LMFDB - Embedded newform 538.3.c.b.351.21

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			351.21
Character	$\chi$	$=$	538.351
Dual form			538.3.c.b.187.21

$q$-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 $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	3.13497	−	3.13497i	1.04499	−	1.04499i	0.0460501	−	0.998939i	$-0.485337\pi$
$3$	3.13497	−	3.13497i	1.04499	−	1.04499i	0.998939	−	0.0460501i	$-0.0146634\pi$
$4$		−	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	0.808029	−	0.589142i	$-0.200534\pi$
$7$	1.53221	+	1.53221i	0.218887	+	0.218887i	−0.589142	+	0.808029i	$0.700534\pi$
$8$	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	$0.330002\pi$
$11$			18.9364i			1.72149i	−0.509035	+	0.860746i	$0.669998\pi$
$12$	−6.26994	−	6.26994i	−0.522495	−	0.522495i
$13$			14.4148i			1.10883i	0.832241	+	0.554414i	$0.187058\pi$
$13$			14.4148i			1.10883i	−0.832241	+	0.554414i	$0.812942\pi$
$14$	−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	−0.679213	−	0.733941i	$-0.737679\pi$
$17$	0.930364	−	0.930364i	0.0547273	−	0.0547273i	0.733941	+	0.679213i	$0.237679\pi$
$18$	10.6560	+	10.6560i	0.592002	+	0.592002i
$19$	12.0460	+	12.0460i	0.633999	+	0.633999i	0.949068	−	0.315070i	$-0.102028\pi$
$19$	12.0460	+	12.0460i	0.633999	+	0.633999i	−0.315070	+	0.949068i	$0.602028\pi$
$20$			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	0.411851	−	0.911251i	$-0.364883\pi$
$29$	−14.4826	−	14.4826i	−0.499401	−	0.499401i	−0.911251	+	0.411851i	$0.864883\pi$
$30$		−	19.4708i		−	0.649027i
$31$	27.4178	+	27.4178i	0.884444	+	0.884444i	0.993983	−	0.109538i	$-0.0349372\pi$
$31$	27.4178	+	27.4178i	0.884444	+	0.884444i	−0.109538	+	0.993983i	$0.534937\pi$
$32$	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	$-0.840354\pi$
$43$		−	41.3469i		−	0.961556i	0.876842	−	0.480778i	$-0.159646\pi$
$44$	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	0.924428	−	0.381357i	$-0.124543\pi$
$59$	32.0412	+	32.0412i	0.543071	+	0.543071i	−0.381357	+	0.924428i	$0.624543\pi$
$60$	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	0.638390	−	0.769713i	$-0.279601\pi$
$71$	−9.32389	−	9.32389i	−0.131322	−	0.131322i	−0.769713	+	0.638390i	$0.779601\pi$
$72$	21.3121	−	21.3121i	0.296001	−	0.296001i
$73$		−	52.8575i		−	0.724076i	−0.932163	−	0.362038i	$-0.882081\pi$
$73$		−	52.8575i		−	0.724076i	0.932163	−	0.362038i	$-0.117919\pi$
$74$	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	$0.167671\pi$
$79$			79.4315i			1.00546i	−0.864443	+	0.502731i	$0.832329\pi$
$80$	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	0.997683	−	0.0680387i	$-0.0216741\pi$
$83$	77.1605	+	77.1605i	0.929644	+	0.929644i	−0.0680387	+	0.997683i	$0.521674\pi$
$84$		−	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	$0.157539\pi$
$89$			84.5435i			0.949927i	−0.880005	+	0.474964i	$0.842461\pi$
$90$	−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	$0.0489292\pi$
$97$			29.7035i			0.306222i	−0.988209	+	0.153111i	$0.951071\pi$
$98$	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	−0.390954	+	0.920410i	$0.627855\pi$
$101$	−132.448	+	132.448i	−1.31136	+	1.31136i	−0.920410	+	0.390954i	$0.872145\pi$
$102$	5.83332	+	5.83332i	0.0571895	+	0.0571895i
$103$			163.138i			1.58386i	0.610609	+	0.791932i	$0.290925\pi$
$103$			163.138i			1.58386i	−0.610609	+	0.791932i	$0.709075\pi$
$104$	−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	−0.984842	−	0.173455i	$-0.944507\pi$
$107$	−123.938	−	123.938i	−1.15830	−	1.15830i	−0.173455	−	0.984842i	$-0.555493\pi$
$108$	−10.3833	+	10.3833i	−0.0961416	+	0.0961416i
$109$	25.1483	+	25.1483i	0.230719	+	0.230719i	0.812993	−	0.582274i	$-0.197837\pi$
$109$	25.1483	+	25.1483i	0.230719	+	0.230719i	−0.582274	+	0.812993i	$0.697837\pi$
$110$	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	0.350908	−	0.936410i	$-0.385873\pi$
$113$	−66.1617	−	66.1617i	−0.585502	−	0.585502i	−0.936410	+	0.350908i	$0.885873\pi$
$114$	−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	$0.128925\pi$
$127$			100.087i			0.788090i	−0.919091	+	0.394045i	$0.871075\pi$
$128$	−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	0.949662	+	0.313275i	$0.101426\pi$
$137$	173.022	+	173.022i	1.26294	+	1.26294i	0.313275	+	0.949662i	$0.398574\pi$
$138$			210.355i			1.52431i
$139$	21.4620	−	21.4620i	0.154403	−	0.154403i	−0.625678	−	0.780081i	$-0.715178\pi$
$139$	21.4620	−	21.4620i	0.154403	−	0.154403i	0.780081	+	0.625678i	$0.215178\pi$
$140$	−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	$-0.794191\pi$
$149$		−	179.530i		−	1.20490i	0.798157	−	0.602450i	$-0.205809\pi$
$150$		−	96.2833i		−	0.641889i
$151$		−	49.9023i		−	0.330479i	−0.986253	−	0.165240i	$-0.947160\pi$
$151$		−	49.9023i		−	0.330479i	0.986253	−	0.165240i	$-0.0528397\pi$
$152$			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	0.230523	−	0.973067i	$-0.425956\pi$
$157$	188.964	−	188.964i	1.20359	−	1.20359i	0.973067	−	0.230523i	$-0.0740435\pi$
$158$	−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	0.0238344	−	0.999716i	$-0.492413\pi$
$163$	−159.069	−	159.069i	−0.975881	−	0.975881i	−0.999716	+	0.0238344i	$0.992413\pi$
$164$		−	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	−0.279892	−	0.960032i	$-0.590299\pi$
$167$	113.583	−	113.583i	0.680140	−	0.680140i	0.960032	+	0.279892i	$0.0902986\pi$
$168$	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	−0.713805	−	0.700344i	$-0.753030\pi$
$179$	−2.40947	+	2.40947i	−0.0134608	+	0.0134608i	0.700344	+	0.713805i	$0.253030\pi$
$180$	66.1831			0.367684
$181$	41.5849	+	41.5849i	0.229751	+	0.229751i	0.812589	−	0.582838i	$-0.198058\pi$
$181$	41.5849	+	41.5849i	0.229751	+	0.229751i	−0.582838	+	0.812589i	$0.698058\pi$
$182$		−	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	$0.116193\pi$
$191$			136.365i			0.713954i	−0.934113	+	0.356977i	$0.883807\pi$
$192$	25.0797	+	25.0797i	0.130624	+	0.130624i
$193$	−247.200	−	247.200i	−1.28083	−	1.28083i	−0.940196	−	0.340634i	$-0.889358\pi$
$193$	−247.200	−	247.200i	−1.28083	−	1.28083i	−0.340634	−	0.940196i	$-0.610642\pi$
$194$	−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	0.731217	−	0.682145i	$-0.238953\pi$
$197$	9.66704	+	9.66704i	0.0490713	+	0.0490713i	−0.682145	+	0.731217i	$0.738953\pi$
$198$	−201.787	+	201.787i	−1.01913	+	1.01913i
$199$		−	243.218i		−	1.22220i	−0.791552	−	0.611102i	$-0.790727\pi$
$199$		−	243.218i		−	1.22220i	0.791552	−	0.611102i	$-0.209273\pi$
$200$	−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	$0.0901694\pi$
$211$			117.950i			0.559004i	−0.960145	+	0.279502i	$0.909831\pi$
$212$		−	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	0.890001	−	0.455958i	$-0.150703\pi$
$223$	96.7915	+	96.7915i	0.434043	+	0.434043i	−0.455958	+	0.890001i	$0.650703\pi$
$224$	12.2577			0.0547218
$225$			163.638i			0.727280i
$226$	132.323			0.585502
$227$	−193.589	−	193.589i	−0.852817	−	0.852817i	0.137663	−	0.990479i	$-0.456041\pi$
$227$	−193.589	−	193.589i	−0.852817	−	0.852817i	−0.990479	+	0.137663i	$0.956041\pi$
$228$		−	151.055i		−	0.662522i
$229$	−53.4738	+	53.4738i	−0.233510	+	0.233510i	−0.814156	−	0.580646i	$-0.802800\pi$
$229$	−53.4738	+	53.4738i	−0.233510	+	0.233510i	0.580646	+	0.814156i	$0.302800\pi$
$230$	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	$-0.959098\pi$
$233$		−	59.7154i		−	0.256289i	0.991755	−	0.128145i	$-0.0409022\pi$
$234$	−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	0.261755	−	0.965134i	$-0.415699\pi$
$241$	−169.514	−	169.514i	−0.703379	−	0.703379i	−0.965134	+	0.261755i	$0.915699\pi$
$242$	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	0.0561455	−	0.998423i	$-0.482119\pi$
$251$	264.697	−	264.697i	1.05457	−	1.05457i	0.998423	−	0.0561455i	$-0.0178811\pi$
$252$	−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	0.253052	−	0.967453i	$-0.418566\pi$
$257$	313.670	−	313.670i	1.22050	−	1.22050i	0.967453	−	0.253052i	$-0.0814344\pi$
$258$	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	−0.756685	−	0.653780i	$-0.773182\pi$
$271$	−27.8872	+	27.8872i	−0.102905	+	0.102905i	0.653780	+	0.756685i	$0.273182\pi$
$272$	−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	0.466039	−	0.884764i	$-0.345681\pi$
$277$	−115.987	−	115.987i	−0.418725	−	0.418725i	−0.884764	+	0.466039i	$0.845681\pi$
$278$			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	−0.982362	−	0.186989i	$-0.940127\pi$
$281$	−328.588	−	328.588i	−1.16935	−	1.16935i	−0.186989	−	0.982362i	$-0.559873\pi$
$282$			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	0.495638	−	0.868529i	$-0.334934\pi$
$311$	424.256	−	424.256i	1.36417	−	1.36417i	0.868529	−	0.495638i	$-0.165066\pi$
$312$			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	−0.885799	−	0.464069i	$-0.846389\pi$
$317$	−133.688	+	133.688i	−0.421730	+	0.421730i	0.464069	+	0.885799i	$0.346389\pi$
$318$			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	0.560653	−	0.828051i	$-0.310550\pi$
$337$	−90.1132	−	90.1132i	−0.267398	−	0.267398i	−0.828051	+	0.560653i	$0.810550\pi$
$338$	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	$-0.876779\pi$
$353$		−	266.525i		−	0.755027i	0.926004	−	0.377514i	$-0.123221\pi$
$354$	−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	0.991020	−	0.133714i	$-0.0426903\pi$
$359$	307.773	+	307.773i	0.857306	+	0.857306i	−0.133714	+	0.991020i	$0.542690\pi$
$360$	−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	0.671762	−	0.740767i	$-0.265538\pi$
$367$	−25.3251	−	25.3251i	−0.0690057	−	0.0690057i	−0.740767	+	0.671762i	$0.765538\pi$
$368$	−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	−0.209954	−	0.977711i	$-0.567332\pi$
$373$	286.373	−	286.373i	0.767757	−	0.767757i	0.977711	+	0.209954i	$0.0673315\pi$
$374$	−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	0.634310	−	0.773079i	$-0.281284\pi$
$379$	−52.5935	−	52.5935i	−0.138769	−	0.138769i	−0.773079	+	0.634310i	$0.781284\pi$
$380$	−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	−0.485310	−	0.874342i	$-0.661293\pi$
$383$	148.999	−	148.999i	0.389032	−	0.389032i	0.874342	+	0.485310i	$0.161293\pi$
$384$	−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	0.937220	−	0.348740i	$-0.113390\pi$
$397$	233.627	+	233.627i	0.588480	+	0.588480i	−0.348740	+	0.937220i	$0.613390\pi$
$398$	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	−0.0810836	+	0.996707i	$0.525838\pi$
$401$	−432.194	+	432.194i	−1.07779	+	1.07779i	−0.996707	+	0.0810836i	$0.974162\pi$
$402$		−	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	−0.354452	−	0.935074i	$-0.615333\pi$
$409$	237.474	−	237.474i	0.580622	−	0.580622i	0.935074	+	0.354452i	$0.115333\pi$
$410$	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	$-0.969777\pi$
$419$		−	79.4467i		−	0.189610i	0.995496	−	0.0948051i	$-0.0302228\pi$
$420$			59.6668i			0.142064i
$421$		−	318.129i		−	0.755650i	−0.925877	−	0.377825i	$-0.876672\pi$
$421$		−	318.129i		−	0.755650i	0.925877	−	0.377825i	$-0.123328\pi$
$422$	−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	−0.905885	−	0.423524i	$-0.860793\pi$
$431$	−207.897	+	207.897i	−0.482360	+	0.482360i	0.423524	+	0.905885i	$0.360793\pi$
$432$	20.7666	+	20.7666i	0.0480708	+	0.0480708i
$433$			566.939i			1.30933i	0.755920	+	0.654664i	$0.227190\pi$
$433$			566.939i			1.30933i	−0.755920	+	0.654664i	$0.772810\pi$
$434$	−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	$-0.948375\pi$
$439$		−	141.773i		−	0.322946i	0.986877	−	0.161473i	$-0.0516245\pi$
$440$	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	−0.652440	−	0.757841i	$-0.726254\pi$
$443$	46.6925	−	46.6925i	0.105401	−	0.105401i	0.757841	+	0.652440i	$0.226254\pi$
$444$	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	$0.246512\pi$
$457$			639.175i			1.39863i	−0.714812	+	0.699316i	$0.753488\pi$
$458$		−	106.948i		−	0.233510i
$459$	−9.66025			−0.0210463
$460$			208.372i			0.452984i
$461$	489.462	+	489.462i	1.06174	+	1.06174i	0.997964	+	0.0637747i	$0.0203139\pi$
$461$	489.462	+	489.462i	1.06174	+	1.06174i	0.0637747	+	0.997964i	$0.479686\pi$
$462$	−181.920	−	181.920i	−0.393765	−	0.393765i
$463$	416.736	+	416.736i	0.900077	+	0.900077i	0.995442	−	0.0953650i	$-0.0304018\pi$
$463$	416.736	+	416.736i	0.900077	+	0.900077i	−0.0953650	+	0.995442i	$0.530402\pi$
$464$	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	−0.392655	−	0.919686i	$-0.628443\pi$
$467$	246.123	−	246.123i	0.527031	−	0.527031i	0.919686	+	0.392655i	$0.128443\pi$
$468$		−	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	−0.989669	−	0.143374i	$-0.954205\pi$
$479$	−405.375	+	405.375i	−0.846295	+	0.846295i	0.143374	+	0.989669i	$0.454205\pi$
$480$			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	$-0.715302\pi$
$491$		−	765.799i		−	1.55967i	0.625983	−	0.779836i	$-0.284698\pi$
$492$	−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	−0.985079	−	0.172103i	$-0.944944\pi$
$499$	−405.675	+	405.675i	−0.812976	+	0.812976i	0.172103	+	0.985079i	$0.444944\pi$
$500$		−	250.647i		−	0.501294i
$501$		−	712.160i		−	1.42148i
$502$			529.393i			1.05457i
$503$	242.673	−	242.673i	0.482452	−	0.482452i	−0.423462	−	0.905914i	$-0.639185\pi$
$503$	242.673	−	242.673i	0.482452	−	0.482452i	0.905914	+	0.423462i	$0.139185\pi$
$504$	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	−0.0277604	−	0.999615i	$-0.508838\pi$
$509$	494.674	−	494.674i	0.971854	−	0.971854i	0.999615	+	0.0277604i	$0.00883756\pi$
$510$	−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	0.618015	−	0.786166i	$-0.287937\pi$
$521$	−87.6064	−	87.6064i	−0.168150	−	0.168150i	−0.786166	+	0.618015i	$0.787937\pi$
$522$		−	308.655i		−	0.591293i
$523$	−473.039	−	473.039i	−0.904473	−	0.904473i	0.0913465	−	0.995819i	$-0.470883\pi$
$523$	−473.039	−	473.039i	−0.904473	−	0.904473i	−0.995819	+	0.0913465i	$0.970883\pi$
$524$		−	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	−0.190538	−	0.981680i	$-0.561023\pi$
$541$	428.008	−	428.008i	0.791142	−	0.791142i	0.981680	+	0.190538i	$0.0610231\pi$
$542$		−	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	$-0.883810\pi$
$547$		−	390.526i		−	0.713941i	0.934116	−	0.356970i	$-0.116190\pi$
$548$	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	0.814655	−	0.579947i	$-0.196927\pi$
$557$	130.732	+	130.732i	0.234708	+	0.234708i	−0.579947	+	0.814655i	$0.696927\pi$
$558$			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	0.237759	−	0.971324i	$-0.423587\pi$
$569$	−417.398	−	417.398i	−0.733565	−	0.733565i	−0.971324	+	0.237759i	$0.923587\pi$
$570$	234.545	−	234.545i	0.411482	−	0.411482i
$571$	183.766	+	183.766i	0.321832	+	0.321832i	0.849470	−	0.527637i	$-0.176922\pi$
$571$	183.766	+	183.766i	0.321832	+	0.321832i	−0.527637	+	0.849470i	$0.676922\pi$
$572$			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	0.684598	−	0.728921i	$-0.259978\pi$
$577$	−25.5743	−	25.5743i	−0.0443229	−	0.0443229i	−0.728921	+	0.684598i	$0.759978\pi$
$578$	−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	$-0.882071\pi$
$587$		−	425.068i		−	0.724137i	0.932152	−	0.362068i	$-0.117929\pi$
$588$	−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	$0.122903\pi$
$593$			446.633i			0.753175i	−0.926381	+	0.376588i	$0.877097\pi$
$594$			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	−0.804353	−	0.594152i	$-0.797488\pi$
$601$	−126.331	+	126.331i	−0.210202	+	0.210202i	0.594152	+	0.804353i	$0.297488\pi$
$602$			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	−0.714450	−	0.699686i	$-0.753323\pi$
$607$	−8.96170	+	8.96170i	−0.0147639	+	0.0147639i	0.699686	+	0.714450i	$0.253323\pi$
$608$	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	−0.341982	−	0.939706i	$-0.611098\pi$
$613$	366.405	−	366.405i	0.597724	−	0.597724i	0.939706	+	0.341982i	$0.111098\pi$
$614$	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	$-0.726583\pi$
$617$		−	934.344i		−	1.51433i	0.653221	−	0.757167i	$-0.273417\pi$
$618$	−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	$-0.914055\pi$
$641$		−	341.953i		−	0.533468i	0.963770	−	0.266734i	$-0.0859446\pi$
$642$	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	0.814912	−	0.579585i	$-0.196785\pi$
$647$	152.256	+	152.256i	0.235327	+	0.235327i	−0.579585	+	0.814912i	$0.696785\pi$
$648$	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	−0.942376	−	0.334555i	$-0.891414\pi$
$661$	−401.769	+	401.769i	−0.607821	+	0.607821i	0.334555	+	0.942376i	$0.391414\pi$
$662$	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	0.973868	+	0.227116i	$0.0729295\pi$
$673$	808.262	+	808.262i	1.20098	+	1.20098i	0.227116	+	0.973868i	$0.427071\pi$
$674$	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	−0.128933	+	0.991653i	$0.541155\pi$
$677$	−758.637	+	758.637i	−1.12059	+	1.12059i	−0.991653	+	0.128933i	$0.958845\pi$
$678$	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	0.977185	+	0.212389i	$0.0681244\pi$
$683$	812.479	+	812.479i	1.18957	+	1.18957i	0.212389	+	0.977185i	$0.431876\pi$
$684$	−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	−0.987548	−	0.157318i	$-0.949715\pi$
$691$	−791.102	−	791.102i	−1.14487	−	1.14487i	−0.157318	−	0.987548i	$-0.550285\pi$
$692$			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	0.878486	−	0.477768i	$-0.158554\pi$
$701$	280.903	+	280.903i	0.400718	+	0.400718i	−0.477768	+	0.878486i	$0.658554\pi$
$702$			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	0.0864567	−	0.996256i	$-0.472446\pi$
$709$	767.643	−	767.643i	1.08271	−	1.08271i	0.996256	−	0.0864567i	$-0.0275544\pi$
$710$	−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	0.151010	−	0.988532i	$-0.451748\pi$
$719$	−602.179	−	602.179i	−0.837523	−	0.837523i	−0.988532	+	0.151010i	$0.951748\pi$
$720$		−	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	$-0.959125\pi$
$727$		−	186.199i		−	0.256120i	0.991766	−	0.128060i	$-0.0408749\pi$
$728$	−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	0.523643	−	0.851938i	$-0.324573\pi$
$733$	−240.640	−	240.640i	−0.328295	−	0.328295i	−0.851938	+	0.523643i	$0.824573\pi$
$734$	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	−0.231215	−	0.972903i	$-0.574270\pi$
$739$	548.108	−	548.108i	0.741688	−	0.741688i	0.972903	+	0.231215i	$0.0742699\pi$
$740$		−	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	0.975891	+	0.218260i	$0.0700379\pi$
$757$	903.972	+	903.972i	1.19415	+	1.19415i	0.218260	+	0.975891i	$0.429962\pi$
$758$	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	0.389354	−	0.921088i	$-0.372698\pi$
$761$	−404.650	−	404.650i	−0.531735	−	0.531735i	−0.921088	+	0.389354i	$0.872698\pi$
$762$	−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	$-0.694851\pi$
$769$		−	1258.73i		−	1.63684i	0.574622	−	0.818419i	$-0.305149\pi$
$770$			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	−0.995950	−	0.0899054i	$-0.971344\pi$
$797$	−865.427	−	865.427i	−1.08586	−	1.08586i	−0.0899054	−	0.995950i	$-0.528656\pi$
$798$	−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	−0.334241	−	0.942488i	$-0.608480\pi$
$809$	492.072	−	492.072i	0.608247	−	0.608247i	0.942488	+	0.334241i	$0.108480\pi$
$810$	196.738	−	196.738i	0.242887	−	0.242887i
$811$		−	1239.46i		−	1.52831i	−0.645035	−	0.764153i	$-0.723157\pi$
$811$		−	1239.46i		−	1.52831i	0.645035	−	0.764153i	$-0.276843\pi$
$812$	−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	$0.290958\pi$
$827$			1309.96i			1.58399i	−0.610527	+	0.791996i	$0.709042\pi$
$828$	−715.016			−0.863546
$829$	278.811	+	278.811i	0.336323	+	0.336323i	0.854981	−	0.518659i	$-0.173568\pi$
$829$	278.811	+	278.811i	0.336323	+	0.336323i	−0.518659	+	0.854981i	$0.673568\pi$
$830$	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	−0.281548	−	0.959547i	$-0.590848\pi$
$839$	568.841	−	568.841i	0.677999	−	0.677999i	0.959547	+	0.281548i	$0.0908480\pi$
$840$	−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	−0.0256336	+	0.999671i	$0.508160\pi$
$853$	−874.585	+	874.585i	−1.02530	+	1.02530i	−0.999671	+	0.0256336i	$0.991840\pi$
$854$	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	−0.131631	−	0.991299i	$-0.542021\pi$
$857$	736.735	−	736.735i	0.859668	−	0.859668i	0.991299	+	0.131631i	$0.0420214\pi$
$858$		−	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	$-0.718396\pi$
$863$		−	1335.43i		−	1.54743i	0.633534	−	0.773715i	$-0.281604\pi$
$864$	−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	−0.430542	−	0.902571i	$-0.641677\pi$
$881$	415.858	−	415.858i	0.472029	−	0.472029i	0.902571	+	0.430542i	$0.141677\pi$
$882$	472.112	−	472.112i	0.535275	−	0.535275i
$883$	−274.673	+	274.673i	−0.311068	+	0.311068i	−0.845323	−	0.534256i	$-0.820592\pi$
$883$	−274.673	+	274.673i	−0.311068	+	0.311068i	0.534256	+	0.845323i	$0.320592\pi$
$884$	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	$-0.986828\pi$
$907$		−	75.0436i		−	0.0827382i	0.999144	−	0.0413691i	$-0.0131720\pi$
$908$	−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	−0.191827	−	0.981429i	$-0.561441\pi$
$911$	719.327	−	719.327i	0.789602	−	0.789602i	0.981429	+	0.191827i	$0.0614413\pi$
$912$	−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	0.999863	+	0.0165293i	$0.00526168\pi$
$919$	934.065	+	934.065i	1.01639	+	1.01639i	0.0165293	+	0.999863i	$0.494738\pi$
$920$	−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	−0.0606982	−	0.998156i	$-0.519333\pi$
$929$	870.898	−	870.898i	0.937458	−	0.937458i	0.998156	+	0.0606982i	$0.0193327\pi$
$930$	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	0.125377	−	0.992109i	$-0.459986\pi$
$937$	−812.128	−	812.128i	−0.866732	−	0.866732i	−0.992109	+	0.125377i	$0.959986\pi$
$938$	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	−0.763974	−	0.645248i	$-0.776754\pi$
$941$	−111.721	+	111.721i	−0.118726	+	0.118726i	0.645248	+	0.763974i	$0.276754\pi$
$942$	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	−0.234898	+	0.972020i	$0.575476\pi$
$947$	−1142.95	+	1142.95i	−1.20692	+	1.20692i	−0.972020	+	0.234898i	$0.924524\pi$
$948$	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	0.993176	−	0.116629i	$-0.0372090\pi$
$953$	835.348	+	835.348i	0.876546	+	0.876546i	−0.116629	+	0.993176i	$0.537209\pi$
$954$	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	−0.330081	−	0.943953i	$-0.607076\pi$
$967$	593.614	−	593.614i	0.613872	−	0.613872i	0.943953	+	0.330081i	$0.107076\pi$
$968$	−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	$0.276261\pi$
$971$			1481.69i			1.52595i	−0.646430	+	0.762973i	$0.723739\pi$
$972$	−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	$0.205517\pi$
$977$			1175.76i			1.20344i	−0.798709	+	0.601718i	$0.794483\pi$
$978$	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	$0.231815\pi$
$983$			1308.53i			1.33116i	−0.746328	+	0.665578i	$0.768185\pi$
$984$	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	0.478257	−	0.878220i	$-0.341269\pi$
$991$	−396.364	−	396.364i	−0.399964	−	0.399964i	−0.878220	+	0.478257i	$0.841269\pi$
$992$	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

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.21	✓	46	269.187	odd	4	inner
538.3.c.b.351.21	yes	46	1.1	even	1	trivial

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(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

Introduction

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