LMFDB - Embedded newform 169.5.d.c.99.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,5,Mod(70,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.70"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	169.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$17.4695237612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 $ x^16 + 152x^14 + 9190x^12 + 285720x^10 + 4862025x^8 + 43573680x^6 + 169417008x^4 + 100636992*x^2 + 3779136
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 13^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.6
Root			$-0.816521i$ of defining polynomial
Character	$\chi$	$=$	169.99
Dual form			169.5.d.c.70.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74699 + 1.74699i) q^{2} -8.51417 q^{3} -9.89603i q^{4} +(-16.9748 - 16.9748i) q^{5} +(-14.8742 - 14.8742i) q^{6} +(-36.7630 + 36.7630i) q^{7} +(45.2402 - 45.2402i) q^{8} -8.50884 q^{9} -59.3096i q^{10} +(63.9068 - 63.9068i) q^{11} +84.2565i q^{12} -128.449 q^{14} +(144.526 + 144.526i) q^{15} -0.267886 q^{16} +252.147i q^{17} +(-14.8649 - 14.8649i) q^{18} +(251.226 + 251.226i) q^{19} +(-167.983 + 167.983i) q^{20} +(313.007 - 313.007i) q^{21} +223.289 q^{22} +848.711i q^{23} +(-385.183 + 385.183i) q^{24} -48.7139i q^{25} +762.094 q^{27} +(363.808 + 363.808i) q^{28} +887.583 q^{29} +504.973i q^{30} +(-407.191 - 407.191i) q^{31} +(-724.311 - 724.311i) q^{32} +(-544.114 + 544.114i) q^{33} +(-440.500 + 440.500i) q^{34} +1248.09 q^{35} +84.2038i q^{36} +(-1879.26 + 1879.26i) q^{37} +877.782i q^{38} -1535.88 q^{40} +(-549.240 - 549.240i) q^{41} +1093.64 q^{42} +2425.04i q^{43} +(-632.424 - 632.424i) q^{44} +(144.436 + 144.436i) q^{45} +(-1482.69 + 1482.69i) q^{46} +(858.063 - 858.063i) q^{47} +2.28083 q^{48} -302.036i q^{49} +(85.1029 - 85.1029i) q^{50} -2146.83i q^{51} +39.2320 q^{53} +(1331.37 + 1331.37i) q^{54} -2169.61 q^{55} +3326.33i q^{56} +(-2138.99 - 2138.99i) q^{57} +(1550.60 + 1550.60i) q^{58} +(838.081 - 838.081i) q^{59} +(1430.24 - 1430.24i) q^{60} +4821.85 q^{61} -1422.72i q^{62} +(312.811 - 312.811i) q^{63} -2526.45i q^{64} -1901.13 q^{66} +(-2576.35 - 2576.35i) q^{67} +2495.26 q^{68} -7226.07i q^{69} +(2180.40 + 2180.40i) q^{70} +(451.353 + 451.353i) q^{71} +(-384.942 + 384.942i) q^{72} +(-1000.63 + 1000.63i) q^{73} -6566.11 q^{74} +414.759i q^{75} +(2486.14 - 2486.14i) q^{76} +4698.81i q^{77} +3698.19 q^{79} +(4.54730 + 4.54730i) q^{80} -5799.38 q^{81} -1919.04i q^{82} +(3629.57 + 3629.57i) q^{83} +(-3097.52 - 3097.52i) q^{84} +(4280.14 - 4280.14i) q^{85} +(-4236.52 + 4236.52i) q^{86} -7557.04 q^{87} -5782.31i q^{88} +(2105.28 - 2105.28i) q^{89} +504.656i q^{90} +8398.87 q^{92} +(3466.90 + 3466.90i) q^{93} +2998.06 q^{94} -8529.02i q^{95} +(6166.91 + 6166.91i) q^{96} +(-77.3660 - 77.3660i) q^{97} +(527.655 - 527.655i) q^{98} +(-543.773 + 543.773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 4 q^{3} - 8 q^{5} + 128 q^{6} - 56 q^{7} - 90 q^{8} + 328 q^{9} - 500 q^{11} + 808 q^{14} - 844 q^{15} - 460 q^{16} - 2434 q^{18} - 1712 q^{19} - 838 q^{20} + 1076 q^{21} + 3048 q^{22}+ \cdots + 21632 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 + 4 * q^3 - 8 * q^5 + 128 * q^6 - 56 * q^7 - 90 * q^8 + 328 * q^9 - 500 * q^11 + 808 * q^14 - 844 * q^15 - 460 * q^16 - 2434 * q^18 - 1712 * q^19 - 838 * q^20 + 1076 * q^21 + 3048 * q^22 - 5772 * q^24 + 3352 * q^27 - 2980 * q^28 - 1628 * q^29 - 4060 * q^31 - 3662 * q^32 + 860 * q^33 + 2502 * q^34 + 9784 * q^35 - 10468 * q^37 + 18816 * q^40 - 3440 * q^41 + 2408 * q^42 - 10736 * q^44 + 1004 * q^45 - 11436 * q^46 - 1484 * q^47 + 6004 * q^48 - 21616 * q^50 + 7204 * q^53 - 6760 * q^54 - 13872 * q^55 - 12736 * q^57 - 7974 * q^58 + 4840 * q^59 + 6472 * q^60 + 324 * q^61 + 13988 * q^63 - 23872 * q^66 - 2216 * q^67 + 12888 * q^68 + 34524 * q^70 + 1240 * q^71 + 6606 * q^72 + 15448 * q^73 + 5764 * q^74 + 39688 * q^76 - 17064 * q^79 + 37630 * q^80 - 4256 * q^81 - 12788 * q^83 + 7736 * q^84 + 22884 * q^85 - 67260 * q^86 - 58684 * q^87 + 37624 * q^89 - 49884 * q^92 + 2492 * q^93 + 61212 * q^94 + 94664 * q^96 + 57056 * q^97 - 27950 * q^98 + 21632 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.74699	+	1.74699i	0.436748	+	0.436748i	0.890916	−	0.454168i	$-0.150063\pi$
$2$	1.74699	+	1.74699i	0.436748	+	0.436748i	−0.454168	+	0.890916i	$0.650063\pi$
$3$	−8.51417			−0.946019			−0.473010	−	0.881057i	$-0.656832\pi$
$3$	−8.51417			−0.946019			−0.473010	+	0.881057i	$0.656832\pi$
$4$		−	9.89603i		−	0.618502i
$5$	−16.9748	−	16.9748i	−0.678991	−	0.678991i	0.280781	−	0.959772i	$-0.409407\pi$
$5$	−16.9748	−	16.9748i	−0.678991	−	0.678991i	−0.959772	+	0.280781i	$0.909407\pi$
$6$	−14.8742	−	14.8742i	−0.413172	−	0.413172i
$7$	−36.7630	+	36.7630i	−0.750265	+	0.750265i	−0.974529	−	0.224263i	$-0.928002\pi$
$7$	−36.7630	+	36.7630i	−0.750265	+	0.750265i	0.224263	+	0.974529i	$0.428002\pi$
$8$	45.2402	−	45.2402i	0.706878	−	0.706878i
$9$	−8.50884			−0.105047
$10$		−	59.3096i		−	0.593096i
$11$	63.9068	−	63.9068i	0.528155	−	0.528155i	−0.391867	−	0.920022i	$-0.628171\pi$
$11$	63.9068	−	63.9068i	0.528155	−	0.528155i	0.920022	+	0.391867i	$0.128171\pi$
$12$			84.2565i			0.585115i
$13$		0			0
$13$		0			0
$14$	−128.449			−0.655354
$15$	144.526	+	144.526i	0.642339	+	0.642339i
$16$	−0.267886			−0.00104643
$17$			252.147i			0.872482i	0.899830	+	0.436241i	$0.143691\pi$
$17$			252.147i			0.872482i	−0.899830	+	0.436241i	$0.856309\pi$
$18$	−14.8649	−	14.8649i	−0.0458793	−	0.0458793i
$19$	251.226	+	251.226i	0.695918	+	0.695918i	0.963527	−	0.267609i	$-0.0862337\pi$
$19$	251.226	+	251.226i	0.695918	+	0.695918i	−0.267609	+	0.963527i	$0.586234\pi$
$20$	−167.983	+	167.983i	−0.419957	+	0.419957i
$21$	313.007	−	313.007i	0.709765	−	0.709765i
$22$	223.289			0.461342
$23$			848.711i			1.60437i	0.597077	+	0.802184i	$0.296329\pi$
$23$			848.711i			1.60437i	−0.597077	+	0.802184i	$0.703671\pi$
$24$	−385.183	+	385.183i	−0.668720	+	0.668720i
$25$		−	48.7139i		−	0.0779423i
$26$		0			0
$27$	762.094			1.04540
$28$	363.808	+	363.808i	0.464040	+	0.464040i
$29$	887.583			1.05539			0.527695	−	0.849434i	$-0.323056\pi$
$29$	887.583			1.05539			0.527695	+	0.849434i	$0.323056\pi$
$30$			504.973i			0.561081i
$31$	−407.191	−	407.191i	−0.423716	−	0.423716i	0.462765	−	0.886481i	$-0.346857\pi$
$31$	−407.191	−	407.191i	−0.423716	−	0.423716i	−0.886481	+	0.462765i	$0.846857\pi$
$32$	−724.311	−	724.311i	−0.707335	−	0.707335i
$33$	−544.114	+	544.114i	−0.499645	+	0.499645i
$34$	−440.500	+	440.500i	−0.381055	+	0.381055i
$35$	1248.09			1.01885
$36$			84.2038i			0.0649720i
$37$	−1879.26	+	1879.26i	−1.37273	+	1.37273i	−0.516344	+	0.856381i	$0.672707\pi$
$37$	−1879.26	+	1879.26i	−1.37273	+	1.37273i	−0.856381	+	0.516344i	$0.827293\pi$
$38$			877.782i			0.607882i
$39$		0			0
$40$	−1535.88			−0.959928
$41$	−549.240	−	549.240i	−0.326734	−	0.326734i	0.524609	−	0.851343i	$-0.324211\pi$
$41$	−549.240	−	549.240i	−0.326734	−	0.326734i	−0.851343	+	0.524609i	$0.824211\pi$
$42$	1093.64			0.619978
$43$			2425.04i			1.31154i	0.754961	+	0.655769i	$0.227656\pi$
$43$			2425.04i			1.31154i	−0.754961	+	0.655769i	$0.772344\pi$
$44$	−632.424	−	632.424i	−0.326665	−	0.326665i
$45$	144.436	+	144.436i	0.0713263	+	0.0713263i
$46$	−1482.69	+	1482.69i	−0.700705	+	0.700705i
$47$	858.063	−	858.063i	0.388440	−	0.388440i	−0.485691	−	0.874131i	$-0.661432\pi$
$47$	858.063	−	858.063i	0.388440	−	0.388440i	0.874131	+	0.485691i	$0.161432\pi$
$48$	2.28083			0.000989942
$49$		−	302.036i		−	0.125796i
$50$	85.1029	−	85.1029i	0.0340412	−	0.0340412i
$51$		−	2146.83i		−	0.825385i
$52$		0			0
$53$	39.2320			0.0139665			0.00698326	−	0.999976i	$-0.497777\pi$
$53$	39.2320			0.0139665			0.00698326	+	0.999976i	$0.497777\pi$
$54$	1331.37	+	1331.37i	0.456575	+	0.456575i
$55$	−2169.61			−0.717225
$56$			3326.33i			1.06069i
$57$	−2138.99	−	2138.99i	−0.658352	−	0.658352i
$58$	1550.60	+	1550.60i	0.460940	+	0.460940i
$59$	838.081	−	838.081i	0.240759	−	0.240759i	−0.576405	−	0.817164i	$-0.695545\pi$
$59$	838.081	−	838.081i	0.240759	−	0.240759i	0.817164	+	0.576405i	$0.195545\pi$
$60$	1430.24	−	1430.24i	0.397288	−	0.397288i
$61$	4821.85			1.29585			0.647923	−	0.761705i	$-0.275638\pi$
$61$	4821.85			1.29585			0.647923	+	0.761705i	$0.275638\pi$
$62$		−	1422.72i		−	0.370114i
$63$	312.811	−	312.811i	0.0788135	−	0.0788135i
$64$		−	2526.45i		−	0.616808i
$65$		0			0
$66$	−1901.13			−0.436438
$67$	−2576.35	−	2576.35i	−0.573926	−	0.573926i	0.359297	−	0.933223i	$-0.383016\pi$
$67$	−2576.35	−	2576.35i	−0.573926	−	0.573926i	−0.933223	+	0.359297i	$0.883016\pi$
$68$	2495.26			0.539632
$69$		−	7226.07i		−	1.51776i
$70$	2180.40	+	2180.40i	0.444980	+	0.444980i
$71$	451.353	+	451.353i	0.0895363	+	0.0895363i	0.750456	−	0.660920i	$-0.229834\pi$
$71$	451.353	+	451.353i	0.0895363	+	0.0895363i	−0.660920	+	0.750456i	$0.729834\pi$
$72$	−384.942	+	384.942i	−0.0742557	+	0.0742557i
$73$	−1000.63	+	1000.63i	−0.187771	+	0.187771i	−0.794732	−	0.606961i	$-0.792388\pi$
$73$	−1000.63	+	1000.63i	−0.187771	+	0.187771i	0.606961	+	0.794732i	$0.292388\pi$
$74$	−6566.11			−1.19907
$75$			414.759i			0.0737349i
$76$	2486.14	−	2486.14i	0.430427	−	0.430427i
$77$			4698.81i			0.792513i
$78$		0			0
$79$	3698.19			0.592564			0.296282	−	0.955100i	$-0.404253\pi$
$79$	3698.19			0.592564			0.296282	+	0.955100i	$0.404253\pi$
$80$	4.54730	+	4.54730i	0.000710516	+	0.000710516i
$81$	−5799.38			−0.883918
$82$		−	1919.04i		−	0.285401i
$83$	3629.57	+	3629.57i	0.526865	+	0.526865i	0.919636	−	0.392771i	$-0.128484\pi$
$83$	3629.57	+	3629.57i	0.526865	+	0.526865i	−0.392771	+	0.919636i	$0.628484\pi$
$84$	−3097.52	−	3097.52i	−0.438991	−	0.438991i
$85$	4280.14	−	4280.14i	0.592408	−	0.592408i
$86$	−4236.52	+	4236.52i	−0.572812	+	0.572812i
$87$	−7557.04			−0.998420
$88$		−	5782.31i		−	0.746683i
$89$	2105.28	−	2105.28i	0.265785	−	0.265785i	−0.561614	−	0.827399i	$-0.689820\pi$
$89$	2105.28	−	2105.28i	0.265785	−	0.265785i	0.827399	+	0.561614i	$0.189820\pi$
$90$			504.656i			0.0623033i
$91$		0			0
$92$	8398.87			0.992305
$93$	3466.90	+	3466.90i	0.400844	+	0.400844i
$94$	2998.06			0.339301
$95$		−	8529.02i		−	0.945044i
$96$	6166.91	+	6166.91i	0.669153	+	0.669153i
$97$	−77.3660	−	77.3660i	−0.00822255	−	0.00822255i	0.702984	−	0.711206i	$-0.251851\pi$
$97$	−77.3660	−	77.3660i	−0.00822255	−	0.00822255i	−0.711206	+	0.702984i	$0.751851\pi$
$98$	527.655	−	527.655i	0.0549411	−	0.0549411i
$99$	−543.773	+	543.773i	−0.0554814	+	0.0554814i
$100$	−482.074			−0.0482074
$101$			18200.3i			1.78417i	0.451871	+	0.892083i	$0.350757\pi$
$101$			18200.3i			1.78417i	−0.451871	+	0.892083i	$0.649243\pi$
$102$	3750.49	−	3750.49i	0.360485	−	0.360485i
$103$			12486.6i			1.17698i	0.808505	+	0.588489i	$0.200277\pi$
$103$			12486.6i			1.17698i	−0.808505	+	0.588489i	$0.799723\pi$
$104$		0			0
$105$	−10626.4			−0.963849
$106$	68.5380	+	68.5380i	0.00609986	+	0.00609986i
$107$	−9365.30			−0.818001			−0.409001	−	0.912534i	$-0.634123\pi$
$107$	−9365.30			−0.818001			−0.409001	+	0.912534i	$0.634123\pi$
$108$		−	7541.70i		−	0.646580i
$109$	−5548.06	−	5548.06i	−0.466969	−	0.466969i	0.433962	−	0.900931i	$-0.357115\pi$
$109$	−5548.06	−	5548.06i	−0.466969	−	0.466969i	−0.900931	+	0.433962i	$0.857115\pi$
$110$	−3790.29	−	3790.29i	−0.313247	−	0.313247i
$111$	16000.4	−	16000.4i	1.29862	−	1.29862i
$112$	9.84828	−	9.84828i	0.000785099	−	0.000785099i
$113$	−7951.37			−0.622709			−0.311355	−	0.950294i	$-0.600783\pi$
$113$	−7951.37			−0.622709			−0.311355	+	0.950294i	$0.600783\pi$
$114$		−	7473.59i		−	0.575068i
$115$	14406.7	−	14406.7i	1.08935	−	1.08935i
$116$		−	8783.55i		−	0.652761i
$117$		0			0
$118$	2928.24			0.210302
$119$	−9269.69	−	9269.69i	−0.654593	−	0.654593i
$120$	13076.8			0.908110
$121$			6472.84i			0.442104i
$122$	8423.73	+	8423.73i	0.565959	+	0.565959i
$123$	4676.32	+	4676.32i	0.309097	+	0.309097i
$124$	−4029.57	+	4029.57i	−0.262069	+	0.262069i
$125$	−11436.1	+	11436.1i	−0.731913	+	0.731913i
$126$	1092.96			0.0688433
$127$		−	18915.3i		−	1.17275i	−0.810039	−	0.586376i	$-0.800554\pi$
$127$		−	18915.3i		−	1.17275i	0.810039	−	0.586376i	$-0.199446\pi$
$128$	−7175.29	+	7175.29i	−0.437945	+	0.437945i
$129$		−	20647.2i		−	1.24074i
$130$		0			0
$131$	−3296.47			−0.192091			−0.0960454	−	0.995377i	$-0.530619\pi$
$131$	−3296.47			−0.192091			−0.0960454	+	0.995377i	$0.530619\pi$
$132$	5384.56	+	5384.56i	0.309031	+	0.309031i
$133$	−18471.7			−1.04425
$134$		−	9001.74i		−	0.501322i
$135$	−12936.4	−	12936.4i	−0.709815	−	0.709815i
$136$	11407.2	+	11407.2i	0.616738	+	0.616738i
$137$	−17255.4	+	17255.4i	−0.919355	+	0.919355i	−0.996982	−	0.0776272i	$-0.975266\pi$
$137$	−17255.4	+	17255.4i	−0.919355	+	0.919355i	0.0776272	+	0.996982i	$0.475266\pi$
$138$	12623.9	−	12623.9i	0.662881	−	0.662881i
$139$	1576.13			0.0815758			0.0407879	−	0.999168i	$-0.487013\pi$
$139$	1576.13			0.0815758			0.0407879	+	0.999168i	$0.487013\pi$
$140$		−	12351.1i		−	0.630159i
$141$	−7305.70	+	7305.70i	−0.367471	+	0.367471i
$142$			1577.02i			0.0782097i
$143$		0			0
$144$	2.27940			0.000109925
$145$	−15066.5	−	15066.5i	−0.716601	−	0.716601i
$146$	−3496.19			−0.164017
$147$			2571.59i			0.119005i
$148$	18597.2	+	18597.2i	0.849033	+	0.849033i
$149$	−5559.67	−	5559.67i	−0.250424	−	0.250424i	0.570720	−	0.821145i	$-0.306664\pi$
$149$	−5559.67	−	5559.67i	−0.250424	−	0.250424i	−0.821145	+	0.570720i	$0.806664\pi$
$150$	−724.581	+	724.581i	−0.0322036	+	0.0322036i
$151$	13112.6	−	13112.6i	0.575089	−	0.575089i	−0.358457	−	0.933546i	$-0.616697\pi$
$151$	13112.6	−	13112.6i	0.575089	−	0.575089i	0.933546	+	0.358457i	$0.116697\pi$
$152$	22731.1			0.983858
$153$		−	2145.48i		−	0.0916520i
$154$	−8208.79	+	8208.79i	−0.346129	+	0.346129i
$155$			13824.0i			0.575399i
$156$		0			0
$157$	212.325			0.00861394			0.00430697	−	0.999991i	$-0.498629\pi$
$157$	212.325			0.00861394			0.00430697	+	0.999991i	$0.498629\pi$
$158$	6460.72	+	6460.72i	0.258802	+	0.258802i
$159$	−334.028			−0.0132126
$160$			24590.0i			0.960548i
$161$	−31201.2	−	31201.2i	−1.20370	−	1.20370i
$162$	−10131.5	−	10131.5i	−0.386049	−	0.386049i
$163$	3851.14	−	3851.14i	0.144948	−	0.144948i	−0.630909	−	0.775857i	$-0.717318\pi$
$163$	3851.14	−	3851.14i	0.144948	−	0.144948i	0.775857	+	0.630909i	$0.217318\pi$
$164$	−5435.29	+	5435.29i	−0.202086	+	0.202086i
$165$	18472.4			0.678509
$166$			12681.7i			0.460215i
$167$	−16193.2	+	16193.2i	−0.580629	+	0.580629i	−0.935076	−	0.354447i	$-0.884669\pi$
$167$	−16193.2	+	16193.2i	−0.580629	+	0.580629i	0.354447	+	0.935076i	$0.384669\pi$
$168$		−	28320.9i		−	1.00343i
$169$		0			0
$170$	14954.8			0.517466
$171$	−2137.65	−	2137.65i	−0.0731044	−	0.0731044i
$172$	23998.2			0.811189
$173$			35476.3i			1.18535i	0.805443	+	0.592674i	$0.201928\pi$
$173$			35476.3i			1.18535i	−0.805443	+	0.592674i	$0.798072\pi$
$174$	−13202.1	−	13202.1i	−0.436058	−	0.436058i
$175$	1790.87	+	1790.87i	0.0584774	+	0.0584774i
$176$	−17.1197	+	17.1197i	−0.000552677	+	0.000552677i
$177$	−7135.57	+	7135.57i	−0.227762	+	0.227762i
$178$	7355.82			0.232162
$179$			49231.4i			1.53651i	0.640142	+	0.768256i	$0.278875\pi$
$179$			49231.4i			1.53651i	−0.640142	+	0.768256i	$0.721125\pi$
$180$	1429.34	−	1429.34i	0.0441154	−	0.0441154i
$181$			45485.8i			1.38841i	0.719775	+	0.694207i	$0.244245\pi$
$181$			45485.8i			1.38841i	−0.719775	+	0.694207i	$0.755755\pi$
$182$		0			0
$183$	−41054.0			−1.22590
$184$	38395.8	+	38395.8i	1.13409	+	1.13409i
$185$	63800.1			1.86414
$186$			12113.3i			0.350135i
$187$	16113.9	+	16113.9i	0.460806	+	0.460806i
$188$	−8491.42	−	8491.42i	−0.240251	−	0.240251i
$189$	−28016.9	+	28016.9i	−0.784324	+	0.784324i
$190$	14900.1	−	14900.1i	0.412746	−	0.412746i
$191$	−19068.1			−0.522686			−0.261343	−	0.965246i	$-0.584165\pi$
$191$	−19068.1			−0.522686			−0.261343	+	0.965246i	$0.584165\pi$
$192$			21510.6i			0.583512i
$193$	−18288.4	+	18288.4i	−0.490976	+	0.490976i	−0.908614	−	0.417638i	$-0.862858\pi$
$193$	−18288.4	+	18288.4i	−0.490976	+	0.490976i	0.417638	+	0.908614i	$0.362858\pi$
$194$		−	270.316i		−	0.00718237i
$195$		0			0
$196$	−2988.96			−0.0778050
$197$	12689.3	+	12689.3i	0.326969	+	0.326969i	0.851433	−	0.524464i	$-0.175734\pi$
$197$	12689.3	+	12689.3i	0.326969	+	0.326969i	−0.524464	+	0.851433i	$0.675734\pi$
$198$	−1899.94			−0.0484628
$199$			3020.21i			0.0762660i	0.999273	+	0.0381330i	$0.0121410\pi$
$199$			3020.21i			0.0762660i	−0.999273	+	0.0381330i	$0.987859\pi$
$200$	−2203.83	−	2203.83i	−0.0550957	−	0.0550957i
$201$	21935.5	+	21935.5i	0.542945	+	0.542945i
$202$	−31795.8	+	31795.8i	−0.779232	+	0.779232i
$203$	−32630.2	+	32630.2i	−0.791823	+	0.791823i
$204$	−21245.1			−0.510502
$205$			18646.4i			0.443699i
$206$	−21813.9	+	21813.9i	−0.514043	+	0.514043i
$207$		−	7221.55i		−	0.168535i
$208$		0			0
$209$	32110.1			0.735106
$210$	−18564.3	−	18564.3i	−0.420959	−	0.420959i
$211$	−76384.5			−1.71570			−0.857848	−	0.513903i	$-0.828199\pi$
$211$	−76384.5			−1.71570			−0.857848	+	0.513903i	$0.828199\pi$
$212$		−	388.241i		−	0.00863832i
$213$	−3842.90	−	3842.90i	−0.0847031	−	0.0847031i
$214$	−16361.1	−	16361.1i	−0.357261	−	0.357261i
$215$	41164.4	−	41164.4i	0.890523	−	0.890523i
$216$	34477.3	−	34477.3i	0.738968	−	0.738968i
$217$	29939.1			0.635799
$218$		−	19384.8i		−	0.407896i
$219$	8519.54	−	8519.54i	0.177635	−	0.177635i
$220$			21470.5i			0.443605i
$221$		0			0
$222$	55905.0			1.13434
$223$	13445.1	+	13445.1i	0.270367	+	0.270367i	0.829248	−	0.558881i	$-0.188769\pi$
$223$	13445.1	+	13445.1i	0.270367	+	0.270367i	−0.558881	+	0.829248i	$0.688769\pi$
$224$	53255.7			1.06138
$225$			414.499i			0.00818764i
$226$	−13891.0	−	13891.0i	−0.271967	−	0.271967i
$227$	−2679.72	−	2679.72i	−0.0520041	−	0.0520041i	0.680626	−	0.732631i	$-0.261708\pi$
$227$	−2679.72	−	2679.72i	−0.0520041	−	0.0520041i	−0.732631	+	0.680626i	$0.761708\pi$
$228$	−21167.5	+	21167.5i	−0.407192	+	0.407192i
$229$	57344.9	−	57344.9i	1.09351	−	1.09351i	0.0983628	−	0.995151i	$-0.468639\pi$
$229$	57344.9	−	57344.9i	1.09351	−	1.09351i	0.995151	−	0.0983628i	$-0.0313606\pi$
$230$	50336.7			0.951545
$231$		−	40006.5i		−	0.749733i
$232$	40154.4	−	40154.4i	0.746032	−	0.746032i
$233$			6475.98i			0.119287i	0.998220	+	0.0596436i	$0.0189964\pi$
$233$			6475.98i			0.119287i	−0.998220	+	0.0596436i	$0.981004\pi$
$234$		0			0
$235$	−29130.9			−0.527494
$236$	−8293.68	−	8293.68i	−0.148910	−	0.148910i
$237$	−31487.1			−0.560577
$238$		−	32388.2i		−	0.571785i
$239$	34428.3	+	34428.3i	0.602725	+	0.602725i	0.941035	−	0.338310i	$-0.109855\pi$
$239$	34428.3	+	34428.3i	0.602725	+	0.602725i	−0.338310	+	0.941035i	$0.609855\pi$
$240$	−38.7165	−	38.7165i	−0.000672162	−	0.000672162i
$241$	5044.21	−	5044.21i	0.0868478	−	0.0868478i	−0.662348	−	0.749196i	$-0.730440\pi$
$241$	5044.21	−	5044.21i	0.0868478	−	0.0868478i	0.749196	+	0.662348i	$0.230440\pi$
$242$	−11308.0	+	11308.0i	−0.193088	+	0.193088i
$243$	−12352.6			−0.209193
$244$		−	47717.1i		−	0.801484i
$245$	−5126.99	+	5126.99i	−0.0854143	+	0.0854143i
$246$			16339.0i			0.269995i
$247$		0			0
$248$	−36842.8			−0.599031
$249$	−30902.8	−	30902.8i	−0.498425	−	0.498425i
$250$	−39957.7			−0.639324
$251$		−	85899.5i		−	1.36346i	−0.731603	−	0.681731i	$-0.761227\pi$
$251$		−	85899.5i		−	1.36346i	0.731603	−	0.681731i	$-0.238773\pi$
$252$	−3095.58	−	3095.58i	−0.0487463	−	0.0487463i
$253$	54238.4	+	54238.4i	0.847356	+	0.847356i
$254$	33044.9	−	33044.9i	0.512197	−	0.512197i
$255$	−36441.9	+	36441.9i	−0.560429	+	0.560429i
$256$	−65493.5			−0.999352
$257$			25727.8i			0.389525i	0.980850	+	0.194763i	$0.0623937\pi$
$257$			25727.8i			0.389525i	−0.980850	+	0.194763i	$0.937606\pi$
$258$	36070.5	−	36070.5i	0.541892	−	0.541892i
$259$		−	138175.i		−	2.05982i
$260$		0			0
$261$	−7552.31			−0.110866
$262$	−5758.91	−	5758.91i	−0.0838953	−	0.0838953i
$263$	27569.5			0.398582			0.199291	−	0.979940i	$-0.436136\pi$
$263$	27569.5			0.398582			0.199291	+	0.979940i	$0.436136\pi$
$264$			49231.6i			0.706376i
$265$	−665.954	−	665.954i	−0.00948315	−	0.00948315i
$266$	−32269.9	−	32269.9i	−0.456073	−	0.456073i
$267$	−17924.7	+	17924.7i	−0.251437	+	0.251437i
$268$	−25495.7	+	25495.7i	−0.354974	+	0.354974i
$269$	−48109.2			−0.664849			−0.332425	−	0.943130i	$-0.607867\pi$
$269$	−48109.2			−0.664849			−0.332425	+	0.943130i	$0.607867\pi$
$270$		−	45199.5i		−	0.620021i
$271$	18041.9	−	18041.9i	0.245665	−	0.245665i	−0.573524	−	0.819189i	$-0.694424\pi$
$271$	18041.9	−	18041.9i	0.245665	−	0.245665i	0.819189	+	0.573524i	$0.194424\pi$
$272$		−	67.5467i		−	0.000912990i
$273$		0			0
$274$	−60290.1			−0.803054
$275$	−3113.15	−	3113.15i	−0.0411656	−	0.0411656i
$276$	−71509.4			−0.938739
$277$			52704.1i			0.686886i	0.939174	+	0.343443i	$0.111593\pi$
$277$			52704.1i			0.686886i	−0.939174	+	0.343443i	$0.888407\pi$
$278$	2753.48	+	2753.48i	0.0356281	+	0.0356281i
$279$	3464.73	+	3464.73i	0.0445103	+	0.0445103i
$280$	56463.7	−	56463.7i	0.720200	−	0.720200i
$281$	−88394.7	+	88394.7i	−1.11947	+	1.11947i	−0.127654	+	0.991819i	$0.540745\pi$
$281$	−88394.7	+	88394.7i	−1.11947	+	1.11947i	−0.991819	+	0.127654i	$0.959255\pi$
$282$	−25526.0			−0.320985
$283$		−	60370.6i		−	0.753794i	−0.926255	−	0.376897i	$-0.876991\pi$
$283$		−	60370.6i		−	0.753794i	0.926255	−	0.376897i	$-0.123009\pi$
$284$	4466.60	−	4466.60i	0.0553784	−	0.0553784i
$285$			72617.6i			0.894030i
$286$		0			0
$287$	40383.4			0.490274
$288$	6163.05	+	6163.05i	0.0743037	+	0.0743037i
$289$	19942.7			0.238775
$290$		−	52642.2i		−	0.625948i
$291$	658.708	+	658.708i	0.00777869	+	0.00777869i
$292$	9902.26	+	9902.26i	0.116136	+	0.116136i
$293$	47402.3	−	47402.3i	0.552159	−	0.552159i	−0.374905	−	0.927063i	$-0.622325\pi$
$293$	47402.3	−	47402.3i	0.552159	−	0.552159i	0.927063	+	0.374905i	$0.122325\pi$
$294$	−4492.54	+	4492.54i	−0.0519754	+	0.0519754i
$295$	−28452.5			−0.326946
$296$			170036.i			1.94070i
$297$	48703.0	−	48703.0i	0.552132	−	0.552132i
$298$		−	19425.4i		−	0.218745i
$299$		0			0
$300$	4104.46			0.0456052
$301$	−89151.6	−	89151.6i	−0.984002	−	0.984002i
$302$	45815.3			0.502339
$303$		−	154960.i		−	1.68786i
$304$	−67.3000	−	67.3000i	−0.000728228	−	0.000728228i
$305$	−81849.8	−	81849.8i	−0.879868	−	0.879868i
$306$	3748.14	−	3748.14i	0.0400289	−	0.0400289i
$307$	56466.7	−	56466.7i	0.599122	−	0.599122i	−0.340957	−	0.940079i	$-0.610751\pi$
$307$	56466.7	−	56466.7i	0.599122	−	0.599122i	0.940079	+	0.340957i	$0.110751\pi$
$308$	46499.6			0.490171
$309$		−	106313.i		−	1.11344i
$310$	−24150.4	+	24150.4i	−0.251304	+	0.251304i
$311$			23649.5i			0.244513i	0.992499	+	0.122256i	$0.0390130\pi$
$311$			23649.5i			0.244513i	−0.992499	+	0.122256i	$0.960987\pi$
$312$		0			0
$313$	86256.6			0.880447			0.440224	−	0.897888i	$-0.354899\pi$
$313$	86256.6			0.880447			0.440224	+	0.897888i	$0.354899\pi$
$314$	370.930	+	370.930i	0.00376212	+	0.00376212i
$315$	−10619.8			−0.107027
$316$		−	36597.4i		−	0.366502i
$317$	108363.	+	108363.i	1.07836	+	1.07836i	0.996657	+	0.0817010i	$0.0260353\pi$
$317$	108363.	+	108363.i	1.07836	+	1.07836i	0.0817010	+	0.996657i	$0.473965\pi$
$318$	−583.544	−	583.544i	−0.00577058	−	0.00577058i
$319$	56722.6	−	56722.6i	0.557410	−	0.557410i
$320$	−42885.9	+	42885.9i	−0.418807	+	0.418807i
$321$	79737.8			0.773845
$322$		−	109016.i		−	1.05143i
$323$	−63346.1	+	63346.1i	−0.607176	+	0.607176i
$324$			57390.9i			0.546705i
$325$		0			0
$326$	13455.8			0.126612
$327$	47237.2	+	47237.2i	0.441762	+	0.441762i
$328$	−49695.4			−0.461922
$329$			63089.9i			0.582866i
$330$	32271.2	+	32271.2i	0.296338	+	0.296338i
$331$	−69512.0	−	69512.0i	−0.634459	−	0.634459i	0.314724	−	0.949183i	$-0.398088\pi$
$331$	−69512.0	−	69512.0i	−0.634459	−	0.634459i	−0.949183	+	0.314724i	$0.898088\pi$
$332$	35918.4	−	35918.4i	0.325867	−	0.325867i
$333$	15990.3	−	15990.3i	0.144201	−	0.144201i
$334$	−56578.6			−0.507177
$335$			87466.0i			0.779381i
$336$	−83.8500	+	83.8500i	−0.000742719	+	0.000742719i
$337$		−	30291.6i		−	0.266725i	−0.991067	−	0.133362i	$-0.957423\pi$
$337$		−	30291.6i		−	0.266725i	0.991067	−	0.133362i	$-0.0425774\pi$
$338$		0			0
$339$	67699.4			0.589095
$340$	−42356.4	−	42356.4i	−0.366405	−	0.366405i
$341$	−52044.5			−0.447576
$342$		−	7468.91i		−	0.0638565i
$343$	−77164.2	−	77164.2i	−0.655885	−	0.655885i
$344$	109709.	+	109709.i	0.927098	+	0.927098i
$345$	−122661.	+	122661.i	−1.03055	+	1.03055i
$346$	−61976.8	+	61976.8i	−0.517699	+	0.517699i
$347$	−185945.			−1.54428			−0.772141	−	0.635452i	$-0.780814\pi$
$347$	−185945.			−1.54428			−0.772141	+	0.635452i	$0.780814\pi$
$348$			74784.7i			0.617524i
$349$	113915.	−	113915.i	0.935252	−	0.935252i	−0.0627755	−	0.998028i	$-0.519995\pi$
$349$	113915.	−	113915.i	0.935252	−	0.935252i	0.998028	+	0.0627755i	$0.0199952\pi$
$350$			6257.27i			0.0510798i
$351$		0			0
$352$	−92576.8			−0.747165
$353$	135896.	+	135896.i	1.09058	+	1.09058i	0.995467	+	0.0951102i	$0.0303203\pi$
$353$	135896.	+	135896.i	1.09058	+	1.09058i	0.0951102	+	0.995467i	$0.469680\pi$
$354$	−24931.6			−0.198950
$355$		−	15323.2i		−	0.121589i
$356$	−20833.9	−	20833.9i	−0.164388	−	0.164388i
$357$	78923.8	+	78923.8i	0.619258	+	0.619258i
$358$	−86006.9	+	86006.9i	−0.671069	+	0.671069i
$359$	111215.	−	111215.i	0.862925	−	0.862925i	−0.128751	−	0.991677i	$-0.541097\pi$
$359$	111215.	−	111215.i	0.862925	−	0.862925i	0.991677	+	0.128751i	$0.0410970\pi$
$360$	13068.6			0.100838
$361$		−	4091.59i		−	0.0313963i
$362$	−79463.5	+	79463.5i	−0.606388	+	0.606388i
$363$		−	55110.9i		−	0.418239i
$364$		0			0
$365$	33970.9			0.254989
$366$	−71721.1	−	71721.1i	−0.535408	−	0.535408i
$367$	224411.			1.66614			0.833072	−	0.553165i	$-0.186580\pi$
$367$	224411.			1.66614			0.833072	+	0.553165i	$0.186580\pi$
$368$		−	227.357i		−	0.00167886i
$369$	4673.39	+	4673.39i	0.0343226	+	0.0343226i
$370$	111458.	+	111458.i	0.814158	+	0.814158i
$371$	−1442.29	+	1442.29i	−0.0104786	+	0.0104786i
$372$	34308.5	−	34308.5i	0.247922	−	0.247922i
$373$	201930.			1.45139			0.725693	−	0.688019i	$-0.241519\pi$
$373$	201930.			1.45139			0.725693	+	0.688019i	$0.241519\pi$
$374$			56301.8i			0.402512i
$375$	97369.3	−	97369.3i	0.692404	−	0.692404i
$376$		−	77637.9i		−	0.549159i
$377$		0			0
$378$	−97890.5			−0.685105
$379$	98134.8	+	98134.8i	0.683195	+	0.683195i	0.960719	−	0.277524i	$-0.0895138\pi$
$379$	98134.8	+	98134.8i	0.683195	+	0.683195i	−0.277524	+	0.960719i	$0.589514\pi$
$380$	−84403.5			−0.584512
$381$			161048.i			1.10945i
$382$	−33311.9	−	33311.9i	−0.228282	−	0.228282i
$383$	−124265.	−	124265.i	−0.847134	−	0.847134i	0.142641	−	0.989775i	$-0.454441\pi$
$383$	−124265.	−	124265.i	−0.847134	−	0.847134i	−0.989775	+	0.142641i	$0.954441\pi$
$384$	61091.7	−	61091.7i	0.414304	−	0.414304i
$385$	79761.3	−	79761.3i	0.538109	−	0.538109i
$386$	−63899.3			−0.428866
$387$		−	20634.2i		−	0.137774i
$388$	−765.616	+	765.616i	−0.00508566	+	0.00508566i
$389$			172903.i			1.14262i	0.820733	+	0.571312i	$0.193565\pi$
$389$			172903.i			1.14262i	−0.820733	+	0.571312i	$0.806435\pi$
$390$		0			0
$391$	−214000.			−1.39978
$392$	−13664.2	−	13664.2i	−0.0889223	−	0.0889223i
$393$	28066.7			0.181722
$394$			44336.4i			0.285606i
$395$	−62776.0	−	62776.0i	−0.402346	−	0.402346i
$396$	5381.19	+	5381.19i	0.0343153	+	0.0343153i
$397$	−115477.	+	115477.i	−0.732683	+	0.732683i	−0.971150	−	0.238467i	$-0.923355\pi$
$397$	−115477.	+	115477.i	−0.732683	+	0.732683i	0.238467	+	0.971150i	$0.423355\pi$
$398$	−5276.28	+	5276.28i	−0.0333090	+	0.0333090i
$399$	157271.			0.987877
$400$			13.0498i			8.15610e-5i
$401$	−150205.	+	150205.i	−0.934104	+	0.934104i	−0.997959	−	0.0638548i	$-0.979661\pi$
$401$	−150205.	+	150205.i	−0.934104	+	0.934104i	0.0638548	+	0.997959i	$0.479661\pi$
$402$			76642.4i			0.474260i
$403$		0			0
$404$	180111.			1.10351
$405$	98443.2	+	98443.2i	0.600172	+	0.600172i
$406$	−114010.			−0.691654
$407$			240195.i			1.45002i
$408$	−97122.8	−	97122.8i	−0.583446	−	0.583446i
$409$	−86795.0	−	86795.0i	−0.518857	−	0.518857i	0.398368	−	0.917226i	$-0.369577\pi$
$409$	−86795.0	−	86795.0i	−0.518857	−	0.518857i	−0.917226	+	0.398368i	$0.869577\pi$
$410$	−32575.2	+	32575.2i	−0.193785	+	0.193785i
$411$	146915.	−	146915.i	0.869728	−	0.869728i
$412$	123567.			0.727963
$413$			61620.8i			0.361266i
$414$	12616.0	−	12616.0i	0.0736073	−	0.0736073i
$415$		−	123222.i		−	0.715474i
$416$		0			0
$417$	−13419.4			−0.0771723
$418$	56096.2	+	56096.2i	0.321056	+	0.321056i
$419$	228319.			1.30051			0.650254	−	0.759717i	$-0.274662\pi$
$419$	228319.			1.30051			0.650254	+	0.759717i	$0.274662\pi$
$420$			105159.i			0.596142i
$421$	−29630.8	−	29630.8i	−0.167178	−	0.167178i	0.618560	−	0.785738i	$-0.287716\pi$
$421$	−29630.8	−	29630.8i	−0.167178	−	0.167178i	−0.785738	+	0.618560i	$0.787716\pi$
$422$	−133443.	−	133443.i	−0.749327	−	0.749327i
$423$	−7301.13	+	7301.13i	−0.0408046	+	0.0408046i
$424$	1774.86	−	1774.86i	0.00987263	−	0.00987263i
$425$	12283.1			0.0680032
$426$		−	13427.0i		−	0.0739879i
$427$	−177266.	+	177266.i	−0.972229	+	0.972229i
$428$			92679.2i			0.505935i
$429$		0			0
$430$	143828.			0.777869
$431$	−101306.	−	101306.i	−0.545358	−	0.545358i	0.379737	−	0.925095i	$-0.376015\pi$
$431$	−101306.	−	101306.i	−0.545358	−	0.545358i	−0.925095	+	0.379737i	$0.876015\pi$
$432$	−204.154			−0.00109393
$433$		−	202761.i		−	1.08146i	−0.841198	−	0.540728i	$-0.818149\pi$
$433$		−	202761.i		−	1.08146i	0.841198	−	0.540728i	$-0.181851\pi$
$434$	52303.5	+	52303.5i	0.277684	+	0.277684i
$435$	128279.	+	128279.i	0.677918	+	0.677918i
$436$	−54903.8	+	54903.8i	−0.288821	+	0.288821i
$437$	−213219.	+	213219.i	−1.11651	+	1.11651i
$438$	29767.1			0.155163
$439$		−	5953.77i		−	0.0308932i	−0.999881	−	0.0154466i	$-0.995083\pi$
$439$		−	5953.77i		−	0.0308932i	0.999881	−	0.0154466i	$-0.00491700\pi$
$440$	−98153.4	+	98153.4i	−0.506991	+	0.506991i
$441$			2569.98i			0.0132145i
$442$		0			0
$443$	−25178.3			−0.128298			−0.0641489	−	0.997940i	$-0.520433\pi$
$443$	−25178.3			−0.128298			−0.0641489	+	0.997940i	$0.520433\pi$
$444$	−158340.	−	158340.i	−0.803202	−	0.803202i
$445$	−71473.3			−0.360931
$446$			46977.0i			0.236165i
$447$	47336.0	+	47336.0i	0.236906	+	0.236906i
$448$	92879.7	+	92879.7i	0.462770	+	0.462770i
$449$	−143200.	+	143200.i	−0.710315	+	0.710315i	−0.966601	−	0.256286i	$-0.917501\pi$
$449$	−143200.	+	143200.i	−0.710315	+	0.710315i	0.256286	+	0.966601i	$0.417501\pi$
$450$	−724.127	+	724.127i	−0.00357594	+	0.00357594i
$451$	−70200.3			−0.345132
$452$			78687.0i			0.385147i
$453$	−111643.	+	111643.i	−0.544046	+	0.544046i
$454$		−	9362.91i		−	0.0454254i
$455$		0			0
$456$	−193536.			−0.930749
$457$	−22101.2	−	22101.2i	−0.105824	−	0.105824i	0.652212	−	0.758036i	$-0.273841\pi$
$457$	−22101.2	−	22101.2i	−0.105824	−	0.105824i	−0.758036	+	0.652212i	$0.773841\pi$
$458$	200362.			0.955180
$459$			192160.i			0.912090i
$460$	−142569.	−	142569.i	−0.673766	−	0.673766i
$461$	−37293.6	−	37293.6i	−0.175482	−	0.175482i	0.613901	−	0.789383i	$-0.289599\pi$
$461$	−37293.6	−	37293.6i	−0.175482	−	0.175482i	−0.789383	+	0.613901i	$0.789599\pi$
$462$	69891.1	−	69891.1i	0.327444	−	0.327444i
$463$	−81704.7	+	81704.7i	−0.381140	+	0.381140i	−0.871513	−	0.490372i	$-0.836861\pi$
$463$	−81704.7	+	81704.7i	−0.381140	+	0.381140i	0.490372	+	0.871513i	$0.336861\pi$
$464$	−237.771			−0.00110439
$465$		−	117700.i		−	0.544338i
$466$	−11313.5	+	11313.5i	−0.0520985	+	0.0520985i
$467$		−	267324.i		−	1.22576i	−0.790177	−	0.612878i	$-0.790012\pi$
$467$		−	267324.i		−	1.22576i	0.790177	−	0.612878i	$-0.209988\pi$
$468$		0			0
$469$	189429.			0.861193
$470$	−50891.4	−	50891.4i	−0.230382	−	0.230382i
$471$	−1807.77			−0.00814895
$472$		−	75829.9i		−	0.340374i
$473$	154976.	+	154976.i	0.692696	+	0.692696i
$474$	−55007.7	−	55007.7i	−0.244831	−	0.244831i
$475$	12238.2	−	12238.2i	0.0542414	−	0.0542414i
$476$	−91733.1	+	91733.1i	−0.404867	+	0.404867i
$477$	−333.819			−0.00146715
$478$			120292.i			0.526478i
$479$	−74292.0	+	74292.0i	−0.323796	+	0.323796i	−0.850221	−	0.526425i	$-0.823532\pi$
$479$	−74292.0	+	74292.0i	−0.323796	+	0.323796i	0.526425	+	0.850221i	$0.323532\pi$
$480$		−	209364.i		−	0.908697i
$481$		0			0
$482$	17624.4			0.0758613
$483$	265652.	+	265652.i	1.13873	+	1.13873i
$484$	64055.5			0.273442
$485$			2626.54i			0.0111661i
$486$	−21580.0	−	21580.0i	−0.0913647	−	0.0913647i
$487$	−120533.	−	120533.i	−0.508216	−	0.508216i	0.405762	−	0.913979i	$-0.367006\pi$
$487$	−120533.	−	120533.i	−0.508216	−	0.508216i	−0.913979	+	0.405762i	$0.867006\pi$
$488$	218141.	−	218141.i	0.916006	−	0.916006i
$489$	−32789.2	+	32789.2i	−0.137124	+	0.137124i
$490$	−17913.6			−0.0746091
$491$			32615.3i			0.135288i	0.997710	+	0.0676439i	$0.0215482\pi$
$491$			32615.3i			0.135288i	−0.997710	+	0.0676439i	$0.978452\pi$
$492$	46277.0	−	46277.0i	0.191177	−	0.191177i
$493$			223802.i			0.920809i
$494$		0			0
$495$	18460.8			0.0753427
$496$	109.081	+	109.081i	0.000443388	+	0.000443388i
$497$	−33186.2			−0.134352
$498$		−	107974.i		−	0.435372i
$499$	39397.8	+	39397.8i	0.158223	+	0.158223i	0.781779	−	0.623556i	$-0.214313\pi$
$499$	39397.8	+	39397.8i	0.158223	+	0.158223i	−0.623556	+	0.781779i	$0.714313\pi$
$500$	113172.	+	113172.i	0.452690	+	0.452690i
$501$	137871.	−	137871.i	0.549286	−	0.549286i
$502$	150066.	−	150066.i	0.595490	−	0.595490i
$503$	390430.			1.54315			0.771573	−	0.636141i	$-0.219470\pi$
$503$	390430.			1.54315			0.771573	+	0.636141i	$0.219470\pi$
$504$		−	28303.2i		−	0.111423i
$505$	308946.	−	308946.i	1.21143	−	1.21143i
$506$			189508.i			0.740162i
$507$		0			0
$508$	−187186.			−0.725349
$509$	−329416.	−	329416.i	−1.27148	−	1.27148i	−0.945313	−	0.326165i	$-0.894243\pi$
$509$	−329416.	−	329416.i	−1.27148	−	1.27148i	−0.326165	−	0.945313i	$-0.605757\pi$
$510$	−127327.			−0.489533
$511$		−	73572.3i		−	0.281756i
$512$	387.940	+	387.940i	0.00147987	+	0.00147987i
$513$	191458.	+	191458.i	0.727510	+	0.727510i
$514$	−44946.2	+	44946.2i	−0.170125	+	0.170125i
$515$	211957.	−	211957.i	0.799157	−	0.799157i
$516$	−204325.			−0.767401
$517$		−	109672.i		−	0.410313i
$518$	241390.	−	241390.i	0.899621	−	0.899621i
$519$		−	302051.i		−	1.12136i
$520$		0			0
$521$	66489.1			0.244949			0.122474	−	0.992472i	$-0.460917\pi$
$521$	66489.1			0.244949			0.122474	+	0.992472i	$0.460917\pi$
$522$	−13193.8	−	13193.8i	−0.0484206	−	0.0484206i
$523$	−199419.			−0.729061			−0.364530	−	0.931192i	$-0.618770\pi$
$523$	−199419.			−0.729061			−0.364530	+	0.931192i	$0.618770\pi$
$524$			32622.0i			0.118809i
$525$	−15247.8	−	15247.8i	−0.0553207	−	0.0553207i
$526$	48163.7	+	48163.7i	0.174080	+	0.174080i
$527$	102672.	−	102672.i	0.369685	−	0.369685i
$528$	145.760	−	145.760i	0.000522843	−	0.000522843i
$529$	−440469.			−1.57400
$530$		−	2326.83i		−	0.00828350i
$531$	−7131.10	+	7131.10i	−0.0252911	+	0.0252911i
$532$			182796.i			0.645868i
$533$		0			0
$534$	−62628.7			−0.219630
$535$	158974.	+	158974.i	0.555416	+	0.555416i
$536$	−233109.			−0.811391
$537$		−	419165.i		−	1.45357i
$538$	−84046.4	−	84046.4i	−0.290372	−	0.290372i
$539$	−19302.1	−	19302.1i	−0.0664397	−	0.0664397i
$540$	−128019.	+	128019.i	−0.439022	+	0.439022i
$541$	−142965.	+	142965.i	−0.488467	+	0.488467i	−0.907822	−	0.419355i	$-0.862256\pi$
$541$	−142965.	+	142965.i	−0.488467	+	0.488467i	0.419355	+	0.907822i	$0.362256\pi$
$542$	63038.1			0.214588
$543$		−	387274.i		−	1.31347i
$544$	182633.	−	182633.i	0.617137	−	0.617137i
$545$			188354.i			0.634136i
$546$		0			0
$547$	−34633.5			−0.115750			−0.0578750	−	0.998324i	$-0.518432\pi$
$547$	−34633.5			−0.115750			−0.0578750	+	0.998324i	$0.518432\pi$
$548$	170760.	+	170760.i	0.568623	+	0.568623i
$549$	−41028.3			−0.136125
$550$		−	10877.3i		−	0.0359580i
$551$	222984.	+	222984.i	0.734465	+	0.734465i
$552$	−326909.	−	326909.i	−1.07287	−	1.07287i
$553$	−135957.	+	135957.i	−0.444581	+	0.444581i
$554$	−92073.7	+	92073.7i	−0.299996	+	0.299996i
$555$	−543205.			−1.76351
$556$		−	15597.4i		−	0.0504548i
$557$	284385.	−	284385.i	0.916635	−	0.916635i	−0.0801481	−	0.996783i	$-0.525539\pi$
$557$	284385.	−	284385.i	0.916635	−	0.916635i	0.996783	+	0.0801481i	$0.0255393\pi$
$558$			12105.7i			0.0388796i
$559$		0			0
$560$	−334.345			−0.00106615
$561$	−137197.	−	137197.i	−0.435931	−	0.435931i
$562$	−308850.			−0.977856
$563$		−	282597.i		−	0.891562i	−0.895142	−	0.445781i	$-0.852926\pi$
$563$		−	282597.i		−	0.891562i	0.895142	−	0.445781i	$-0.147074\pi$
$564$	72297.4	+	72297.4i	0.227282	+	0.227282i
$565$	134973.	+	134973.i	0.422814	+	0.422814i
$566$	105467.	−	105467.i	0.329218	−	0.329218i
$567$	213203.	−	213203.i	0.663173	−	0.663173i
$568$	40838.6			0.126583
$569$		−	115427.i		−	0.356520i	−0.983983	−	0.178260i	$-0.942953\pi$
$569$		−	115427.i		−	0.356520i	0.983983	−	0.178260i	$-0.0570467\pi$
$570$	−126862.	+	126862.i	−0.390466	+	0.390466i
$571$			75184.3i			0.230598i	0.993331	+	0.115299i	$0.0367826\pi$
$571$			75184.3i			0.230598i	−0.993331	+	0.115299i	$0.963217\pi$
$572$		0			0
$573$	162349.			0.494471
$574$	70549.5	+	70549.5i	0.214126	+	0.214126i
$575$	41344.0			0.125048
$576$			21497.1i			0.0647941i
$577$	198197.	+	198197.i	0.595313	+	0.595313i	0.939062	−	0.343749i	$-0.111697\pi$
$577$	198197.	+	198197.i	0.595313	+	0.595313i	−0.343749	+	0.939062i	$0.611697\pi$
$578$	34839.8	+	34839.8i	0.104285	+	0.104285i
$579$	155710.	−	155710.i	0.464473	−	0.464473i
$580$	−149099.	+	149099.i	−0.443219	+	0.443219i
$581$	−266868.			−0.790577
$582$			2301.52i			0.00679466i
$583$	2507.19	−	2507.19i	0.00737650	−	0.00737650i
$584$			90537.4i			0.265462i
$585$		0			0
$586$	165623.			0.482309
$587$	−18461.4	−	18461.4i	−0.0535784	−	0.0535784i	0.679810	−	0.733388i	$-0.262062\pi$
$587$	−18461.4	−	18461.4i	−0.0535784	−	0.0535784i	−0.733388	+	0.679810i	$0.762062\pi$
$588$	25448.5			0.0736050
$589$		−	204594.i		−	0.589743i
$590$	−49706.3	−	49706.3i	−0.142793	−	0.142793i
$591$	−108039.	−	108039.i	−0.309319	−	0.309319i
$592$	503.427	−	503.427i	0.00143646	−	0.00143646i
$593$	−444924.	+	444924.i	−1.26525	+	1.26525i	−0.316736	+	0.948514i	$0.602587\pi$
$593$	−444924.	+	444924.i	−1.26525	+	1.26525i	−0.948514	+	0.316736i	$0.897413\pi$
$594$	170168.			0.482285
$595$			314702.i			0.888926i
$596$	−55018.6	+	55018.6i	−0.154888	+	0.154888i
$597$		−	25714.6i		−	0.0721491i
$598$		0			0
$599$	−174476.			−0.486275			−0.243138	−	0.969992i	$-0.578177\pi$
$599$	−174476.			−0.486275			−0.243138	+	0.969992i	$0.578177\pi$
$600$	18763.8	+	18763.8i	0.0521216	+	0.0521216i
$601$	503463.			1.39386			0.696929	−	0.717140i	$-0.254549\pi$
$601$	503463.			1.39386			0.696929	+	0.717140i	$0.254549\pi$
$602$		−	311494.i		−	0.859522i
$603$	21921.8	+	21921.8i	0.0602894	+	0.0602894i
$604$	−129763.	−	129763.i	−0.355694	−	0.355694i
$605$	109875.	−	109875.i	0.300185	−	0.300185i
$606$	270715.	−	270715.i	0.737168	−	0.737168i
$607$	−54701.1			−0.148463			−0.0742316	−	0.997241i	$-0.523650\pi$
$607$	−54701.1			−0.148463			−0.0742316	+	0.997241i	$0.523650\pi$
$608$		−	363932.i		−	0.984494i
$609$	277819.	−	277819.i	0.749080	−	0.749080i
$610$		−	285982.i		−	0.768562i
$611$		0			0
$612$	−21231.8			−0.0566869
$613$	−394238.	−	394238.i	−1.04915	−	1.04915i	−0.998728	−	0.0504228i	$-0.983943\pi$
$613$	−394238.	−	394238.i	−1.04915	−	1.04915i	−0.0504228	−	0.998728i	$-0.516057\pi$
$614$	197294.			0.523331
$615$		−	158759.i		−	0.419748i
$616$	212575.	+	212575.i	0.560210	+	0.560210i
$617$	128366.	+	128366.i	0.337193	+	0.337193i	0.855310	−	0.518117i	$-0.173367\pi$
$617$	128366.	+	128366.i	0.337193	+	0.337193i	−0.518117	+	0.855310i	$0.673367\pi$
$618$	185728.	−	185728.i	0.486295	−	0.486295i
$619$	−44147.8	+	44147.8i	−0.115220	+	0.115220i	−0.762366	−	0.647146i	$-0.775962\pi$
$619$	−44147.8	+	44147.8i	−0.115220	+	0.115220i	0.647146	+	0.762366i	$0.275962\pi$
$620$	136802.			0.355885
$621$			646797.i			1.67720i
$622$	−41315.5	+	41315.5i	−0.106790	+	0.106790i
$623$			154793.i			0.398818i
$624$		0			0
$625$	357806.			0.915983
$626$	150690.	+	150690.i	0.384534	+	0.384534i
$627$	−273391.			−0.695424
$628$		−	2101.17i		−	0.00532774i
$629$	−473851.	−	473851.i	−1.19768	−	1.19768i
$630$	−18552.7	−	18552.7i	−0.0467440	−	0.0467440i
$631$	376659.	−	376659.i	0.945998	−	0.945998i	−0.0526170	−	0.998615i	$-0.516756\pi$
$631$	376659.	−	376659.i	0.945998	−	0.945998i	0.998615	+	0.0526170i	$0.0167563\pi$
$632$	167307.	−	167307.i	0.418871	−	0.418871i
$633$	650351.			1.62308
$634$			378619.i			0.941942i
$635$	−321083.	+	321083.i	−0.796288	+	0.796288i
$636$			3305.55i			0.00817202i
$637$		0			0
$638$	198188.			0.486896
$639$	−3840.49	−	3840.49i	−0.00940556	−	0.00940556i
$640$	243598.			0.594721
$641$			789963.i			1.92261i	0.275490	+	0.961304i	$0.411160\pi$
$641$			789963.i			1.92261i	−0.275490	+	0.961304i	$0.588840\pi$
$642$	139301.	+	139301.i	0.337975	+	0.337975i
$643$	310418.	+	310418.i	0.750801	+	0.750801i	0.974629	−	0.223827i	$-0.0718552\pi$
$643$	310418.	+	310418.i	0.750801	+	0.750801i	−0.223827	+	0.974629i	$0.571855\pi$
$644$	−308768.	+	308768.i	−0.744492	+	0.744492i
$645$	−350481.	+	350481.i	−0.842452	+	0.842452i
$646$	−221330.			−0.530366
$647$			172300.i			0.411601i	0.978594	+	0.205801i	$0.0659798\pi$
$647$			172300.i			0.411601i	−0.978594	+	0.205801i	$0.934020\pi$
$648$	−262365.	+	262365.i	−0.624822	+	0.624822i
$649$		−	107118.i		−	0.254316i
$650$		0			0
$651$	−254907.			−0.601478
$652$	−38111.0	−	38111.0i	−0.0896509	−	0.0896509i
$653$	−438961.			−1.02944			−0.514718	−	0.857359i	$-0.672103\pi$
$653$	−438961.			−1.02944			−0.514718	+	0.857359i	$0.672103\pi$
$654$			165046.i			0.385877i
$655$	55956.8	+	55956.8i	0.130428	+	0.130428i
$656$	147.133	+	147.133i	0.000341904	+	0.000341904i
$657$	8514.20	−	8514.20i	0.0197248	−	0.0197248i
$658$	−110218.	+	110218.i	−0.254566	+	0.254566i
$659$	−42262.6			−0.0973163			−0.0486581	−	0.998815i	$-0.515494\pi$
$659$	−42262.6			−0.0973163			−0.0486581	+	0.998815i	$0.515494\pi$
$660$		−	182804.i		−	0.419659i
$661$	−136635.	+	136635.i	−0.312721	+	0.312721i	−0.845963	−	0.533242i	$-0.820974\pi$
$661$	−136635.	+	136635.i	−0.312721	+	0.312721i	0.533242	+	0.845963i	$0.320974\pi$
$662$		−	242874.i		−	0.554198i
$663$		0			0
$664$	328405.			0.744859
$665$	313552.	+	313552.i	0.709034	+	0.709034i
$666$	55870.0			0.125959
$667$			753302.i			1.69323i
$668$	160248.	+	160248.i	0.359120	+	0.359120i
$669$	−114474.	−	114474.i	−0.255773	−	0.255773i
$670$	−152803.	+	152803.i	−0.340393	+	0.340393i
$671$	308149.	−	308149.i	0.684408	−	0.684408i
$672$	−453428.			−1.00408
$673$		−	548835.i		−	1.21175i	−0.795562	−	0.605873i	$-0.792824\pi$
$673$		−	548835.i		−	1.21175i	0.795562	−	0.605873i	$-0.207176\pi$
$674$	52919.3	−	52919.3i	0.116491	−	0.116491i
$675$		−	37124.6i		−	0.0814805i
$676$		0			0
$677$	−427627.			−0.933014			−0.466507	−	0.884518i	$-0.654488\pi$
$677$	−427627.			−0.933014			−0.466507	+	0.884518i	$0.654488\pi$
$678$	118270.	+	118270.i	0.257286	+	0.257286i
$679$	5688.41			0.0123382
$680$		−	387269.i		−	0.837520i
$681$	22815.6	+	22815.6i	0.0491969	+	0.0491969i
$682$	−90921.5	−	90921.5i	−0.195478	−	0.195478i
$683$	−348779.	+	348779.i	−0.747668	+	0.747668i	−0.974041	−	0.226373i	$-0.927313\pi$
$683$	−348779.	+	348779.i	−0.747668	+	0.747668i	0.226373	+	0.974041i	$0.427313\pi$
$684$	−21154.2	+	21154.2i	−0.0452152	+	0.0452152i
$685$	585812.			1.24847
$686$		−	269611.i		−	0.572913i
$687$	−488245.	+	488245.i	−1.03448	+	1.03448i
$688$		−	649.632i		−	0.00137243i
$689$		0			0
$690$	−428576.			−0.900180
$691$	−291105.	−	291105.i	−0.609669	−	0.609669i	0.333191	−	0.942860i	$-0.391875\pi$
$691$	−291105.	−	291105.i	−0.609669	−	0.609669i	−0.942860	+	0.333191i	$0.891875\pi$
$692$	351074.			0.733140
$693$		−	39981.4i		−	0.0832515i
$694$	−324845.	−	324845.i	−0.674462	−	0.674462i
$695$	−26754.4	−	26754.4i	−0.0553892	−	0.0553892i
$696$	−341882.	+	341882.i	−0.705761	+	0.705761i
$697$	138489.	−	138489.i	0.285069	−	0.285069i
$698$	398016.			0.816940
$699$		−	55137.6i		−	0.112848i
$700$	17722.5	−	17722.5i	0.0361684	−	0.0361684i
$701$		−	44529.2i		−	0.0906169i	−0.998973	−	0.0453085i	$-0.985573\pi$
$701$		−	44529.2i		−	0.0906169i	0.998973	−	0.0453085i	$-0.0144271\pi$
$702$		0			0
$703$	−944240.			−1.91061
$704$	−161457.	−	161457.i	−0.325771	−	0.325771i
$705$	248025.			0.499020
$706$			474818.i			0.952615i
$707$	−669097.	−	669097.i	−1.33860	−	1.33860i
$708$	70613.8	+	70613.8i	0.140871	+	0.140871i
$709$	−279385.	+	279385.i	−0.555791	+	0.555791i	−0.928106	−	0.372316i	$-0.878564\pi$
$709$	−279385.	+	279385.i	−0.555791	+	0.555791i	0.372316	+	0.928106i	$0.378564\pi$
$710$	26769.6	−	26769.6i	0.0531037	−	0.0531037i
$711$	−31467.4			−0.0622474
$712$		−	190487.i		−	0.375755i
$713$	345587.	−	345587.i	0.679796	−	0.679796i
$714$			275759.i			0.540919i
$715$		0			0
$716$	487195.			0.950336
$717$	−293128.	−	293128.i	−0.570190	−	0.570190i
$718$	388583.			0.753762
$719$		−	280011.i		−	0.541648i	−0.962629	−	0.270824i	$-0.912704\pi$
$719$		−	280011.i		−	0.541648i	0.962629	−	0.270824i	$-0.0872961\pi$
$720$	−38.6923	−	38.6923i	−7.46379e−5	−	7.46379e-5i
$721$	−459043.	−	459043.i	−0.883045	−	0.883045i
$722$	7147.99	−	7147.99i	0.0137123	−	0.0137123i
$723$	−42947.3	+	42947.3i	−0.0821597	+	0.0821597i
$724$	450129.			0.858737
$725$		−	43237.7i		−	0.0822595i
$726$	96278.4	−	96278.4i	0.182665	−	0.182665i
$727$			133105.i			0.251840i	0.992040	+	0.125920i	$0.0401882\pi$
$727$			133105.i			0.251840i	−0.992040	+	0.125920i	$0.959812\pi$
$728$		0			0
$729$	574923.			1.08182
$730$	59347.0	+	59347.0i	0.111366	+	0.111366i
$731$	−611466.			−1.14429
$732$			406272.i			0.758219i
$733$	−313844.	−	313844.i	−0.584125	−	0.584125i	0.351909	−	0.936034i	$-0.385533\pi$
$733$	−313844.	−	313844.i	−0.584125	−	0.584125i	−0.936034	+	0.351909i	$0.885533\pi$
$734$	392045.	+	392045.i	0.727685	+	0.727685i
$735$	43652.1	−	43652.1i	0.0808035	−	0.0808035i
$736$	614731.	−	614731.i	1.13483	−	1.13483i
$737$	−329293.			−0.606244
$738$			16328.8i			0.0299806i
$739$	−464338.	+	464338.i	−0.850247	+	0.850247i	−0.990163	−	0.139916i	$-0.955317\pi$
$739$	−464338.	+	464338.i	−0.850247	+	0.850247i	0.139916	+	0.990163i	$0.455317\pi$
$740$		−	631367.i		−	1.15297i
$741$		0			0
$742$	−5039.32			−0.00915302
$743$	733957.	+	733957.i	1.32951	+	1.32951i	0.905792	+	0.423723i	$0.139277\pi$
$743$	733957.	+	733957.i	1.32951	+	1.32951i	0.423723	+	0.905792i	$0.360723\pi$
$744$	313686.			0.566695
$745$			188748.i			0.340072i
$746$	352770.	+	352770.i	0.633890	+	0.633890i
$747$	−30883.5	−	30883.5i	−0.0553458	−	0.0553458i
$748$	159464.	−	159464.i	0.285009	−	0.285009i
$749$	344296.	−	344296.i	0.613718	−	0.613718i
$750$	340207.			0.604813
$751$			233455.i			0.413927i	0.978349	+	0.206964i	$0.0663582\pi$
$751$			233455.i			0.413927i	−0.978349	+	0.206964i	$0.933642\pi$
$752$	−229.863	+	229.863i	−0.000406474	+	0.000406474i
$753$			731363.i			1.28986i
$754$		0			0
$755$	−445167.			−0.780961
$756$	277256.	+	277256.i	0.485106	+	0.485106i
$757$	−853576.			−1.48953			−0.744767	−	0.667325i	$-0.767439\pi$
$757$	−853576.			−1.48953			−0.744767	+	0.667325i	$0.767439\pi$
$758$			342882.i			0.596768i
$759$	−461795.	−	461795.i	−0.801615	−	0.801615i
$760$	−385855.	−	385855.i	−0.668031	−	0.668031i
$761$	−779276.	+	779276.i	−1.34562	+	1.34562i	−0.455260	+	0.890359i	$0.650454\pi$
$761$	−779276.	+	779276.i	−1.34562	+	1.34562i	−0.890359	+	0.455260i	$0.849546\pi$
$762$	−281350.	+	281350.i	−0.484548	+	0.484548i
$763$	407927.			0.700702
$764$			188699.i			0.323283i
$765$	−36419.1	+	36419.1i	−0.0622309	+	0.0622309i
$766$		−	434181.i		−	0.739969i
$767$		0			0
$768$	557623.			0.945406
$769$	−39890.5	−	39890.5i	−0.0674555	−	0.0674555i	0.672574	−	0.740030i	$-0.265189\pi$
$769$	−39890.5	−	39890.5i	−0.0674555	−	0.0674555i	−0.740030	+	0.672574i	$0.765189\pi$
$770$	278685.			0.470037
$771$		−	219051.i		−	0.368499i
$772$	180982.	+	180982.i	0.303669	+	0.303669i
$773$	558787.	+	558787.i	0.935163	+	0.935163i	0.998022	−	0.0628590i	$-0.0200218\pi$
$773$	558787.	+	558787.i	0.935163	+	0.935163i	−0.0628590	+	0.998022i	$0.520022\pi$
$774$	36047.9	−	36047.9i	0.0601725	−	0.0601725i
$775$	−19835.9	+	19835.9i	−0.0330254	+	0.0330254i
$776$	−7000.10			−0.0116247
$777$			1.17644e6i			1.94863i
$778$	−302060.	+	302060.i	−0.499039	+	0.499039i
$779$		−	275967.i		−	0.454760i
$780$		0			0
$781$	57689.0			0.0945782
$782$	−373857.	−	373857.i	−0.611353	−	0.611353i
$783$	676422.			1.10330
$784$			80.9111i			0.000131636i
$785$	−3604.17	−	3604.17i	−0.00584879	−	0.00584879i
$786$	49032.4	+	49032.4i	0.0793666	+	0.0793666i
$787$	705380.	−	705380.i	1.13887	−	1.13887i	0.150216	−	0.988653i	$-0.452003\pi$
$787$	705380.	−	705380.i	1.13887	−	1.13887i	0.988653	−	0.150216i	$-0.0479968\pi$
$788$	125574.	−	125574.i	0.202231	−	0.202231i
$789$	−234732.			−0.377066
$790$		−	219339.i		−	0.351448i
$791$	292316.	−	292316.i	0.467197	−	0.467197i
$792$			49200.8i			0.0784371i
$793$		0			0
$794$	−403477.			−0.639996
$795$	5670.05	+	5670.05i	0.00897124	+	0.00897124i
$796$	29888.1			0.0471706
$797$		−	28611.8i		−	0.0450432i	−0.999746	−	0.0225216i	$-0.992831\pi$
$797$		−	28611.8i		−	0.0450432i	0.999746	−	0.0225216i	$-0.00716945\pi$
$798$	274751.	+	274751.i	0.431454	+	0.431454i
$799$	216358.	+	216358.i	0.338907	+	0.338907i
$800$	−35284.0	+	35284.0i	−0.0551313	+	0.0551313i
$801$	−17913.5	+	17913.5i	−0.0279200	+	0.0279200i
$802$	−524814.			−0.815937
$803$			127894.i			0.198344i
$804$	217074.	−	217074.i	0.335812	−	0.335812i
$805$			1.05927e6i			1.63461i
$806$		0			0
$807$	409610.			0.628960
$808$	823384.	+	823384.i	1.26119	+	1.26119i
$809$	−349664.			−0.534261			−0.267131	−	0.963660i	$-0.586076\pi$
$809$	−349664.			−0.534261			−0.267131	+	0.963660i	$0.586076\pi$
$810$			343959.i			0.524248i
$811$	765373.	+	765373.i	1.16367	+	1.16367i	0.983665	+	0.180009i	$0.0576127\pi$
$811$	765373.	+	765373.i	1.16367	+	1.16367i	0.180009	+	0.983665i	$0.442387\pi$
$812$	322910.	+	322910.i	0.489744	+	0.489744i
$813$	−153612.	+	153612.i	−0.232404	+	0.232404i
$814$	−419619.	+	419619.i	−0.633296	+	0.633296i
$815$	−130744.			−0.196837
$816$			575.104i			0.000863706i
$817$	−609233.	+	609233.i	−0.912724	+	0.912724i
$818$		−	303261.i		−	0.453220i
$819$		0			0
$820$	184526.			0.274429
$821$	−223350.	−	223350.i	−0.331360	−	0.331360i	0.521743	−	0.853103i	$-0.325282\pi$
$821$	−223350.	−	223350.i	−0.331360	−	0.331360i	−0.853103	+	0.521743i	$0.825282\pi$
$822$	513320.			0.759704
$823$		−	546927.i		−	0.807477i	−0.914874	−	0.403738i	$-0.867711\pi$
$823$		−	546927.i		−	0.807477i	0.914874	−	0.403738i	$-0.132289\pi$
$824$	564894.	+	564894.i	0.831980	+	0.831980i
$825$	26505.9	+	26505.9i	0.0389435	+	0.0389435i
$826$	−107651.	+	107651.i	−0.157782	+	0.157782i
$827$	322764.	−	322764.i	0.471926	−	0.471926i	−0.430612	−	0.902537i	$-0.641702\pi$
$827$	322764.	−	322764.i	0.471926	−	0.471926i	0.902537	+	0.430612i	$0.141702\pi$
$828$	−71464.6			−0.104239
$829$			378171.i			0.550274i	0.961405	+	0.275137i	$0.0887233\pi$
$829$			378171.i			0.550274i	−0.961405	+	0.275137i	$0.911277\pi$
$830$	215269.	−	215269.i	0.312482	−	0.312482i
$831$		−	448732.i		−	0.649808i
$832$		0			0
$833$	76157.5			0.109755
$834$	−23443.6	−	23443.6i	−0.0337049	−	0.0337049i
$835$	549750.			0.788483
$836$		−	317763.i		−	0.454664i
$837$	−310318.	−	310318.i	−0.442951	−	0.442951i
$838$	398871.	+	398871.i	0.567995	+	0.567995i
$839$	708994.	−	708994.i	1.00721	−	1.00721i	0.00723336	−	0.999974i	$-0.497698\pi$
$839$	708994.	−	708994.i	1.00721	−	1.00721i	0.999974	−	0.00723336i	$-0.00230247\pi$
$840$	−480742.	+	480742.i	−0.681323	+	0.681323i
$841$	80523.2			0.113849
$842$		−	103530.i		−	0.146030i
$843$	752608.	−	752608.i	1.05904	−	1.05904i
$844$			755903.i			1.06116i
$845$		0			0
$846$	−25510.0			−0.0356427
$847$	−237961.	−	237961.i	−0.331695	−	0.331695i
$848$	−10.5097			−1.46150e−5
$849$			514006.i			0.713104i
$850$	21458.5	+	21458.5i	0.0297003	+	0.0297003i
$851$	−1.59495e6	−	1.59495e6i	−2.20236	−	2.20236i
$852$	−38029.4	+	38029.4i	−0.0523890	+	0.0523890i
$853$	−743379.	+	743379.i	−1.02167	+	1.02167i	−0.0219142	+	0.999760i	$0.506976\pi$
$853$	−743379.	+	743379.i	−1.02167	+	1.02167i	−0.999760	+	0.0219142i	$0.993024\pi$
$854$	−619363.			−0.849239
$855$			72572.1i			0.0992745i
$856$	−423688.	+	423688.i	−0.578227	+	0.578227i
$857$			424271.i			0.577672i	0.957379	+	0.288836i	$0.0932683\pi$
$857$			424271.i			0.577672i	−0.957379	+	0.288836i	$0.906732\pi$
$858$		0			0
$859$	396196.			0.536938			0.268469	−	0.963288i	$-0.413482\pi$
$859$	396196.			0.536938			0.268469	+	0.963288i	$0.413482\pi$
$860$	−407364.	−	407364.i	−0.550790	−	0.550790i
$861$	−343831.			−0.463809
$862$		−	353963.i		−	0.476368i
$863$	−908405.	−	908405.i	−1.21971	−	1.21971i	−0.967732	−	0.251982i	$-0.918918\pi$
$863$	−908405.	−	908405.i	−1.21971	−	1.21971i	−0.251982	−	0.967732i	$-0.581082\pi$
$864$	−551993.	−	551993.i	−0.739445	−	0.739445i
$865$	602202.	−	602202.i	0.804840	−	0.804840i
$866$	354222.	−	354222.i	0.472324	−	0.472324i
$867$	−169796.			−0.225886
$868$		−	296278.i		−	0.393243i
$869$	236340.	−	236340.i	0.312966	−	0.312966i
$870$			448205.i			0.592159i
$871$		0			0
$872$	−501991.			−0.660180
$873$	658.295	+	658.295i	0.000863758	+	0.000863758i
$874$	−744983.			−0.975267
$875$		−	840854.i		−	1.09826i
$876$	−84309.6	−	84309.6i	−0.109867	−	0.109867i
$877$	139989.	+	139989.i	0.182009	+	0.182009i	0.792231	−	0.610222i	$-0.208920\pi$
$877$	139989.	+	139989.i	0.182009	+	0.182009i	−0.610222	+	0.792231i	$0.708920\pi$
$878$	10401.2	−	10401.2i	0.0134926	−	0.0134926i
$879$	−403591.	+	403591.i	−0.522353	+	0.522353i
$880$	581.207			0.000750525
$881$		−	1.25593e6i		−	1.61813i	−0.587717	−	0.809066i	$-0.699973\pi$
$881$		−	1.25593e6i		−	1.61813i	0.587717	−	0.809066i	$-0.300027\pi$
$882$	−4489.73	+	4489.73i	−0.00577143	+	0.00577143i
$883$		−	781993.i		−	1.00296i	−0.865171	−	0.501478i	$-0.832790\pi$
$883$		−	781993.i		−	1.00296i	0.865171	−	0.501478i	$-0.167210\pi$
$884$		0			0
$885$	242249.			0.309297
$886$	−43986.3	−	43986.3i	−0.0560338	−	0.0560338i
$887$	−903167.			−1.14794			−0.573972	−	0.818875i	$-0.694598\pi$
$887$	−903167.			−1.14794			−0.573972	+	0.818875i	$0.694598\pi$
$888$		−	1.44772e6i		−	1.83594i
$889$	695384.	+	695384.i	0.879875	+	0.879875i
$890$	−124863.	−	124863.i	−0.157636	−	0.157636i
$891$	−370620.	+	370620.i	−0.466846	+	0.466846i
$892$	133053.	−	133053.i	0.167223	−	0.167223i
$893$	431136.			0.540644
$894$			165391.i			0.206937i
$895$	835692.	−	835692.i	1.04328	−	1.04328i
$896$		−	527570.i		−	0.657150i
$897$		0			0
$898$	−500340.			−0.620458
$899$	−361416.	−	361416.i	−0.447186	−	0.447186i
$900$	4101.90			0.00506407
$901$			9892.24i			0.0121855i
$902$	−122639.	−	122639.i	−0.150736	−	0.150736i
$903$	759052.	+	759052.i	0.930885	+	0.930885i
$904$	−359722.	+	359722.i	−0.440179	+	0.440179i
$905$	772112.	−	772112.i	0.942721	−	0.942721i
$906$	−390079.			−0.475222
$907$			286766.i			0.348589i	0.984694	+	0.174294i	$0.0557644\pi$
$907$			286766.i			0.348589i	−0.984694	+	0.174294i	$0.944236\pi$
$908$	−26518.6	+	26518.6i	−0.0321646	+	0.0321646i
$909$		−	154863.i		−	0.187422i
$910$		0			0
$911$	463939.			0.559016			0.279508	−	0.960143i	$-0.409829\pi$
$911$	463939.			0.559016			0.279508	+	0.960143i	$0.409829\pi$
$912$	573.004	+	573.004i	0.000688918	+	0.000688918i
$913$	463909.			0.556533
$914$		−	77221.2i		−	0.0924367i
$915$	696883.	+	696883.i	0.832373	+	0.832373i
$916$	−567487.	−	567487.i	−0.676340	−	0.676340i
$917$	121188.	−	121188.i	0.144119	−	0.144119i
$918$	−335702.	+	335702.i	−0.398354	+	0.398354i
$919$	−827217.			−0.979464			−0.489732	−	0.871873i	$-0.662905\pi$
$919$	−827217.			−0.979464			−0.489732	+	0.871873i	$0.662905\pi$
$920$		−	1.30352e6i		−	1.54008i
$921$	−480767.	+	480767.i	−0.566781	+	0.566781i
$922$		−	130303.i		−	0.153283i
$923$		0			0
$924$	−395905.			−0.463711
$925$	91546.2	+	91546.2i	0.106993	+	0.106993i
$926$	−285475.			−0.332925
$927$		−	106246.i		−	0.123639i
$928$	−642886.	−	642886.i	−0.746515	−	0.746515i
$929$	895025.	+	895025.i	1.03706	+	1.03706i	0.999286	+	0.0377735i	$0.0120265\pi$
$929$	895025.	+	895025.i	1.03706	+	1.03706i	0.0377735	+	0.999286i	$0.487973\pi$
$930$	205620.	−	205620.i	0.237739	−	0.237739i
$931$	75879.4	−	75879.4i	0.0875436	−	0.0875436i
$932$	64086.5			0.0737793
$933$		−	201356.i		−	0.231314i
$934$	467013.	−	467013.i	0.535347	−	0.535347i
$935$		−	547061.i		−	0.625766i
$936$		0			0
$937$	−134570.			−0.153275			−0.0766374	−	0.997059i	$-0.524418\pi$
$937$	−134570.			−0.153275			−0.0766374	+	0.997059i	$0.524418\pi$
$938$	330931.	+	330931.i	0.376125	+	0.376125i
$939$	−734403.			−0.832920
$940$			288280.i			0.326256i
$941$	−211534.	−	211534.i	−0.238891	−	0.238891i	0.577500	−	0.816391i	$-0.304028\pi$
$941$	−211534.	−	211534.i	−0.238891	−	0.238891i	−0.816391	+	0.577500i	$0.804028\pi$
$942$	−3158.17	−	3158.17i	−0.00355904	−	0.00355904i
$943$	466146.	−	466146.i	0.524201	−	0.524201i
$944$	−224.510	+	224.510i	−0.000251937	+	0.000251937i
$945$	951160.			1.06510
$946$			541485.i			0.605068i
$947$	1.12230e6	−	1.12230e6i	1.25144	−	1.25144i	0.296368	−	0.955074i	$-0.404224\pi$
$947$	1.12230e6	−	1.12230e6i	1.25144	−	1.25144i	0.955074	−	0.296368i	$-0.0957756\pi$
$948$			311597.i			0.346718i
$949$		0			0
$950$	42760.2			0.0473797
$951$	−922622.	−	922622.i	−1.02015	−	1.02015i
$952$	−838725.			−0.925435
$953$			252952.i			0.278517i	0.990256	+	0.139259i	$0.0444720\pi$
$953$			252952.i			0.278517i	−0.990256	+	0.139259i	$0.955528\pi$
$954$	−583.179	−	583.179i	−0.000640775	−	0.000640775i
$955$	323677.	+	323677.i	0.354899	+	0.354899i
$956$	340703.	−	340703.i	0.372787	−	0.372787i
$957$	−482946.	+	482946.i	−0.527321	+	0.527321i
$958$	−259575.			−0.282835
$959$		−	1.26872e6i		−	1.37952i
$960$	365138.	−	365138.i	0.396200	−	0.396200i
$961$		−	591912.i		−	0.640930i
$962$		0			0
$963$	79687.8			0.0859289
$964$	−49917.6	−	49917.6i	−0.0537155	−	0.0537155i
$965$	620882.			0.666736
$966$			928185.i			0.994672i
$967$	422826.	+	422826.i	0.452177	+	0.452177i	0.896077	−	0.443899i	$-0.146405\pi$
$967$	422826.	+	422826.i	0.452177	+	0.452177i	−0.443899	+	0.896077i	$0.646405\pi$
$968$	292833.	+	292833.i	0.312514	+	0.312514i
$969$	539339.	−	539339.i	0.574400	−	0.574400i
$970$	−4588.55	+	4588.55i	−0.00487677	+	0.00487677i
$971$	−1.47528e6			−1.56472			−0.782360	−	0.622826i	$-0.785984\pi$
$971$	−1.47528e6			−1.56472			−0.782360	+	0.622826i	$0.785984\pi$
$972$			122242.i			0.129386i
$973$	−57943.1	+	57943.1i	−0.0612035	+	0.0612035i
$974$		−	421141.i		−	0.443925i
$975$		0			0
$976$	−1291.70			−0.00135601
$977$	−222446.	−	222446.i	−0.233043	−	0.233043i	0.580919	−	0.813962i	$-0.302693\pi$
$977$	−222446.	−	222446.i	−0.233043	−	0.233043i	−0.813962	+	0.580919i	$0.802693\pi$
$978$	−114565.			−0.119777
$979$		−	269083.i		−	0.280751i
$980$	50736.9	+	50736.9i	0.0528289	+	0.0528289i
$981$	47207.6	+	47207.6i	0.0490539	+	0.0490539i
$982$	−56978.7	+	56978.7i	−0.0590867	+	0.0590867i
$983$	−262323.	+	262323.i	−0.271475	+	0.271475i	−0.829694	−	0.558219i	$-0.811485\pi$
$983$	−262323.	+	262323.i	−0.271475	+	0.271475i	0.558219	+	0.829694i	$0.311485\pi$
$984$	423115.			0.436987
$985$		−	430797.i		−	0.444018i
$986$	−390980.	+	390980.i	−0.402162	+	0.402162i
$987$		−	537159.i		−	0.551402i
$988$		0			0
$989$	−2.05815e6			−2.10419
$990$	32251.0	+	32251.0i	0.0329058	+	0.0329058i
$991$	1.14616e6			1.16707			0.583536	−	0.812087i	$-0.301669\pi$
$991$	1.14616e6			1.16707			0.583536	+	0.812087i	$0.301669\pi$
$992$			589866.i			0.599418i
$993$	591837.	+	591837.i	0.600210	+	0.600210i
$994$	−57976.0	−	57976.0i	−0.0586780	−	0.0586780i
$995$	51267.4	−	51267.4i	0.0517839	−	0.0517839i
$996$	−305815.	+	305815.i	−0.308277	+	0.308277i
$997$	507329.			0.510387			0.255193	−	0.966890i	$-0.417861\pi$
$997$	507329.			0.510387			0.255193	+	0.966890i	$0.417861\pi$
$998$			137655.i			0.138208i
$999$	−1.43217e6	+	1.43217e6i	−1.43504	+	1.43504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.5.d.c.99.6		16
13.5	odd	4	inner	169.5.d.c.70.6		16
13.7	odd	12		13.5.f.a.2.3	✓	16
13.8	odd	4		169.5.d.d.70.3		16
13.10	even	6		13.5.f.a.7.3	yes	16
13.12	even	2		169.5.d.d.99.3		16
39.20	even	12		117.5.bd.c.28.2		16
39.23	odd	6		117.5.bd.c.46.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.2.3	✓	16	13.7	odd	12
13.5.f.a.7.3	yes	16	13.10	even	6
117.5.bd.c.28.2		16	39.20	even	12
117.5.bd.c.46.2		16	39.23	odd	6
169.5.d.c.70.6		16	13.5	odd	4	inner
169.5.d.c.99.6		16	1.1	even	1	trivial
169.5.d.d.70.3		16	13.8	odd	4
169.5.d.d.99.3		16	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	169.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74699 + 1.74699i) q^{2} -8.51417 q^{3} -9.89603i q^{4} +(-16.9748 - 16.9748i) q^{5} +(-14.8742 - 14.8742i) q^{6} +(-36.7630 + 36.7630i) q^{7} +(45.2402 - 45.2402i) q^{8} -8.50884 q^{9} -59.3096i q^{10} +(63.9068 - 63.9068i) q^{11} +84.2565i q^{12} -128.449 q^{14} +(144.526 + 144.526i) q^{15} -0.267886 q^{16} +252.147i q^{17} +(-14.8649 - 14.8649i) q^{18} +(251.226 + 251.226i) q^{19} +(-167.983 + 167.983i) q^{20} +(313.007 - 313.007i) q^{21} +223.289 q^{22} +848.711i q^{23} +(-385.183 + 385.183i) q^{24} -48.7139i q^{25} +762.094 q^{27} +(363.808 + 363.808i) q^{28} +887.583 q^{29} +504.973i q^{30} +(-407.191 - 407.191i) q^{31} +(-724.311 - 724.311i) q^{32} +(-544.114 + 544.114i) q^{33} +(-440.500 + 440.500i) q^{34} +1248.09 q^{35} +84.2038i q^{36} +(-1879.26 + 1879.26i) q^{37} +877.782i q^{38} -1535.88 q^{40} +(-549.240 - 549.240i) q^{41} +1093.64 q^{42} +2425.04i q^{43} +(-632.424 - 632.424i) q^{44} +(144.436 + 144.436i) q^{45} +(-1482.69 + 1482.69i) q^{46} +(858.063 - 858.063i) q^{47} +2.28083 q^{48} -302.036i q^{49} +(85.1029 - 85.1029i) q^{50} -2146.83i q^{51} +39.2320 q^{53} +(1331.37 + 1331.37i) q^{54} -2169.61 q^{55} +3326.33i q^{56} +(-2138.99 - 2138.99i) q^{57} +(1550.60 + 1550.60i) q^{58} +(838.081 - 838.081i) q^{59} +(1430.24 - 1430.24i) q^{60} +4821.85 q^{61} -1422.72i q^{62} +(312.811 - 312.811i) q^{63} -2526.45i q^{64} -1901.13 q^{66} +(-2576.35 - 2576.35i) q^{67} +2495.26 q^{68} -7226.07i q^{69} +(2180.40 + 2180.40i) q^{70} +(451.353 + 451.353i) q^{71} +(-384.942 + 384.942i) q^{72} +(-1000.63 + 1000.63i) q^{73} -6566.11 q^{74} +414.759i q^{75} +(2486.14 - 2486.14i) q^{76} +4698.81i q^{77} +3698.19 q^{79} +(4.54730 + 4.54730i) q^{80} -5799.38 q^{81} -1919.04i q^{82} +(3629.57 + 3629.57i) q^{83} +(-3097.52 - 3097.52i) q^{84} +(4280.14 - 4280.14i) q^{85} +(-4236.52 + 4236.52i) q^{86} -7557.04 q^{87} -5782.31i q^{88} +(2105.28 - 2105.28i) q^{89} +504.656i q^{90} +8398.87 q^{92} +(3466.90 + 3466.90i) q^{93} +2998.06 q^{94} -8529.02i q^{95} +(6166.91 + 6166.91i) q^{96} +(-77.3660 - 77.3660i) q^{97} +(527.655 - 527.655i) q^{98} +(-543.773 + 543.773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 4 q^{3} - 8 q^{5} + 128 q^{6} - 56 q^{7} - 90 q^{8} + 328 q^{9} - 500 q^{11} + 808 q^{14} - 844 q^{15} - 460 q^{16} - 2434 q^{18} - 1712 q^{19} - 838 q^{20} + 1076 q^{21} + 3048 q^{22}+ \cdots + 21632 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 4 * q^3 - 8 * q^5 + 128 * q^6 - 56 * q^7 - 90 * q^8 + 328 * q^9 - 500 * q^11 + 808 * q^14 - 844 * q^15 - 460 * q^16 - 2434 * q^18 - 1712 * q^19 - 838 * q^20 + 1076 * q^21 + 3048 * q^22 - 5772 * q^24 + 3352 * q^27 - 2980 * q^28 - 1628 * q^29 - 4060 * q^31 - 3662 * q^32 + 860 * q^33 + 2502 * q^34 + 9784 * q^35 - 10468 * q^37 + 18816 * q^40 - 3440 * q^41 + 2408 * q^42 - 10736 * q^44 + 1004 * q^45 - 11436 * q^46 - 1484 * q^47 + 6004 * q^48 - 21616 * q^50 + 7204 * q^53 - 6760 * q^54 - 13872 * q^55 - 12736 * q^57 - 7974 * q^58 + 4840 * q^59 + 6472 * q^60 + 324 * q^61 + 13988 * q^63 - 23872 * q^66 - 2216 * q^67 + 12888 * q^68 + 34524 * q^70 + 1240 * q^71 + 6606 * q^72 + 15448 * q^73 + 5764 * q^74 + 39688 * q^76 - 17064 * q^79 + 37630 * q^80 - 4256 * q^81 - 12788 * q^83 + 7736 * q^84 + 22884 * q^85 - 67260 * q^86 - 58684 * q^87 + 37624 * q^89 - 49884 * q^92 + 2492 * q^93 + 61212 * q^94 + 94664 * q^96 + 57056 * q^97 - 27950 * q^98 + 21632 * q^99

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