	−	206098.i	−0.0362335	−	0.267352i
$879$			1.13107e6i			1.46390i
$880$	−5725.76	+	3423.06i	−0.00739380	+	0.00442027i
$881$	1.41764e6			1.82648			0.913240	−	0.407421i	$-0.133572\pi$
$881$	1.41764e6			1.82648			0.913240	+	0.407421i	$0.133572\pi$
$882$	158960.	+	1.17290e6i	0.204338	+	1.50773i
$883$	−538491.			−0.690649			−0.345324	−	0.938483i	$-0.612231\pi$
$883$	−538491.			−0.690649			−0.345324	+	0.938483i	$0.612231\pi$
$884$	−281344.	+	77686.4i	−0.360025	+	0.0994124i
$885$		−	6365.31i		−	0.00812705i
$886$	385085.	−	52189.5i	0.490557	−	0.0664837i
$887$	932748.			1.18554			0.592771	−	0.805371i	$-0.298034\pi$
$887$	932748.			1.18554			0.592771	+	0.805371i	$0.298034\pi$
$888$	−385641.	−	901752.i	−0.489054	−	1.14357i
$889$		−	2.10621e6i		−	2.66500i
$890$	8431.63	−	1142.71i	0.0106447	−	0.00144264i
$891$	−733095.			−0.923431
$892$	77476.3	+	280583.i	0.0973732	+	0.352640i
$893$	−11710.0			−0.0146843
$894$	662402.	−	89773.5i	0.828794	−	0.112324i
$895$	517.214			0.000645690
$896$	−1.16804e6	−	847801.i	−1.45493	−	1.05603i
$897$	−260191.			−0.323376
$898$	−37652.5	−	277823.i	−0.0466919	−	0.344521i
$899$	182177.			0.225410
$900$	532166.	−	146945.i	0.656995	−	0.181413i
$901$	376887.			0.464260
$902$	−448802.	+	423902.i	−0.551622	+	0.521018i
$903$		−	2.66692e6i		−	3.27065i
$904$	−192790.	−	450804.i	−0.235910	−	0.551634i
$905$		−	4949.65i		−	0.00604334i
$906$	−87166.3	−	643165.i	−0.106192	−	0.783549i
$907$			153251.i			0.186290i	0.995653	+	0.0931448i	$0.0296920\pi$
$907$			153251.i			0.186290i	−0.995653	+	0.0931448i	$0.970308\pi$
$908$	−1.06255e6	+	293398.i	−1.28878	+	0.355865i
$909$		−	183402.i		−	0.221961i
$910$	18359.8	−	2488.25i	0.0221710	−	0.00300477i
$911$		−	338709.i		−	0.408122i	−0.978958	−	0.204061i	$-0.934586\pi$
$911$		−	338709.i		−	0.408122i	0.978958	−	0.204061i	$-0.0654141\pi$
$912$	23786.2	−	14220.2i	0.0285980	−	0.0170969i
$913$			1.13508e6i			1.36171i
$914$	945884.	−	128193.i	1.13226	−	0.153452i
$915$	−5774.64			−0.00689735
$916$	256159.	+	927687.i	0.305294	+	1.10563i
$917$			1.71190e6i			2.03582i
$918$	117457.	−	15918.6i	0.139378	−	0.0188895i
$919$	714838.			0.846402			0.423201	−	0.906036i	$-0.360906\pi$
$919$	714838.			0.846402			0.423201	+	0.906036i	$0.360906\pi$
$920$	2009.82	−	859.513i	0.00237455	−	0.00101549i
$921$		−	137565.i		−	0.162176i
$922$	60843.5	+	448940.i	0.0715735	+	0.528112i
$923$			791912.i			0.929551i
$924$	1.45584e6	−	401994.i	1.70517	−	0.470843i
$925$	820523.			0.958975
$926$	28369.7	+	209329.i	0.0330852	+	0.244122i
$927$		−	576121.i		−	0.670432i
$928$	109589.	−	87453.8i	0.127253	−	0.101551i
$929$			914438.i			1.05955i	0.848137	+	0.529777i	$0.177724\pi$
$929$			914438.i			1.05955i	−0.848137	+	0.529777i	$0.822276\pi$
$930$	−17470.0	+	2367.66i	−0.0201989	+	0.00273749i
$931$	−49707.5			−0.0573486
$932$	253631.	+	918533.i	0.291992	+	1.05746i
$933$	951489.			1.09305
$934$	251008.	−	34018.4i	0.287736	−	0.0389960i
$935$			2565.92i			0.00293508i
$936$	601927.	−	257419.i	0.687057	−	0.293825i
$937$			435078.i			0.495550i	0.968818	+	0.247775i	$0.0796994\pi$
$937$			435078.i			0.495550i	−0.968818	+	0.247775i	$0.920301\pi$
$938$	−253655.	−	1.87162e6i	−0.288295	−	2.12722i
$939$		−	1.67731e6i		−	1.90231i
$940$	5526.36	−	1525.97i	0.00625437	−	0.00172699i
$941$	−59621.3			−0.0673321			−0.0336660	−	0.999433i	$-0.510718\pi$
$941$	−59621.3			−0.0673321			−0.0336660	+	0.999433i	$0.510718\pi$
$942$	154918.	−	20995.6i	0.174582	−	0.0236607i
$943$	164382.	−	117893.i	0.184855	−	0.132576i
$944$	−252421.	−	422226.i	−0.283258	−	0.473806i
$945$	−7524.16			−0.00842548
$946$	−943996.	+	127937.i	−1.05484	+	0.142960i
$947$			83654.3i			0.0932799i	0.998912	+	0.0466400i	$0.0148514\pi$
$947$			83654.3i			0.0932799i	−0.998912	+	0.0466400i	$0.985149\pi$
$948$	1.10756e6	−	305826.i	1.23240	−	0.340297i
$949$			19495.8i			0.0216475i
$950$	3113.76	+	22975.2i	0.00345015	+	0.0254573i
$951$		−	850324.i		−	0.940207i
$952$	−510432.	+	218290.i	−0.563202	+	0.240857i
$953$	1.40651e6			1.54866			0.774332	−	0.632779i	$-0.218086\pi$
$953$	1.40651e6			1.54866			0.774332	+	0.632779i	$0.218086\pi$
$954$	−837687.	+	113529.i	−0.920417	+	0.124742i
$955$	11690.7			0.0128184
$956$	−1.48810e6	+	410903.i	−1.62823	+	0.449597i
$957$			146717.i			0.160198i
$958$	−224568.	−	1.65700e6i	−0.244691	−	1.80547i
$959$			1.17287e6i			1.27531i
$960$	−9372.50	+	9810.72i	−0.0101698	+	0.0106453i
$961$	−846794.			−0.916919
$962$	964167.	−	130671.i	1.04184	−	0.141198i
$963$			777950.i			0.838879i
$964$	165398.	−	45670.8i	0.177982	−	0.0491456i
$965$		−	14791.3i		−	0.0158837i
$966$	−490407.	+	66463.5i	−0.525536	+	0.0712244i
$967$	−589325.			−0.630234			−0.315117	−	0.949053i	$-0.602044\pi$
$967$	−589325.			−0.630234			−0.315117	+	0.949053i	$0.602044\pi$
$968$	156315.	+	365514.i	0.166821	+	0.390080i
$969$		−	10659.5i		−	0.0113524i
$970$	−16928.2	+	2294.24i	−0.0179915	+	0.00243834i
$971$	1.68175e6			1.78371			0.891853	−	0.452326i	$-0.149406\pi$
$971$	1.68175e6			1.78371			0.891853	+	0.452326i	$0.149406\pi$
$972$	−1.06132e6	+	293057.i	−1.12334	+	0.310184i
$973$		−	2.56398e6i		−	2.70825i
$974$	−624364.	+	84618.2i	−0.658142	+	0.0891961i
$975$			1.35118e6i			1.42136i
$976$	−383045.	+	228997.i	−0.402115	+	0.240398i
$977$			1.79042e6i			1.87571i	0.347021	+	0.937857i	$0.387193\pi$
$977$			1.79042e6i			1.87571i	−0.347021	+	0.937857i	$0.612807\pi$
$978$	1.68556e6	−	228439.i	1.76225	−	0.238832i
$979$			688109.i			0.717946i
$980$	23458.8	−	6477.59i	0.0244261	−	0.00674468i
$981$			368620.i			0.383037i
$982$	961336.	−	130287.i	0.996901	−	0.135107i
$983$		−	1.35023e6i		−	1.39734i	−0.715444	−	0.698670i	$-0.753776\pi$
$983$		−	1.35023e6i		−	1.39734i	0.715444	−	0.698670i	$-0.246224\pi$
$984$	−650412.	+	1.07404e6i	−0.671736	+	1.10925i
$985$	−17132.3			−0.0176581
$986$	−7242.65	−	53440.6i	−0.00744978	−	0.0549689i
$987$	−1.29800e6			−1.33242
$988$	7317.74	+	26501.5i	0.00749658	+	0.0271491i
$989$	312150.			0.319133
$990$	−772.931	−	5703.14i	−0.000788624	−	0.00581894i
$991$	−203565.			−0.207280			−0.103640	−	0.994615i	$-0.533049\pi$
$991$	−203565.			−0.207280			−0.103640	+	0.994615i	$0.533049\pi$
$992$	−1.06493e6	+	849838.i	−1.08218	+	0.863600i
$993$	−2.10855e6			−2.13839
$994$	202287.	+	1.49259e6i	0.204736	+	1.51067i
$995$	10089.7			0.0101914
$996$	614483.	+	2.22537e6i	0.619429	+	2.24328i
$997$		−	1.61503e6i		−	1.62477i	−0.583124	−	0.812383i	$-0.698170\pi$
$997$		−	1.61503e6i		−	1.62477i	0.583124	−	0.812383i	$-0.301830\pi$
$998$	−124422.	−	918059.i	−0.124921	−	0.921742i
$999$	−395133.			−0.395924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.5.d.f.163.39	yes	72
4.3	odd	2	inner	164.5.d.f.163.38	yes	72
41.40	even	2	inner	164.5.d.f.163.40	yes	72
164.163	odd	2	inner	164.5.d.f.163.37	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.5.d.f.163.37	✓	72	164.163	odd	2	inner
164.5.d.f.163.38	yes	72	4.3	odd	2	inner
164.5.d.f.163.39	yes	72	1.1	even	1	trivial
164.5.d.f.163.40	yes	72	41.40	even	2	inner

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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	164.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.537197 + 3.96376i) q^{2} -11.6711 q^{3} +(-15.4228 + 4.25865i) q^{4} -0.283823 q^{5} +(-6.26970 - 46.2616i) q^{6} +88.0916 q^{7} +(-25.1654 - 58.8447i) q^{8} +55.2152 q^{9} +(-0.152469 - 1.12501i) q^{10} +91.8123 q^{11} +(180.002 - 49.7032i) q^{12} +185.258i q^{13} +(47.3226 + 349.174i) q^{14} +3.31253 q^{15} +(219.728 - 131.361i) q^{16} -98.4681i q^{17} +(29.6615 + 218.860i) q^{18} -9.27529 q^{19} +(4.37735 - 1.20870i) q^{20} -1028.13 q^{21} +(49.3213 + 363.922i) q^{22} -120.338i q^{23} +(293.708 + 686.784i) q^{24} -624.919 q^{25} +(-734.320 + 99.5203i) q^{26} +300.938 q^{27} +(-1358.62 + 375.151i) q^{28} -136.920i q^{29} +(1.77948 + 13.1301i) q^{30} +1330.53i q^{31} +(638.721 + 800.382i) q^{32} -1071.55 q^{33} +(390.304 - 52.8968i) q^{34} -25.0024 q^{35} +(-851.575 + 235.142i) q^{36} -1313.01 q^{37} +(-4.98266 - 36.7651i) q^{38} -2162.17i q^{39} +(7.14251 + 16.7015i) q^{40} +(979.684 + 1366.01i) q^{41} +(-552.308 - 4075.26i) q^{42} +2593.95i q^{43} +(-1416.01 + 390.996i) q^{44} -15.6713 q^{45} +(476.990 - 64.6451i) q^{46} +1262.49 q^{47} +(-2564.47 + 1533.13i) q^{48} +5359.13 q^{49} +(-335.705 - 2477.03i) q^{50} +1149.23i q^{51} +(-788.950 - 2857.21i) q^{52} +3827.50i q^{53} +(161.663 + 1192.85i) q^{54} -26.0584 q^{55} +(-2216.86 - 5183.73i) q^{56} +108.253 q^{57} +(542.720 - 73.5532i) q^{58} -1921.58i q^{59} +(-51.0886 + 14.1069i) q^{60} -1743.27 q^{61} +(-5273.91 + 714.758i) q^{62} +4864.00 q^{63} +(-2829.41 + 2961.70i) q^{64} -52.5805i q^{65} +(-575.635 - 4247.38i) q^{66} -5360.12 q^{67} +(419.341 + 1518.66i) q^{68} +1404.48i q^{69} +(-13.4312 - 99.1036i) q^{70} +4274.63 q^{71} +(-1389.51 - 3249.12i) q^{72} +105.236 q^{73} +(-705.343 - 5204.44i) q^{74} +7293.51 q^{75} +(143.051 - 39.5002i) q^{76} +8087.89 q^{77} +(8570.34 - 1161.51i) q^{78} +6153.05 q^{79} +(-62.3638 + 37.2832i) q^{80} -7984.71 q^{81} +(-4888.25 + 4617.05i) q^{82} +12363.0i q^{83} +(15856.7 - 4378.44i) q^{84} +27.9475i q^{85} +(-10281.8 + 1393.46i) q^{86} +1598.01i q^{87} +(-2310.49 - 5402.67i) q^{88} +7494.74i q^{89} +(-8.41860 - 62.1174i) q^{90} +16319.7i q^{91} +(512.476 + 1855.95i) q^{92} -15528.8i q^{93} +(678.206 + 5004.21i) q^{94} +2.63254 q^{95} +(-7454.59 - 9341.37i) q^{96} -15047.2i q^{97} +(2878.91 + 21242.3i) q^{98} +5069.43 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40}+ \cdots + 2902 q^{98}+O(q^{100}) \) 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

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