LMFDB - Embedded newform 169.5.d.c.70.7

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			70.7
Root			$-3.98977i$ of defining polynomial
Character	$\chi$	$=$	169.70
Dual form			169.5.d.c.99.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.03282 - 4.03282i) q^{2} +8.56159 q^{3} -16.5272i q^{4} +(29.3294 - 29.3294i) q^{5} +(34.5273 - 34.5273i) q^{6} +(33.5543 + 33.5543i) q^{7} +(-2.12627 - 2.12627i) q^{8} -7.69920 q^{9} -236.560i q^{10} +(-31.3041 - 31.3041i) q^{11} -141.499i q^{12} +270.637 q^{14} +(251.106 - 251.106i) q^{15} +247.286 q^{16} +237.462i q^{17} +(-31.0495 + 31.0495i) q^{18} +(-348.888 + 348.888i) q^{19} +(-484.734 - 484.734i) q^{20} +(287.279 + 287.279i) q^{21} -252.488 q^{22} -298.164i q^{23} +(-18.2042 - 18.2042i) q^{24} -1095.43i q^{25} -759.406 q^{27} +(554.561 - 554.561i) q^{28} -371.384 q^{29} -2025.33i q^{30} +(-625.946 + 625.946i) q^{31} +(1031.28 - 1031.28i) q^{32} +(-268.013 - 268.013i) q^{33} +(957.641 + 957.641i) q^{34} +1968.26 q^{35} +127.247i q^{36} +(-540.096 - 540.096i) q^{37} +2814.01i q^{38} -124.724 q^{40} +(-491.434 + 491.434i) q^{41} +2317.08 q^{42} -1126.26i q^{43} +(-517.371 + 517.371i) q^{44} +(-225.813 + 225.813i) q^{45} +(-1202.44 - 1202.44i) q^{46} +(-609.937 - 609.937i) q^{47} +2117.16 q^{48} -149.212i q^{49} +(-4417.66 - 4417.66i) q^{50} +2033.05i q^{51} +897.855 q^{53} +(-3062.55 + 3062.55i) q^{54} -1836.26 q^{55} -142.691i q^{56} +(-2987.04 + 2987.04i) q^{57} +(-1497.72 + 1497.72i) q^{58} +(351.769 + 351.769i) q^{59} +(-4150.10 - 4150.10i) q^{60} +248.429 q^{61} +5048.65i q^{62} +(-258.342 - 258.342i) q^{63} -4361.35i q^{64} -2161.69 q^{66} +(1319.92 - 1319.92i) q^{67} +3924.59 q^{68} -2552.76i q^{69} +(7937.63 - 7937.63i) q^{70} +(-2121.75 + 2121.75i) q^{71} +(16.3705 + 16.3705i) q^{72} +(6818.40 + 6818.40i) q^{73} -4356.22 q^{74} -9378.61i q^{75} +(5766.16 + 5766.16i) q^{76} -2100.78i q^{77} +2503.91 q^{79} +(7252.76 - 7252.76i) q^{80} -5878.09 q^{81} +3963.73i q^{82} +(-7971.73 + 7971.73i) q^{83} +(4747.92 - 4747.92i) q^{84} +(6964.62 + 6964.62i) q^{85} +(-4541.98 - 4541.98i) q^{86} -3179.64 q^{87} +133.122i q^{88} +(10252.7 + 10252.7i) q^{89} +1821.33i q^{90} -4927.83 q^{92} +(-5359.09 + 5359.09i) q^{93} -4919.53 q^{94} +20465.4i q^{95} +(8829.40 - 8829.40i) q^{96} +(5238.81 - 5238.81i) q^{97} +(-601.744 - 601.744i) q^{98} +(241.017 + 241.017i) 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	4.03282	−	4.03282i	1.00820	−	1.00820i	0.00823842	−	0.999966i	$-0.497378\pi$
$2$	4.03282	−	4.03282i	1.00820	−	1.00820i	0.999966	−	0.00823842i	$-0.00262240\pi$
$3$	8.56159			0.951288			0.475644	−	0.879638i	$-0.342215\pi$
$3$	8.56159			0.951288			0.475644	+	0.879638i	$0.342215\pi$
$4$		−	16.5272i		−	1.03295i
$5$	29.3294	−	29.3294i	1.17318	−	1.17318i	0.191728	−	0.981448i	$-0.438591\pi$
$5$	29.3294	−	29.3294i	1.17318	−	1.17318i	0.981448	−	0.191728i	$-0.0614093\pi$
$6$	34.5273	−	34.5273i	0.959092	−	0.959092i
$7$	33.5543	+	33.5543i	0.684783	+	0.684783i	0.961074	−	0.276291i	$-0.0891055\pi$
$7$	33.5543	+	33.5543i	0.684783	+	0.684783i	−0.276291	+	0.961074i	$0.589105\pi$
$8$	−2.12627	−	2.12627i	−0.0332229	−	0.0332229i
$9$	−7.69920			−0.0950518
$10$		−	236.560i		−	2.36560i
$11$	−31.3041	−	31.3041i	−0.258712	−	0.258712i	0.565818	−	0.824530i	$-0.308560\pi$
$11$	−31.3041	−	31.3041i	−0.258712	−	0.258712i	−0.824530	+	0.565818i	$0.808560\pi$
$12$		−	141.499i		−	0.982635i
$13$		0			0
$13$		0			0
$14$	270.637			1.38080
$15$	251.106	−	251.106i	1.11603	−	1.11603i
$16$	247.286			0.965962
$17$			237.462i			0.821668i	0.911710	+	0.410834i	$0.134762\pi$
$17$			237.462i			0.821668i	−0.911710	+	0.410834i	$0.865238\pi$
$18$	−31.0495	+	31.0495i	−0.0958317	+	0.0958317i
$19$	−348.888	+	348.888i	−0.966449	+	0.966449i	−0.999455	−	0.0330058i	$-0.989492\pi$
$19$	−348.888	+	348.888i	−0.966449	+	0.966449i	0.0330058	+	0.999455i	$0.489492\pi$
$20$	−484.734	−	484.734i	−1.21184	−	1.21184i
$21$	287.279	+	287.279i	0.651425	+	0.651425i
$22$	−252.488			−0.521669
$23$		−	298.164i		−	0.563638i	−0.959468	−	0.281819i	$-0.909062\pi$
$23$		−	298.164i		−	0.563638i	0.959468	−	0.281819i	$-0.0909377\pi$
$24$	−18.2042	−	18.2042i	−0.0316045	−	0.0316045i
$25$		−	1095.43i		−	1.75269i
$26$		0			0
$27$	−759.406			−1.04171
$28$	554.561	−	554.561i	0.707348	−	0.707348i
$29$	−371.384			−0.441598			−0.220799	−	0.975319i	$-0.570866\pi$
$29$	−371.384			−0.441598			−0.220799	+	0.975319i	$0.570866\pi$
$30$		−	2025.33i		−	2.25037i
$31$	−625.946	+	625.946i	−0.651348	+	0.651348i	−0.953318	−	0.301969i	$-0.902356\pi$
$31$	−625.946	+	625.946i	−0.651348	+	0.651348i	0.301969	+	0.953318i	$0.402356\pi$
$32$	1031.28	−	1031.28i	1.00711	−	1.00711i
$33$	−268.013	−	268.013i	−0.246109	−	0.246109i
$34$	957.641	+	957.641i	0.828409	+	0.828409i
$35$	1968.26			1.60674
$36$			127.247i			0.0981840i
$37$	−540.096	−	540.096i	−0.394518	−	0.394518i	0.481776	−	0.876294i	$-0.339992\pi$
$37$	−540.096	−	540.096i	−0.394518	−	0.394518i	−0.876294	+	0.481776i	$0.839992\pi$
$38$			2814.01i			1.94876i
$39$		0			0
$40$	−124.724			−0.0779527
$41$	−491.434	+	491.434i	−0.292346	+	0.292346i	−0.838006	−	0.545660i	$-0.816279\pi$
$41$	−491.434	+	491.434i	−0.292346	+	0.292346i	0.545660	+	0.838006i	$0.316279\pi$
$42$	2317.08			1.31354
$43$		−	1126.26i		−	0.609116i	−0.952494	−	0.304558i	$-0.901491\pi$
$43$		−	1126.26i		−	0.609116i	0.952494	−	0.304558i	$-0.0985087\pi$
$44$	−517.371	+	517.371i	−0.267237	+	0.267237i
$45$	−225.813	+	225.813i	−0.111513	+	0.111513i
$46$	−1202.44	−	1202.44i	−0.568262	−	0.568262i
$47$	−609.937	−	609.937i	−0.276114	−	0.276114i	0.555441	−	0.831556i	$-0.312549\pi$
$47$	−609.937	−	609.937i	−0.276114	−	0.276114i	−0.831556	+	0.555441i	$0.812549\pi$
$48$	2117.16			0.918907
$49$		−	149.212i		−	0.0621457i
$50$	−4417.66	−	4417.66i	−1.76707	−	1.76707i
$51$			2033.05i			0.781642i
$52$		0			0
$53$	897.855			0.319635			0.159818	−	0.987147i	$-0.448909\pi$
$53$	897.855			0.319635			0.159818	+	0.987147i	$0.448909\pi$
$54$	−3062.55	+	3062.55i	−1.05026	+	1.05026i
$55$	−1836.26			−0.607029
$56$		−	142.691i		−	0.0455009i
$57$	−2987.04	+	2987.04i	−0.919371	+	0.919371i
$58$	−1497.72	+	1497.72i	−0.445221	+	0.445221i
$59$	351.769	+	351.769i	0.101054	+	0.101054i	0.755826	−	0.654772i	$-0.227235\pi$
$59$	351.769	+	351.769i	0.101054	+	0.101054i	−0.654772	+	0.755826i	$0.727235\pi$
$60$	−4150.10	−	4150.10i	−1.15280	−	1.15280i
$61$	248.429			0.0667640			0.0333820	−	0.999443i	$-0.489372\pi$
$61$	248.429			0.0667640			0.0333820	+	0.999443i	$0.489372\pi$
$62$			5048.65i			1.31338i
$63$	−258.342	−	258.342i	−0.0650898	−	0.0650898i
$64$		−	4361.35i		−	1.06478i
$65$		0			0
$66$	−2161.69			−0.496257
$67$	1319.92	−	1319.92i	0.294034	−	0.294034i	−0.544638	−	0.838672i	$-0.683333\pi$
$67$	1319.92	−	1319.92i	0.294034	−	0.294034i	0.838672	+	0.544638i	$0.183333\pi$
$68$	3924.59			0.848744
$69$		−	2552.76i		−	0.536182i
$70$	7937.63	−	7937.63i	1.61992	−	1.61992i
$71$	−2121.75	+	2121.75i	−0.420898	+	0.420898i	−0.885513	−	0.464615i	$-0.846193\pi$
$71$	−2121.75	+	2121.75i	−0.420898	+	0.420898i	0.464615	+	0.885513i	$0.346193\pi$
$72$	16.3705	+	16.3705i	0.00315790	+	0.00315790i
$73$	6818.40	+	6818.40i	1.27949	+	1.27949i	0.940953	+	0.338536i	$0.109932\pi$
$73$	6818.40	+	6818.40i	1.27949	+	1.27949i	0.338536	+	0.940953i	$0.390068\pi$
$74$	−4356.22			−0.795510
$75$		−	9378.61i		−	1.66731i
$76$	5766.16	+	5766.16i	0.998296	+	0.998296i
$77$		−	2100.78i		−	0.354323i
$78$		0			0
$79$	2503.91			0.401204			0.200602	−	0.979673i	$-0.435710\pi$
$79$	2503.91			0.401204			0.200602	+	0.979673i	$0.435710\pi$
$80$	7252.76	−	7252.76i	1.13324	−	1.13324i
$81$	−5878.09			−0.895913
$82$			3963.73i			0.589489i
$83$	−7971.73	+	7971.73i	−1.15717	+	1.15717i	−0.172086	+	0.985082i	$0.555051\pi$
$83$	−7971.73	+	7971.73i	−1.15717	+	1.15717i	−0.985082	+	0.172086i	$0.944949\pi$
$84$	4747.92	−	4747.92i	0.672891	−	0.672891i
$85$	6964.62	+	6964.62i	0.963961	+	0.963961i
$86$	−4541.98	−	4541.98i	−0.614113	−	0.614113i
$87$	−3179.64			−0.420087
$88$			133.122i			0.0171903i
$89$	10252.7	+	10252.7i	1.29437	+	1.29437i	0.932056	+	0.362314i	$0.118013\pi$
$89$	10252.7	+	10252.7i	1.29437	+	1.29437i	0.362314	+	0.932056i	$0.381987\pi$
$90$			1821.33i			0.224855i
$91$		0			0
$92$	−4927.83			−0.582211
$93$	−5359.09	+	5359.09i	−0.619619	+	0.619619i
$94$	−4919.53			−0.556760
$95$			20465.4i			2.26763i
$96$	8829.40	−	8829.40i	0.958051	−	0.958051i
$97$	5238.81	−	5238.81i	0.556787	−	0.556787i	−0.371605	−	0.928391i	$-0.621192\pi$
$97$	5238.81	−	5238.81i	0.556787	−	0.556787i	0.928391	+	0.371605i	$0.121192\pi$
$98$	−601.744	−	601.744i	−0.0626555	−	0.0626555i
$99$	241.017	+	241.017i	0.0245910	+	0.0245910i
$100$	−18104.4			−1.81044
$101$			246.646i			0.0241786i	0.999927	+	0.0120893i	$0.00384824\pi$
$101$			246.646i			0.0241786i	−0.999927	+	0.0120893i	$0.996152\pi$
$102$	8198.93	+	8198.93i	0.788055	+	0.788055i
$103$		−	6944.63i		−	0.654598i	−0.944921	−	0.327299i	$-0.893862\pi$
$103$		−	6944.63i		−	0.654598i	0.944921	−	0.327299i	$-0.106138\pi$
$104$		0			0
$105$	16851.4			1.52847
$106$	3620.89	−	3620.89i	0.322258	−	0.322258i
$107$	−1489.08			−0.130062			−0.0650311	−	0.997883i	$-0.520715\pi$
$107$	−1489.08			−0.130062			−0.0650311	+	0.997883i	$0.520715\pi$
$108$			12550.9i			1.07604i
$109$	12063.2	−	12063.2i	1.01534	−	1.01534i	0.0154553	−	0.999881i	$-0.495080\pi$
$109$	12063.2	−	12063.2i	1.01534	−	1.01534i	0.999881	−	0.0154553i	$-0.00491977\pi$
$110$	−7405.31	+	7405.31i	−0.612009	+	0.612009i
$111$	−4624.08	−	4624.08i	−0.375300	−	0.375300i
$112$	8297.53	+	8297.53i	0.661474	+	0.661474i
$113$	9077.08			0.710869			0.355434	−	0.934701i	$-0.384333\pi$
$113$	9077.08			0.710869			0.355434	+	0.934701i	$0.384333\pi$
$114$			24092.4i			1.85383i
$115$	−8744.99	−	8744.99i	−0.661247	−	0.661247i
$116$			6137.95i			0.456150i
$117$		0			0
$118$	2837.24			0.203766
$119$	−7967.88	+	7967.88i	−0.562664	+	0.562664i
$120$	−1067.84			−0.0741554
$121$		−	12681.1i		−	0.866137i
$122$	1001.87	−	1001.87i	0.0673118	−	0.0673118i
$123$	−4207.45	+	4207.45i	−0.278105	+	0.278105i
$124$	10345.2	+	10345.2i	0.672812	+	0.672812i
$125$	−13797.4	−	13797.4i	−0.883033	−	0.883033i
$126$	−2083.69			−0.131248
$127$		−	258.250i		−	0.0160115i	−0.999968	−	0.00800577i	$-0.997452\pi$
$127$		−	258.250i		−	0.0160115i	0.999968	−	0.00800577i	$-0.00254834\pi$
$128$	−1088.06	−	1088.06i	−0.0664097	−	0.0664097i
$129$		−	9642.53i		−	0.579444i
$130$		0			0
$131$	−19031.9			−1.10902			−0.554511	−	0.832177i	$-0.687095\pi$
$131$	−19031.9			−1.10902			−0.554511	+	0.832177i	$0.687095\pi$
$132$	−4429.51	+	4429.51i	−0.254219	+	0.254219i
$133$	−23413.4			−1.32362
$134$		−	10646.0i		−	0.592893i
$135$	−22272.9	+	22272.9i	−1.22211	+	1.22211i
$136$	504.907	−	504.907i	0.0272982	−	0.0272982i
$137$	23164.2	+	23164.2i	1.23418	+	1.23418i	0.962345	+	0.271830i	$0.0876288\pi$
$137$	23164.2	+	23164.2i	1.23418	+	1.23418i	0.271830	+	0.962345i	$0.412371\pi$
$138$	−10294.8	−	10294.8i	−0.540581	−	0.540581i
$139$	18205.8			0.942283			0.471141	−	0.882058i	$-0.343842\pi$
$139$	18205.8			0.942283			0.471141	+	0.882058i	$0.343842\pi$
$140$		−	32529.9i		−	1.65969i
$141$	−5222.03	−	5222.03i	−0.262664	−	0.262664i
$142$			17113.2i			0.848702i
$143$		0			0
$144$	−1903.91			−0.0918164
$145$	−10892.5	+	10892.5i	−0.518072	+	0.518072i
$146$	54994.7			2.57997
$147$		−	1277.49i		−	0.0591184i
$148$	−8926.29	+	8926.29i	−0.407519	+	0.407519i
$149$	7548.87	−	7548.87i	0.340024	−	0.340024i	−0.516352	−	0.856376i	$-0.672711\pi$
$149$	7548.87	−	7548.87i	0.340024	−	0.340024i	0.856376	+	0.516352i	$0.172711\pi$
$150$	−37822.2	−	37822.2i	−1.68099	−	1.68099i
$151$	−6497.73	−	6497.73i	−0.284976	−	0.284976i	0.550114	−	0.835090i	$-0.314584\pi$
$151$	−6497.73	−	6497.73i	−0.284976	−	0.284976i	−0.835090	+	0.550114i	$0.814584\pi$
$152$	1483.66			0.0642165
$153$		−	1828.27i		−	0.0781010i
$154$	−8472.06	−	8472.06i	−0.357230	−	0.357230i
$155$			36717.2i			1.52829i
$156$		0			0
$157$	−41173.9			−1.67041			−0.835203	−	0.549941i	$-0.814650\pi$
$157$	−41173.9			−1.67041			−0.835203	+	0.549941i	$0.814650\pi$
$158$	10097.8	−	10097.8i	0.404496	−	0.404496i
$159$	7687.06			0.304065
$160$		−	60493.7i		−	2.36303i
$161$	10004.7	−	10004.7i	0.385969	−	0.385969i
$162$	−23705.3	+	23705.3i	−0.903264	+	0.903264i
$163$	184.071	+	184.071i	0.00692805	+	0.00692805i	0.710562	−	0.703634i	$-0.248441\pi$
$163$	184.071	+	184.071i	0.00692805	+	0.00692805i	−0.703634	+	0.710562i	$0.748441\pi$
$164$	8122.04	+	8122.04i	0.301980	+	0.301980i
$165$	−15721.3			−0.577459
$166$			64297.1i			2.33332i
$167$	−30782.0	−	30782.0i	−1.10373	−	1.10373i	−0.993956	−	0.109777i	$-0.964986\pi$
$167$	−30782.0	−	30782.0i	−1.10373	−	1.10373i	−0.109777	−	0.993956i	$-0.535014\pi$
$168$		−	1221.66i		−	0.0432845i
$169$		0			0
$170$	56174.1			1.94374
$171$	2686.16	−	2686.16i	0.0918628	−	0.0918628i
$172$	−18613.9			−0.629188
$173$			26014.5i			0.869206i	0.900622	+	0.434603i	$0.143111\pi$
$173$			26014.5i			0.869206i	−0.900622	+	0.434603i	$0.856889\pi$
$174$	−12822.9	+	12822.9i	−0.423533	+	0.423533i
$175$	36756.4	−	36756.4i	1.20021	−	1.20021i
$176$	−7741.07	−	7741.07i	−0.249906	−	0.249906i
$177$	3011.70	+	3011.70i	0.0961315	+	0.0961315i
$178$	82694.6			2.60998
$179$		−	34894.6i		−	1.08906i	−0.838742	−	0.544530i	$-0.816708\pi$
$179$		−	34894.6i		−	1.08906i	0.838742	−	0.544530i	$-0.183292\pi$
$180$	3732.07	+	3732.07i	0.115187	+	0.115187i
$181$		−	38784.9i		−	1.18387i	−0.805984	−	0.591937i	$-0.798363\pi$
$181$		−	38784.9i		−	1.18387i	0.805984	−	0.591937i	$-0.201637\pi$
$182$		0			0
$183$	2126.95			0.0635118
$184$	−633.977	+	633.977i	−0.0187257	+	0.0187257i
$185$	−31681.4			−0.925679
$186$			43224.5i			1.24941i
$187$	7433.54	−	7433.54i	0.212575	−	0.212575i
$188$	−10080.6	+	10080.6i	−0.285213	+	0.285213i
$189$	−25481.4	−	25481.4i	−0.713344	−	0.713344i
$190$	82533.1	+	82533.1i	2.28624	+	2.28624i
$191$	−47264.1			−1.29558			−0.647791	−	0.761818i	$-0.724307\pi$
$191$	−47264.1			−1.29558			−0.647791	+	0.761818i	$0.724307\pi$
$192$		−	37340.1i		−	1.01292i
$193$	15720.9	+	15720.9i	0.422049	+	0.422049i	0.885909	−	0.463859i	$-0.153536\pi$
$193$	15720.9	+	15720.9i	0.422049	+	0.422049i	−0.463859	+	0.885909i	$0.653536\pi$
$194$		−	42254.3i		−	1.12271i
$195$		0			0
$196$	−2466.06			−0.0641935
$197$	3331.72	−	3331.72i	0.0858492	−	0.0858492i	−0.662878	−	0.748727i	$-0.730665\pi$
$197$	3331.72	−	3331.72i	0.0858492	−	0.0858492i	0.748727	+	0.662878i	$0.230665\pi$
$198$	1943.95			0.0495856
$199$		−	67470.8i		−	1.70377i	−0.523732	−	0.851883i	$-0.675461\pi$
$199$		−	67470.8i		−	1.70377i	0.523732	−	0.851883i	$-0.324539\pi$
$200$	−2329.17	+	2329.17i	−0.0582293	+	0.0582293i
$201$	11300.6	−	11300.6i	0.279711	−	0.279711i
$202$	994.679	+	994.679i	0.0243770	+	0.0243770i
$203$	−12461.5	−	12461.5i	−0.302399	−	0.302399i
$204$	33600.7			0.807399
$205$			28826.9i			0.685947i
$206$	−28006.4	−	28006.4i	−0.659969	−	0.659969i
$207$			2295.63i			0.0535748i
$208$		0			0
$209$	21843.3			0.500063
$210$	67958.7	−	67958.7i	1.54101	−	1.54101i
$211$	34787.0			0.781363			0.390681	−	0.920526i	$-0.372239\pi$
$211$	34787.0			0.781363			0.390681	+	0.920526i	$0.372239\pi$
$212$		−	14839.1i		−	0.330168i
$213$	−18165.5	+	18165.5i	−0.400395	+	0.400395i
$214$	−6005.20	+	6005.20i	−0.131129	+	0.131129i
$215$	−33032.4	−	33032.4i	−0.714600	−	0.714600i
$216$	1614.70	+	1614.70i	0.0346086	+	0.0346086i
$217$	−42006.4			−0.892064
$218$		−	97297.4i		−	2.04733i
$219$	58376.3	+	58376.3i	1.21716	+	1.21716i
$220$			30348.4i			0.627032i
$221$		0			0
$222$	−37296.1			−0.756759
$223$	22684.9	−	22684.9i	0.456171	−	0.456171i	−0.441225	−	0.897396i	$-0.645456\pi$
$223$	22684.9	−	22684.9i	0.456171	−	0.456171i	0.897396	+	0.441225i	$0.145456\pi$
$224$	69207.9			1.37930
$225$			8433.92i			0.166596i
$226$	36606.2	−	36606.2i	0.716701	−	0.716701i
$227$	−45810.4	+	45810.4i	−0.889021	+	0.889021i	−0.994429	−	0.105408i	$-0.966385\pi$
$227$	−45810.4	+	45810.4i	−0.889021	+	0.889021i	0.105408	+	0.994429i	$0.466385\pi$
$228$	49367.5	+	49367.5i	0.949667	+	0.949667i
$229$	−54161.9	−	54161.9i	−1.03282	−	1.03282i	−0.999443	−	0.0333737i	$-0.989375\pi$
$229$	−54161.9	−	54161.9i	−1.03282	−	1.03282i	−0.0333737	−	0.999443i	$-0.510625\pi$
$230$	−70533.9			−1.33334
$231$		−	17986.0i		−	0.337063i
$232$	789.661	+	789.661i	0.0146712	+	0.0146712i
$233$		−	61901.5i		−	1.14022i	−0.821568	−	0.570111i	$-0.806900\pi$
$233$		−	61901.5i		−	1.14022i	0.821568	−	0.570111i	$-0.193100\pi$
$234$		0			0
$235$	−35778.2			−0.647862
$236$	5813.77	−	5813.77i	0.104384	−	0.104384i
$237$	21437.5			0.381660
$238$			64266.0i			1.13456i
$239$	−34967.7	+	34967.7i	−0.612169	+	0.612169i	−0.943511	−	0.331342i	$-0.892499\pi$
$239$	−34967.7	+	34967.7i	−0.612169	+	0.612169i	0.331342	+	0.943511i	$0.392499\pi$
$240$	62095.1	−	62095.1i	1.07804	−	1.07804i
$241$	−1194.63	−	1194.63i	−0.0205684	−	0.0205684i	0.696748	−	0.717316i	$-0.254630\pi$
$241$	−1194.63	−	1194.63i	−0.0205684	−	0.0205684i	−0.717316	+	0.696748i	$0.754630\pi$
$242$	−51140.6	−	51140.6i	−0.873243	−	0.873243i
$243$	11186.1			0.189438
$244$		−	4105.84i		−	0.0689640i
$245$	−4376.29	−	4376.29i	−0.0729078	−	0.0729078i
$246$			33935.8i			0.560774i
$247$		0			0
$248$	2661.85			0.0432794
$249$	−68250.7	+	68250.7i	−1.10080	+	1.10080i
$250$	−111285.			−1.78056
$251$		−	45604.5i		−	0.723870i	−0.932203	−	0.361935i	$-0.882116\pi$
$251$		−	45604.5i		−	0.723870i	0.932203	−	0.361935i	$-0.117884\pi$
$252$	−4269.67	+	4269.67i	−0.0672347	+	0.0672347i
$253$	−9333.77	+	9333.77i	−0.145820	+	0.145820i
$254$	−1041.48	−	1041.48i	−0.0161429	−	0.0161429i
$255$	59628.2	+	59628.2i	0.917004	+	0.917004i
$256$	61005.8			0.930874
$257$			13013.4i			0.197027i	0.995136	+	0.0985134i	$0.0314087\pi$
$257$			13013.4i			0.197027i	−0.995136	+	0.0985134i	$0.968591\pi$
$258$	−38886.6	−	38886.6i	−0.584198	−	0.584198i
$259$		−	36245.1i		−	0.540319i
$260$		0			0
$261$	2859.36			0.0419747
$262$	−76752.2	+	76752.2i	−1.11812	+	1.11812i
$263$	−19388.3			−0.280304			−0.140152	−	0.990130i	$-0.544759\pi$
$263$	−19388.3			−0.280304			−0.140152	+	0.990130i	$0.544759\pi$
$264$			1139.73i			0.0163529i
$265$	26333.6	−	26333.6i	0.374988	−	0.374988i
$266$	−94422.1	+	94422.1i	−1.33447	+	1.33447i
$267$	87779.4	+	87779.4i	1.23132	+	1.23132i
$268$	−21814.6	−	21814.6i	−0.303723	−	0.303723i
$269$	21911.2			0.302804			0.151402	−	0.988472i	$-0.451621\pi$
$269$	21911.2			0.302804			0.151402	+	0.988472i	$0.451621\pi$
$270$			179645.i			2.46427i
$271$	−30254.4	−	30254.4i	−0.411956	−	0.411956i	0.470464	−	0.882419i	$-0.344087\pi$
$271$	−30254.4	−	30254.4i	−0.411956	−	0.411956i	−0.882419	+	0.470464i	$0.844087\pi$
$272$			58721.0i			0.793699i
$273$		0			0
$274$	186834.			2.48860
$275$	−34291.4	+	34291.4i	−0.453440	+	0.453440i
$276$	−42190.1			−0.553850
$277$			96564.2i			1.25851i	0.777199	+	0.629255i	$0.216640\pi$
$277$			96564.2i			1.25851i	−0.777199	+	0.629255i	$0.783360\pi$
$278$	73420.8	−	73420.8i	0.950013	−	0.950013i
$279$	4819.28	−	4819.28i	0.0619118	−	0.0619118i
$280$	−4185.04	−	4185.04i	−0.0533806	−	0.0533806i
$281$	−50030.4	−	50030.4i	−0.633609	−	0.633609i	0.315362	−	0.948971i	$-0.397874\pi$
$281$	−50030.4	−	50030.4i	−0.633609	−	0.633609i	−0.948971	+	0.315362i	$0.897874\pi$
$282$	−42119.0			−0.529639
$283$			147680.i			1.84394i	0.387256	+	0.921972i	$0.373423\pi$
$283$			147680.i			1.84394i	−0.387256	+	0.921972i	$0.626577\pi$
$284$	35066.6	+	35066.6i	0.434768	+	0.434768i
$285$			175216.i			2.15717i
$286$		0			0
$287$	−32979.5			−0.400387
$288$	−7940.03	+	7940.03i	−0.0957276	+	0.0957276i
$289$	27132.8			0.324862
$290$			87854.7i			1.04465i
$291$	44852.5	−	44852.5i	0.529664	−	0.529664i
$292$	112689.	−	112689.i	1.32165	−	1.32165i
$293$	−7052.35	−	7052.35i	−0.0821483	−	0.0821483i	0.664839	−	0.746987i	$-0.268500\pi$
$293$	−7052.35	−	7052.35i	−0.0821483	−	0.0821483i	−0.746987	+	0.664839i	$0.768500\pi$
$294$	−5151.88	−	5151.88i	−0.0596034	−	0.0596034i
$295$	20634.4			0.237108
$296$			2296.77i			0.0262141i
$297$	23772.5	+	23772.5i	0.269502	+	0.269502i
$298$		−	60886.4i		−	0.685627i
$299$		0			0
$300$	−155003.			−1.72225
$301$	37790.8	−	37790.8i	0.417112	−	0.417112i
$302$	−52408.3			−0.574628
$303$			2111.68i			0.0230008i
$304$	−86275.2	+	86275.2i	−0.933553	+	0.933553i
$305$	7286.27	−	7286.27i	0.0783259	−	0.0783259i
$306$	−7373.07	−	7373.07i	−0.0787418	−	0.0787418i
$307$	58686.7	+	58686.7i	0.622677	+	0.622677i	0.946215	−	0.323538i	$-0.104872\pi$
$307$	58686.7	+	58686.7i	0.622677	+	0.622677i	−0.323538	+	0.946215i	$0.604872\pi$
$308$	−34720.1			−0.365998
$309$		−	59457.1i		−	0.622711i
$310$	148074.	+	148074.i	1.54083	+	1.54083i
$311$			38813.8i			0.401296i	0.979663	+	0.200648i	$0.0643048\pi$
$311$			38813.8i			0.401296i	−0.979663	+	0.200648i	$0.935695\pi$
$312$		0			0
$313$	−98727.3			−1.00774			−0.503870	−	0.863779i	$-0.668091\pi$
$313$	−98727.3			−1.00774			−0.503870	+	0.863779i	$0.668091\pi$
$314$	−166047.	+	166047.i	−1.68411	+	1.68411i
$315$	−15154.0			−0.152724
$316$		−	41382.8i		−	0.414425i
$317$	−49531.4	+	49531.4i	−0.492904	+	0.492904i	−0.909220	−	0.416316i	$-0.863321\pi$
$317$	−49531.4	+	49531.4i	−0.492904	+	0.492904i	0.416316	+	0.909220i	$0.363321\pi$
$318$	31000.5	−	31000.5i	0.306560	−	0.306560i
$319$	11625.8	+	11625.8i	0.114247	+	0.114247i
$320$	−127916.	−	127916.i	−1.24918	−	1.24918i
$321$	−12748.9			−0.123727
$322$		−	80694.4i		−	0.778272i
$323$	−82847.7	−	82847.7i	−0.794100	−	0.794100i
$324$			97148.6i			0.925436i
$325$		0			0
$326$	1484.65			0.0139698
$327$	103280.	−	103280.i	0.965876	−	0.965876i
$328$	2089.84			0.0194252
$329$		−	40932.1i		−	0.378157i
$330$	−63401.2	+	63401.2i	−0.582197	+	0.582197i
$331$	−47550.4	+	47550.4i	−0.434009	+	0.434009i	−0.889990	−	0.455981i	$-0.849289\pi$
$331$	−47550.4	+	47550.4i	−0.434009	+	0.434009i	0.455981	+	0.889990i	$0.349289\pi$
$332$	131751.	+	131751.i	1.19530	+	1.19530i
$333$	4158.30	+	4158.30i	0.0374997	+	0.0374997i
$334$	−248277.			−2.22558
$335$		−	77424.9i		−	0.689907i
$336$	71040.0	+	71040.0i	0.629252	+	0.629252i
$337$		−	104833.i		−	0.923075i	−0.887121	−	0.461538i	$-0.847298\pi$
$337$		−	104833.i		−	0.923075i	0.887121	−	0.461538i	$-0.152702\pi$
$338$		0			0
$339$	77714.3			0.676241
$340$	115106.	−	115106.i	0.995726	−	0.995726i
$341$	39189.3			0.337023
$342$		−	21665.6i		−	0.185233i
$343$	85570.7	−	85570.7i	0.727339	−	0.727339i
$344$	−2394.72	+	2394.72i	−0.0202366	+	0.0202366i
$345$	−74871.0	−	74871.0i	−0.629036	−	0.629036i
$346$	104912.	+	104912.i	0.876338	+	0.876338i
$347$	152401.			1.26569			0.632846	−	0.774277i	$-0.281887\pi$
$347$	152401.			1.26569			0.632846	+	0.774277i	$0.281887\pi$
$348$			52550.6i			0.433930i
$349$	150748.	+	150748.i	1.23766	+	1.23766i	0.960956	+	0.276699i	$0.0892407\pi$
$349$	150748.	+	150748.i	1.23766	+	1.23766i	0.276699	+	0.960956i	$0.410759\pi$
$350$		−	296464.i		−	2.42011i
$351$		0			0
$352$	−64566.6			−0.521102
$353$	146322.	−	146322.i	1.17425	−	1.17425i	0.193066	−	0.981186i	$-0.438157\pi$
$353$	146322.	−	146322.i	1.17425	−	1.17425i	0.981186	−	0.193066i	$-0.0618431\pi$
$354$	24291.3			0.193840
$355$			124459.i			0.987575i
$356$	169449.	−	169449.i	1.33702	−	1.33702i
$357$	−68217.7	+	68217.7i	−0.535255	+	0.535255i
$358$	−140723.	−	140723.i	−1.09799	−	1.09799i
$359$	100758.	+	100758.i	0.781795	+	0.781795i	0.980134	−	0.198339i	$-0.0635546\pi$
$359$	100758.	+	100758.i	0.781795	+	0.781795i	−0.198339	+	0.980134i	$0.563555\pi$
$360$	960.277			0.00740954
$361$		−	113125.i		−	0.868049i
$362$	−156412.	−	156412.i	−1.19359	−	1.19359i
$363$		−	108570.i		−	0.823945i
$364$		0			0
$365$	399959.			3.00213
$366$	8577.58	−	8577.58i	0.0640328	−	0.0640328i
$367$	−100859.			−0.748832			−0.374416	−	0.927261i	$-0.622157\pi$
$367$	−100859.			−0.748832			−0.374416	+	0.927261i	$0.622157\pi$
$368$		−	73731.9i		−	0.544452i
$369$	3783.65	−	3783.65i	0.0277880	−	0.0277880i
$370$	−127765.	+	127765.i	−0.933274	+	0.933274i
$371$	30126.9	+	30126.9i	0.218881	+	0.218881i
$372$	88571.0	+	88571.0i	0.640038	+	0.640038i
$373$	82341.2			0.591834			0.295917	−	0.955214i	$-0.404375\pi$
$373$	82341.2			0.591834			0.295917	+	0.955214i	$0.404375\pi$
$374$		−	59956.2i		−	0.428638i
$375$	−118128.	−	118128.i	−0.840018	−	0.840018i
$376$			2593.78i			0.0183467i
$377$		0			0
$378$	−205523.			−1.43839
$379$	−25664.7	+	25664.7i	−0.178673	+	0.178673i	−0.790777	−	0.612104i	$-0.790323\pi$
$379$	−25664.7	+	25664.7i	−0.178673	+	0.178673i	0.612104	+	0.790777i	$0.290323\pi$
$380$	338236.			2.34236
$381$		−	2211.03i		−	0.0152316i
$382$	−190608.	+	190608.i	−1.30621	+	1.30621i
$383$	108692.	−	108692.i	0.740972	−	0.740972i	−0.231793	−	0.972765i	$-0.574459\pi$
$383$	108692.	−	108692.i	0.740972	−	0.740972i	0.972765	+	0.231793i	$0.0744592\pi$
$384$	−9315.50	−	9315.50i	−0.0631748	−	0.0631748i
$385$	−61614.6	−	61614.6i	−0.415683	−	0.415683i
$386$	126799.			0.851024
$387$			8671.26i			0.0578976i
$388$	−86583.0	−	86583.0i	−0.575134	−	0.575134i
$389$		−	15749.1i		−	0.104077i	−0.998645	−	0.0520387i	$-0.983428\pi$
$389$		−	15749.1i		−	0.104077i	0.998645	−	0.0520387i	$-0.0165719\pi$
$390$		0			0
$391$	70802.7			0.463123
$392$	−317.264	+	317.264i	−0.00206466	+	0.00206466i
$393$	−162943.			−1.05500
$394$		−	26872.4i		−	0.173107i
$395$	73438.3	−	73438.3i	0.470683	−	0.470683i
$396$	3983.34	−	3983.34i	0.0254014	−	0.0254014i
$397$	−144465.	−	144465.i	−0.916605	−	0.916605i	0.0801760	−	0.996781i	$-0.474452\pi$
$397$	−144465.	−	144465.i	−0.916605	−	0.916605i	−0.996781	+	0.0801760i	$0.974452\pi$
$398$	−272098.	−	272098.i	−1.71774	−	1.71774i
$399$	−200456.			−1.25914
$400$		−	270884.i		−	1.69303i
$401$	−83242.2	−	83242.2i	−0.517672	−	0.517672i	0.399194	−	0.916866i	$-0.369290\pi$
$401$	−83242.2	−	83242.2i	−0.517672	−	0.517672i	−0.916866	+	0.399194i	$0.869290\pi$
$402$		−	91146.5i		−	0.564011i
$403$		0			0
$404$	4076.38			0.0249754
$405$	−172401.	+	172401.i	−1.05106	+	1.05106i
$406$	−100510.			−0.609759
$407$			33814.4i			0.204133i
$408$	4322.81	−	4322.81i	0.0259684	−	0.0259684i
$409$	42949.5	−	42949.5i	0.256751	−	0.256751i	−0.566980	−	0.823731i	$-0.691888\pi$
$409$	42949.5	−	42949.5i	0.256751	−	0.256751i	0.823731	+	0.566980i	$0.191888\pi$
$410$	116254.	+	116254.i	0.691575	+	0.691575i
$411$	198323.	+	198323.i	1.17406	+	1.17406i
$412$	−114776.			−0.676169
$413$			23606.8i			0.138400i
$414$	9257.85	+	9257.85i	0.0540144	+	0.0540144i
$415$			467612.i			2.71512i
$416$		0			0
$417$	155871.			0.896382
$418$	88089.9	−	88089.9i	0.504166	−	0.504166i
$419$	325761.			1.85554			0.927770	−	0.373152i	$-0.121723\pi$
$419$	325761.			1.85554			0.927770	+	0.373152i	$0.121723\pi$
$420$		−	278507.i		−	1.57884i
$421$	−84760.5	+	84760.5i	−0.478222	+	0.478222i	−0.904563	−	0.426341i	$-0.859802\pi$
$421$	−84760.5	+	84760.5i	−0.478222	+	0.478222i	0.426341	+	0.904563i	$0.359802\pi$
$422$	140290.	−	140290.i	0.787773	−	0.787773i
$423$	4696.03	+	4696.03i	0.0262452	+	0.0262452i
$424$	−1909.08	−	1909.08i	−0.0106192	−	0.0106192i
$425$	260123.			1.44013
$426$			146516.i			0.807360i
$427$	8335.87	+	8335.87i	0.0457188	+	0.0457188i
$428$			24610.4i			0.134348i
$429$		0			0
$430$	−266427.			−1.44093
$431$	220269.	−	220269.i	1.18576	−	1.18576i	0.207537	−	0.978227i	$-0.433455\pi$
$431$	220269.	−	220269.i	1.18576	−	1.18576i	0.978227	−	0.207537i	$-0.0665447\pi$
$432$	−187791.			−1.00625
$433$		−	65965.0i		−	0.351834i	−0.984405	−	0.175917i	$-0.943711\pi$
$433$		−	65965.0i		−	0.351834i	0.984405	−	0.175917i	$-0.0562890\pi$
$434$	−169404.	+	169404.i	−0.899383	+	0.899383i
$435$	−93256.9	+	93256.9i	−0.492836	+	0.492836i
$436$	−199371.	−	199371.i	−1.04879	−	1.04879i
$437$	104026.	+	104026.i	0.544727	+	0.544727i
$438$	470842.			2.45430
$439$			159531.i			0.827784i	0.910326	+	0.413892i	$0.135831\pi$
$439$			159531.i			0.827784i	−0.910326	+	0.413892i	$0.864169\pi$
$440$	3904.38	+	3904.38i	0.0201673	+	0.0201673i
$441$			1148.81i			0.00590706i
$442$		0			0
$443$	−372577.			−1.89849			−0.949246	−	0.314535i	$-0.898151\pi$
$443$	−372577.			−1.89849			−0.949246	+	0.314535i	$0.898151\pi$
$444$	−76423.2	+	76423.2i	−0.387668	+	0.387668i
$445$	601411.			3.03705
$446$		−	182968.i		−	0.919828i
$447$	64630.3	−	64630.3i	0.323460	−	0.323460i
$448$	146342.	−	146342.i	0.729145	−	0.729145i
$449$	−51939.7	−	51939.7i	−0.257636	−	0.257636i	0.566456	−	0.824092i	$-0.308314\pi$
$449$	−51939.7	−	51939.7i	−0.257636	−	0.257636i	−0.824092	+	0.566456i	$0.808314\pi$
$450$	34012.5	+	34012.5i	0.167963	+	0.167963i
$451$	30767.8			0.151267
$452$		−	150019.i		−	0.734294i
$453$	−55630.9	−	55630.9i	−0.271094	−	0.271094i
$454$			369490.i			1.79263i
$455$		0			0
$456$	12702.5			0.0610884
$457$	−227956.	+	227956.i	−1.09149	+	1.09149i	−0.0961183	+	0.995370i	$0.530643\pi$
$457$	−227956.	+	227956.i	−1.09149	+	1.09149i	−0.995370	+	0.0961183i	$0.969357\pi$
$458$	−436850.			−2.08258
$459$		−	180330.i		−	0.855939i
$460$	−144530.	+	144530.i	−0.683036	+	0.683036i
$461$	−122668.	+	122668.i	−0.577202	+	0.577202i	−0.934131	−	0.356929i	$-0.883824\pi$
$461$	−122668.	+	122668.i	−0.577202	+	0.577202i	0.356929	+	0.934131i	$0.383824\pi$
$462$	−72534.3	−	72534.3i	−0.339828	−	0.339828i
$463$	−88275.9	−	88275.9i	−0.411794	−	0.411794i	0.470569	−	0.882363i	$-0.344049\pi$
$463$	−88275.9	−	88275.9i	−0.411794	−	0.411794i	−0.882363	+	0.470569i	$0.844049\pi$
$464$	−91838.1			−0.426567
$465$			314358.i			1.45385i
$466$	−249637.	−	249637.i	−1.14958	−	1.14958i
$467$		−	2610.83i		−	0.0119714i	−0.999982	−	0.00598570i	$-0.998095\pi$
$467$		−	2610.83i		−	0.0119714i	0.999982	−	0.00598570i	$-0.00190532\pi$
$468$		0			0
$469$	88578.0			0.402699
$470$	−144287.	+	144287.i	−0.653177	+	0.653177i
$471$	−352514.			−1.58904
$472$		−	1495.91i		−	0.00671462i
$473$	−35256.4	+	35256.4i	−0.157585	+	0.157585i
$474$	86453.5	−	86453.5i	0.384792	−	0.384792i
$475$	382182.	+	382182.i	1.69388	+	1.69388i
$476$	131687.	+	131687.i	0.581205	+	0.581205i
$477$	−6912.76			−0.0303819
$478$			282037.i			1.23438i
$479$	244175.	+	244175.i	1.06422	+	1.06422i	0.997791	+	0.0664278i	$0.0211602\pi$
$479$	244175.	+	244175.i	1.06422	+	1.06422i	0.0664278	+	0.997791i	$0.478840\pi$
$480$		−	517922.i		−	2.24793i
$481$		0			0
$482$	−9635.48			−0.0414743
$483$	85656.2	−	85656.2i	0.367168	−	0.367168i
$484$	−209584.			−0.894678
$485$		−	307302.i		−	1.30642i
$486$	45111.6	−	45111.6i	0.190992	−	0.190992i
$487$	−219809.	+	219809.i	−0.926805	+	0.926805i	−0.997498	−	0.0706935i	$-0.977479\pi$
$487$	−219809.	+	219809.i	−0.926805	+	0.926805i	0.0706935	+	0.997498i	$0.477479\pi$
$488$	−528.226	−	528.226i	−0.00221809	−	0.00221809i
$489$	1575.94	+	1575.94i	0.00659057	+	0.00659057i
$490$	−35297.6			−0.147012
$491$		−	16431.7i		−	0.0681583i	−0.999419	−	0.0340791i	$-0.989150\pi$
$491$		−	16431.7i		−	0.0681583i	0.999419	−	0.0340791i	$-0.0108498\pi$
$492$	69537.6	+	69537.6i	0.287269	+	0.287269i
$493$		−	88189.5i		−	0.362847i
$494$		0			0
$495$	14137.7			0.0576992
$496$	−154788.	+	154788.i	−0.629177	+	0.629177i
$497$	−142388.			−0.576447
$498$			550485.i			2.21966i
$499$	−165805.	+	165805.i	−0.665883	+	0.665883i	−0.956760	−	0.290877i	$-0.906053\pi$
$499$	−165805.	+	165805.i	−0.665883	+	0.665883i	0.290877	+	0.956760i	$0.406053\pi$
$500$	−228033.	+	228033.i	−0.912131	+	0.912131i
$501$	−263543.	−	263543.i	−1.04997	−	1.04997i
$502$	−183915.	−	183915.i	−0.729809	−	0.729809i
$503$	−305660.			−1.20810			−0.604050	−	0.796946i	$-0.706447\pi$
$503$	−305660.			−1.20810			−0.604050	+	0.796946i	$0.706447\pi$
$504$			1098.61i			0.00432495i
$505$	7233.99	+	7233.99i	0.0283658	+	0.0283658i
$506$			75282.8i			0.294032i
$507$		0			0
$508$	−4268.16			−0.0165392
$509$	98134.2	−	98134.2i	0.378778	−	0.378778i	−0.491883	−	0.870661i	$-0.663691\pi$
$509$	98134.2	−	98134.2i	0.378778	−	0.378778i	0.870661	+	0.491883i	$0.163691\pi$
$510$	480939.			1.84906
$511$			457574.i			1.75234i
$512$	263434.	−	263434.i	1.00492	−	1.00492i
$513$	264948.	−	264948.i	1.00676	−	1.00676i
$514$	52480.8	+	52480.8i	0.198643	+	0.198643i
$515$	−203682.	−	203682.i	−0.767959	−	0.767959i
$516$	−159364.			−0.598538
$517$			38187.1i			0.142868i
$518$	−146170.	−	146170.i	−0.544752	−	0.544752i
$519$			222725.i			0.826865i
$520$		0			0
$521$	−82330.3			−0.303308			−0.151654	−	0.988434i	$-0.548460\pi$
$521$	−82330.3			−0.303308			−0.151654	+	0.988434i	$0.548460\pi$
$522$	11531.3	−	11531.3i	0.0423191	−	0.0423191i
$523$	352506.			1.28873			0.644367	−	0.764717i	$-0.277121\pi$
$523$	352506.			1.28873			0.644367	+	0.764717i	$0.277121\pi$
$524$			314545.i			1.14557i
$525$	314693.	−	314693.i	1.14174	−	1.14174i
$526$	−78189.6	+	78189.6i	−0.282603	+	0.282603i
$527$	−148638.	−	148638.i	−0.535192	−	0.535192i
$528$	−66275.9	−	66275.9i	−0.237732	−	0.237732i
$529$	190939.			0.682312
$530$		−	212397.i		−	0.756130i
$531$	−2708.34	−	2708.34i	−0.00960537	−	0.00960537i
$532$			386959.i			1.36723i
$533$		0			0
$534$	707997.			2.48284
$535$	−43673.9	+	43673.9i	−0.152586	+	0.152586i
$536$	−5613.00			−0.0195373
$537$		−	298753.i		−	1.03601i
$538$	88363.7	−	88363.7i	0.305288	−	0.305288i
$539$	−4670.94	+	4670.94i	−0.0160778	+	0.0160778i
$540$	368110.	+	368110.i	1.26238	+	1.26238i
$541$	−148284.	−	148284.i	−0.506642	−	0.506642i	0.406852	−	0.913494i	$-0.366626\pi$
$541$	−148284.	−	148284.i	−0.506642	−	0.506642i	−0.913494	+	0.406852i	$0.866626\pi$
$542$	−244021.			−0.830671
$543$		−	332060.i		−	1.12620i
$544$	244890.	+	244890.i	0.827509	+	0.827509i
$545$		−	707613.i		−	2.38234i
$546$		0			0
$547$	−103249.			−0.345075			−0.172537	−	0.985003i	$-0.555197\pi$
$547$	−103249.			−0.345075			−0.172537	+	0.985003i	$0.555197\pi$
$548$	382841.	−	382841.i	1.27484	−	1.27484i
$549$	−1912.70			−0.00634604
$550$			276582.i			0.914321i
$551$	129571.	−	129571.i	0.426782	−	0.426782i
$552$	−5427.85	+	5427.85i	−0.0178135	+	0.0178135i
$553$	84017.2	+	84017.2i	0.274737	+	0.274737i
$554$	389426.	+	389426.i	1.26883	+	1.26883i
$555$	−271243.			−0.880587
$556$		−	300892.i		−	0.973333i
$557$	107744.	+	107744.i	0.347281	+	0.347281i	0.859096	−	0.511815i	$-0.171027\pi$
$557$	107744.	+	107744.i	0.347281	+	0.347281i	−0.511815	+	0.859096i	$0.671027\pi$
$558$		−	38870.6i		−	0.124840i
$559$		0			0
$560$	486723.			1.55205
$561$	63642.9	−	63642.9i	0.202220	−	0.202220i
$562$	−403527.			−1.27762
$563$			522914.i			1.64973i	0.565328	+	0.824866i	$0.308750\pi$
$563$			522914.i			1.64973i	−0.565328	+	0.824866i	$0.691250\pi$
$564$	−86305.7	+	86305.7i	−0.271320	+	0.271320i
$565$	266226.	−	266226.i	0.833974	−	0.833974i
$566$	595565.	+	595565.i	1.85907	+	1.85907i
$567$	−197235.	−	197235.i	−0.613506	−	0.613506i
$568$	9022.80			0.0279669
$569$		−	315341.i		−	0.973994i	−0.873404	−	0.486997i	$-0.838092\pi$
$569$		−	315341.i		−	0.973994i	0.873404	−	0.486997i	$-0.161908\pi$
$570$	706615.	+	706615.i	2.17487	+	2.17487i
$571$		−	6380.52i		−	0.0195697i	−0.999952	−	0.00978484i	$-0.996885\pi$
$571$		−	6380.52i		−	0.0195697i	0.999952	−	0.00978484i	$-0.00311466\pi$
$572$		0			0
$573$	−404656.			−1.23247
$574$	−133000.	+	133000.i	−0.403672	+	0.403672i
$575$	−326618.			−0.987880
$576$			33578.9i			0.101210i
$577$	78575.8	−	78575.8i	0.236014	−	0.236014i	−0.579184	−	0.815197i	$-0.696629\pi$
$577$	78575.8	−	78575.8i	0.236014	−	0.236014i	0.815197	+	0.579184i	$0.196629\pi$
$578$	109422.	−	109422.i	0.327528	−	0.327528i
$579$	134596.	+	134596.i	0.401490	+	0.401490i
$580$	180022.	+	180022.i	0.535144	+	0.535144i
$581$	−534972.			−1.58482
$582$		−	361764.i		−	1.06802i
$583$	−28106.6	−	28106.6i	−0.0826933	−	0.0826933i
$584$		−	28995.5i		−	0.0850167i
$585$		0			0
$586$	−56881.7			−0.165645
$587$	−84677.0	+	84677.0i	−0.245748	+	0.245748i	−0.819223	−	0.573475i	$-0.805595\pi$
$587$	−84677.0	+	84677.0i	−0.245748	+	0.245748i	0.573475	+	0.819223i	$0.305595\pi$
$588$	−21113.4			−0.0610665
$589$		−	436770.i		−	1.25899i
$590$	83214.6	−	83214.6i	0.239054	−	0.239054i
$591$	28524.8	−	28524.8i	0.0816672	−	0.0816672i
$592$	−133558.	−	133558.i	−0.381090	−	0.381090i
$593$	−86441.2	−	86441.2i	−0.245817	−	0.245817i	0.573435	−	0.819251i	$-0.305611\pi$
$593$	−86441.2	−	86441.2i	−0.245817	−	0.245817i	−0.819251	+	0.573435i	$0.805611\pi$
$594$	191741.			0.543427
$595$			467386.i			1.32021i
$596$	−124762.	−	124762.i	−0.351228	−	0.351228i
$597$		−	577657.i		−	1.62077i
$598$		0			0
$599$	−256983.			−0.716228			−0.358114	−	0.933678i	$-0.616580\pi$
$599$	−256983.			−0.716228			−0.358114	+	0.933678i	$0.616580\pi$
$600$	−19941.4	+	19941.4i	−0.0553928	+	0.0553928i
$601$	−344146.			−0.952781			−0.476391	−	0.879234i	$-0.658055\pi$
$601$	−344146.			−0.952781			−0.476391	+	0.879234i	$0.658055\pi$
$602$		−	304806.i		−	0.841068i
$603$	−10162.3	+	10162.3i	−0.0279485	+	0.0279485i
$604$	−107390.	+	107390.i	−0.294366	+	0.294366i
$605$	−371929.	−	371929.i	−1.01613	−	1.01613i
$606$	8516.03	+	8516.03i	0.0231895	+	0.0231895i
$607$	−158686.			−0.430688			−0.215344	−	0.976538i	$-0.569087\pi$
$607$	−158686.			−0.430688			−0.215344	+	0.976538i	$0.569087\pi$
$608$			719603.i			1.94664i
$609$	−106691.	−	106691.i	−0.287668	−	0.287668i
$610$		−	58768.4i		−	0.157937i
$611$		0			0
$612$	−30216.2			−0.0806746
$613$	464914.	−	464914.i	1.23723	−	1.23723i	0.276105	−	0.961127i	$-0.410956\pi$
$613$	464914.	−	464914.i	1.23723	−	1.23723i	0.961127	−	0.276105i	$-0.0890438\pi$
$614$	473345.			1.25557
$615$			246804.i			0.652533i
$616$	−4466.81	+	4466.81i	−0.0117716	+	0.0117716i
$617$	−82086.7	+	82086.7i	−0.215627	+	0.215627i	−0.806653	−	0.591026i	$-0.798723\pi$
$617$	−82086.7	+	82086.7i	−0.215627	+	0.215627i	0.591026	+	0.806653i	$0.298723\pi$
$618$	−239779.	−	239779.i	−0.627820	−	0.627820i
$619$	349306.	+	349306.i	0.911644	+	0.911644i	0.996402	−	0.0847577i	$-0.0270116\pi$
$619$	349306.	+	349306.i	0.911644	+	0.911644i	−0.0847577	+	0.996402i	$0.527012\pi$
$620$	606834.			1.57865
$621$			226428.i			0.587147i
$622$	156529.	+	156529.i	0.404589	+	0.404589i
$623$			688046.i			1.77272i
$624$		0			0
$625$	−124696.			−0.319221
$626$	−398149.	+	398149.i	−1.01601	+	1.01601i
$627$	187013.			0.475704
$628$			680490.i			1.72545i
$629$	128252.	−	128252.i	0.324163	−	0.324163i
$630$	−61113.4	+	61113.4i	−0.153977	+	0.153977i
$631$	−29344.9	−	29344.9i	−0.0737011	−	0.0737011i	0.669295	−	0.742996i	$-0.266596\pi$
$631$	−29344.9	−	29344.9i	−0.0737011	−	0.0737011i	−0.742996	+	0.669295i	$0.766596\pi$
$632$	−5323.99	−	5323.99i	−0.0133292	−	0.0133292i
$633$	297832.			0.743301
$634$			399502.i			0.993896i
$635$	−7574.33	−	7574.33i	−0.0187844	−	0.0187844i
$636$		−	127046.i		−	0.314085i
$637$		0			0
$638$	93769.8			0.230368
$639$	16335.7	−	16335.7i	0.0400071	−	0.0400071i
$640$	−63824.2			−0.155821
$641$		−	74714.1i		−	0.181839i	−0.995858	−	0.0909194i	$-0.971019\pi$
$641$		−	74714.1i		−	0.181839i	0.995858	−	0.0909194i	$-0.0289806\pi$
$642$	−51414.1	+	51414.1i	−0.124742	+	0.124742i
$643$	−464484.	+	464484.i	−1.12344	+	1.12344i	−0.132216	+	0.991221i	$0.542209\pi$
$643$	−464484.	+	464484.i	−1.12344	+	1.12344i	−0.991221	+	0.132216i	$0.957791\pi$
$644$	−165350.	−	165350.i	−0.398688	−	0.398688i
$645$	−282810.	−	282810.i	−0.679790	−	0.679790i
$646$	−668219.			−1.60123
$647$			431810.i			1.03153i	0.856729	+	0.515767i	$0.172493\pi$
$647$			431810.i			1.03153i	−0.856729	+	0.515767i	$0.827507\pi$
$648$	12498.4	+	12498.4i	0.0297648	+	0.0297648i
$649$		−	22023.6i		−	0.0522877i
$650$		0			0
$651$	−359641.			−0.848609
$652$	3042.19	−	3042.19i	0.00715635	−	0.00715635i
$653$	−562003.			−1.31799			−0.658995	−	0.752147i	$-0.729018\pi$
$653$	−562003.			−1.31799			−0.658995	+	0.752147i	$0.729018\pi$
$654$		−	833020.i		−	1.94760i
$655$	−558195.	+	558195.i	−1.30108	+	1.30108i
$656$	−121525.	+	121525.i	−0.282395	+	0.282395i
$657$	−52496.2	−	52496.2i	−0.121618	−	0.121618i
$658$	−165072.	−	165072.i	−0.381259	−	0.381259i
$659$	−765929.			−1.76367			−0.881835	−	0.471557i	$-0.843692\pi$
$659$	−765929.			−1.76367			−0.881835	+	0.471557i	$0.843692\pi$
$660$			259830.i			0.596488i
$661$	−158559.	−	158559.i	−0.362900	−	0.362900i	0.501979	−	0.864880i	$-0.332605\pi$
$661$	−158559.	−	158559.i	−0.362900	−	0.362900i	−0.864880	+	0.501979i	$0.832605\pi$
$662$			383524.i			0.875139i
$663$		0			0
$664$	33900.0			0.0768889
$665$	−686702.	+	686702.i	−1.55283	+	1.55283i
$666$	33539.4			0.0756147
$667$			110733.i			0.248901i
$668$	−508742.	+	508742.i	−1.14010	+	1.14010i
$669$	194219.	−	194219.i	0.433950	−	0.433950i
$670$	−312240.	−	312240.i	−0.695568	−	0.695568i
$671$	−7776.84	−	7776.84i	−0.0172726	−	0.0172726i
$672$	592529.			1.31211
$673$		−	532008.i		−	1.17459i	−0.809372	−	0.587297i	$-0.800192\pi$
$673$		−	532008.i		−	1.17459i	0.809372	−	0.587297i	$-0.199808\pi$
$674$	−422771.	−	422771.i	−0.930649	−	0.930649i
$675$			831875.i			1.82579i
$676$		0			0
$677$	538896.			1.17578			0.587892	−	0.808940i	$-0.299958\pi$
$677$	538896.			1.17578			0.587892	+	0.808940i	$0.299958\pi$
$678$	313407.	−	313407.i	0.681789	−	0.681789i
$679$	351569.			0.762556
$680$		−	29617.3i		−	0.0640512i
$681$	−392209.	+	392209.i	−0.845715	+	0.845715i
$682$	158043.	−	158043.i	0.339788	−	0.339788i
$683$	548460.	+	548460.i	1.17572	+	1.17572i	0.980824	+	0.194895i	$0.0624365\pi$
$683$	548460.	+	548460.i	1.17572	+	1.17572i	0.194895	+	0.980824i	$0.437564\pi$
$684$	−44394.8	−	44394.8i	−0.0948899	−	0.0948899i
$685$	1.35879e6			2.89581
$686$		−	690182.i		−	1.46661i
$687$	−463712.	−	463712.i	−0.982506	−	0.982506i
$688$		−	278507.i		−	0.588382i
$689$		0			0
$690$	−603882.			−1.26839
$691$	−468251.	+	468251.i	−0.980670	+	0.980670i	−0.999817	−	0.0191471i	$-0.993905\pi$
$691$	−468251.	+	468251.i	−0.980670	+	0.980670i	0.0191471	+	0.999817i	$0.493905\pi$
$692$	429947.			0.897849
$693$			16174.3i			0.0336790i
$694$	614605.	−	614605.i	1.27608	−	1.27608i
$695$	533967.	−	533967.i	1.10546	−	1.10546i
$696$	6760.75	+	6760.75i	0.0139565	+	0.0139565i
$697$	−116697.	−	116697.i	−0.240211	−	0.240211i
$698$	1.21588e6			2.49562
$699$		−	529975.i		−	1.08468i
$700$	−607482.	−	607482.i	−1.23976	−	1.23976i
$701$			263737.i			0.536705i	0.963321	+	0.268352i	$0.0864791\pi$
$701$			263737.i			0.536705i	−0.963321	+	0.268352i	$0.913521\pi$
$702$		0			0
$703$	376866.			0.762564
$704$	−136528.	+	136528.i	−0.275472	+	0.275472i
$705$	−306318.			−0.616303
$706$		−	1.18018e6i		−	2.36777i
$707$	−8276.05	+	8276.05i	−0.0165571	+	0.0165571i
$708$	49775.1	−	49775.1i	0.0992992	−	0.0992992i
$709$	342335.	+	342335.i	0.681018	+	0.681018i	0.960230	−	0.279212i	$-0.0900732\pi$
$709$	342335.	+	342335.i	0.681018	+	0.681018i	−0.279212	+	0.960230i	$0.590073\pi$
$710$	501921.	+	501921.i	0.995678	+	0.995678i
$711$	−19278.1			−0.0381352
$712$		−	43600.0i		−	0.0860055i
$713$	186635.	+	186635.i	0.367124	+	0.367124i
$714$			550219.i			1.07929i
$715$		0			0
$716$	−576711.			−1.12495
$717$	−299379.	+	299379.i	−0.582348	+	0.582348i
$718$	812681.			1.57642
$719$		−	477053.i		−	0.922802i	−0.887192	−	0.461401i	$-0.847347\pi$
$719$		−	477053.i		−	0.922802i	0.887192	−	0.461401i	$-0.152653\pi$
$720$	−55840.4	+	55840.4i	−0.107717	+	0.107717i
$721$	233022.	−	233022.i	0.448257	−	0.448257i
$722$	−456212.	−	456212.i	−0.875171	−	0.875171i
$723$	−10228.0	−	10228.0i	−0.0195665	−	0.0195665i
$724$	−641007.			−1.22289
$725$			406825.i			0.773982i
$726$	−437845.	−	437845.i	−0.830705	−	0.830705i
$727$		−	1.00958e6i		−	1.91017i	−0.296330	−	0.955086i	$-0.595763\pi$
$727$		−	1.00958e6i		−	1.91017i	0.296330	−	0.955086i	$-0.404237\pi$
$728$		0			0
$729$	571896.			1.07612
$730$	1.61296e6	−	1.61296e6i	3.02676	−	3.02676i
$731$	267443.			0.500491
$732$		−	35152.5i		−	0.0656046i
$733$	438348.	−	438348.i	0.815851	−	0.815851i	−0.169653	−	0.985504i	$-0.554265\pi$
$733$	438348.	−	438348.i	0.815851	−	0.815851i	0.985504	+	0.169653i	$0.0542647\pi$
$734$	−406748.	+	406748.i	−0.754975	+	0.754975i
$735$	−37468.0	−	37468.0i	−0.0693563	−	0.0693563i
$736$	−307491.	−	307491.i	−0.567645	−	0.567645i
$737$	−82637.8			−0.152140
$738$		−	30517.5i		−	0.0560320i
$739$	396206.	+	396206.i	0.725491	+	0.725491i	0.969718	−	0.244227i	$-0.0785342\pi$
$739$	396206.	+	396206.i	0.725491	+	0.725491i	−0.244227	+	0.969718i	$0.578534\pi$
$740$			523606.i			0.956183i
$741$		0			0
$742$	242993.			0.441353
$743$	323825.	−	323825.i	0.586587	−	0.586587i	−0.350118	−	0.936706i	$-0.613859\pi$
$743$	323825.	−	323825.i	0.586587	−	0.586587i	0.936706	+	0.350118i	$0.113859\pi$
$744$	22789.7			0.0411711
$745$		−	442808.i		−	0.797816i
$746$	332067.	−	332067.i	0.596689	−	0.596689i
$747$	61375.9	−	61375.9i	0.109991	−	0.109991i
$748$	−122856.	−	122856.i	−0.219580	−	0.219580i
$749$	−49965.2	−	49965.2i	−0.0890644	−	0.0890644i
$750$	−952774.			−1.69382
$751$		−	833642.i		−	1.47809i	−0.673658	−	0.739043i	$-0.735278\pi$
$751$		−	833642.i		−	1.47809i	0.673658	−	0.739043i	$-0.264722\pi$
$752$	−150829.	−	150829.i	−0.266716	−	0.266716i
$753$		−	390447.i		−	0.688608i
$754$		0			0
$755$	−381149.			−0.668653
$756$	−421137.	+	421137.i	−0.736851	+	0.736851i
$757$	299160.			0.522050			0.261025	−	0.965332i	$-0.415940\pi$
$757$	299160.			0.522050			0.261025	+	0.965332i	$0.415940\pi$
$758$			207002.i			0.360277i
$759$	−79911.9	+	79911.9i	−0.138716	+	0.138716i
$760$	43514.8	−	43514.8i	0.0753373	−	0.0753373i
$761$	−332199.	−	332199.i	−0.573627	−	0.573627i	0.359513	−	0.933140i	$-0.382943\pi$
$761$	−332199.	−	332199.i	−0.573627	−	0.573627i	−0.933140	+	0.359513i	$0.882943\pi$
$762$	−8916.69	−	8916.69i	−0.0153566	−	0.0153566i
$763$	809546.			1.39057
$764$			781146.i			1.33827i
$765$	−53622.0	−	53622.0i	−0.0916263	−	0.0916263i
$766$		−	876674.i		−	1.49410i
$767$		0			0
$768$	522306.			0.885529
$769$	−501329.	+	501329.i	−0.847754	+	0.847754i	−0.989853	−	0.142098i	$-0.954615\pi$
$769$	−501329.	+	501329.i	−0.847754	+	0.847754i	0.142098	+	0.989853i	$0.454615\pi$
$770$	−496961.			−0.838187
$771$			111416.i			0.187429i
$772$	259823.	−	259823.i	0.435957	−	0.435957i
$773$	−266737.	+	266737.i	−0.446400	+	0.446400i	−0.894156	−	0.447756i	$-0.852223\pi$
$773$	−266737.	+	266737.i	−0.446400	+	0.446400i	0.447756	+	0.894156i	$0.352223\pi$
$774$	34969.6	+	34969.6i	0.0583726	+	0.0583726i
$775$	685679.	+	685679.i	1.14161	+	1.14161i
$776$	−22278.2			−0.0369961
$777$		−	310316.i		−	0.513998i
$778$	−63513.2	−	63513.2i	−0.104931	−	0.104931i
$779$		−	342911.i		−	0.565075i
$780$		0			0
$781$	132839.			0.217782
$782$	285534.	−	285534.i	0.466923	−	0.466923i
$783$	282031.			0.460017
$784$		−	36898.0i		−	0.0600303i
$785$	−1.20761e6	+	1.20761e6i	−1.95968	+	1.95968i
$786$	−657121.	+	657121.i	−1.06365	+	1.06365i
$787$	282531.	+	282531.i	0.456159	+	0.456159i	0.897392	−	0.441234i	$-0.145459\pi$
$787$	282531.	+	282531.i	0.456159	+	0.456159i	−0.441234	+	0.897392i	$0.645459\pi$
$788$	−55064.1	−	55064.1i	−0.0886781	−	0.0886781i
$789$	−165995.			−0.266649
$790$		−	592327.i		−	0.949090i
$791$	304576.	+	304576.i	0.486791	+	0.486791i
$792$		−	1024.93i		−	0.00163397i
$793$		0			0
$794$	−1.16520e6			−1.84825
$795$	225457.	−	225457.i	0.356722	−	0.356722i
$796$	−1.11511e6			−1.75991
$797$			577074.i			0.908479i	0.890880	+	0.454240i	$0.150089\pi$
$797$			577074.i			0.908479i	−0.890880	+	0.454240i	$0.849911\pi$
$798$	−808403.	+	808403.i	−1.26947	+	1.26947i
$799$	144837.	−	144837.i	0.226874	−	0.226874i
$800$	−1.12969e6	−	1.12969e6i	−1.76515	−	1.76515i
$801$	−78937.6	−	78937.6i	−0.123032	−	0.123032i
$802$	−671401.			−1.04384
$803$		−	426888.i		−	0.662038i
$804$	−186768.	−	186768.i	−0.288928	−	0.288928i
$805$		−	586865.i		−	0.905620i
$806$		0			0
$807$	187594.			0.288053
$808$	524.435	−	524.435i	0.000803284	−	0.000803284i
$809$	−88438.0			−0.135127			−0.0675635	−	0.997715i	$-0.521523\pi$
$809$	−88438.0			−0.135127			−0.0675635	+	0.997715i	$0.521523\pi$
$810$			1.39052e6i			2.11938i
$811$	342385.	−	342385.i	0.520562	−	0.520562i	−0.397179	−	0.917741i	$-0.630011\pi$
$811$	342385.	−	342385.i	0.520562	−	0.520562i	0.917741	+	0.397179i	$0.130011\pi$
$812$	−205955.	+	205955.i	−0.312363	+	0.312363i
$813$	−259026.	−	259026.i	−0.391889	−	0.391889i
$814$	136367.	+	136367.i	0.205808	+	0.205808i
$815$	10797.4			0.0162556
$816$			502745.i			0.755036i
$817$	392937.	+	392937.i	0.588680	+	0.588680i
$818$		−	346415.i		−	0.517715i
$819$		0			0
$820$	476430.			0.708551
$821$	391227.	−	391227.i	0.580421	−	0.580421i	−0.354598	−	0.935019i	$-0.615382\pi$
$821$	391227.	−	391227.i	0.580421	−	0.580421i	0.935019	+	0.354598i	$0.115382\pi$
$822$	1.59960e6			2.36738
$823$			328220.i			0.484579i	0.970204	+	0.242290i	$0.0778984\pi$
$823$			328220.i			0.484579i	−0.970204	+	0.242290i	$0.922102\pi$
$824$	−14766.1	+	14766.1i	−0.0217476	+	0.0217476i
$825$	−293589.	+	293589.i	−0.431352	+	0.431352i
$826$	95201.8	+	95201.8i	0.139536	+	0.139536i
$827$	440313.	+	440313.i	0.643800	+	0.643800i	0.951487	−	0.307688i	$-0.0995552\pi$
$827$	440313.	+	440313.i	0.643800	+	0.643800i	−0.307688	+	0.951487i	$0.599555\pi$
$828$	37940.4			0.0553402
$829$		−	44855.4i		−	0.0652687i	−0.999467	−	0.0326344i	$-0.989610\pi$
$829$		−	44855.4i		−	0.0652687i	0.999467	−	0.0326344i	$-0.0103897\pi$
$830$	1.88579e6	+	1.88579e6i	2.73740	+	2.73740i
$831$			826743.i			1.19720i
$832$		0			0
$833$	35432.1			0.0510631
$834$	628599.	−	628599.i	0.903736	−	0.903736i
$835$	−1.80564e6			−2.58975
$836$		−	361009.i		−	0.516542i
$837$	475347.	−	475347.i	0.678515	−	0.678515i
$838$	1.31373e6	−	1.31373e6i	1.87076	−	1.87076i
$839$	449717.	+	449717.i	0.638874	+	0.638874i	0.950278	−	0.311404i	$-0.100799\pi$
$839$	449717.	+	449717.i	0.638874	+	0.638874i	−0.311404	+	0.950278i	$0.600799\pi$
$840$	−35830.6	−	35830.6i	−0.0507803	−	0.0507803i
$841$	−569355.			−0.804991
$842$			683647.i			0.964291i
$843$	−428340.	−	428340.i	−0.602745	−	0.602745i
$844$		−	574934.i		−	0.807110i
$845$		0			0
$846$	37876.4			0.0529210
$847$	425506.	−	425506.i	0.593115	−	0.593115i
$848$	222027.			0.308755
$849$			1.26437e6i			1.75412i
$850$	1.04903e6	−	1.04903e6i	1.45194	−	1.45194i
$851$	−161037.	+	161037.i	−0.222365	+	0.222365i
$852$	300226.	+	300226.i	0.413589	+	0.413589i
$853$	467145.	+	467145.i	0.642027	+	0.642027i	0.951053	−	0.309026i	$-0.100003\pi$
$853$	467145.	+	467145.i	0.642027	+	0.642027i	−0.309026	+	0.951053i	$0.600003\pi$
$854$	67234.1			0.0921878
$855$		−	157567.i		−	0.215543i
$856$	3166.19	+	3166.19i	0.00432105	+	0.00432105i
$857$			481160.i			0.655131i	0.944829	+	0.327565i	$0.106228\pi$
$857$			481160.i			0.655131i	−0.944829	+	0.327565i	$0.893772\pi$
$858$		0			0
$859$	480348.			0.650983			0.325491	−	0.945545i	$-0.394470\pi$
$859$	480348.			0.650983			0.325491	+	0.945545i	$0.394470\pi$
$860$	−545934.	+	545934.i	−0.738148	+	0.738148i
$861$	−282357.			−0.380883
$862$		−	1.77661e6i		−	2.39099i
$863$	−415207.	+	415207.i	−0.557497	+	0.557497i	−0.928594	−	0.371097i	$-0.878982\pi$
$863$	−415207.	+	415207.i	−0.557497	+	0.557497i	0.371097	+	0.928594i	$0.378982\pi$
$864$	−783161.	+	783161.i	−1.04912	+	1.04912i
$865$	762989.	+	762989.i	1.01973	+	1.01973i
$866$	−266025.	−	266025.i	−0.354721	−	0.354721i
$867$	232300.			0.309038
$868$			694250.i			0.921460i
$869$	−78382.8	−	78382.8i	−0.103796	−	0.103796i
$870$			752176.i			0.993759i
$871$		0			0
$872$	−51299.2			−0.0674648
$873$	−40334.6	+	40334.6i	−0.0529236	+	0.0529236i
$874$	839036.			1.09839
$875$		−	925925.i		−	1.20937i
$876$	964800.	−	964800.i	1.25727	−	1.25727i
$877$	−39229.5	+	39229.5i	−0.0510051	+	0.0510051i	−0.732149	−	0.681144i	$-0.761483\pi$
$877$	−39229.5	+	39229.5i	−0.0510051	+	0.0510051i	0.681144	+	0.732149i	$0.261483\pi$
$878$	643361.	+	643361.i	0.834576	+	0.834576i
$879$	−60379.3	−	60379.3i	−0.0781467	−	0.0781467i
$880$	−454082.			−0.586367
$881$		−	466304.i		−	0.600783i	−0.953816	−	0.300391i	$-0.902883\pi$
$881$		−	466304.i		−	0.600783i	0.953816	−	0.300391i	$-0.0971173\pi$
$882$	4632.95	+	4632.95i	0.00595552	+	0.00595552i
$883$			280955.i			0.360343i	0.983635	+	0.180171i	$0.0576652\pi$
$883$			280955.i			0.360343i	−0.983635	+	0.180171i	$0.942335\pi$
$884$		0			0
$885$	176663.			0.225558
$886$	−1.50254e6	+	1.50254e6i	−1.91407	+	1.91407i
$887$	−881569.			−1.12049			−0.560246	−	0.828326i	$-0.689293\pi$
$887$	−881569.			−1.12049			−0.560246	+	0.828326i	$0.689293\pi$
$888$			19664.0i			0.0249371i
$889$	8665.42	−	8665.42i	0.0109644	−	0.0109644i
$890$	2.42538e6	−	2.42538e6i	3.06197	−	3.06197i
$891$	184008.	+	184008.i	0.231783	+	0.231783i
$892$	−374919.	−	374919.i	−0.471203	−	0.471203i
$893$	425600.			0.533701
$894$		−	521284.i		−	0.652228i
$895$	−1.02344e6	−	1.02344e6i	−1.27766	−	1.27766i
$896$		−	73018.1i		−	0.0909525i
$897$		0			0
$898$	−418927.			−0.519500
$899$	232466.	−	232466.i	0.287634	−	0.287634i
$900$	139389.			0.172086
$901$			213206.i			0.262634i
$902$	124081.	−	124081.i	0.152508	−	0.152508i
$903$	323549.	−	323549.i	0.396793	−	0.396793i
$904$	−19300.3	−	19300.3i	−0.0236171	−	0.0236171i
$905$	−1.13754e6	−	1.13754e6i	−1.38889	−	1.38889i
$906$	−448699.			−0.546636
$907$			692963.i			0.842356i	0.906978	+	0.421178i	$0.138383\pi$
$907$			692963.i			0.842356i	−0.906978	+	0.421178i	$0.861617\pi$
$908$	757119.	+	757119.i	0.918316	+	0.918316i
$909$		−	1898.98i		−	0.00229822i
$910$		0			0
$911$	−1.13827e6			−1.37154			−0.685769	−	0.727819i	$-0.740534\pi$
$911$	−1.13827e6			−1.37154			−0.685769	+	0.727819i	$0.740534\pi$
$912$	−738653.	+	738653.i	−0.888077	+	0.888077i
$913$	499096.			0.598746
$914$			1.83861e6i			2.20089i
$915$	62382.1	−	62382.1i	0.0745105	−	0.0745105i
$916$	−895147.	+	895147.i	−1.06685	+	1.06685i
$917$	−638603.	−	638603.i	−0.759438	−	0.759438i
$918$	−727238.	−	727238.i	−0.862961	−	0.862961i
$919$	1.25828e6			1.48986			0.744930	−	0.667143i	$-0.232483\pi$
$919$	1.25828e6			1.48986			0.744930	+	0.667143i	$0.232483\pi$
$920$			37188.3i			0.0439371i
$921$	502451.	+	502451.i	0.592345	+	0.592345i
$922$			989392.i			1.16388i
$923$		0			0
$924$	−297259.			−0.348170
$925$	−591636.	+	591636.i	−0.691467	+	0.691467i
$926$	−712002.			−0.830346
$927$			53468.1i			0.0622207i
$928$	−383001.	+	383001.i	−0.444738	+	0.444738i
$929$	271956.	−	271956.i	0.315114	−	0.315114i	−0.531773	−	0.846887i	$-0.678474\pi$
$929$	271956.	−	271956.i	0.315114	−	0.315114i	0.846887	+	0.531773i	$0.178474\pi$
$930$	1.26775e6	+	1.26775e6i	1.46577	+	1.46577i
$931$	52058.2	+	52058.2i	0.0600606	+	0.0600606i
$932$	−1.02306e6			−1.17779
$933$			332308.i			0.381748i
$934$	−10529.0	−	10529.0i	−0.0120696	−	0.0120696i
$935$		−	436042.i		−	0.498776i
$936$		0			0
$937$	−310991.			−0.354216			−0.177108	−	0.984191i	$-0.556674\pi$
$937$	−310991.			−0.354216			−0.177108	+	0.984191i	$0.556674\pi$
$938$	357219.	−	357219.i	0.406003	−	0.406003i
$939$	−845263.			−0.958651
$940$			591315.i			0.669211i
$941$	−685037.	+	685037.i	−0.773633	+	0.773633i	−0.978740	−	0.205107i	$-0.934246\pi$
$941$	−685037.	+	685037.i	−0.773633	+	0.773633i	0.205107	+	0.978740i	$0.434246\pi$
$942$	−1.42162e6	+	1.42162e6i	−1.60207	+	1.60207i
$943$	146528.	+	146528.i	0.164777	+	0.164777i
$944$	86987.6	+	86987.6i	0.0976143	+	0.0976143i
$945$	−1.49471e6			−1.67376
$946$			284365.i			0.317757i
$947$	−700532.	−	700532.i	−0.781139	−	0.781139i	0.198884	−	0.980023i	$-0.436268\pi$
$947$	−700532.	−	700532.i	−0.781139	−	0.781139i	−0.980023	+	0.198884i	$0.936268\pi$
$948$		−	354302.i		−	0.394237i
$949$		0			0
$950$	3.08254e6			3.41556
$951$	−424068.	+	424068.i	−0.468893	+	0.468893i
$952$	33883.7			0.0373866
$953$			981938.i			1.08118i	0.841286	+	0.540590i	$0.181799\pi$
$953$			981938.i			1.08118i	−0.841286	+	0.540590i	$0.818201\pi$
$954$	−27877.9	+	27877.9i	−0.0306312	+	0.0306312i
$955$	−1.38623e6	+	1.38623e6i	−1.51995	+	1.51995i
$956$	577919.	+	577919.i	0.632341	+	0.632341i
$957$	99535.7	+	99535.7i	0.108681	+	0.108681i
$958$	1.96943e6			2.14590
$959$			1.55452e6i			1.69028i
$960$	−1.09516e6	−	1.09516e6i	−1.18833	−	1.18833i
$961$			139905.i			0.151491i
$962$		0			0
$963$	11464.7			0.0123627
$964$	−19744.0	+	19744.0i	−0.0212462	+	0.0212462i
$965$	922171.			0.990277
$966$		−	690872.i		−	0.740361i
$967$	751098.	−	751098.i	0.803237	−	0.803237i	−0.180363	−	0.983600i	$-0.557727\pi$
$967$	751098.	−	751098.i	0.803237	−	0.803237i	0.983600	+	0.180363i	$0.0577273\pi$
$968$	−26963.4	+	26963.4i	−0.0287756	+	0.0287756i
$969$	−709308.	−	709308.i	−0.755418	−	0.755418i
$970$	−1.23929e6	−	1.23929e6i	−1.31714	−	1.31714i
$971$	−373637.			−0.396288			−0.198144	−	0.980173i	$-0.563491\pi$
$971$	−373637.			−0.396288			−0.198144	+	0.980173i	$0.563491\pi$
$972$		−	184876.i		−	0.195680i
$973$	610885.	+	610885.i	0.645259	+	0.645259i
$974$			1.77290e6i			1.86882i
$975$		0			0
$976$	61433.0			0.0644915
$977$	−22942.7	+	22942.7i	−0.0240356	+	0.0240356i	−0.719022	−	0.694987i	$-0.755410\pi$
$977$	−22942.7	+	22942.7i	−0.0240356	+	0.0240356i	0.694987	+	0.719022i	$0.255410\pi$
$978$	12711.0			0.0132893
$979$		−	641904.i		−	0.669737i
$980$	−72328.0	+	72328.0i	−0.0753103	+	0.0753103i
$981$	−92877.0	+	92877.0i	−0.0965095	+	0.0965095i
$982$	−66265.9	−	66265.9i	−0.0687175	−	0.0687175i
$983$	−7991.46	−	7991.46i	−0.00827026	−	0.00827026i	0.702960	−	0.711230i	$-0.251861\pi$
$983$	−7991.46	−	7991.46i	−0.00827026	−	0.00827026i	−0.711230	+	0.702960i	$0.751861\pi$
$984$	17892.3			0.0184789
$985$		−	195435.i		−	0.201432i
$986$	−355652.	−	355652.i	−0.365824	−	0.365824i
$987$		−	350444.i		−	0.359736i
$988$		0			0
$989$	−335809.			−0.343321
$990$	57015.0	−	57015.0i	0.0581726	−	0.0581726i
$991$	1.30914e6			1.33303			0.666515	−	0.745491i	$-0.267785\pi$
$991$	1.30914e6			1.33303			0.666515	+	0.745491i	$0.267785\pi$
$992$			1.29105e6i			1.31196i
$993$	−407107.	+	407107.i	−0.412867	+	0.412867i
$994$	−574223.	+	574223.i	−0.581177	+	0.581177i
$995$	−1.97888e6	−	1.97888e6i	−1.99882	−	1.99882i
$996$	1.12799e6	+	1.12799e6i	1.13707	+	1.13707i
$997$	−624154.			−0.627916			−0.313958	−	0.949437i	$-0.601655\pi$
$997$	−624154.			−0.627916			−0.313958	+	0.949437i	$0.601655\pi$
$998$			1.33733e6i			1.34269i
$999$	410152.	+	410152.i	0.410973	+	0.410973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.5.d.c.70.7		16
13.2	odd	12		13.5.f.a.7.4	yes	16
13.4	even	6		13.5.f.a.2.4	✓	16
13.5	odd	4		169.5.d.d.99.2		16
13.8	odd	4	inner	169.5.d.c.99.7		16
13.12	even	2		169.5.d.d.70.2		16
39.2	even	12		117.5.bd.c.46.1		16
39.17	odd	6		117.5.bd.c.28.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.2.4	✓	16	13.4	even	6
13.5.f.a.7.4	yes	16	13.2	odd	12
117.5.bd.c.28.1		16	39.17	odd	6
117.5.bd.c.46.1		16	39.2	even	12
169.5.d.c.70.7		16	1.1	even	1	trivial
169.5.d.c.99.7		16	13.8	odd	4	inner
169.5.d.d.70.2		16	13.12	even	2
169.5.d.d.99.2		16	13.5	odd	4

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+(4.03282 - 4.03282i) q^{2} +8.56159 q^{3} -16.5272i q^{4} +(29.3294 - 29.3294i) q^{5} +(34.5273 - 34.5273i) q^{6} +(33.5543 + 33.5543i) q^{7} +(-2.12627 - 2.12627i) q^{8} -7.69920 q^{9} -236.560i q^{10} +(-31.3041 - 31.3041i) q^{11} -141.499i q^{12} +270.637 q^{14} +(251.106 - 251.106i) q^{15} +247.286 q^{16} +237.462i q^{17} +(-31.0495 + 31.0495i) q^{18} +(-348.888 + 348.888i) q^{19} +(-484.734 - 484.734i) q^{20} +(287.279 + 287.279i) q^{21} -252.488 q^{22} -298.164i q^{23} +(-18.2042 - 18.2042i) q^{24} -1095.43i q^{25} -759.406 q^{27} +(554.561 - 554.561i) q^{28} -371.384 q^{29} -2025.33i q^{30} +(-625.946 + 625.946i) q^{31} +(1031.28 - 1031.28i) q^{32} +(-268.013 - 268.013i) q^{33} +(957.641 + 957.641i) q^{34} +1968.26 q^{35} +127.247i q^{36} +(-540.096 - 540.096i) q^{37} +2814.01i q^{38} -124.724 q^{40} +(-491.434 + 491.434i) q^{41} +2317.08 q^{42} -1126.26i q^{43} +(-517.371 + 517.371i) q^{44} +(-225.813 + 225.813i) q^{45} +(-1202.44 - 1202.44i) q^{46} +(-609.937 - 609.937i) q^{47} +2117.16 q^{48} -149.212i q^{49} +(-4417.66 - 4417.66i) q^{50} +2033.05i q^{51} +897.855 q^{53} +(-3062.55 + 3062.55i) q^{54} -1836.26 q^{55} -142.691i q^{56} +(-2987.04 + 2987.04i) q^{57} +(-1497.72 + 1497.72i) q^{58} +(351.769 + 351.769i) q^{59} +(-4150.10 - 4150.10i) q^{60} +248.429 q^{61} +5048.65i q^{62} +(-258.342 - 258.342i) q^{63} -4361.35i q^{64} -2161.69 q^{66} +(1319.92 - 1319.92i) q^{67} +3924.59 q^{68} -2552.76i q^{69} +(7937.63 - 7937.63i) q^{70} +(-2121.75 + 2121.75i) q^{71} +(16.3705 + 16.3705i) q^{72} +(6818.40 + 6818.40i) q^{73} -4356.22 q^{74} -9378.61i q^{75} +(5766.16 + 5766.16i) q^{76} -2100.78i q^{77} +2503.91 q^{79} +(7252.76 - 7252.76i) q^{80} -5878.09 q^{81} +3963.73i q^{82} +(-7971.73 + 7971.73i) q^{83} +(4747.92 - 4747.92i) q^{84} +(6964.62 + 6964.62i) q^{85} +(-4541.98 - 4541.98i) q^{86} -3179.64 q^{87} +133.122i q^{88} +(10252.7 + 10252.7i) q^{89} +1821.33i q^{90} -4927.83 q^{92} +(-5359.09 + 5359.09i) q^{93} -4919.53 q^{94} +20465.4i q^{95} +(8829.40 - 8829.40i) q^{96} +(5238.81 - 5238.81i) q^{97} +(-601.744 - 601.744i) q^{98} +(241.017 + 241.017i) 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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