LMFDB - Embedded newform 538.3.c.b.187.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$538 = 2 \cdot 269$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	538.c (of order $4$ , degree $2$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.21
Character	$\chi$	$=$	538.187
Dual form			538.3.c.b.351.21

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(3.13497 + 3.13497i) q^{3} +2.00000i q^{4} -3.10542 q^{5} -6.26994i q^{6} +(1.53221 - 1.53221i) q^{7} +(2.00000 - 2.00000i) q^{8} +10.6560i q^{9} +(3.10542 + 3.10542i) q^{10} -18.9364i q^{11} +(-6.26994 + 6.26994i) q^{12} -14.4148i q^{13} -3.06442 q^{14} +(-9.73540 - 9.73540i) q^{15} -4.00000 q^{16} +(0.930364 + 0.930364i) q^{17} +(10.6560 - 10.6560i) q^{18} +(12.0460 - 12.0460i) q^{19} -6.21085i q^{20} +9.60687 q^{21} +(-18.9364 + 18.9364i) q^{22} +33.5498 q^{23} +12.5399 q^{24} -15.3563 q^{25} +(-14.4148 + 14.4148i) q^{26} +(-5.19165 + 5.19165i) q^{27} +(3.06442 + 3.06442i) q^{28} +(-14.4826 + 14.4826i) q^{29} +19.4708i q^{30} +(27.4178 - 27.4178i) q^{31} +(4.00000 + 4.00000i) q^{32} +(59.3650 - 59.3650i) q^{33} -1.86073i q^{34} +(-4.75816 + 4.75816i) q^{35} -21.3121 q^{36} -51.5072 q^{37} -24.0919 q^{38} +(45.1898 - 45.1898i) q^{39} +(-6.21085 + 6.21085i) q^{40} +18.4910 q^{41} +(-9.60687 - 9.60687i) q^{42} +41.3469i q^{43} +37.8728 q^{44} -33.0915i q^{45} +(-33.5498 - 33.5498i) q^{46} +73.3404 q^{47} +(-12.5399 - 12.5399i) q^{48} +44.3047i q^{49} +(15.3563 + 15.3563i) q^{50} +5.83332i q^{51} +28.8295 q^{52} +32.0050 q^{53} +10.3833 q^{54} +58.8056i q^{55} -6.12885i q^{56} +75.5275 q^{57} +28.9652 q^{58} +(32.0412 - 32.0412i) q^{59} +(19.4708 - 19.4708i) q^{60} -35.3265 q^{61} -54.8355 q^{62} +(16.3273 + 16.3273i) q^{63} -8.00000i q^{64} +44.7640i q^{65} -118.730 q^{66} -76.5063 q^{67} +(-1.86073 + 1.86073i) q^{68} +(105.177 + 105.177i) q^{69} +9.51633 q^{70} +(-9.32389 + 9.32389i) q^{71} +(21.3121 + 21.3121i) q^{72} +52.8575i q^{73} +(51.5072 + 51.5072i) q^{74} +(-48.1417 - 48.1417i) q^{75} +(24.0919 + 24.0919i) q^{76} +(-29.0146 - 29.0146i) q^{77} -90.3797 q^{78} -79.4315i q^{79} +12.4217 q^{80} +63.3531 q^{81} +(-18.4910 - 18.4910i) q^{82} +(77.1605 - 77.1605i) q^{83} +19.2137i q^{84} +(-2.88918 - 2.88918i) q^{85} +(41.3469 - 41.3469i) q^{86} -90.8051 q^{87} +(-37.8728 - 37.8728i) q^{88} -84.5435i q^{89} +(-33.0915 + 33.0915i) q^{90} +(-22.0865 - 22.0865i) q^{91} +67.0995i q^{92} +171.908 q^{93} +(-73.3404 - 73.3404i) q^{94} +(-37.4078 + 37.4078i) q^{95} +25.0797i q^{96} -29.7035i q^{97} +(44.3047 - 44.3047i) q^{98} +201.787 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100})$ 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$ .

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	3.13497	+	3.13497i	1.04499	+	1.04499i	0.998939	+	0.0460501i	$0.0146634\pi$
$3$	3.13497	+	3.13497i	1.04499	+	1.04499i	0.0460501	+	0.998939i	$0.485337\pi$
$4$			2.00000i			0.500000i
$5$	−3.10542			−0.621085			−0.310542	−	0.950560i	$-0.600511\pi$
$5$	−3.10542			−0.621085			−0.310542	+	0.950560i	$0.600511\pi$
$6$		−	6.26994i		−	1.04499i
$7$	1.53221	−	1.53221i	0.218887	−	0.218887i	−0.589142	−	0.808029i	$-0.700534\pi$
$7$	1.53221	−	1.53221i	0.218887	−	0.218887i	0.808029	+	0.589142i	$0.200534\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			10.6560i			1.18400i
$10$	3.10542	+	3.10542i	0.310542	+	0.310542i
$11$		−	18.9364i		−	1.72149i	−0.509035	−	0.860746i	$-0.669998\pi$
$11$		−	18.9364i		−	1.72149i	0.509035	−	0.860746i	$-0.330002\pi$
$12$	−6.26994	+	6.26994i	−0.522495	+	0.522495i
$13$		−	14.4148i		−	1.10883i	−0.832241	−	0.554414i	$-0.812942\pi$
$13$		−	14.4148i		−	1.10883i	0.832241	−	0.554414i	$-0.187058\pi$
$14$	−3.06442			−0.218887
$15$	−9.73540	−	9.73540i	−0.649027	−	0.649027i
$16$	−4.00000			−0.250000
$17$	0.930364	+	0.930364i	0.0547273	+	0.0547273i	0.733941	−	0.679213i	$-0.237679\pi$
$17$	0.930364	+	0.930364i	0.0547273	+	0.0547273i	−0.679213	+	0.733941i	$0.737679\pi$
$18$	10.6560	−	10.6560i	0.592002	−	0.592002i
$19$	12.0460	−	12.0460i	0.633999	−	0.633999i	−0.315070	−	0.949068i	$-0.602028\pi$
$19$	12.0460	−	12.0460i	0.633999	−	0.633999i	0.949068	+	0.315070i	$0.102028\pi$
$20$		−	6.21085i		−	0.310542i
$21$	9.60687			0.457470
$22$	−18.9364	+	18.9364i	−0.860746	+	0.860746i
$23$	33.5498			1.45869			0.729343	−	0.684148i	$-0.239826\pi$
$23$	33.5498			1.45869			0.729343	+	0.684148i	$0.239826\pi$
$24$	12.5399			0.522495
$25$	−15.3563			−0.614254
$26$	−14.4148	+	14.4148i	−0.554414	+	0.554414i
$27$	−5.19165	+	5.19165i	−0.192283	+	0.192283i
$28$	3.06442	+	3.06442i	0.109444	+	0.109444i
$29$	−14.4826	+	14.4826i	−0.499401	+	0.499401i	−0.911251	−	0.411851i	$-0.864883\pi$
$29$	−14.4826	+	14.4826i	−0.499401	+	0.499401i	0.411851	+	0.911251i	$0.364883\pi$
$30$			19.4708i			0.649027i
$31$	27.4178	−	27.4178i	0.884444	−	0.884444i	−0.109538	−	0.993983i	$-0.534937\pi$
$31$	27.4178	−	27.4178i	0.884444	−	0.884444i	0.993983	+	0.109538i	$0.0349372\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	59.3650	−	59.3650i	1.79894	−	1.79894i
$34$		−	1.86073i		−	0.0547273i
$35$	−4.75816	+	4.75816i	−0.135948	+	0.135948i
$36$	−21.3121			−0.592002
$37$	−51.5072			−1.39209			−0.696044	−	0.718000i	$-0.745058\pi$
$37$	−51.5072			−1.39209			−0.696044	+	0.718000i	$0.745058\pi$
$38$	−24.0919			−0.633999
$39$	45.1898	−	45.1898i	1.15871	−	1.15871i
$40$	−6.21085	+	6.21085i	−0.155271	+	0.155271i
$41$	18.4910			0.451000			0.225500	−	0.974243i	$-0.427598\pi$
$41$	18.4910			0.451000			0.225500	+	0.974243i	$0.427598\pi$
$42$	−9.60687	−	9.60687i	−0.228735	−	0.228735i
$43$			41.3469i			0.961556i	0.876842	+	0.480778i	$0.159646\pi$
$43$			41.3469i			0.961556i	−0.876842	+	0.480778i	$0.840354\pi$
$44$	37.8728			0.860746
$45$		−	33.0915i		−	0.735367i
$46$	−33.5498	−	33.5498i	−0.729343	−	0.729343i
$47$	73.3404			1.56043			0.780217	−	0.625509i	$-0.215109\pi$
$47$	73.3404			1.56043			0.780217	+	0.625509i	$0.215109\pi$
$48$	−12.5399	−	12.5399i	−0.261247	−	0.261247i
$49$			44.3047i			0.904177i
$50$	15.3563	+	15.3563i	0.307127	+	0.307127i
$51$			5.83332i			0.114379i
$52$	28.8295			0.554414
$53$	32.0050			0.603868			0.301934	−	0.953329i	$-0.402368\pi$
$53$	32.0050			0.603868			0.301934	+	0.953329i	$0.402368\pi$
$54$	10.3833			0.192283
$55$			58.8056i			1.06919i
$56$		−	6.12885i		−	0.109444i
$57$	75.5275			1.32504
$58$	28.9652			0.499401
$59$	32.0412	−	32.0412i	0.543071	−	0.543071i	−0.381357	−	0.924428i	$-0.624543\pi$
$59$	32.0412	−	32.0412i	0.543071	−	0.543071i	0.924428	+	0.381357i	$0.124543\pi$
$60$	19.4708	−	19.4708i	0.324513	−	0.324513i
$61$	−35.3265			−0.579124			−0.289562	−	0.957159i	$-0.593510\pi$
$61$	−35.3265			−0.579124			−0.289562	+	0.957159i	$0.593510\pi$
$62$	−54.8355			−0.884444
$63$	16.3273	+	16.3273i	0.259164	+	0.259164i
$64$		−	8.00000i		−	0.125000i
$65$			44.7640i			0.688676i
$66$	−118.730			−1.79894
$67$	−76.5063			−1.14188			−0.570942	−	0.820990i	$-0.693422\pi$
$67$	−76.5063			−1.14188			−0.570942	+	0.820990i	$0.693422\pi$
$68$	−1.86073	+	1.86073i	−0.0273637	+	0.0273637i
$69$	105.177	+	105.177i	1.52431	+	1.52431i
$70$	9.51633			0.135948
$71$	−9.32389	+	9.32389i	−0.131322	+	0.131322i	−0.769713	−	0.638390i	$-0.779601\pi$
$71$	−9.32389	+	9.32389i	−0.131322	+	0.131322i	0.638390	+	0.769713i	$0.279601\pi$
$72$	21.3121	+	21.3121i	0.296001	+	0.296001i
$73$			52.8575i			0.724076i	0.932163	+	0.362038i	$0.117919\pi$
$73$			52.8575i			0.724076i	−0.932163	+	0.362038i	$0.882081\pi$
$74$	51.5072	+	51.5072i	0.696044	+	0.696044i
$75$	−48.1417	−	48.1417i	−0.641889	−	0.641889i
$76$	24.0919	+	24.0919i	0.316999	+	0.316999i
$77$	−29.0146	−	29.0146i	−0.376813	−	0.376813i
$78$	−90.3797			−1.15871
$79$		−	79.4315i		−	1.00546i	−0.864443	−	0.502731i	$-0.832329\pi$
$79$		−	79.4315i		−	1.00546i	0.864443	−	0.502731i	$-0.167671\pi$
$80$	12.4217			0.155271
$81$	63.3531			0.782137
$82$	−18.4910	−	18.4910i	−0.225500	−	0.225500i
$83$	77.1605	−	77.1605i	0.929644	−	0.929644i	−0.0680387	−	0.997683i	$-0.521674\pi$
$83$	77.1605	−	77.1605i	0.929644	−	0.929644i	0.997683	+	0.0680387i	$0.0216741\pi$
$84$			19.2137i			0.228735i
$85$	−2.88918	−	2.88918i	−0.0339903	−	0.0339903i
$86$	41.3469	−	41.3469i	0.480778	−	0.480778i
$87$	−90.8051			−1.04374
$88$	−37.8728	−	37.8728i	−0.430373	−	0.430373i
$89$		−	84.5435i		−	0.949927i	−0.880005	−	0.474964i	$-0.842461\pi$
$89$		−	84.5435i		−	0.949927i	0.880005	−	0.474964i	$-0.157539\pi$
$90$	−33.0915	+	33.0915i	−0.367684	+	0.367684i
$91$	−22.0865	−	22.0865i	−0.242708	−	0.242708i
$92$			67.0995i			0.729343i
$93$	171.908			1.84847
$94$	−73.3404	−	73.3404i	−0.780217	−	0.780217i
$95$	−37.4078	+	37.4078i	−0.393767	+	0.393767i
$96$			25.0797i			0.261247i
$97$		−	29.7035i		−	0.306222i	−0.988209	−	0.153111i	$-0.951071\pi$
$97$		−	29.7035i		−	0.306222i	0.988209	−	0.153111i	$-0.0489292\pi$
$98$	44.3047	−	44.3047i	0.452088	−	0.452088i
$99$	201.787			2.03826
$100$		−	30.7127i		−	0.307127i
$101$	−132.448	−	132.448i	−1.31136	−	1.31136i	−0.920410	−	0.390954i	$-0.872145\pi$
$101$	−132.448	−	132.448i	−1.31136	−	1.31136i	−0.390954	−	0.920410i	$-0.627855\pi$
$102$	5.83332	−	5.83332i	0.0571895	−	0.0571895i
$103$		−	163.138i		−	1.58386i	−0.610609	−	0.791932i	$-0.709075\pi$
$103$		−	163.138i		−	1.58386i	0.610609	−	0.791932i	$-0.290925\pi$
$104$	−28.8295	−	28.8295i	−0.277207	−	0.277207i
$105$	−29.8334			−0.284127
$106$	−32.0050	−	32.0050i	−0.301934	−	0.301934i
$107$	−123.938	+	123.938i	−1.15830	+	1.15830i	−0.173455	+	0.984842i	$0.555493\pi$
$107$	−123.938	+	123.938i	−1.15830	+	1.15830i	−0.984842	+	0.173455i	$0.944507\pi$
$108$	−10.3833	−	10.3833i	−0.0961416	−	0.0961416i
$109$	25.1483	−	25.1483i	0.230719	−	0.230719i	−0.582274	−	0.812993i	$-0.697837\pi$
$109$	25.1483	−	25.1483i	0.230719	−	0.230719i	0.812993	+	0.582274i	$0.197837\pi$
$110$	58.8056	−	58.8056i	0.534596	−	0.534596i
$111$	−161.473	−	161.473i	−1.45472	−	1.45472i
$112$	−6.12885	+	6.12885i	−0.0547218	+	0.0547218i
$113$	−66.1617	+	66.1617i	−0.585502	+	0.585502i	−0.936410	−	0.350908i	$-0.885873\pi$
$113$	−66.1617	+	66.1617i	−0.585502	+	0.585502i	0.350908	+	0.936410i	$0.385873\pi$
$114$	−75.5275	−	75.5275i	−0.662522	−	0.662522i
$115$	−104.186			−0.905967
$116$	−28.9652	−	28.9652i	−0.249700	−	0.249700i
$117$	153.604			1.31286
$118$	−64.0824			−0.543071
$119$	2.85103			0.0239582
$120$	−38.9416			−0.324513
$121$	−237.588			−1.96353
$122$	35.3265	+	35.3265i	0.289562	+	0.289562i
$123$	57.9687	+	57.9687i	0.471291	+	0.471291i
$124$	54.8355	+	54.8355i	0.442222	+	0.442222i
$125$	125.324			1.00259
$126$		−	32.6546i		−	0.259164i
$127$		−	100.087i		−	0.788090i	−0.919091	−	0.394045i	$-0.871075\pi$
$127$		−	100.087i		−	0.788090i	0.919091	−	0.394045i	$-0.128925\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	−129.621	+	129.621i	−1.00482	+	1.00482i
$130$	44.7640	−	44.7640i	0.344338	−	0.344338i
$131$	40.6002			0.309925			0.154963	−	0.987920i	$-0.450474\pi$
$131$	40.6002			0.309925			0.154963	+	0.987920i	$0.450474\pi$
$132$	118.730	+	118.730i	0.899470	+	0.899470i
$133$		−	36.9140i		−	0.277549i
$134$	76.5063	+	76.5063i	0.570942	+	0.570942i
$135$	16.1223	−	16.1223i	0.119424	−	0.119424i
$136$	3.72146			0.0273637
$137$	173.022	−	173.022i	1.26294	−	1.26294i	0.313275	−	0.949662i	$-0.398574\pi$
$137$	173.022	−	173.022i	1.26294	−	1.26294i	0.949662	−	0.313275i	$-0.101426\pi$
$138$		−	210.355i		−	1.52431i
$139$	21.4620	+	21.4620i	0.154403	+	0.154403i	0.780081	−	0.625678i	$-0.215178\pi$
$139$	21.4620	+	21.4620i	0.154403	+	0.154403i	−0.625678	+	0.780081i	$0.715178\pi$
$140$	−9.51633	−	9.51633i	−0.0679738	−	0.0679738i
$141$	229.920	+	229.920i	1.63064	+	1.63064i
$142$	18.6478			0.131322
$143$	−272.964			−1.90884
$144$		−	42.6242i		−	0.296001i
$145$	44.9747	−	44.9747i	0.310170	−	0.310170i
$146$	52.8575	−	52.8575i	0.362038	−	0.362038i
$147$	−138.894	+	138.894i	−0.944855	+	0.944855i
$148$		−	103.014i		−	0.696044i
$149$			179.530i			1.20490i	0.798157	+	0.602450i	$0.205809\pi$
$149$			179.530i			1.20490i	−0.798157	+	0.602450i	$0.794191\pi$
$150$			96.2833i			0.641889i
$151$			49.9023i			0.330479i	0.986253	+	0.165240i	$0.0528397\pi$
$151$			49.9023i			0.330479i	−0.986253	+	0.165240i	$0.947160\pi$
$152$		−	48.1839i		−	0.316999i
$153$	−9.91400	+	9.91400i	−0.0647974	+	0.0647974i
$154$			58.0292i			0.376813i
$155$	−85.1438	+	85.1438i	−0.549315	+	0.549315i
$156$	90.3797	+	90.3797i	0.579357	+	0.579357i
$157$	188.964	+	188.964i	1.20359	+	1.20359i	0.973067	+	0.230523i	$0.0740435\pi$
$157$	188.964	+	188.964i	1.20359	+	1.20359i	0.230523	+	0.973067i	$0.425956\pi$
$158$	−79.4315	+	79.4315i	−0.502731	+	0.502731i
$159$	100.335	+	100.335i	0.631035	+	0.631035i
$160$	−12.4217	−	12.4217i	−0.0776356	−	0.0776356i
$161$	51.4053	−	51.4053i	0.319288	−	0.319288i
$162$	−63.3531	−	63.3531i	−0.391069	−	0.391069i
$163$	−159.069	+	159.069i	−0.975881	+	0.975881i	−0.999716	−	0.0238344i	$-0.992413\pi$
$163$	−159.069	+	159.069i	−0.975881	+	0.975881i	0.0238344	+	0.999716i	$0.492413\pi$
$164$			36.9820i			0.225500i
$165$	−184.354	+	184.354i	−1.11729	+	1.11729i
$166$	−154.321			−0.929644
$167$	113.583	+	113.583i	0.680140	+	0.680140i	0.960032	−	0.279892i	$-0.0902986\pi$
$167$	113.583	+	113.583i	0.680140	+	0.680140i	−0.279892	+	0.960032i	$0.590299\pi$
$168$	19.2137	−	19.2137i	0.114367	−	0.114367i
$169$	−38.7855			−0.229500
$170$			5.77835i			0.0339903i
$171$	128.362	+	128.362i	0.750658	+	0.750658i
$172$	−82.6938			−0.480778
$173$	−27.9682			−0.161666			−0.0808330	−	0.996728i	$-0.525758\pi$
$173$	−27.9682			−0.161666			−0.0808330	+	0.996728i	$0.525758\pi$
$174$	90.8051	+	90.8051i	0.521868	+	0.521868i
$175$	−23.5292	+	23.5292i	−0.134452	+	0.134452i
$176$			75.7456i			0.430373i
$177$	200.896			1.13501
$178$	−84.5435	+	84.5435i	−0.474964	+	0.474964i
$179$	−2.40947	−	2.40947i	−0.0134608	−	0.0134608i	0.700344	−	0.713805i	$-0.253030\pi$
$179$	−2.40947	−	2.40947i	−0.0134608	−	0.0134608i	−0.713805	+	0.700344i	$0.753030\pi$
$180$	66.1831			0.367684
$181$	41.5849	−	41.5849i	0.229751	−	0.229751i	−0.582838	−	0.812589i	$-0.698058\pi$
$181$	41.5849	−	41.5849i	0.229751	−	0.229751i	0.812589	+	0.582838i	$0.198058\pi$
$182$			44.1729i			0.242708i
$183$	−110.748	−	110.748i	−0.605178	−	0.605178i
$184$	67.0995	−	67.0995i	0.364671	−	0.364671i
$185$	159.952			0.864604
$186$	−171.908	−	171.908i	−0.924235	−	0.924235i
$187$	17.6178	−	17.6178i	0.0942126	−	0.0942126i
$188$			146.681i			0.780217i
$189$			15.9094i			0.0841767i
$190$	74.8157			0.393767
$191$		−	136.365i		−	0.713954i	−0.934113	−	0.356977i	$-0.883807\pi$
$191$		−	136.365i		−	0.713954i	0.934113	−	0.356977i	$-0.116193\pi$
$192$	25.0797	−	25.0797i	0.130624	−	0.130624i
$193$	−247.200	+	247.200i	−1.28083	+	1.28083i	−0.340634	+	0.940196i	$0.610642\pi$
$193$	−247.200	+	247.200i	−1.28083	+	1.28083i	−0.940196	+	0.340634i	$0.889358\pi$
$194$	−29.7035	+	29.7035i	−0.153111	+	0.153111i
$195$	−140.334	+	140.334i	−0.719659	+	0.719659i
$196$	−88.6093			−0.452088
$197$	9.66704	−	9.66704i	0.0490713	−	0.0490713i	−0.682145	−	0.731217i	$-0.738953\pi$
$197$	9.66704	−	9.66704i	0.0490713	−	0.0490713i	0.731217	+	0.682145i	$0.238953\pi$
$198$	−201.787	−	201.787i	−1.01913	−	1.01913i
$199$			243.218i			1.22220i	0.791552	+	0.611102i	$0.209273\pi$
$199$			243.218i			1.22220i	−0.791552	+	0.611102i	$0.790727\pi$
$200$	−30.7127	+	30.7127i	−0.153563	+	0.153563i
$201$	−239.845	−	239.845i	−1.19326	−	1.19326i
$202$			264.896i			1.31136i
$203$			44.3809i			0.218625i
$204$	−11.6666			−0.0571895
$205$	−57.4224			−0.280109
$206$	−163.138	+	163.138i	−0.791932	+	0.791932i
$207$			357.508i			1.72709i
$208$			57.6591i			0.277207i
$209$	−228.108	−	228.108i	−1.09142	−	1.09142i
$210$	29.8334	+	29.8334i	0.142064	+	0.142064i
$211$		−	117.950i		−	0.559004i	−0.960145	−	0.279502i	$-0.909831\pi$
$211$		−	117.950i		−	0.559004i	0.960145	−	0.279502i	$-0.0901694\pi$
$212$			64.0100i			0.301934i
$213$	−58.4602			−0.274461
$214$	247.876			1.15830
$215$		−	128.400i		−	0.597208i
$216$			20.7666i			0.0961416i
$217$		−	84.0197i		−	0.387187i
$218$	−50.2967			−0.230719
$219$	−165.707	+	165.707i	−0.756652	+	0.756652i
$220$	−117.611			−0.534596
$221$	13.4110	−	13.4110i	0.0606832	−	0.0606832i
$222$			322.947i			1.45472i
$223$	96.7915	−	96.7915i	0.434043	−	0.434043i	−0.455958	−	0.890001i	$-0.650703\pi$
$223$	96.7915	−	96.7915i	0.434043	−	0.434043i	0.890001	+	0.455958i	$0.150703\pi$
$224$	12.2577			0.0547218
$225$		−	163.638i		−	0.727280i
$226$	132.323			0.585502
$227$	−193.589	+	193.589i	−0.852817	+	0.852817i	−0.990479	−	0.137663i	$-0.956041\pi$
$227$	−193.589	+	193.589i	−0.852817	+	0.852817i	0.137663	+	0.990479i	$0.456041\pi$
$228$			151.055i			0.662522i
$229$	−53.4738	−	53.4738i	−0.233510	−	0.233510i	0.580646	−	0.814156i	$-0.302800\pi$
$229$	−53.4738	−	53.4738i	−0.233510	−	0.233510i	−0.814156	+	0.580646i	$0.802800\pi$
$230$	104.186	+	104.186i	0.452984	+	0.452984i
$231$		−	181.920i		−	0.787531i
$232$			57.9305i			0.249700i
$233$			59.7154i			0.256289i	0.991755	+	0.128145i	$0.0409022\pi$
$233$			59.7154i			0.256289i	−0.991755	+	0.128145i	$0.959098\pi$
$234$	−153.604	−	153.604i	−0.656429	−	0.656429i
$235$	−227.753			−0.969162
$236$	64.0824	+	64.0824i	0.271536	+	0.271536i
$237$	249.015	−	249.015i	1.05070	−	1.05070i
$238$	−2.85103	−	2.85103i	−0.0119791	−	0.0119791i
$239$	67.0954			0.280734			0.140367	−	0.990100i	$-0.455172\pi$
$239$	67.0954			0.280734			0.140367	+	0.990100i	$0.455172\pi$
$240$	38.9416	+	38.9416i	0.162257	+	0.162257i
$241$	−169.514	+	169.514i	−0.703379	+	0.703379i	−0.965134	−	0.261755i	$-0.915699\pi$
$241$	−169.514	+	169.514i	−0.703379	+	0.703379i	0.261755	+	0.965134i	$0.415699\pi$
$242$	237.588	+	237.588i	0.981767	+	0.981767i
$243$	245.335	+	245.335i	1.00961	+	1.00961i
$244$		−	70.6531i		−	0.289562i
$245$		−	137.585i		−	0.561570i
$246$		−	115.937i		−	0.471291i
$247$	−173.640	−	173.640i	−0.702996	−	0.702996i
$248$		−	109.671i		−	0.442222i
$249$	483.791			1.94294
$250$	−125.324	−	125.324i	−0.501294	−	0.501294i
$251$	264.697	+	264.697i	1.05457	+	1.05457i	0.998423	+	0.0561455i	$0.0178811\pi$
$251$	264.697	+	264.697i	1.05457	+	1.05457i	0.0561455	+	0.998423i	$0.482119\pi$
$252$	−32.6546	+	32.6546i	−0.129582	+	0.129582i
$253$		−	635.312i		−	2.51112i
$254$	−100.087	+	100.087i	−0.394045	+	0.394045i
$255$		−	18.1149i		−	0.0710390i
$256$	16.0000			0.0625000
$257$	313.670	+	313.670i	1.22050	+	1.22050i	0.967453	+	0.253052i	$0.0814344\pi$
$257$	313.670	+	313.670i	1.22050	+	1.22050i	0.253052	+	0.967453i	$0.418566\pi$
$258$	259.243			1.00482
$259$	−78.9199	+	78.9199i	−0.304710	+	0.304710i
$260$	−89.5279			−0.344338
$261$	−154.327	−	154.327i	−0.591293	−	0.591293i
$262$	−40.6002	−	40.6002i	−0.154963	−	0.154963i
$263$	283.691			1.07867			0.539336	−	0.842090i	$-0.318675\pi$
$263$	283.691			1.07867			0.539336	+	0.842090i	$0.318675\pi$
$264$		−	237.460i		−	0.899470i
$265$	−99.3891			−0.375053
$266$	−36.9140	+	36.9140i	−0.138774	+	0.138774i
$267$	265.041	−	265.041i	0.992664	−	0.992664i
$268$		−	153.013i		−	0.570942i
$269$	97.9596	−	250.529i	0.364162	−	0.931336i
$269$	97.9596	−	250.529i	0.364162	−	0.931336i
$270$	−32.2445			−0.119424
$271$	−27.8872	−	27.8872i	−0.102905	−	0.102905i	0.653780	−	0.756685i	$-0.273182\pi$
$271$	−27.8872	−	27.8872i	−0.102905	−	0.102905i	−0.756685	+	0.653780i	$0.773182\pi$
$272$	−3.72146	−	3.72146i	−0.0136818	−	0.0136818i
$273$		−	138.481i		−	0.507255i
$274$	−346.045			−1.26294
$275$			290.794i			1.05743i
$276$	−210.355	+	210.355i	−0.762155	+	0.762155i
$277$	−115.987	+	115.987i	−0.418725	+	0.418725i	−0.884764	−	0.466039i	$-0.845681\pi$
$277$	−115.987	+	115.987i	−0.418725	+	0.418725i	0.466039	+	0.884764i	$0.345681\pi$
$278$		−	42.9239i		−	0.154403i
$279$	292.165	+	292.165i	1.04719	+	1.04719i
$280$			19.0327i			0.0679738i
$281$	−328.588	+	328.588i	−1.16935	+	1.16935i	−0.186989	+	0.982362i	$0.559873\pi$
$281$	−328.588	+	328.588i	−1.16935	+	1.16935i	−0.982362	+	0.186989i	$0.940127\pi$
$282$		−	459.840i		−	1.63064i
$283$	−263.473			−0.931000			−0.465500	−	0.885048i	$-0.654125\pi$
$283$	−263.473			−0.931000			−0.465500	+	0.885048i	$0.654125\pi$
$284$	−18.6478	−	18.6478i	−0.0656612	−	0.0656612i
$285$	−234.545			−0.822964
$286$	272.964	+	272.964i	0.954420	+	0.954420i
$287$	28.3321	−	28.3321i	0.0987183	−	0.0987183i
$288$	−42.6242	+	42.6242i	−0.148001	+	0.148001i
$289$		−	287.269i		−	0.994010i
$290$	−89.9493			−0.310170
$291$	93.1196	−	93.1196i	0.319999	−	0.319999i
$292$	−105.715			−0.362038
$293$	−43.1690			−0.147335			−0.0736673	−	0.997283i	$-0.523470\pi$
$293$	−43.1690			−0.147335			−0.0736673	+	0.997283i	$0.523470\pi$
$294$	277.787			0.944855
$295$	−99.5015	+	99.5015i	−0.337293	+	0.337293i
$296$	−103.014	+	103.014i	−0.348022	+	0.348022i
$297$	98.3112	+	98.3112i	0.331014	+	0.331014i
$298$	179.530	−	179.530i	0.602450	−	0.602450i
$299$		−	483.612i		−	1.61743i
$300$	96.2833	−	96.2833i	0.320944	−	0.320944i
$301$	63.3522	+	63.3522i	0.210473	+	0.210473i
$302$	49.9023	−	49.9023i	0.165240	−	0.165240i
$303$		−	830.439i		−	2.74072i
$304$	−48.1839	+	48.1839i	−0.158500	+	0.158500i
$305$	109.704			0.359685
$306$	19.8280			0.0647974
$307$	−34.0861			−0.111029			−0.0555147	−	0.998458i	$-0.517680\pi$
$307$	−34.0861			−0.111029			−0.0555147	+	0.998458i	$0.517680\pi$
$308$	58.0292	−	58.0292i	0.188406	−	0.188406i
$309$	511.432	−	511.432i	1.65512	−	1.65512i
$310$	170.288			0.549315
$311$	424.256	+	424.256i	1.36417	+	1.36417i	0.868529	+	0.495638i	$0.165066\pi$
$311$	424.256	+	424.256i	1.36417	+	1.36417i	0.495638	+	0.868529i	$0.334934\pi$
$312$		−	180.759i		−	0.579357i
$313$	−16.5274			−0.0528031			−0.0264016	−	0.999651i	$-0.508405\pi$
$313$	−16.5274			−0.0528031			−0.0264016	+	0.999651i	$0.508405\pi$
$314$		−	377.927i		−	1.20359i
$315$	−50.7032	−	50.7032i	−0.160963	−	0.160963i
$316$	158.863			0.502731
$317$	−133.688	−	133.688i	−0.421730	−	0.421730i	0.464069	−	0.885799i	$-0.346389\pi$
$317$	−133.688	−	133.688i	−0.421730	−	0.421730i	−0.885799	+	0.464069i	$0.846389\pi$
$318$		−	200.669i		−	0.631035i
$319$	274.249	+	274.249i	0.859714	+	0.859714i
$320$			24.8434i			0.0776356i
$321$	−777.082			−2.42082
$322$	−102.811			−0.319288
$323$	22.4143			0.0693941
$324$			126.706i			0.391069i
$325$			221.358i			0.681102i
$326$	318.137			0.975881
$327$	157.678			0.482197
$328$	36.9820	−	36.9820i	0.112750	−	0.112750i
$329$	112.373	−	112.373i	0.341559	−	0.341559i
$330$	368.707			1.11729
$331$	−18.0652			−0.0545776			−0.0272888	−	0.999628i	$-0.508687\pi$
$331$	−18.0652			−0.0545776			−0.0272888	+	0.999628i	$0.508687\pi$
$332$	154.321	+	154.321i	0.464822	+	0.464822i
$333$		−	548.863i		−	1.64824i
$334$		−	227.167i		−	0.680140i
$335$	237.584			0.709207
$336$	−38.4275			−0.114367
$337$	−90.1132	+	90.1132i	−0.267398	+	0.267398i	−0.828051	−	0.560653i	$-0.810550\pi$
$337$	−90.1132	+	90.1132i	−0.267398	+	0.267398i	0.560653	+	0.828051i	$0.310550\pi$
$338$	38.7855	+	38.7855i	0.114750	+	0.114750i
$339$	−414.829			−1.22369
$340$	5.77835	−	5.77835i	0.0169951	−	0.0169951i
$341$	−519.194	−	519.194i	−1.52256	−	1.52256i
$342$		−	256.725i		−	0.750658i
$343$	142.962	+	142.962i	0.416800	+	0.416800i
$344$	82.6938	+	82.6938i	0.240389	+	0.240389i
$345$	−326.620	−	326.620i	−0.946726	−	0.946726i
$346$	27.9682	+	27.9682i	0.0808330	+	0.0808330i
$347$	−96.5159			−0.278144			−0.139072	−	0.990282i	$-0.544412\pi$
$347$	−96.5159			−0.278144			−0.139072	+	0.990282i	$0.544412\pi$
$348$		−	181.610i		−	0.521868i
$349$	−416.690			−1.19396			−0.596978	−	0.802258i	$-0.703632\pi$
$349$	−416.690			−1.19396			−0.596978	+	0.802258i	$0.703632\pi$
$350$	47.0583			0.134452
$351$	74.8364	+	74.8364i	0.213209	+	0.213209i
$352$	75.7456	−	75.7456i	0.215187	−	0.215187i
$353$			266.525i			0.755027i	0.926004	+	0.377514i	$0.123221\pi$
$353$			266.525i			0.755027i	−0.926004	+	0.377514i	$0.876779\pi$
$354$	−200.896	−	200.896i	−0.567504	−	0.567504i
$355$	28.9546	−	28.9546i	0.0815623	−	0.0815623i
$356$	169.087			0.474964
$357$	8.93789	+	8.93789i	0.0250361	+	0.0250361i
$358$			4.81895i			0.0134608i
$359$	307.773	−	307.773i	0.857306	−	0.857306i	−0.133714	−	0.991020i	$-0.542690\pi$
$359$	307.773	−	307.773i	0.857306	−	0.857306i	0.991020	+	0.133714i	$0.0426903\pi$
$360$	−66.1831	−	66.1831i	−0.183842	−	0.183842i
$361$			70.7890i			0.196091i
$362$	−83.1698			−0.229751
$363$	−744.830	−	744.830i	−2.05187	−	2.05187i
$364$	44.1729	−	44.1729i	0.121354	−	0.121354i
$365$		−	164.145i		−	0.449712i
$366$			221.495i			0.605178i
$367$	−25.3251	+	25.3251i	−0.0690057	+	0.0690057i	−0.740767	−	0.671762i	$-0.765538\pi$
$367$	−25.3251	+	25.3251i	−0.0690057	+	0.0690057i	0.671762	+	0.740767i	$0.265538\pi$
$368$	−134.199			−0.364671
$369$			197.041i			0.533987i
$370$	−159.952	−	159.952i	−0.432302	−	0.432302i
$371$	49.0384	−	49.0384i	0.132179	−	0.132179i
$372$			343.815i			0.924235i
$373$	286.373	+	286.373i	0.767757	+	0.767757i	0.977711	−	0.209954i	$-0.0673315\pi$
$373$	286.373	+	286.373i	0.767757	+	0.767757i	−0.209954	+	0.977711i	$0.567332\pi$
$374$	−35.2355			−0.0942126
$375$	392.885	+	392.885i	1.04769	+	1.04769i
$376$	146.681	−	146.681i	0.390109	−	0.390109i
$377$	208.764	+	208.764i	0.553749	+	0.553749i
$378$	15.9094	−	15.9094i	0.0420884	−	0.0420884i
$379$	−52.5935	+	52.5935i	−0.138769	+	0.138769i	−0.773079	−	0.634310i	$-0.781284\pi$
$379$	−52.5935	+	52.5935i	−0.138769	+	0.138769i	0.634310	+	0.773079i	$0.281284\pi$
$380$	−74.8157	−	74.8157i	−0.196883	−	0.196883i
$381$	313.771	−	313.771i	0.823545	−	0.823545i
$382$	−136.365	+	136.365i	−0.356977	+	0.356977i
$383$	148.999	+	148.999i	0.389032	+	0.389032i	0.874342	−	0.485310i	$-0.161293\pi$
$383$	148.999	+	148.999i	0.389032	+	0.389032i	−0.485310	+	0.874342i	$0.661293\pi$
$384$	−50.1595			−0.130624
$385$	90.1026	+	90.1026i	0.234033	+	0.234033i
$386$	494.400			1.28083
$387$	−440.595			−1.13849
$388$	59.4071			0.153111
$389$	−573.341			−1.47389			−0.736943	−	0.675955i	$-0.763731\pi$
$389$	−573.341			−1.47389			−0.736943	+	0.675955i	$0.763731\pi$
$390$	280.667			0.719659
$391$	31.2135	+	31.2135i	0.0798300	+	0.0798300i
$392$	88.6093	+	88.6093i	0.226044	+	0.226044i
$393$	127.280	+	127.280i	0.323868	+	0.323868i
$394$	−19.3341			−0.0490713
$395$			246.669i			0.624477i
$396$			403.575i			1.01913i
$397$	233.627	−	233.627i	0.588480	−	0.588480i	−0.348740	−	0.937220i	$-0.613390\pi$
$397$	233.627	−	233.627i	0.588480	−	0.588480i	0.937220	+	0.348740i	$0.113390\pi$
$398$	243.218	−	243.218i	0.611102	−	0.611102i
$399$	115.724	−	115.724i	0.290035	−	0.290035i
$400$	61.4254			0.153563
$401$	−432.194	−	432.194i	−1.07779	−	1.07779i	−0.996707	−	0.0810836i	$-0.974162\pi$
$401$	−432.194	−	432.194i	−1.07779	−	1.07779i	−0.0810836	−	0.996707i	$-0.525838\pi$
$402$			479.689i			1.19326i
$403$	−395.221	−	395.221i	−0.980697	−	0.980697i
$404$	264.896	−	264.896i	0.655682	−	0.655682i
$405$	−196.738			−0.485773
$406$	44.3809	−	44.3809i	0.109312	−	0.109312i
$407$			975.362i			2.39647i
$408$	11.6666	+	11.6666i	0.0285947	+	0.0285947i
$409$	237.474	+	237.474i	0.580622	+	0.580622i	0.935074	−	0.354452i	$-0.115333\pi$
$409$	237.474	+	237.474i	0.580622	+	0.580622i	−0.354452	+	0.935074i	$0.615333\pi$
$410$	57.4224	+	57.4224i	0.140055	+	0.140055i
$411$	1084.84			2.63951
$412$	326.276			0.791932
$413$		−	98.1878i		−	0.237743i
$414$	357.508	−	357.508i	0.863546	−	0.863546i
$415$	−239.616	+	239.616i	−0.577388	+	0.577388i
$416$	57.6591	−	57.6591i	0.138604	−	0.138604i
$417$			134.565i			0.322698i
$418$			456.215i			1.09142i
$419$			79.4467i			0.189610i	0.995496	+	0.0948051i	$0.0302228\pi$
$419$			79.4467i			0.189610i	−0.995496	+	0.0948051i	$0.969777\pi$
$420$		−	59.6668i		−	0.142064i
$421$			318.129i			0.755650i	0.925877	+	0.377825i	$0.123328\pi$
$421$			318.129i			0.755650i	−0.925877	+	0.377825i	$0.876672\pi$
$422$	−117.950	+	117.950i	−0.279502	+	0.279502i
$423$			781.519i			1.84756i
$424$	64.0100	−	64.0100i	0.150967	−	0.150967i
$425$	−14.2870	−	14.2870i	−0.0336165	−	0.0336165i
$426$	58.4602	+	58.4602i	0.137231	+	0.137231i
$427$	−54.1277	+	54.1277i	−0.126763	+	0.126763i
$428$	−247.876	−	247.876i	−0.579148	−	0.579148i
$429$	−855.733	−	855.733i	−1.99472	−	1.99472i
$430$	−128.400	+	128.400i	−0.298604	+	0.298604i
$431$	−207.897	−	207.897i	−0.482360	−	0.482360i	0.423524	−	0.905885i	$-0.360793\pi$
$431$	−207.897	−	207.897i	−0.482360	−	0.482360i	−0.905885	+	0.423524i	$0.860793\pi$
$432$	20.7666	−	20.7666i	0.0480708	−	0.0480708i
$433$		−	566.939i		−	1.30933i	−0.755920	−	0.654664i	$-0.772810\pi$
$433$		−	566.939i		−	1.30933i	0.755920	−	0.654664i	$-0.227190\pi$
$434$	−84.0197	+	84.0197i	−0.193594	+	0.193594i
$435$	281.988			0.648249
$436$	50.2967	+	50.2967i	0.115359	+	0.115359i
$437$	404.140	−	404.140i	0.924805	−	0.924805i
$438$	331.413			0.756652
$439$			141.773i			0.322946i	0.986877	+	0.161473i	$0.0516245\pi$
$439$			141.773i			0.322946i	−0.986877	+	0.161473i	$0.948375\pi$
$440$	117.611	+	117.611i	0.267298	+	0.267298i
$441$	−472.112			−1.07055
$442$	−26.8220			−0.0606832
$443$	46.6925	+	46.6925i	0.105401	+	0.105401i	0.757841	−	0.652440i	$-0.226254\pi$
$443$	46.6925	+	46.6925i	0.105401	+	0.105401i	−0.652440	+	0.757841i	$0.726254\pi$
$444$	322.947	−	322.947i	0.727358	−	0.727358i
$445$			262.543i			0.589985i
$446$	−193.583			−0.434043
$447$	−562.821	+	562.821i	−1.25911	+	1.25911i
$448$	−12.2577	−	12.2577i	−0.0273609	−	0.0273609i
$449$	240.453			0.535531			0.267765	−	0.963484i	$-0.413715\pi$
$449$	240.453			0.535531			0.267765	+	0.963484i	$0.413715\pi$
$450$	−163.638	+	163.638i	−0.363640	+	0.363640i
$451$		−	350.154i		−	0.776394i
$452$	−132.323	−	132.323i	−0.292751	−	0.292751i
$453$	−156.442	+	156.442i	−0.345347	+	0.345347i
$454$	387.179			0.852817
$455$	68.5878	+	68.5878i	0.150742	+	0.150742i
$456$	151.055	−	151.055i	0.331261	−	0.331261i
$457$		−	639.175i		−	1.39863i	−0.714812	−	0.699316i	$-0.753488\pi$
$457$		−	639.175i		−	1.39863i	0.714812	−	0.699316i	$-0.246512\pi$
$458$			106.948i			0.233510i
$459$	−9.66025			−0.0210463
$460$		−	208.372i		−	0.452984i
$461$	489.462	−	489.462i	1.06174	−	1.06174i	0.0637747	−	0.997964i	$-0.479686\pi$
$461$	489.462	−	489.462i	1.06174	−	1.06174i	0.997964	−	0.0637747i	$-0.0203139\pi$
$462$	−181.920	+	181.920i	−0.393765	+	0.393765i
$463$	416.736	−	416.736i	0.900077	−	0.900077i	−0.0953650	−	0.995442i	$-0.530402\pi$
$463$	416.736	−	416.736i	0.900077	−	0.900077i	0.995442	+	0.0953650i	$0.0304018\pi$
$464$	57.9305	−	57.9305i	0.124850	−	0.124850i
$465$	−533.846			−1.14806
$466$	59.7154	−	59.7154i	0.128145	−	0.128145i
$467$	246.123	+	246.123i	0.527031	+	0.527031i	0.919686	−	0.392655i	$-0.128443\pi$
$467$	246.123	+	246.123i	0.527031	+	0.527031i	−0.392655	+	0.919686i	$0.628443\pi$
$468$			307.209i			0.656429i
$469$	−117.224	+	117.224i	−0.249944	+	0.249944i
$470$	227.753	+	227.753i	0.484581	+	0.484581i
$471$			1184.79i			2.51548i
$472$		−	128.165i		−	0.271536i
$473$	782.962			1.65531
$474$	−498.031			−1.05070
$475$	−184.982	+	184.982i	−0.389436	+	0.389436i
$476$			5.70206i			0.0119791i
$477$			341.047i			0.714983i
$478$	−67.0954	−	67.0954i	−0.140367	−	0.140367i
$479$	−405.375	−	405.375i	−0.846295	−	0.846295i	0.143374	−	0.989669i	$-0.454205\pi$
$479$	−405.375	−	405.375i	−0.846295	−	0.846295i	−0.989669	+	0.143374i	$0.954205\pi$
$480$		−	77.8832i		−	0.162257i
$481$			742.465i			1.54359i
$482$	339.029			0.703379
$483$	322.308			0.667305
$484$		−	475.175i		−	0.981767i
$485$			92.2421i			0.190190i
$486$		−	490.670i		−	1.00961i
$487$	−85.8008			−0.176182			−0.0880911	−	0.996112i	$-0.528077\pi$
$487$	−85.8008			−0.176182			−0.0880911	+	0.996112i	$0.528077\pi$
$488$	−70.6531	+	70.6531i	−0.144781	+	0.144781i
$489$	−997.350			−2.03957
$490$	−137.585	+	137.585i	−0.280785	+	0.280785i
$491$			765.799i			1.55967i	0.625983	+	0.779836i	$0.284698\pi$
$491$			765.799i			1.55967i	−0.625983	+	0.779836i	$0.715302\pi$
$492$	−115.937	+	115.937i	−0.235645	+	0.235645i
$493$	−26.9482			−0.0546617
$494$			347.280i			0.702996i
$495$	−626.635			−1.26593
$496$	−109.671	+	109.671i	−0.221111	+	0.221111i
$497$			28.5723i			0.0574896i
$498$	−483.791	−	483.791i	−0.971468	−	0.971468i
$499$	−405.675	−	405.675i	−0.812976	−	0.812976i	0.172103	−	0.985079i	$-0.444944\pi$
$499$	−405.675	−	405.675i	−0.812976	−	0.812976i	−0.985079	+	0.172103i	$0.944944\pi$
$500$			250.647i			0.501294i
$501$			712.160i			1.42148i
$502$		−	529.393i		−	1.05457i
$503$	242.673	+	242.673i	0.482452	+	0.482452i	0.905914	−	0.423462i	$-0.139185\pi$
$503$	242.673	+	242.673i	0.482452	+	0.482452i	−0.423462	+	0.905914i	$0.639185\pi$
$504$	65.3093			0.129582
$505$	411.306	+	411.306i	0.814468	+	0.814468i
$506$	−635.312	+	635.312i	−1.25556	+	1.25556i
$507$	−121.591	−	121.591i	−0.239825	−	0.239825i
$508$	200.175			0.394045
$509$	494.674	+	494.674i	0.971854	+	0.971854i	0.999615	−	0.0277604i	$-0.00883756\pi$
$509$	494.674	+	494.674i	0.971854	+	0.971854i	−0.0277604	+	0.999615i	$0.508838\pi$
$510$	−18.1149	+	18.1149i	−0.0355195	+	0.0355195i
$511$	80.9889	+	80.9889i	0.158491	+	0.158491i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$			125.077i			0.243815i
$514$		−	627.339i		−	1.22050i
$515$			506.613i			0.983714i
$516$	−259.243	−	259.243i	−0.502408	−	0.502408i
$517$		−	1388.80i		−	2.68628i
$518$	157.840			0.304710
$519$	−87.6794	−	87.6794i	−0.168939	−	0.168939i
$520$	89.5279	+	89.5279i	0.172169	+	0.172169i
$521$	−87.6064	+	87.6064i	−0.168150	+	0.168150i	−0.786166	−	0.618015i	$-0.787937\pi$
$521$	−87.6064	+	87.6064i	−0.168150	+	0.168150i	0.618015	+	0.786166i	$0.287937\pi$
$522$			308.655i			0.591293i
$523$	−473.039	+	473.039i	−0.904473	+	0.904473i	−0.995819	−	0.0913465i	$-0.970883\pi$
$523$	−473.039	+	473.039i	−0.904473	+	0.904473i	0.0913465	+	0.995819i	$0.470883\pi$
$524$			81.2004i			0.154963i
$525$	−147.526			−0.281003
$526$	−283.691	−	283.691i	−0.539336	−	0.539336i
$527$	51.0170			0.0968065
$528$	−237.460	+	237.460i	−0.449735	+	0.449735i
$529$	596.587			1.12776
$530$	99.3891	+	99.3891i	0.187527	+	0.187527i
$531$	341.433	+	341.433i	0.642999	+	0.642999i
$532$	73.8279			0.138774
$533$		−	266.544i		−	0.500082i
$534$	−530.082			−0.992664
$535$	384.879	−	384.879i	0.719400	−	0.719400i
$536$	−153.013	+	153.013i	−0.285471	+	0.285471i
$537$		−	15.1073i		−	0.0281327i
$538$	−348.489	+	152.570i	−0.647749	+	0.283587i
$539$	838.971			1.55653
$540$	32.2445	+	32.2445i	0.0597121	+	0.0597121i
$541$	428.008	+	428.008i	0.791142	+	0.791142i	0.981680	−	0.190538i	$-0.0610231\pi$
$541$	428.008	+	428.008i	0.791142	+	0.791142i	−0.190538	+	0.981680i	$0.561023\pi$
$542$			55.7745i			0.102905i
$543$	260.735			0.480175
$544$			7.44292i			0.0136818i
$545$	−78.0962	+	78.0962i	−0.143296	+	0.143296i
$546$	−138.481	+	138.481i	−0.253628	+	0.253628i
$547$			390.526i			0.713941i	0.934116	+	0.356970i	$0.116190\pi$
$547$			390.526i			0.713941i	−0.934116	+	0.356970i	$0.883810\pi$
$548$	346.045	+	346.045i	0.631469	+	0.631469i
$549$		−	376.441i		−	0.685685i
$550$	290.794	−	290.794i	0.528717	−	0.528717i
$551$			348.914i			0.633239i
$552$	420.710			0.762155
$553$	−121.706	−	121.706i	−0.220083	−	0.220083i
$554$	231.974			0.418725
$555$	501.443	+	501.443i	0.903502	+	0.903502i
$556$	−42.9239	+	42.9239i	−0.0772013	+	0.0772013i
$557$	130.732	−	130.732i	0.234708	−	0.234708i	−0.579947	−	0.814655i	$-0.696927\pi$
$557$	130.732	−	130.732i	0.234708	−	0.234708i	0.814655	+	0.579947i	$0.196927\pi$
$558$		−	584.330i		−	1.04719i
$559$	596.006			1.06620
$560$	19.0327	−	19.0327i	0.0339869	−	0.0339869i
$561$	110.462			0.196902
$562$	657.175			1.16935
$563$	−423.905			−0.752940			−0.376470	−	0.926429i	$-0.622862\pi$
$563$	−423.905			−0.752940			−0.376470	+	0.926429i	$0.622862\pi$
$564$	−459.840	+	459.840i	−0.815319	+	0.815319i
$565$	205.460	−	205.460i	0.363646	−	0.363646i
$566$	263.473	+	263.473i	0.465500	+	0.465500i
$567$	97.0704	−	97.0704i	0.171200	−	0.171200i
$568$			37.2956i			0.0656612i
$569$	−417.398	+	417.398i	−0.733565	+	0.733565i	−0.971324	−	0.237759i	$-0.923587\pi$
$569$	−417.398	+	417.398i	−0.733565	+	0.733565i	0.237759	+	0.971324i	$0.423587\pi$
$570$	234.545	+	234.545i	0.411482	+	0.411482i
$571$	183.766	−	183.766i	0.321832	−	0.321832i	−0.527637	−	0.849470i	$-0.676922\pi$
$571$	183.766	−	183.766i	0.321832	−	0.321832i	0.849470	+	0.527637i	$0.176922\pi$
$572$		−	545.928i		−	0.954420i
$573$	427.501	−	427.501i	0.746074	−	0.746074i
$574$	−56.6643			−0.0987183
$575$	−515.202			−0.896003
$576$	85.2484			0.148001
$577$	−25.5743	+	25.5743i	−0.0443229	+	0.0443229i	−0.728921	−	0.684598i	$-0.759978\pi$
$577$	−25.5743	+	25.5743i	−0.0443229	+	0.0443229i	0.684598	+	0.728921i	$0.259978\pi$
$578$	−287.269	+	287.269i	−0.497005	+	0.497005i
$579$	−1549.93			−2.67691
$580$	89.9493	+	89.9493i	0.155085	+	0.155085i
$581$		−	236.452i		−	0.406975i
$582$	−186.239			−0.319999
$583$		−	606.060i		−	1.03955i
$584$	105.715	+	105.715i	0.181019	+	0.181019i
$585$	−477.007			−0.815396
$586$	43.1690	+	43.1690i	0.0736673	+	0.0736673i
$587$			425.068i			0.724137i	0.932152	+	0.362068i	$0.117929\pi$
$587$			425.068i			0.724137i	−0.932152	+	0.362068i	$0.882071\pi$
$588$	−277.787	−	277.787i	−0.472427	−	0.472427i
$589$		−	660.548i		−	1.12147i
$590$	199.003			0.337293
$591$	60.6117			0.102558
$592$	206.029			0.348022
$593$		−	446.633i		−	0.753175i	−0.926381	−	0.376588i	$-0.877097\pi$
$593$		−	446.633i		−	0.753175i	0.926381	−	0.376588i	$-0.122903\pi$
$594$		−	196.622i		−	0.331014i
$595$	−8.85365			−0.0148801
$596$	−359.060			−0.602450
$597$	−762.482	+	762.482i	−1.27719	+	1.27719i
$598$	−483.612	+	483.612i	−0.808716	+	0.808716i
$599$	−653.142			−1.09039			−0.545193	−	0.838310i	$-0.683544\pi$
$599$	−653.142			−1.09039			−0.545193	+	0.838310i	$0.683544\pi$
$600$	−192.567			−0.320944
$601$	−126.331	−	126.331i	−0.210202	−	0.210202i	0.594152	−	0.804353i	$-0.297488\pi$
$601$	−126.331	−	126.331i	−0.210202	−	0.210202i	−0.804353	+	0.594152i	$0.797488\pi$
$602$		−	126.704i		−	0.210473i
$603$		−	815.254i		−	1.35200i
$604$	−99.8047			−0.165240
$605$	737.810			1.21952
$606$	−830.439	+	830.439i	−1.37036	+	1.37036i
$607$	−8.96170	−	8.96170i	−0.0147639	−	0.0147639i	0.699686	−	0.714450i	$-0.253323\pi$
$607$	−8.96170	−	8.96170i	−0.0147639	−	0.0147639i	−0.714450	+	0.699686i	$0.753323\pi$
$608$	96.3678			0.158500
$609$	−139.133	+	139.133i	−0.228461	+	0.228461i
$610$	−109.704	−	109.704i	−0.179842	−	0.179842i
$611$		−	1057.19i		−	1.73025i
$612$	−19.8280	−	19.8280i	−0.0323987	−	0.0323987i
$613$	366.405	+	366.405i	0.597724	+	0.597724i	0.939706	−	0.341982i	$-0.111098\pi$
$613$	366.405	+	366.405i	0.597724	+	0.597724i	−0.341982	+	0.939706i	$0.611098\pi$
$614$	34.0861	+	34.0861i	0.0555147	+	0.0555147i
$615$	−180.017	−	180.017i	−0.292711	−	0.292711i
$616$	−116.058			−0.188406
$617$			934.344i			1.51433i	0.653221	+	0.757167i	$0.273417\pi$
$617$			934.344i			1.51433i	−0.653221	+	0.757167i	$0.726583\pi$
$618$	−1022.86			−1.65512
$619$	−210.208			−0.339593			−0.169797	−	0.985479i	$-0.554311\pi$
$619$	−210.208			−0.339593			−0.169797	+	0.985479i	$0.554311\pi$
$620$	−170.288	−	170.288i	−0.274657	−	0.274657i
$621$	−174.179	+	174.179i	−0.280481	+	0.280481i
$622$		−	848.512i		−	1.36417i
$623$	−129.539	−	129.539i	−0.207927	−	0.207927i
$624$	−180.759	+	180.759i	−0.289678	+	0.289678i
$625$	−5.27391			−0.00843825
$626$	16.5274	+	16.5274i	0.0264016	+	0.0264016i
$627$		−	1430.22i		−	2.28105i
$628$	−377.927	+	377.927i	−0.601795	+	0.601795i
$629$	−47.9205	−	47.9205i	−0.0761852	−	0.0761852i
$630$			101.406i			0.160963i
$631$	568.563			0.901050			0.450525	−	0.892764i	$-0.351237\pi$
$631$	568.563			0.901050			0.450525	+	0.892764i	$0.351237\pi$
$632$	−158.863	−	158.863i	−0.251366	−	0.251366i
$633$	369.769	−	369.769i	0.584153	−	0.584153i
$634$			267.377i			0.421730i
$635$			310.814i			0.489470i
$636$	−200.669	+	200.669i	−0.315518	+	0.315518i
$637$	638.641			1.00258
$638$		−	548.498i		−	0.859714i
$639$	−99.3558	−	99.3558i	−0.155486	−	0.155486i
$640$	24.8434	−	24.8434i	0.0388178	−	0.0388178i
$641$			341.953i			0.533468i	0.963770	+	0.266734i	$0.0859446\pi$
$641$			341.953i			0.533468i	−0.963770	+	0.266734i	$0.914055\pi$
$642$	777.082	+	777.082i	1.21041	+	1.21041i
$643$	960.068			1.49311			0.746554	−	0.665325i	$-0.231707\pi$
$643$	960.068			1.49311			0.746554	+	0.665325i	$0.231707\pi$
$644$	102.811	+	102.811i	0.159644	+	0.159644i
$645$	402.529	−	402.529i	0.624076	−	0.624076i
$646$	−22.4143	−	22.4143i	−0.0346970	−	0.0346970i
$647$	152.256	−	152.256i	0.235327	−	0.235327i	−0.579585	−	0.814912i	$-0.696785\pi$
$647$	152.256	−	152.256i	0.235327	−	0.235327i	0.814912	+	0.579585i	$0.196785\pi$
$648$	126.706	−	126.706i	0.195534	−	0.195534i
$649$	−606.746	−	606.746i	−0.934893	−	0.934893i
$650$	221.358	−	221.358i	0.340551	−	0.340551i
$651$	263.399	−	263.399i	0.404607	−	0.404607i
$652$	−318.137	−	318.137i	−0.487941	−	0.487941i
$653$	40.5452			0.0620907			0.0310453	−	0.999518i	$-0.490116\pi$
$653$	40.5452			0.0620907			0.0310453	+	0.999518i	$0.490116\pi$
$654$	−157.678	−	157.678i	−0.241098	−	0.241098i
$655$	−126.081			−0.192490
$656$	−73.9641			−0.112750
$657$	−563.252			−0.857310
$658$	−224.746			−0.341559
$659$	−97.3853			−0.147777			−0.0738887	−	0.997266i	$-0.523541\pi$
$659$	−97.3853			−0.147777			−0.0738887	+	0.997266i	$0.523541\pi$
$660$	−368.707	−	368.707i	−0.558647	−	0.558647i
$661$	−401.769	−	401.769i	−0.607821	−	0.607821i	0.334555	−	0.942376i	$-0.391414\pi$
$661$	−401.769	−	401.769i	−0.607821	−	0.607821i	−0.942376	+	0.334555i	$0.891414\pi$
$662$	18.0652	+	18.0652i	0.0272888	+	0.0272888i
$663$	84.0860			0.126827
$664$		−	308.642i		−	0.464822i
$665$			114.633i			0.172381i
$666$	−548.863	+	548.863i	−0.824119	+	0.824119i
$667$	−485.888	+	485.888i	−0.728468	+	0.728468i
$668$	−227.167	+	227.167i	−0.340070	+	0.340070i
$669$	606.877			0.907140
$670$	−237.584	−	237.584i	−0.354604	−	0.354604i
$671$			668.958i			0.996957i
$672$	38.4275	+	38.4275i	0.0571837	+	0.0571837i
$673$	808.262	−	808.262i	1.20098	−	1.20098i	0.227116	−	0.973868i	$-0.427071\pi$
$673$	808.262	−	808.262i	1.20098	−	1.20098i	0.973868	−	0.227116i	$-0.0729295\pi$
$674$	180.226			0.267398
$675$	79.7247	−	79.7247i	0.118111	−	0.118111i
$676$		−	77.5710i		−	0.114750i
$677$	−758.637	−	758.637i	−1.12059	−	1.12059i	−0.991653	−	0.128933i	$-0.958845\pi$
$677$	−758.637	−	758.637i	−1.12059	−	1.12059i	−0.128933	−	0.991653i	$-0.541155\pi$
$678$	414.829	+	414.829i	0.611843	+	0.611843i
$679$	−45.5121	−	45.5121i	−0.0670281	−	0.0670281i
$680$	−11.5567			−0.0169951
$681$	−1213.79			−1.78237
$682$			1038.39i			1.52256i
$683$	812.479	−	812.479i	1.18957	−	1.18957i	0.212389	−	0.977185i	$-0.431876\pi$
$683$	812.479	−	812.479i	1.18957	−	1.18957i	0.977185	−	0.212389i	$-0.0681244\pi$
$684$	−256.725	+	256.725i	−0.375329	+	0.375329i
$685$	−537.308	+	537.308i	−0.784391	+	0.784391i
$686$		−	285.925i		−	0.416800i
$687$		−	335.277i		−	0.488031i
$688$		−	165.388i		−	0.240389i
$689$		−	461.345i		−	0.669586i
$690$			653.241i			0.946726i
$691$	−791.102	+	791.102i	−1.14487	+	1.14487i	−0.157318	+	0.987548i	$0.550285\pi$
$691$	−791.102	+	791.102i	−1.14487	+	1.14487i	−0.987548	+	0.157318i	$0.949715\pi$
$692$		−	55.9364i		−	0.0808330i
$693$	309.181	−	309.181i	0.446148	−	0.446148i
$694$	96.5159	+	96.5159i	0.139072	+	0.139072i
$695$	−66.6485	−	66.6485i	−0.0958971	−	0.0958971i
$696$	−181.610	+	181.610i	−0.260934	+	0.260934i
$697$	17.2034	+	17.2034i	0.0246820	+	0.0246820i
$698$	416.690	+	416.690i	0.596978	+	0.596978i
$699$	−187.206	+	187.206i	−0.267820	+	0.267820i
$700$	−47.0583	−	47.0583i	−0.0672262	−	0.0672262i
$701$	280.903	−	280.903i	0.400718	−	0.400718i	−0.477768	−	0.878486i	$-0.658554\pi$
$701$	280.903	−	280.903i	0.400718	−	0.400718i	0.878486	+	0.477768i	$0.158554\pi$
$702$		−	149.673i		−	0.213209i
$703$	−620.455	+	620.455i	−0.882581	+	0.882581i
$704$	−151.491			−0.215187
$705$	−713.998	−	713.998i	−1.01276	−	1.01276i
$706$	266.525	−	266.525i	0.377514	−	0.377514i
$707$	−405.876			−0.574082
$708$			401.793i			0.567504i
$709$	767.643	+	767.643i	1.08271	+	1.08271i	0.996256	+	0.0864567i	$0.0275544\pi$
$709$	767.643	+	767.643i	1.08271	+	1.08271i	0.0864567	+	0.996256i	$0.472446\pi$
$710$	−57.9093			−0.0815623
$711$	846.426			1.19047
$712$	−169.087	−	169.087i	−0.237482	−	0.237482i
$713$	919.860	−	919.860i	1.29013	−	1.29013i
$714$		−	17.8758i		−	0.0250361i
$715$	847.669			1.18555
$716$	4.81895	−	4.81895i	0.00673038	−	0.00673038i
$717$	210.342	+	210.342i	0.293364	+	0.293364i
$718$	−615.546			−0.857306
$719$	−602.179	+	602.179i	−0.837523	+	0.837523i	−0.988532	−	0.151010i	$-0.951748\pi$
$719$	−602.179	+	602.179i	−0.837523	+	0.837523i	0.151010	+	0.988532i	$0.451748\pi$
$720$			132.366i			0.183842i
$721$	−249.962	−	249.962i	−0.346688	−	0.346688i
$722$	70.7890	−	70.7890i	0.0980457	−	0.0980457i
$723$	−1062.84			−1.47005
$724$	83.1698	+	83.1698i	0.114875	+	0.114875i
$725$	222.400	−	222.400i	0.306759	−	0.306759i
$726$			1489.66i			2.05187i
$727$			186.199i			0.256120i	0.991766	+	0.128060i	$0.0408749\pi$
$727$			186.199i			0.256120i	−0.991766	+	0.128060i	$0.959125\pi$
$728$	−88.3459			−0.121354
$729$			968.055i			1.32792i
$730$	−164.145	+	164.145i	−0.224856	+	0.224856i
$731$	−38.4677	+	38.4677i	−0.0526234	+	0.0526234i
$732$	221.495	−	221.495i	0.302589	−	0.302589i
$733$	−240.640	+	240.640i	−0.328295	+	0.328295i	−0.851938	−	0.523643i	$-0.824573\pi$
$733$	−240.640	+	240.640i	−0.328295	+	0.328295i	0.523643	+	0.851938i	$0.324573\pi$
$734$	50.6502			0.0690057
$735$	431.324	−	431.324i	0.586835	−	0.586835i
$736$	134.199	+	134.199i	0.182336	+	0.182336i
$737$			1448.75i			1.96575i
$738$	197.041	−	197.041i	0.266993	−	0.266993i
$739$	548.108	+	548.108i	0.741688	+	0.741688i	0.972903	−	0.231215i	$-0.0742699\pi$
$739$	548.108	+	548.108i	0.741688	+	0.741688i	−0.231215	+	0.972903i	$0.574270\pi$
$740$			319.903i			0.432302i
$741$		−	1088.71i		−	1.46925i
$742$	−98.0769			−0.132179
$743$	1004.35			1.35175			0.675876	−	0.737016i	$-0.263766\pi$
$743$	1004.35			1.35175			0.675876	+	0.737016i	$0.263766\pi$
$744$	343.815	−	343.815i	0.462117	−	0.462117i
$745$		−	557.517i		−	0.748345i
$746$		−	572.747i		−	0.767757i
$747$	822.225	+	822.225i	1.10070	+	1.10070i
$748$	35.2355	+	35.2355i	0.0471063	+	0.0471063i
$749$			379.798i			0.507073i
$750$		−	785.770i		−	1.04769i
$751$	−157.505			−0.209727			−0.104863	−	0.994487i	$-0.533441\pi$
$751$	−157.505			−0.209727			−0.104863	+	0.994487i	$0.533441\pi$
$752$	−293.362			−0.390109
$753$			1659.63i			2.20402i
$754$		−	417.527i		−	0.553749i
$755$		−	154.968i		−	0.205255i
$756$	−31.8188			−0.0420884
$757$	903.972	−	903.972i	1.19415	−	1.19415i	0.218260	−	0.975891i	$-0.429962\pi$
$757$	903.972	−	903.972i	1.19415	−	1.19415i	0.975891	−	0.218260i	$-0.0700379\pi$
$758$	105.187			0.138769
$759$	1991.68	−	1991.68i	2.62409	−	2.62409i
$760$			149.631i			0.196883i
$761$	−404.650	+	404.650i	−0.531735	+	0.531735i	−0.921088	−	0.389354i	$-0.872698\pi$
$761$	−404.650	+	404.650i	−0.531735	+	0.531735i	0.389354	+	0.921088i	$0.372698\pi$
$762$	−627.542			−0.823545
$763$		−	77.0651i		−	0.101003i
$764$	272.730			0.356977
$765$	30.7872	−	30.7872i	0.0402447	−	0.0402447i
$766$		−	297.998i		−	0.389032i
$767$	−461.867	−	461.867i	−0.602173	−	0.602173i
$768$	50.1595	+	50.1595i	0.0653118	+	0.0653118i
$769$			1258.73i			1.63684i	0.574622	+	0.818419i	$0.305149\pi$
$769$			1258.73i			1.63684i	−0.574622	+	0.818419i	$0.694851\pi$
$770$		−	180.205i		−	0.234033i
$771$			1966.69i			2.55083i
$772$	−494.400	−	494.400i	−0.640415	−	0.640415i
$773$	203.913			0.263794			0.131897	−	0.991263i	$-0.457893\pi$
$773$	203.913			0.263794			0.131897	+	0.991263i	$0.457893\pi$
$774$	440.595	+	440.595i	0.569244	+	0.569244i
$775$	−421.037	+	421.037i	−0.543273	+	0.543273i
$776$	−59.4071	−	59.4071i	−0.0765555	−	0.0765555i
$777$	−494.823			−0.636838
$778$	573.341	+	573.341i	0.736943	+	0.736943i
$779$	222.742	−	222.742i	0.285934	−	0.285934i
$780$	−280.667	−	280.667i	−0.359830	−	0.359830i
$781$	176.561	+	176.561i	0.226070	+	0.226070i
$782$		−	62.4270i		−	0.0798300i
$783$		−	150.377i		−	0.192053i
$784$		−	177.219i		−	0.226044i
$785$	−586.812	−	586.812i	−0.747531	−	0.747531i
$786$		−	254.561i		−	0.323868i
$787$	−824.518			−1.04767			−0.523836	−	0.851819i	$-0.675500\pi$
$787$	−824.518			−1.04767			−0.523836	+	0.851819i	$0.675500\pi$
$788$	19.3341	+	19.3341i	0.0245356	+	0.0245356i
$789$	889.362	+	889.362i	1.12720	+	1.12720i
$790$	246.669	−	246.669i	0.312239	−	0.312239i
$791$			202.747i			0.256318i
$792$	403.575	−	403.575i	0.509564	−	0.509564i
$793$			509.224i			0.642149i
$794$	−467.253			−0.588480
$795$	−311.582	−	311.582i	−0.391926	−	0.391926i
$796$	−486.437			−0.611102
$797$	−865.427	+	865.427i	−1.08586	+	1.08586i	−0.0899054	+	0.995950i	$0.528656\pi$
$797$	−865.427	+	865.427i	−1.08586	+	1.08586i	−0.995950	+	0.0899054i	$0.971344\pi$
$798$	−231.448			−0.290035
$799$	68.2333	+	68.2333i	0.0853984	+	0.0853984i
$800$	−61.4254	−	61.4254i	−0.0767817	−	0.0767817i
$801$	900.899			1.12472
$802$			864.388i			1.07779i
$803$	1000.93			1.24649
$804$	479.689	−	479.689i	0.596629	−	0.596629i
$805$	−159.635	+	159.635i	−0.198305	+	0.198305i
$806$			790.442i			0.980697i
$807$	1092.50	−	478.301i	1.35378	−	0.592690i
$808$	−529.791			−0.655682
$809$	492.072	+	492.072i	0.608247	+	0.608247i	0.942488	−	0.334241i	$-0.108480\pi$
$809$	492.072	+	492.072i	0.608247	+	0.608247i	−0.334241	+	0.942488i	$0.608480\pi$
$810$	196.738	+	196.738i	0.242887	+	0.242887i
$811$			1239.46i			1.52831i	0.645035	+	0.764153i	$0.276843\pi$
$811$			1239.46i			1.52831i	−0.645035	+	0.764153i	$0.723157\pi$
$812$	−88.7617			−0.109312
$813$		−	174.851i		−	0.215069i
$814$	975.362	−	975.362i	1.19823	−	1.19823i
$815$	493.976	−	493.976i	0.606105	−	0.606105i
$816$		−	23.3333i		−	0.0285947i
$817$	498.064	+	498.064i	0.609625	+	0.609625i
$818$		−	474.949i		−	0.580622i
$819$	235.354	−	235.354i	0.287368	−	0.287368i
$820$		−	114.845i		−	0.140055i
$821$	−1271.41			−1.54861			−0.774304	−	0.632813i	$-0.781900\pi$
$821$	−1271.41			−1.54861			−0.774304	+	0.632813i	$0.781900\pi$
$822$	−1084.84	−	1084.84i	−1.31976	−	1.31976i
$823$	−370.372			−0.450027			−0.225013	−	0.974356i	$-0.572243\pi$
$823$	−370.372			−0.450027			−0.225013	+	0.974356i	$0.572243\pi$
$824$	−326.276	−	326.276i	−0.395966	−	0.395966i
$825$	−911.630	+	911.630i	−1.10501	+	1.10501i
$826$	−98.1878	+	98.1878i	−0.118871	+	0.118871i
$827$		−	1309.96i		−	1.58399i	−0.610527	−	0.791996i	$-0.709042\pi$
$827$		−	1309.96i		−	1.58399i	0.610527	−	0.791996i	$-0.290958\pi$
$828$	−715.016			−0.863546
$829$	278.811	−	278.811i	0.336323	−	0.336323i	−0.518659	−	0.854981i	$-0.673568\pi$
$829$	278.811	−	278.811i	0.336323	−	0.336323i	0.854981	+	0.518659i	$0.173568\pi$
$830$	479.232			0.577388
$831$	−727.231			−0.875127
$832$	−115.318			−0.138604
$833$	−41.2195	+	41.2195i	−0.0494832	+	0.0494832i
$834$	134.565	−	134.565i	0.161349	−	0.161349i
$835$	−352.724	−	352.724i	−0.422424	−	0.422424i
$836$	456.215	−	456.215i	0.545712	−	0.545712i
$837$			284.687i			0.340128i
$838$	79.4467	−	79.4467i	0.0948051	−	0.0948051i
$839$	568.841	+	568.841i	0.677999	+	0.677999i	0.959547	−	0.281548i	$-0.0908480\pi$
$839$	568.841	+	568.841i	0.677999	+	0.677999i	−0.281548	+	0.959547i	$0.590848\pi$
$840$	−59.6668	+	59.6668i	−0.0710319	+	0.0710319i
$841$			421.508i			0.501198i
$842$	318.129	−	318.129i	0.377825	−	0.377825i
$843$	−2060.22			−2.44392
$844$	235.900			0.279502
$845$	120.445			0.142539
$846$	781.519	−	781.519i	0.923781	−	0.923781i
$847$	−364.035	+	364.035i	−0.429793	+	0.429793i
$848$	−128.020			−0.150967
$849$	−825.979	−	825.979i	−0.972885	−	0.972885i
$850$			28.5740i			0.0336165i
$851$	−1728.06			−2.03062
$852$		−	116.920i		−	0.137231i
$853$	−874.585	−	874.585i	−1.02530	−	1.02530i	−0.999671	−	0.0256336i	$-0.991840\pi$
$853$	−874.585	−	874.585i	−1.02530	−	1.02530i	−0.0256336	−	0.999671i	$-0.508160\pi$
$854$	108.255			0.126763
$855$	−398.620	−	398.620i	−0.466222	−	0.466222i
$856$			495.751i			0.579148i
$857$	736.735	+	736.735i	0.859668	+	0.859668i	0.991299	−	0.131631i	$-0.0420214\pi$
$857$	736.735	+	736.735i	0.859668	+	0.859668i	−0.131631	+	0.991299i	$0.542021\pi$
$858$			1711.47i			1.99472i
$859$	432.328			0.503293			0.251646	−	0.967819i	$-0.419028\pi$
$859$	432.328			0.503293			0.251646	+	0.967819i	$0.419028\pi$
$860$	256.799			0.298604
$861$	177.641			0.206319
$862$			415.795i			0.482360i
$863$			1335.43i			1.54743i	0.633534	+	0.773715i	$0.281604\pi$
$863$			1335.43i			1.54743i	−0.633534	+	0.773715i	$0.718396\pi$
$864$	−41.5332			−0.0480708
$865$	86.8531			0.100408
$866$	−566.939	+	566.939i	−0.654664	+	0.654664i
$867$	900.579	−	900.579i	1.03873	−	1.03873i
$868$	168.039			0.193594
$869$	−1504.15			−1.73090
$870$	−281.988	−	281.988i	−0.324124	−	0.324124i
$871$			1102.82i			1.26615i
$872$		−	100.593i		−	0.115359i
$873$	316.522			0.362568
$874$	−808.279			−0.924805
$875$	192.022	−	192.022i	0.219454	−	0.219454i
$876$	−331.413	−	331.413i	−0.378326	−	0.378326i
$877$	−52.8766			−0.0602926			−0.0301463	−	0.999545i	$-0.509597\pi$
$877$	−52.8766			−0.0602926			−0.0301463	+	0.999545i	$0.509597\pi$
$878$	141.773	−	141.773i	0.161473	−	0.161473i
$879$	−135.334	−	135.334i	−0.153963	−	0.153963i
$880$		−	235.222i		−	0.267298i
$881$	415.858	+	415.858i	0.472029	+	0.472029i	0.902571	−	0.430542i	$-0.141677\pi$
$881$	415.858	+	415.858i	0.472029	+	0.472029i	−0.430542	+	0.902571i	$0.641677\pi$
$882$	472.112	+	472.112i	0.535275	+	0.535275i
$883$	−274.673	−	274.673i	−0.311068	−	0.311068i	0.534256	−	0.845323i	$-0.320592\pi$
$883$	−274.673	−	274.673i	−0.311068	−	0.311068i	−0.845323	+	0.534256i	$0.820592\pi$
$884$	26.8220	+	26.8220i	0.0303416	+	0.0303416i
$885$	−623.868			−0.704936
$886$		−	93.3850i		−	0.105401i
$887$	1094.34			1.23375			0.616876	−	0.787060i	$-0.288398\pi$
$887$	1094.34			1.23375			0.616876	+	0.787060i	$0.288398\pi$
$888$	−645.894			−0.727358
$889$	−153.355	−	153.355i	−0.172503	−	0.172503i
$890$	262.543	−	262.543i	0.294993	−	0.294993i
$891$		−	1199.68i		−	1.34644i
$892$	193.583	+	193.583i	0.217021	+	0.217021i
$893$	883.457	−	883.457i	0.989313	−	0.989313i
$894$	1125.64			1.25911
$895$	7.48244	+	7.48244i	0.00836027	+	0.00836027i
$896$			24.5154i			0.0273609i
$897$	1516.11	−	1516.11i	1.69020	−	1.69020i
$898$	−240.453	−	240.453i	−0.267765	−	0.267765i
$899$			794.162i			0.883384i
$900$	327.276			0.363640
$901$	29.7763	+	29.7763i	0.0330481	+	0.0330481i
$902$	−350.154	+	350.154i	−0.388197	+	0.388197i
$903$			397.214i			0.439883i
$904$			264.647i			0.292751i
$905$	−129.139	+	129.139i	−0.142695	+	0.142695i
$906$	312.884			0.345347
$907$			75.0436i			0.0827382i	0.999144	+	0.0413691i	$0.0131720\pi$
$907$			75.0436i			0.0827382i	−0.999144	+	0.0413691i	$0.986828\pi$
$908$	−387.179	−	387.179i	−0.426408	−	0.426408i
$909$	1411.37	−	1411.37i	1.55266	−	1.55266i
$910$		−	137.176i		−	0.150742i
$911$	719.327	+	719.327i	0.789602	+	0.789602i	0.981429	−	0.191827i	$-0.0614413\pi$
$911$	719.327	+	719.327i	0.789602	+	0.789602i	−0.191827	+	0.981429i	$0.561441\pi$
$912$	−302.110			−0.331261
$913$	−1461.14	−	1461.14i	−1.60037	−	1.60037i
$914$	−639.175	+	639.175i	−0.699316	+	0.699316i
$915$	343.918	+	343.918i	0.375867	+	0.375867i
$916$	106.948	−	106.948i	0.116755	−	0.116755i
$917$	62.2081	−	62.2081i	0.0678387	−	0.0678387i
$918$	9.66025	+	9.66025i	0.0105231	+	0.0105231i
$919$	934.065	−	934.065i	1.01639	−	1.01639i	0.0165293	−	0.999863i	$-0.494738\pi$
$919$	934.065	−	934.065i	1.01639	−	1.01639i	0.999863	−	0.0165293i	$-0.00526168\pi$
$920$	−208.372	+	208.372i	−0.226492	+	0.226492i
$921$	−106.859	−	106.859i	−0.116025	−	0.116025i
$922$	−978.923			−1.06174
$923$	134.402	+	134.402i	0.145614	+	0.145614i
$924$	363.839			0.393765
$925$	790.963			0.855095
$926$	−833.472			−0.900077
$927$	1738.41			1.87530
$928$	−115.861			−0.124850
$929$	870.898	+	870.898i	0.937458	+	0.937458i	0.998156	−	0.0606982i	$-0.0193327\pi$
$929$	870.898	+	870.898i	0.937458	+	0.937458i	−0.0606982	+	0.998156i	$0.519333\pi$
$930$	533.846	+	533.846i	0.574028	+	0.574028i
$931$	533.693	+	533.693i	0.573247	+	0.573247i
$932$	−119.431			−0.128145
$933$			2660.06i			2.85108i
$934$		−	492.247i		−	0.527031i
$935$	−54.7106	+	54.7106i	−0.0585140	+	0.0585140i
$936$	307.209	−	307.209i	0.328215	−	0.328215i
$937$	−812.128	+	812.128i	−0.866732	+	0.866732i	−0.992109	−	0.125377i	$-0.959986\pi$
$937$	−812.128	+	812.128i	−0.866732	+	0.866732i	0.125377	+	0.992109i	$0.459986\pi$
$938$	234.448			0.249944
$939$	−51.8128	−	51.8128i	−0.0551787	−	0.0551787i
$940$		−	455.506i		−	0.484581i
$941$	−111.721	−	111.721i	−0.118726	−	0.118726i	0.645248	−	0.763974i	$-0.276754\pi$
$941$	−111.721	−	111.721i	−0.118726	−	0.118726i	−0.763974	+	0.645248i	$0.776754\pi$
$942$	1184.79	−	1184.79i	1.25774	−	1.25774i
$943$	620.369			0.657868
$944$	−128.165	+	128.165i	−0.135768	+	0.135768i
$945$		−	49.4054i		−	0.0522809i
$946$	−782.962	−	782.962i	−0.827656	−	0.827656i
$947$	−1142.95	−	1142.95i	−1.20692	−	1.20692i	−0.972020	−	0.234898i	$-0.924524\pi$
$947$	−1142.95	−	1142.95i	−1.20692	−	1.20692i	−0.234898	−	0.972020i	$-0.575476\pi$
$948$	498.031	+	498.031i	0.525349	+	0.525349i
$949$	761.929			0.802876
$950$	369.964			0.389436
$951$		−	838.217i		−	0.881406i
$952$	5.70206	−	5.70206i	0.00598956	−	0.00598956i
$953$	835.348	−	835.348i	0.876546	−	0.876546i	−0.116629	−	0.993176i	$-0.537209\pi$
$953$	835.348	−	835.348i	0.876546	−	0.876546i	0.993176	+	0.116629i	$0.0372090\pi$
$954$	341.047	−	341.047i	0.357491	−	0.357491i
$955$			423.472i			0.443426i
$956$			134.191i			0.140367i
$957$			1719.52i			1.79678i
$958$			810.751i			0.846295i
$959$		−	530.214i		−	0.552882i
$960$	−77.8832	+	77.8832i	−0.0811283	+	0.0811283i
$961$		−	542.469i		−	0.564484i
$962$	742.465	−	742.465i	0.771793	−	0.771793i
$963$	−1320.69	−	1320.69i	−1.37143	−	1.37143i
$964$	−339.029	−	339.029i	−0.351690	−	0.351690i
$965$	767.661	−	767.661i	0.795504	−	0.795504i
$966$	−322.308	−	322.308i	−0.333652	−	0.333652i
$967$	593.614	+	593.614i	0.613872	+	0.613872i	0.943953	−	0.330081i	$-0.107076\pi$
$967$	593.614	+	593.614i	0.613872	+	0.613872i	−0.330081	+	0.943953i	$0.607076\pi$
$968$	−475.175	+	475.175i	−0.490884	+	0.490884i
$969$	70.2681	+	70.2681i	0.0725161	+	0.0725161i
$970$	92.2421	−	92.2421i	0.0950949	−	0.0950949i
$971$		−	1481.69i		−	1.52595i	−0.646430	−	0.762973i	$-0.723739\pi$
$971$		−	1481.69i		−	1.52595i	0.646430	−	0.762973i	$-0.276261\pi$
$972$	−490.670	+	490.670i	−0.504804	+	0.504804i
$973$	65.7685			0.0675936
$974$	85.8008	+	85.8008i	0.0880911	+	0.0880911i
$975$	−693.951	+	693.951i	−0.711744	+	0.711744i
$976$	141.306			0.144781
$977$		−	1175.76i		−	1.20344i	−0.798709	−	0.601718i	$-0.794483\pi$
$977$		−	1175.76i		−	1.20344i	0.798709	−	0.601718i	$-0.205517\pi$
$978$	997.350	+	997.350i	1.01979	+	1.01979i
$979$	−1600.95			−1.63529
$980$	275.169			0.280785
$981$	267.982	+	267.982i	0.273172	+	0.273172i
$982$	765.799	−	765.799i	0.779836	−	0.779836i
$983$		−	1308.53i		−	1.33116i	−0.746328	−	0.665578i	$-0.768185\pi$
$983$		−	1308.53i		−	1.33116i	0.746328	−	0.665578i	$-0.231815\pi$
$984$	231.875			0.235645
$985$	−30.0203	+	30.0203i	−0.0304774	+	0.0304774i
$986$	26.9482	+	26.9482i	0.0273309	+	0.0273309i
$987$	704.572			0.713852
$988$	347.280	−	347.280i	0.351498	−	0.351498i
$989$			1387.18i			1.40261i
$990$	626.635	+	626.635i	0.632964	+	0.632964i
$991$	−396.364	+	396.364i	−0.399964	+	0.399964i	−0.878220	−	0.478257i	$-0.841269\pi$
$991$	−396.364	+	396.364i	−0.399964	+	0.399964i	0.478257	+	0.878220i	$0.341269\pi$
$992$	219.342			0.221111
$993$	−56.6337	−	56.6337i	−0.0570330	−	0.0570330i
$994$	28.5723	−	28.5723i	0.0287448	−	0.0287448i
$995$		−	755.296i		−	0.759092i
$996$			967.582i			0.971468i
$997$	1170.53			1.17405			0.587027	−	0.809567i	$-0.300298\pi$
$997$	1170.53			1.17405			0.587027	+	0.809567i	$0.300298\pi$
$998$			811.350i			0.812976i
$999$	267.407	−	267.407i	0.267675	−	0.267675i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.b.187.21	✓	46
269.82	odd	4	inner	538.3.c.b.351.21	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.21	✓	46	1.1	even	1	trivial
538.3.c.b.351.21	yes	46	269.82	odd	4	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	538.3.c.b.187.21

Level	$538$
Weight	$3$
Character	538.187
Analytic conductor	$14.659$
Analytic rank	$0$
Dimension	$46$
Inner twists	$2$