LMFDB - Embedded newform 165.6.c.b.34.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.23
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.57523i q^{2} -9.00000i q^{3} -41.5346 q^{4} +(-51.2624 + 22.2971i) q^{5} +77.1771 q^{6} +178.462i q^{7} -81.7612i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q+8.57523i q^{2} -9.00000i q^{3} -41.5346 q^{4} +(-51.2624 + 22.2971i) q^{5} +77.1771 q^{6} +178.462i q^{7} -81.7612i q^{8} -81.0000 q^{9} +(-191.203 - 439.587i) q^{10} +121.000 q^{11} +373.811i q^{12} +361.980i q^{13} -1530.36 q^{14} +(200.674 + 461.362i) q^{15} -627.985 q^{16} +934.004i q^{17} -694.594i q^{18} -753.929 q^{19} +(2129.16 - 926.102i) q^{20} +1606.16 q^{21} +1037.60i q^{22} -3231.01i q^{23} -735.851 q^{24} +(2130.68 - 2286.01i) q^{25} -3104.06 q^{26} +729.000i q^{27} -7412.36i q^{28} -2606.34 q^{29} +(-3956.29 + 1720.83i) q^{30} +662.215 q^{31} -8001.48i q^{32} -1089.00i q^{33} -8009.30 q^{34} +(-3979.20 - 9148.42i) q^{35} +3364.30 q^{36} -12924.2i q^{37} -6465.11i q^{38} +3257.82 q^{39} +(1823.04 + 4191.28i) q^{40} -2538.56 q^{41} +13773.2i q^{42} -22022.8i q^{43} -5025.68 q^{44} +(4152.26 - 1806.07i) q^{45} +27706.7 q^{46} +20835.4i q^{47} +5651.87i q^{48} -15041.8 q^{49} +(19603.1 + 18271.0i) q^{50} +8406.03 q^{51} -15034.7i q^{52} +27450.5i q^{53} -6251.34 q^{54} +(-6202.76 + 2697.95i) q^{55} +14591.3 q^{56} +6785.36i q^{57} -22350.0i q^{58} -7759.71 q^{59} +(-8334.92 - 19162.5i) q^{60} +38469.2 q^{61} +5678.65i q^{62} -14455.5i q^{63} +48519.0 q^{64} +(-8071.11 - 18556.0i) q^{65} +9338.43 q^{66} +35521.3i q^{67} -38793.4i q^{68} -29079.1 q^{69} +(78449.8 - 34122.5i) q^{70} -62677.1 q^{71} +6622.66i q^{72} -68950.2i q^{73} +110828. q^{74} +(-20574.1 - 19176.1i) q^{75} +31314.1 q^{76} +21594.0i q^{77} +27936.5i q^{78} +17313.8 q^{79} +(32192.1 - 14002.3i) q^{80} +6561.00 q^{81} -21768.7i q^{82} +89017.9i q^{83} -66711.2 q^{84} +(-20825.6 - 47879.3i) q^{85} +188850. q^{86} +23457.1i q^{87} -9893.11i q^{88} -129627. q^{89} +(15487.4 + 35606.6i) q^{90} -64599.8 q^{91} +134199. i q^{92} -5959.94i q^{93} -178668. q^{94} +(38648.2 - 16810.4i) q^{95} -72013.3 q^{96} -136732. i q^{97} -128987. i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			8.57523i			1.51590i	0.652312	+	0.757950i	$0.273799\pi$
$2$			8.57523i			1.51590i	−0.652312	+	0.757950i	$0.726201\pi$
$3$		−	9.00000i		−	0.577350i
$3$		−	9.00000i		−	0.577350i
$4$	−41.5346			−1.29796
$5$	−51.2624	+	22.2971i	−0.917010	+	0.398863i
$5$	−51.2624	+	22.2971i	−0.917010	+	0.398863i
$6$	77.1771			0.875206
$7$			178.462i			1.37658i	0.725435	+	0.688290i	$0.241638\pi$
$7$			178.462i			1.37658i	−0.725435	+	0.688290i	$0.758362\pi$
$8$		−	81.7612i		−	0.451671i
$9$	−81.0000			−0.333333
$10$	−191.203	−	439.587i	−0.604637	−	1.39010i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$			373.811i			0.749375i
$13$			361.980i			0.594054i	0.954869	+	0.297027i	$0.0959951\pi$
$13$			361.980i			0.594054i	−0.954869	+	0.297027i	$0.904005\pi$
$14$	−1530.36			−2.08676
$15$	200.674	+	461.362i	0.230284	+	0.529436i
$16$	−627.985			−0.613267
$17$			934.004i			0.783838i	0.920000	+	0.391919i	$0.128189\pi$
$17$			934.004i			0.783838i	−0.920000	+	0.391919i	$0.871811\pi$
$18$		−	694.594i		−	0.505300i
$19$	−753.929			−0.479122			−0.239561	−	0.970881i	$-0.577004\pi$
$19$	−753.929			−0.479122			−0.239561	+	0.970881i	$0.577004\pi$
$20$	2129.16	−	926.102i	1.19024	−	0.517707i
$21$	1606.16			0.794769
$22$			1037.60i			0.457061i
$23$		−	3231.01i		−	1.27356i	−0.771046	−	0.636780i	$-0.780266\pi$
$23$		−	3231.01i		−	1.27356i	0.771046	−	0.636780i	$-0.219734\pi$
$24$	−735.851			−0.260773
$25$	2130.68	−	2286.01i	0.681816	−	0.731523i
$26$	−3104.06			−0.900527
$27$			729.000i			0.192450i
$28$		−	7412.36i		−	1.78674i
$29$	−2606.34			−0.575488			−0.287744	−	0.957707i	$-0.592905\pi$
$29$	−2606.34			−0.575488			−0.287744	+	0.957707i	$0.592905\pi$
$30$	−3956.29	+	1720.83i	−0.802573	+	0.349087i
$31$	662.215			0.123764			0.0618821	−	0.998083i	$-0.480290\pi$
$31$	662.215			0.123764			0.0618821	+	0.998083i	$0.480290\pi$
$32$		−	8001.48i		−	1.38132i
$33$		−	1089.00i		−	0.174078i
$34$	−8009.30			−1.18822
$35$	−3979.20	−	9148.42i	−0.549067	−	1.26234i
$36$	3364.30			0.432652
$37$		−	12924.2i		−	1.55203i	−0.630717	−	0.776013i	$-0.717239\pi$
$37$		−	12924.2i		−	1.55203i	0.630717	−	0.776013i	$-0.282761\pi$
$38$		−	6465.11i		−	0.726302i
$39$	3257.82			0.342977
$40$	1823.04	+	4191.28i	0.180155	+	0.414187i
$41$	−2538.56			−0.235846			−0.117923	−	0.993023i	$-0.537624\pi$
$41$	−2538.56			−0.235846			−0.117923	+	0.993023i	$0.537624\pi$
$42$			13773.2i			1.20479i
$43$		−	22022.8i		−	1.81636i	−0.418583	−	0.908178i	$-0.637473\pi$
$43$		−	22022.8i		−	1.81636i	0.418583	−	0.908178i	$-0.362527\pi$
$44$	−5025.68			−0.391348
$45$	4152.26	−	1806.07i	0.305670	−	0.132954i
$46$	27706.7			1.93059
$47$			20835.4i			1.37581i	0.725802	+	0.687903i	$0.241469\pi$
$47$			20835.4i			1.37581i	−0.725802	+	0.687903i	$0.758531\pi$
$48$			5651.87i			0.354070i
$49$	−15041.8			−0.894974
$50$	19603.1	+	18271.0i	1.10892	+	1.03357i
$51$	8406.03			0.452549
$52$		−	15034.7i		−	0.771056i
$53$			27450.5i			1.34233i	0.741307	+	0.671166i	$0.234206\pi$
$53$			27450.5i			1.34233i	−0.741307	+	0.671166i	$0.765794\pi$
$54$	−6251.34			−0.291735
$55$	−6202.76	+	2697.95i	−0.276489	+	0.120262i
$56$	14591.3			0.621762
$57$			6785.36i			0.276621i
$58$		−	22350.0i		−	0.872383i
$59$	−7759.71			−0.290212			−0.145106	−	0.989416i	$-0.546352\pi$
$59$	−7759.71			−0.290212			−0.145106	+	0.989416i	$0.546352\pi$
$60$	−8334.92	−	19162.5i	−0.298898	−	0.687185i
$61$	38469.2			1.32370			0.661849	−	0.749638i	$-0.269772\pi$
$61$	38469.2			1.32370			0.661849	+	0.749638i	$0.269772\pi$
$62$			5678.65i			0.187614i
$63$		−	14455.5i		−	0.458860i
$64$	48519.0			1.48068
$65$	−8071.11	−	18556.0i	−0.236946	−	0.544754i
$66$	9338.43			0.263884
$67$			35521.3i			0.966723i	0.875421	+	0.483362i	$0.160584\pi$
$67$			35521.3i			0.966723i	−0.875421	+	0.483362i	$0.839416\pi$
$68$		−	38793.4i		−	1.01739i
$69$	−29079.1			−0.735290
$70$	78449.8	−	34122.5i	1.91358	−	0.832332i
$71$	−62677.1			−1.47558			−0.737790	−	0.675030i	$-0.764131\pi$
$71$	−62677.1			−1.47558			−0.737790	+	0.675030i	$0.764131\pi$
$72$			6622.66i			0.150557i
$73$		−	68950.2i		−	1.51436i	−0.653208	−	0.757179i	$-0.726577\pi$
$73$		−	68950.2i		−	1.51436i	0.653208	−	0.757179i	$-0.273423\pi$
$74$	110828.			2.35272
$75$	−20574.1	−	19176.1i	−0.422345	−	0.393647i
$76$	31314.1			0.621879
$77$			21594.0i			0.415055i
$78$			27936.5i			0.519919i
$79$	17313.8			0.312123			0.156061	−	0.987747i	$-0.450120\pi$
$79$	17313.8			0.312123			0.156061	+	0.987747i	$0.450120\pi$
$80$	32192.1	−	14002.3i	0.562372	−	0.244610i
$81$	6561.00			0.111111
$82$		−	21768.7i		−	0.357518i
$83$			89017.9i			1.41835i	0.705035	+	0.709173i	$0.250931\pi$
$83$			89017.9i			1.41835i	−0.705035	+	0.709173i	$0.749069\pi$
$84$	−66711.2			−1.03158
$85$	−20825.6	−	47879.3i	−0.312644	−	0.718787i
$86$	188850.			2.75342
$87$			23457.1i			0.332258i
$88$		−	9893.11i		−	0.136184i
$89$	−129627.			−1.73468			−0.867341	−	0.497714i	$-0.834173\pi$
$89$	−129627.			−1.73468			−0.867341	+	0.497714i	$0.834173\pi$
$90$	15487.4	+	35606.6i	0.201546	+	0.463366i
$91$	−64599.8			−0.817763
$92$			134199.i			1.65302i
$93$		−	5959.94i		−	0.0714553i
$94$	−178668.			−2.08559
$95$	38648.2	−	16810.4i	0.439360	−	0.191104i
$96$	−72013.3			−0.797507
$97$		−	136732.i		−	1.47551i	−0.675069	−	0.737755i	$-0.735886\pi$
$97$		−	136732.i		−	1.47551i	0.675069	−	0.737755i	$-0.264114\pi$
$98$		−	128987.i		−	1.35669i
$99$	−9801.00			−0.100504
$100$	−88496.7	+	94948.5i	−0.884967	+	0.949485i
$101$	51376.9			0.501146			0.250573	−	0.968098i	$-0.419381\pi$
$101$	51376.9			0.501146			0.250573	+	0.968098i	$0.419381\pi$
$102$			72083.7i			0.686019i
$103$			94899.7i			0.881398i	0.897655	+	0.440699i	$0.145269\pi$
$103$			94899.7i			0.881398i	−0.897655	+	0.440699i	$0.854731\pi$
$104$	29595.9			0.268317
$105$	−82335.8	+	35812.8i	−0.728812	+	0.317004i
$106$	−235394.			−2.03484
$107$		−	52232.6i		−	0.441045i	−0.975382	−	0.220522i	$-0.929224\pi$
$107$		−	52232.6i		−	0.441045i	0.975382	−	0.220522i	$-0.0707762\pi$
$108$		−	30278.7i		−	0.249792i
$109$	−138553.			−1.11699			−0.558496	−	0.829507i	$-0.688622\pi$
$109$	−138553.			−1.11699			−0.558496	+	0.829507i	$0.688622\pi$
$110$	−23135.6	−	53190.1i	−0.182305	−	0.419130i
$111$	−116318.			−0.896063
$112$		−	112072.i		−	0.844211i
$113$			136642.i			1.00667i	0.864091	+	0.503336i	$0.167894\pi$
$113$			136642.i			1.00667i	−0.864091	+	0.503336i	$0.832106\pi$
$114$	−58186.0			−0.419330
$115$	72042.3	+	165630.i	0.507976	+	1.16787i
$116$	108253.			0.746958
$117$		−	29320.4i		−	0.198018i
$118$		−	66541.3i		−	0.439933i
$119$	−166685.			−1.07902
$120$	37721.5	−	16407.4i	0.239131	−	0.104013i
$121$	14641.0			0.0909091
$122$			329882.i			2.00659i
$123$			22847.0i			0.136165i
$124$	−27504.8			−0.160640
$125$	−58252.2	+	164694.i	−0.333455	+	0.942766i
$126$	123959.			0.695587
$127$			23888.8i			0.131427i	0.997839	+	0.0657136i	$0.0209324\pi$
$127$			23888.8i			0.131427i	−0.997839	+	0.0657136i	$0.979068\pi$
$128$			160014.i			0.863244i
$129$	−198205.			−1.04867
$130$	159122.	−	69211.6i	0.825793	−	0.359187i
$131$	67597.5			0.344154			0.172077	−	0.985084i	$-0.444952\pi$
$131$	67597.5			0.344154			0.172077	+	0.985084i	$0.444952\pi$
$132$			45231.2i			0.225945i
$133$		−	134548.i		−	0.659550i
$134$	−304604.			−1.46546
$135$	−16254.6	−	37370.3i	−0.0767613	−	0.176479i
$136$	76365.3			0.354037
$137$		−	205843.i		−	0.936991i	−0.883466	−	0.468496i	$-0.844796\pi$
$137$		−	205843.i		−	0.936991i	0.883466	−	0.468496i	$-0.155204\pi$
$138$		−	249360.i		−	1.11463i
$139$	−43495.6			−0.190945			−0.0954724	−	0.995432i	$-0.530436\pi$
$139$	−43495.6			−0.190945			−0.0954724	+	0.995432i	$0.530436\pi$
$140$	165274.	+	379976.i	0.712665	+	1.63846i
$141$	187519.			0.794323
$142$		−	537470.i		−	2.23683i
$143$			43799.6i			0.179114i
$144$	50866.8			0.204422
$145$	133607.	−	58113.9i	0.527728	−	0.229541i
$146$	591264.			2.29562
$147$			135376.i			0.516713i
$148$			536801.i			2.01446i
$149$	−219355.			−0.809436			−0.404718	−	0.914442i	$-0.632630\pi$
$149$	−219355.			−0.809436			−0.404718	+	0.914442i	$0.632630\pi$
$150$	164439.	−	176428.i	0.596730	−	0.640234i
$151$	−32928.1			−0.117523			−0.0587616	−	0.998272i	$-0.518715\pi$
$151$	−32928.1			−0.117523			−0.0587616	+	0.998272i	$0.518715\pi$
$152$			61642.1i			0.216406i
$153$		−	75654.3i		−	0.261279i
$154$	−185173.			−0.629182
$155$	−33946.8	+	14765.5i	−0.113493	+	0.0493650i
$156$	−135312.			−0.445169
$157$			457292.i			1.48062i	0.672265	+	0.740311i	$0.265322\pi$
$157$			457292.i			1.48062i	−0.672265	+	0.740311i	$0.734678\pi$
$158$			148470.i			0.473147i
$159$	247054.			0.774996
$160$	178410.	+	410175.i	0.550959	+	1.26669i
$161$	576614.			1.75316
$162$			56262.1i			0.168433i
$163$			52822.0i			0.155721i	0.996964	+	0.0778603i	$0.0248088\pi$
$163$			52822.0i			0.155721i	−0.996964	+	0.0778603i	$0.975191\pi$
$164$	105438.			0.306117
$165$	24281.6	+	55824.8i	0.0694332	+	0.159631i
$166$	−763349.			−2.15007
$167$		−	327606.i		−	0.908993i	−0.890748	−	0.454497i	$-0.849819\pi$
$167$		−	327606.i		−	0.908993i	0.890748	−	0.454497i	$-0.150181\pi$
$168$		−	131322.i		−	0.358974i
$169$	240264.			0.647100
$170$	410576.	−	178584.i	1.08961	−	0.473937i
$171$	61068.2			0.159707
$172$			914707.i			2.35755i
$173$		−	246387.i		−	0.625897i	−0.949770	−	0.312949i	$-0.898683\pi$
$173$		−	246387.i		−	0.625897i	0.949770	−	0.312949i	$-0.101317\pi$
$174$	−201150.			−0.503670
$175$	407967.	+	380246.i	1.00700	+	0.938575i
$176$	−75986.2			−0.184907
$177$			69837.4i			0.167554i
$178$		−	1.11158e6i		−	2.62961i
$179$	−302341.			−0.705285			−0.352643	−	0.935758i	$-0.614717\pi$
$179$	−302341.			−0.705285			−0.352643	+	0.935758i	$0.614717\pi$
$180$	−172462.	+	75014.3i	−0.396746	+	0.172569i
$181$	−465374.			−1.05586			−0.527929	−	0.849288i	$-0.677031\pi$
$181$	−465374.			−1.05586			−0.527929	+	0.849288i	$0.677031\pi$
$182$		−	553958.i		−	1.23965i
$183$		−	346223.i		−	0.764237i
$184$	−264172.			−0.575230
$185$	288172.	+	662526.i	0.619046	+	1.42322i
$186$	51107.8			0.108319
$187$			113014.i			0.236336i
$188$		−	865390.i		−	1.78574i
$189$	−130099.			−0.264923
$190$	144153.	+	331417.i	0.289695	+	0.666026i
$191$	294182.			0.583489			0.291745	−	0.956496i	$-0.405764\pi$
$191$	294182.			0.583489			0.291745	+	0.956496i	$0.405764\pi$
$192$		−	436671.i		−	0.854872i
$193$			280529.i			0.542106i	0.962564	+	0.271053i	$0.0873718\pi$
$193$			280529.i			0.542106i	−0.962564	+	0.271053i	$0.912628\pi$
$194$	1.17251e6			2.23673
$195$	−167004.	+	72640.0i	−0.314514	+	0.136801i
$196$	624756.			1.16164
$197$		−	241625.i		−	0.443585i	−0.975094	−	0.221792i	$-0.928809\pi$
$197$		−	241625.i		−	0.443585i	0.975094	−	0.221792i	$-0.0711907\pi$
$198$		−	84045.8i		−	0.152354i
$199$	−621763.			−1.11299			−0.556496	−	0.830850i	$-0.687855\pi$
$199$	−621763.			−1.11299			−0.556496	+	0.830850i	$0.687855\pi$
$200$	−186907.	−	174207.i	−0.330408	−	0.307957i
$201$	319692.			0.558138
$202$			440569.i			0.759688i
$203$		−	465134.i		−	0.792205i
$204$	−349141.			−0.587389
$205$	130133.	−	56602.6i	0.216273	−	0.0940701i
$206$	−813787.			−1.33611
$207$			261712.i			0.424520i
$208$		−	227318.i		−	0.364314i
$209$	−91225.4			−0.144461
$210$	−307103.	−	706048.i	−0.480547	−	1.10481i
$211$	−446582.			−0.690550			−0.345275	−	0.938502i	$-0.612214\pi$
$211$	−446582.			−0.690550			−0.345275	+	0.938502i	$0.612214\pi$
$212$		−	1.14014e6i		−	1.74229i
$213$			564094.i			0.851927i
$214$	447907.			0.668580
$215$	491045.	+	1.12894e6i	0.724478	+	1.66562i
$216$	59603.9			0.0869242
$217$			118181.i			0.170371i
$218$		−	1.18813e6i		−	1.69325i
$219$	−620552.			−0.874314
$220$	257629.	−	112058.i	0.358871	−	0.156094i
$221$	−338090.			−0.465642
$222$		−	997451.i		−	1.35834i
$223$		−	29867.7i		−	0.0402198i	−0.999798	−	0.0201099i	$-0.993598\pi$
$223$		−	29867.7i		−	0.0402198i	0.999798	−	0.0201099i	$-0.00640161\pi$
$224$	1.42796e6			1.90150
$225$	−172585.	+	185167.i	−0.227272	+	0.243841i
$226$	−1.17174e6			−1.52602
$227$			425464.i			0.548022i	0.961726	+	0.274011i	$0.0883505\pi$
$227$			425464.i			0.548022i	−0.961726	+	0.274011i	$0.911649\pi$
$228$		−	281827.i		−	0.359042i
$229$	1.31835e6			1.66127			0.830637	−	0.556814i	$-0.187977\pi$
$229$	1.31835e6			1.66127			0.830637	+	0.556814i	$0.187977\pi$
$230$	−1.42031e6	+	617780.i	−1.77037	+	0.770041i
$231$	194346.			0.239632
$232$			213098.i			0.259931i
$233$			320062.i			0.386228i	0.981176	+	0.193114i	$0.0618588\pi$
$233$			320062.i			0.386228i	−0.981176	+	0.193114i	$0.938141\pi$
$234$	251429.			0.300176
$235$	−464570.	−	1.06807e6i	−0.548759	−	1.26163i
$236$	322296.			0.376683
$237$		−	155825.i		−	0.180204i
$238$		−	1.42936e6i		−	1.63568i
$239$	−1.25534e6			−1.42156			−0.710781	−	0.703414i	$-0.751658\pi$
$239$	−1.25534e6			−1.42156			−0.710781	+	0.703414i	$0.751658\pi$
$240$	−126020.	−	289728.i	−0.141225	−	0.324686i
$241$	−1.07813e6			−1.19572			−0.597859	−	0.801601i	$-0.703982\pi$
$241$	−1.07813e6			−1.19572			−0.597859	+	0.801601i	$0.703982\pi$
$242$			125550.i			0.137809i
$243$		−	59049.0i		−	0.0641500i
$244$	−1.59780e6			−1.71810
$245$	771081.	−	335390.i	0.820700	−	0.356972i
$246$	−195919.			−0.206413
$247$		−	272907.i		−	0.284624i
$248$		−	54143.5i		−	0.0559007i
$249$	801161.			0.818882
$250$	−1.41229e6	−	499526.i	−1.42914	−	0.505485i
$251$	−918775.			−0.920502			−0.460251	−	0.887789i	$-0.652241\pi$
$251$	−918775.			−0.920502			−0.460251	+	0.887789i	$0.652241\pi$
$252$			600401.i			0.595580i
$253$		−	390953.i		−	0.383993i
$254$	−204852.			−0.199231
$255$	−430914.	+	187430.i	−0.414992	+	0.180505i
$256$	180449.			0.172089
$257$			797355.i			0.753041i	0.926408	+	0.376521i	$0.122880\pi$
$257$			797355.i			0.753041i	−0.926408	+	0.376521i	$0.877120\pi$
$258$		−	1.69965e6i		−	1.58969i
$259$	2.30648e6			2.13649
$260$	335230.	+	770714.i	0.307546	+	0.707066i
$261$	211114.			0.191829
$262$			579664.i			0.521703i
$263$			980563.i			0.874150i	0.899425	+	0.437075i	$0.143986\pi$
$263$			980563.i			0.874150i	−0.899425	+	0.437075i	$0.856014\pi$
$264$	−89038.0			−0.0786259
$265$	−612067.	−	1.40718e6i	−0.535407	−	1.23093i
$266$	1.15378e6			0.999813
$267$			1.16664e6i			1.00152i
$268$		−	1.47536e6i		−	1.25476i
$269$	1.32137e6			1.11338			0.556691	−	0.830719i	$-0.312071\pi$
$269$	1.32137e6			1.11338			0.556691	+	0.830719i	$0.312071\pi$
$270$	320459.	−	139387.i	0.267524	−	0.116362i
$271$	−62864.5			−0.0519975			−0.0259987	−	0.999662i	$-0.508277\pi$
$271$	−62864.5			−0.0519975			−0.0259987	+	0.999662i	$0.508277\pi$
$272$		−	586540.i		−	0.480702i
$273$			581398.i			0.472136i
$274$	1.76515e6			1.42039
$275$	257812.	−	276607.i	0.205575	−	0.220563i
$276$	1.20779e6			0.954374
$277$			1.44313e6i			1.13007i	0.825066	+	0.565037i	$0.191138\pi$
$277$			1.44313e6i			1.13007i	−0.825066	+	0.565037i	$0.808862\pi$
$278$		−	372984.i		−	0.289453i
$279$	−53639.4			−0.0412547
$280$	−747986.	+	325344.i	−0.570162	+	0.247998i
$281$	−143939.			−0.108746			−0.0543731	−	0.998521i	$-0.517316\pi$
$281$	−143939.			−0.108746			−0.0543731	+	0.998521i	$0.517316\pi$
$282$			1.60802e6i			1.20411i
$283$			9060.12i			0.00672462i	0.999994	+	0.00336231i	$0.00107026\pi$
$283$			9060.12i			0.00672462i	−0.999994	+	0.00336231i	$0.998930\pi$
$284$	2.60327e6			1.91524
$285$	−151294.	−	347834.i	−0.110334	−	0.253665i
$286$	−375591.			−0.271519
$287$		−	453037.i		−	0.324660i
$288$			648120.i			0.460441i
$289$	547494.			0.385598
$290$	498340.	+	1.14571e6i	0.347961	+	0.799984i
$291$	−1.23059e6			−0.851886
$292$			2.86382e6i			1.96557i
$293$			1.85674e6i			1.26352i	0.775165	+	0.631759i	$0.217667\pi$
$293$			1.85674e6i			1.26352i	−0.775165	+	0.631759i	$0.782333\pi$
$294$	−1.16088e6			−0.783286
$295$	397782.	−	173019.i	0.266128	−	0.115755i
$296$	−1.05670e6			−0.701006
$297$			88209.0i			0.0580259i
$298$		−	1.88102e6i		−	1.22703i
$299$	1.16956e6			0.756563
$300$	854536.	+	796471.i	0.548185	+	0.510936i
$301$	3.93024e6			2.50036
$302$		−	282366.i		−	0.178154i
$303$		−	462392.i		−	0.289337i
$304$	473456.			0.293830
$305$	−1.97203e6	+	857753.i	−1.21384	+	0.527974i
$306$	648753.			0.396074
$307$		−	504688.i		−	0.305617i	−0.988256	−	0.152808i	$-0.951168\pi$
$307$		−	504688.i		−	0.305617i	0.988256	−	0.152808i	$-0.0488318\pi$
$308$		−	896896.i		−	0.538723i
$309$	854097.			0.508875
$310$	−126618.	−	291101.i	−0.0748324	−	0.172044i
$311$	−448511.			−0.262950			−0.131475	−	0.991320i	$-0.541971\pi$
$311$	−448511.			−0.262950			−0.131475	+	0.991320i	$0.541971\pi$
$312$		−	266363.i		−	0.154913i
$313$		−	825146.i		−	0.476069i	−0.971257	−	0.238035i	$-0.923497\pi$
$313$		−	825146.i		−	0.476069i	0.971257	−	0.238035i	$-0.0765031\pi$
$314$	−3.92138e6			−2.24448
$315$	322315.	+	741022.i	0.183022	+	0.420780i
$316$	−719123.			−0.405122
$317$			3.26266e6i			1.82358i	0.410659	+	0.911789i	$0.365299\pi$
$317$			3.26266e6i			1.82358i	−0.410659	+	0.911789i	$0.634701\pi$
$318$			2.11855e6i			1.17482i
$319$	−315367.			−0.173516
$320$	−2.48720e6	+	1.08183e6i	−1.35780	+	0.590589i
$321$	−470094.			−0.254637
$322$			4.94460e6i			2.65761i
$323$		−	704172.i		−	0.375554i
$324$	−272508.			−0.144217
$325$	827490.	+	771262.i	0.434564	+	0.405036i
$326$	−452961.			−0.236057
$327$			1.24698e6i			0.644896i
$328$			207556.i			0.106525i
$329$	−3.71834e6			−1.89391
$330$	−478711.	+	208220.i	−0.241985	+	0.105254i
$331$	−3.48175e6			−1.74674			−0.873369	−	0.487059i	$-0.838070\pi$
$331$	−3.48175e6			−1.74674			−0.873369	+	0.487059i	$0.838070\pi$
$332$		−	3.69732e6i		−	1.84095i
$333$			1.04686e6i			0.517342i
$334$	2.80930e6			1.37794
$335$	−792024.	−	1.82091e6i	−0.385590	−	0.886495i
$336$	−1.00865e6			−0.487406
$337$		−	1.52759e6i		−	0.732710i	−0.930475	−	0.366355i	$-0.880606\pi$
$337$		−	1.52759e6i		−	0.732710i	0.930475	−	0.366355i	$-0.119394\pi$
$338$			2.06032e6i			0.980939i
$339$	1.22978e6			0.581203
$340$	864982.	+	1.98865e6i	0.405798	+	0.932954i
$341$	80128.0			0.0373163
$342$			523674.i			0.242101i
$343$			315017.i			0.144577i
$344$	−1.80061e6			−0.820396
$345$	1.49067e6	−	648381.i	0.674268	−	0.293280i
$346$	2.11283e6			0.948798
$347$		−	4.01479e6i		−	1.78994i	−0.446122	−	0.894972i	$-0.647195\pi$
$347$		−	4.01479e6i		−	1.78994i	0.446122	−	0.894972i	$-0.352805\pi$
$348$		−	974279.i		−	0.431256i
$349$	511478.			0.224783			0.112391	−	0.993664i	$-0.464149\pi$
$349$	511478.			0.224783			0.112391	+	0.993664i	$0.464149\pi$
$350$	−3.26069e6	+	3.49841e6i	−1.42279	+	1.52651i
$351$	−263883.			−0.114326
$352$		−	968179.i		−	0.416485i
$353$			722636.i			0.308662i	0.988019	+	0.154331i	$0.0493221\pi$
$353$			722636.i			0.308662i	−0.988019	+	0.154331i	$0.950678\pi$
$354$	−598872.			−0.253995
$355$	3.21298e6	−	1.39752e6i	1.35312	−	0.588555i
$356$	5.38400e6			2.25154
$357$			1.50016e6i			0.622970i
$358$		−	2.59264e6i		−	1.06914i
$359$	−393345.			−0.161078			−0.0805392	−	0.996751i	$-0.525664\pi$
$359$	−393345.			−0.161078			−0.0805392	+	0.996751i	$0.525664\pi$
$360$	−147666.	−	339494.i	−0.0600517	−	0.138062i
$361$	−1.90769e6			−0.770442
$362$		−	3.99069e6i		−	1.60058i
$363$		−	131769.i		−	0.0524864i
$364$	2.68312e6			1.06142
$365$	1.53739e6	+	3.53455e6i	0.604021	+	1.38868i
$366$	2.96894e6			1.15851
$367$		−	2.87578e6i		−	1.11453i	−0.830336	−	0.557264i	$-0.811851\pi$
$367$		−	2.87578e6i		−	1.11453i	0.830336	−	0.557264i	$-0.188149\pi$
$368$			2.02903e6i			0.781032i
$369$	205623.			0.0786152
$370$	−5.68131e6	+	2.47114e6i	−2.15747	+	0.938413i
$371$	−4.89888e6			−1.84783
$372$			247543.i			0.0927458i
$373$		−	3.86030e6i		−	1.43665i	−0.695710	−	0.718323i	$-0.744910\pi$
$373$		−	3.86030e6i		−	1.43665i	0.695710	−	0.718323i	$-0.255090\pi$
$374$	−969125.			−0.358262
$375$	1.48225e6	+	524270.i	0.544306	+	0.192520i
$376$	1.70353e6			0.621412
$377$		−	943443.i		−	0.341871i
$378$		−	1.11563e6i		−	0.401597i
$379$	1.63355e6			0.584162			0.292081	−	0.956394i	$-0.405652\pi$
$379$	1.63355e6			0.584162			0.292081	+	0.956394i	$0.405652\pi$
$380$	−1.60524e6	+	698215.i	−0.570270	+	0.248045i
$381$	214999.			0.0758795
$382$			2.52268e6i			0.884512i
$383$		−	3.86858e6i		−	1.34758i	−0.738923	−	0.673790i	$-0.764665\pi$
$383$		−	3.86858e6i		−	1.34758i	0.738923	−	0.673790i	$-0.235335\pi$
$384$	1.44013e6			0.498394
$385$	−481483.	−	1.10696e6i	−0.165550	−	0.380609i
$386$	−2.40560e6			−0.821779
$387$			1.78385e6i			0.605452i
$388$			5.67912e6i			1.91515i
$389$	10040.7			0.00336428			0.00168214	−	0.999999i	$-0.499465\pi$
$389$	10040.7			0.00336428			0.00168214	+	0.999999i	$0.499465\pi$
$390$	−622905.	−	1.43210e6i	−0.207377	−	0.476772i
$391$	3.01778e6			0.998264
$392$			1.22984e6i			0.404234i
$393$		−	608378.i		−	0.198697i
$394$	2.07199e6			0.672431
$395$	−887550.	+	386049.i	−0.286220	+	0.124494i
$396$	407080.			0.130449
$397$		−	3.77944e6i		−	1.20352i	−0.798679	−	0.601758i	$-0.794467\pi$
$397$		−	3.77944e6i		−	1.20352i	0.798679	−	0.601758i	$-0.205533\pi$
$398$		−	5.33176e6i		−	1.68719i
$399$	−1.21093e6			−0.380791
$400$	−1.33803e6	+	1.43558e6i	−0.418135	+	0.448619i
$401$	−5.77840e6			−1.79451			−0.897256	−	0.441510i	$-0.854443\pi$
$401$	−5.77840e6			−1.79451			−0.897256	+	0.441510i	$0.854443\pi$
$402$			2.74143e6i			0.846082i
$403$			239708.i			0.0735226i
$404$	−2.13392e6			−0.650465
$405$	−336333.	+	146291.i	−0.101890	+	0.0443181i
$406$	3.98863e6			1.20090
$407$		−	1.56383e6i		−	0.467954i
$408$		−	687287.i		−	0.204403i
$409$	−4.93158e6			−1.45773			−0.728866	−	0.684656i	$-0.759952\pi$
$409$	−4.93158e6			−1.45773			−0.728866	+	0.684656i	$0.759952\pi$
$410$	485380.	+	1.11592e6i	0.142601	+	0.327848i
$411$	−1.85259e6			−0.540972
$412$		−	3.94162e6i		−	1.14401i
$413$		−	1.38482e6i		−	0.399501i
$414$	−2.24424e6			−0.643530
$415$	−1.98484e6	−	4.56327e6i	−0.565726	−	1.30064i
$416$	2.89637e6			0.820580
$417$			391460.i			0.110242i
$418$		−	782278.i		−	0.218988i
$419$	4.38879e6			1.22126			0.610632	−	0.791914i	$-0.290915\pi$
$419$	4.38879e6			1.22126			0.610632	+	0.791914i	$0.290915\pi$
$420$	3.41978e6	−	1.48747e6i	0.945965	−	0.411457i
$421$	−6.32905e6			−1.74034			−0.870169	−	0.492754i	$-0.835990\pi$
$421$	−6.32905e6			−1.74034			−0.870169	+	0.492754i	$0.835990\pi$
$422$		−	3.82954e6i		−	1.04681i
$423$		−	1.68767e6i		−	0.458602i
$424$	2.24438e6			0.606293
$425$	2.13514e6	+	1.99006e6i	0.573396	+	0.534433i
$426$	−4.83723e6			−1.29144
$427$			6.86531e6i			1.82218i
$428$			2.16946e6i			0.572456i
$429$	394196.			0.103412
$430$	−9.68094e6	+	4.21082e6i	−2.52491	+	1.09824i
$431$	−4.39779e6			−1.14036			−0.570179	−	0.821520i	$-0.693126\pi$
$431$	−4.39779e6			−1.14036			−0.570179	+	0.821520i	$0.693126\pi$
$432$		−	457801.i		−	0.118023i
$433$			1.57360e6i			0.403344i	0.979453	+	0.201672i	$0.0646375\pi$
$433$			1.57360e6i			0.403344i	−0.979453	+	0.201672i	$0.935362\pi$
$434$	−1.01343e6			−0.258266
$435$	−523025.	−	1.20247e6i	−0.132526	−	0.304684i
$436$	5.75475e6			1.44981
$437$			2.43595e6i			0.610190i
$438$		−	5.32137e6i		−	1.32537i
$439$	7.89299e6			1.95470			0.977351	−	0.211626i	$-0.0678759\pi$
$439$	7.89299e6			1.95470			0.977351	+	0.211626i	$0.0678759\pi$
$440$	220588.	+	507145.i	0.0543188	+	0.124882i
$441$	1.21839e6			0.298325
$442$		−	2.89920e6i		−	0.705867i
$443$			557226.i			0.134903i	0.997723	+	0.0674516i	$0.0214868\pi$
$443$			557226.i			0.134903i	−0.997723	+	0.0674516i	$0.978513\pi$
$444$	4.83121e6			1.16305
$445$	6.64499e6	−	2.89031e6i	1.59072	−	0.691901i
$446$	256123.			0.0609693
$447$			1.97420e6i			0.467328i
$448$			8.65881e6i			2.03828i
$449$	−2.27558e6			−0.532691			−0.266346	−	0.963878i	$-0.585816\pi$
$449$	−2.27558e6			−0.532691			−0.266346	+	0.963878i	$0.585816\pi$
$450$	−1.58785e6	−	1.47995e6i	−0.369639	−	0.344522i
$451$	−307166.			−0.0711101
$452$		−	5.67537e6i		−	1.30662i
$453$			296352.i			0.0678521i
$454$	−3.64845e6			−0.830748
$455$	3.31154e6	−	1.44039e6i	0.749897	−	0.326176i
$456$	554779.			0.124942
$457$			7.50427e6i			1.68081i	0.541961	+	0.840404i	$0.317682\pi$
$457$			7.50427e6i			1.68081i	−0.541961	+	0.840404i	$0.682318\pi$
$458$			1.13051e7i			2.51833i
$459$	−680889.			−0.150850
$460$	−2.99225e6	−	6.87936e6i	−0.659330	−	1.51584i
$461$	436978.			0.0957652			0.0478826	−	0.998853i	$-0.484753\pi$
$461$	436978.			0.0957652			0.0478826	+	0.998853i	$0.484753\pi$
$462$			1.66656e6i			0.363258i
$463$			3.11651e6i			0.675642i	0.941210	+	0.337821i	$0.109690\pi$
$463$			3.11651e6i			0.675642i	−0.941210	+	0.337821i	$0.890310\pi$
$464$	1.63674e6			0.352928
$465$	132889.	+	305521.i	0.0285009	+	0.0655252i
$466$	−2.74460e6			−0.585484
$467$		−	1.89749e6i		−	0.402613i	−0.979528	−	0.201307i	$-0.935481\pi$
$467$		−	1.89749e6i		−	0.402613i	0.979528	−	0.201307i	$-0.0645187\pi$
$468$			1.21781e6i			0.257019i
$469$	−6.33922e6			−1.33077
$470$	9.15898e6	−	3.98379e6i	1.91251	−	0.831864i
$471$	4.11562e6			0.854837
$472$			634444.i			0.131081i
$473$		−	2.66476e6i		−	0.547652i
$474$	1.33623e6			0.273172
$475$	−1.60638e6	+	1.72349e6i	−0.326673	+	0.350489i
$476$	6.92317e6			1.40051
$477$		−	2.22349e6i		−	0.447444i
$478$		−	1.07648e7i		−	2.15495i
$479$	6.10287e6			1.21533			0.607666	−	0.794193i	$-0.292106\pi$
$479$	6.10287e6			1.21533			0.607666	+	0.794193i	$0.292106\pi$
$480$	3.69158e6	−	1.60569e6i	0.731322	−	0.318096i
$481$	4.67830e6			0.921987
$482$		−	9.24522e6i		−	1.81259i
$483$		−	5.18953e6i		−	1.01219i
$484$	−608108.			−0.117996
$485$	3.04874e6	+	7.00924e6i	0.588527	+	1.35306i
$486$	506359.			0.0972451
$487$		−	7.30170e6i		−	1.39509i	−0.716542	−	0.697544i	$-0.754276\pi$
$487$		−	7.30170e6i		−	1.39509i	0.716542	−	0.697544i	$-0.245724\pi$
$488$		−	3.14529e6i		−	0.597876i
$489$	475398.			0.0899053
$490$	2.87604e6	+	6.61220e6i	0.541134	+	1.24410i
$491$	4.40884e6			0.825317			0.412658	−	0.910886i	$-0.364600\pi$
$491$	4.40884e6			0.825317			0.412658	+	0.910886i	$0.364600\pi$
$492$		−	948942.i		−	0.176737i
$493$		−	2.43433e6i		−	0.451089i
$494$	2.34024e6			0.431462
$495$	502423.	−	218534.i	0.0921630	−	0.0400873i
$496$	−415861.			−0.0759004
$497$		−	1.11855e7i		−	2.03125i
$498$			6.87014e6i			1.24134i
$499$	−3.45620e6			−0.621367			−0.310683	−	0.950513i	$-0.600558\pi$
$499$	−3.45620e6			−0.621367			−0.310683	+	0.950513i	$0.600558\pi$
$500$	2.41948e6	−	6.84051e6i	0.432810	−	1.22367i
$501$	−2.94845e6			−0.524808
$502$		−	7.87871e6i		−	1.39539i
$503$		−	5.07651e6i		−	0.894634i	−0.894375	−	0.447317i	$-0.852380\pi$
$503$		−	5.07651e6i		−	0.894634i	0.894375	−	0.447317i	$-0.147620\pi$
$504$	−1.18190e6			−0.207254
$505$	−2.63370e6	+	1.14556e6i	−0.459556	+	0.199889i
$506$	3.35251e6			0.582095
$507$		−	2.16237e6i		−	0.373603i
$508$		−	992212.i		−	0.170587i
$509$	−7.63894e6			−1.30689			−0.653445	−	0.756974i	$-0.726677\pi$
$509$	−7.63894e6			−1.30689			−0.653445	+	0.756974i	$0.726677\pi$
$510$	−1.60726e6	−	3.69518e6i	−0.273628	−	0.629087i
$511$	1.23050e7			2.08463
$512$			6.66784e6i			1.12411i
$513$		−	549614.i		−	0.0922071i
$514$	−6.83750e6			−1.14154
$515$	−2.11599e6	−	4.86479e6i	−0.351557	−	0.808251i
$516$	8.23237e6			1.36113
$517$			2.52109e6i			0.414821i
$518$			1.97786e7i			3.23871i
$519$	−2.21748e6			−0.361362
$520$	−1.51716e6	+	659904.i	−0.246050	+	0.107022i
$521$	−9.46786e6			−1.52812			−0.764060	−	0.645145i	$-0.776797\pi$
$521$	−9.46786e6			−1.52812			−0.764060	+	0.645145i	$0.776797\pi$
$522$			1.81035e6i			0.290794i
$523$			1.12533e6i			0.179898i	0.995946	+	0.0899490i	$0.0286704\pi$
$523$			1.12533e6i			0.179898i	−0.995946	+	0.0899490i	$0.971330\pi$
$524$	−2.80764e6			−0.446696
$525$	3.42221e6	−	3.67170e6i	0.541887	−	0.581392i
$526$	−8.40855e6			−1.32512
$527$			618511.i			0.0970110i
$528$			683876.i			0.106756i
$529$	−4.00311e6			−0.621953
$530$	1.20669e7	−	5.24861e6i	1.86597	−	0.811624i
$531$	628537.			0.0967374
$532$			5.58839e6i			0.856067i
$533$		−	918907.i		−	0.140105i
$534$	−1.00042e7			−1.51820
$535$	1.16464e6	+	2.67757e6i	0.175916	+	0.404442i
$536$	2.90427e6			0.436641
$537$			2.72107e6i			0.407196i
$538$			1.13311e7i			1.68778i
$539$	−1.82006e6			−0.269845
$540$	675128.	+	1.55216e6i	0.0996327	+	0.229062i
$541$	1.05433e7			1.54876			0.774379	−	0.632722i	$-0.218062\pi$
$541$	1.05433e7			1.54876			0.774379	+	0.632722i	$0.218062\pi$
$542$		−	539078.i		−	0.0788230i
$543$			4.18837e6i			0.609600i
$544$	7.47341e6			1.08273
$545$	7.10258e6	−	3.08934e6i	1.02429	−	0.445527i
$546$	−4.98562e6			−0.715711
$547$			9.65329e6i			1.37945i	0.724070	+	0.689727i	$0.242269\pi$
$547$			9.65329e6i			1.37945i	−0.724070	+	0.689727i	$0.757731\pi$
$548$			8.54962e6i			1.21617i
$549$	−3.11601e6			−0.441232
$550$	2.37197e6	+	2.21080e6i	0.334351	+	0.311632i
$551$	1.96499e6			0.275729
$552$			2.37754e6i			0.332109i
$553$			3.08987e6i			0.429662i
$554$	−1.23752e7			−1.71308
$555$	5.96273e6	−	2.59355e6i	0.821699	−	0.357406i
$556$	1.80657e6			0.247838
$557$			4.21289e6i			0.575363i	0.957726	+	0.287682i	$0.0928845\pi$
$557$			4.21289e6i			0.575363i	−0.957726	+	0.287682i	$0.907115\pi$
$558$		−	459970.i		−	0.0625381i
$559$	7.97180e6			1.07901
$560$	2.49888e6	+	5.74507e6i	0.336725	+	0.774150i
$561$	1.01713e6			0.136449
$562$		−	1.23431e6i		−	0.164848i
$563$		−	9.59902e6i		−	1.27631i	−0.769908	−	0.638155i	$-0.779698\pi$
$563$		−	9.59902e6i		−	1.27631i	0.769908	−	0.638155i	$-0.220302\pi$
$564$	−7.78851e6			−1.03100
$565$	−3.04673e6	−	7.00461e6i	−0.401525	−	0.923129i
$566$	−77692.6			−0.0101939
$567$			1.17089e6i			0.152953i
$568$			5.12455e6i			0.666477i
$569$	−4.20682e6			−0.544720			−0.272360	−	0.962195i	$-0.587804\pi$
$569$	−4.20682e6			−0.544720			−0.272360	+	0.962195i	$0.587804\pi$
$570$	2.98276e6	−	1.29738e6i	0.384530	−	0.167255i
$571$	−1.22447e7			−1.57165			−0.785826	−	0.618447i	$-0.787762\pi$
$571$	−1.22447e7			−1.57165			−0.785826	+	0.618447i	$0.787762\pi$
$572$		−	1.81920e6i		−	0.232482i
$573$		−	2.64764e6i		−	0.336878i
$574$	3.88490e6			0.492153
$575$	−7.38613e6	−	6.88424e6i	−0.931638	−	0.868334i
$576$	−3.93004e6			−0.493561
$577$			5.32012e6i			0.665245i	0.943060	+	0.332623i	$0.107934\pi$
$577$			5.32012e6i			0.665245i	−0.943060	+	0.332623i	$0.892066\pi$
$578$			4.69489e6i			0.584529i
$579$	2.52476e6			0.312985
$580$	−5.54933e6	+	2.41374e6i	−0.684968	+	0.297934i
$581$	−1.58863e7			−1.95247
$582$		−	1.05526e7i		−	1.29137i
$583$			3.32151e6i			0.404728i
$584$	−5.63745e6			−0.683992
$585$	653760.	+	1.50303e6i	0.0789821	+	0.181585i
$586$	−1.59220e7			−1.91537
$587$		−	5.70534e6i		−	0.683418i	−0.939806	−	0.341709i	$-0.888994\pi$
$587$		−	5.70534e6i		−	0.683418i	0.939806	−	0.341709i	$-0.111006\pi$
$588$		−	5.62280e6i		−	0.670671i
$589$	−499263.			−0.0592981
$590$	1.48368e6	+	3.41107e6i	0.175473	+	0.403423i
$591$	−2.17463e6			−0.256104
$592$			8.11620e6i			0.951806i
$593$		−	2.15575e6i		−	0.251746i	−0.992046	−	0.125873i	$-0.959827\pi$
$593$		−	2.15575e6i		−	0.251746i	0.992046	−	0.125873i	$-0.0401731\pi$
$594$	−756413.			−0.0879615
$595$	8.54466e6	−	3.71659e6i	0.989469	−	0.430380i
$596$	9.11083e6			1.05061
$597$			5.59587e6i			0.642587i
$598$			1.00293e7i			1.14687i
$599$	−5.13968e6			−0.585287			−0.292643	−	0.956222i	$-0.594535\pi$
$599$	−5.13968e6			−0.585287			−0.292643	+	0.956222i	$0.594535\pi$
$600$	−1.56786e6	+	1.68216e6i	−0.177799	+	0.190761i
$601$	−7.48666e6			−0.845478			−0.422739	−	0.906252i	$-0.638931\pi$
$601$	−7.48666e6			−0.845478			−0.422739	+	0.906252i	$0.638931\pi$
$602$			3.37027e7i			3.79030i
$603$		−	2.87723e6i		−	0.322241i
$604$	1.36765e6			0.152540
$605$	−750533.	+	326452.i	−0.0833646	+	0.0362603i
$606$	3.96512e6			0.438606
$607$		−	8.62794e6i		−	0.950464i	−0.879861	−	0.475232i	$-0.842364\pi$
$607$		−	8.62794e6i		−	0.950464i	0.879861	−	0.475232i	$-0.157636\pi$
$608$			6.03254e6i			0.661822i
$609$	−4.18620e6			−0.457380
$610$	−7.35543e6	−	1.69106e7i	−0.800356	−	1.84007i
$611$	−7.54200e6			−0.817304
$612$			3.14227e6i			0.339129i
$613$			1.44646e7i			1.55473i	0.629047	+	0.777367i	$0.283445\pi$
$613$			1.44646e7i			1.55473i	−0.629047	+	0.777367i	$0.716555\pi$
$614$	4.32782e6			0.463285
$615$	−509423.	−	1.17119e6i	−0.0543114	−	0.124865i
$616$	1.76555e6			0.187468
$617$			5.82746e6i			0.616264i	0.951344	+	0.308132i	$0.0997038\pi$
$617$			5.82746e6i			0.616264i	−0.951344	+	0.308132i	$0.900296\pi$
$618$			7.32408e6i			0.771404i
$619$	2.32647e6			0.244045			0.122023	−	0.992527i	$-0.461062\pi$
$619$	2.32647e6			0.244045			0.122023	+	0.992527i	$0.461062\pi$
$620$	1.40996e6	−	613279.i	0.147309	−	0.0640735i
$621$	2.35541e6			0.245097
$622$		−	3.84609e6i		−	0.398605i
$623$		−	2.31335e7i		−	2.38793i
$624$	−2.04586e6			−0.210337
$625$	−686064.	−	9.74150e6i	−0.0702529	−	0.997529i
$626$	7.07582e6			0.721674
$627$			821028.i			0.0834044i
$628$		−	1.89934e7i		−	1.92178i
$629$	1.20712e7			1.21654
$630$	−6.35443e6	+	2.76393e6i	−0.637860	+	0.277444i
$631$	−398154.			−0.0398087			−0.0199043	−	0.999802i	$-0.506336\pi$
$631$	−398154.			−0.0398087			−0.0199043	+	0.999802i	$0.506336\pi$
$632$		−	1.41560e6i		−	0.140977i
$633$			4.01924e6i			0.398689i
$634$	−2.79781e7			−2.76436
$635$	−532652.	−	1.22460e6i	−0.0524215	−	0.120520i
$636$	−1.02613e7			−1.00591
$637$		−	5.44484e6i		−	0.531663i
$638$		−	2.70435e6i		−	0.263033i
$639$	5.07684e6			0.491860
$640$	−3.56786e6	−	8.20272e6i	−0.344316	−	0.791604i
$641$	1.81586e7			1.74557			0.872784	−	0.488107i	$-0.162312\pi$
$641$	1.81586e7			1.74557			0.872784	+	0.488107i	$0.162312\pi$
$642$		−	4.03116e6i		−	0.386005i
$643$			4.48264e6i			0.427569i	0.976881	+	0.213784i	$0.0685790\pi$
$643$			4.48264e6i			0.427569i	−0.976881	+	0.213784i	$0.931421\pi$
$644$	−2.39494e7			−2.27552
$645$	1.01605e7	−	4.41940e6i	0.961645	−	0.418277i
$646$	6.03844e6			0.569303
$647$			1.75122e7i			1.64467i	0.569003	+	0.822336i	$0.307329\pi$
$647$			1.75122e7i			1.64467i	−0.569003	+	0.822336i	$0.692671\pi$
$648$		−	536435.i		−	0.0501857i
$649$	−938925.			−0.0875023
$650$	−6.61375e6	+	7.09591e6i	−0.613994	+	0.658757i
$651$	1.06362e6			0.0983639
$652$		−	2.19394e6i		−	0.202118i
$653$			1.89639e7i			1.74039i	0.492711	+	0.870193i	$0.336006\pi$
$653$			1.89639e7i			1.74039i	−0.492711	+	0.870193i	$0.663994\pi$
$654$	−1.06931e7			−0.977599
$655$	−3.46521e6	+	1.50723e6i	−0.315593	+	0.137270i
$656$	1.59418e6			0.144636
$657$			5.58496e6i			0.504786i
$658$		−	3.18856e7i		−	2.87098i
$659$	−23732.7			−0.00212879			−0.00106440	−	0.999999i	$-0.500339\pi$
$659$	−23732.7			−0.00212879			−0.00106440	+	0.999999i	$0.500339\pi$
$660$	−1.00852e6	−	2.31866e6i	−0.0901212	−	0.207194i
$661$	1.09938e7			0.978686			0.489343	−	0.872091i	$-0.337237\pi$
$661$	1.09938e7			0.978686			0.489343	+	0.872091i	$0.337237\pi$
$662$		−	2.98568e7i		−	2.64788i
$663$			3.04281e6i			0.268839i
$664$	7.27821e6			0.640626
$665$	3.00003e6	+	6.89725e6i	0.263070	+	0.604814i
$666$	−8.97706e6			−0.784239
$667$			8.42112e6i			0.732918i
$668$			1.36070e7i			1.17983i
$669$	−268810.			−0.0232209
$670$	1.56147e7	−	6.79179e6i	1.34384	−	0.584517i
$671$	4.65477e6			0.399110
$672$		−	1.28517e7i		−	1.09783i
$673$		−	1.19040e6i		−	0.101310i	−0.998716	−	0.0506552i	$-0.983869\pi$
$673$		−	1.19040e6i		−	0.101310i	0.998716	−	0.0506552i	$-0.0161310\pi$
$674$	1.30994e7			1.11072
$675$	1.66650e6	+	1.55326e6i	0.140782	+	0.131216i
$676$	−9.97925e6			−0.839907
$677$		−	2.03890e7i		−	1.70972i	−0.518859	−	0.854860i	$-0.673643\pi$
$677$		−	2.03890e7i		−	1.70972i	0.518859	−	0.854860i	$-0.326357\pi$
$678$			1.05456e7i			0.881046i
$679$	2.44016e7			2.03116
$680$	−3.91467e6	+	1.70273e6i	−0.324656	+	0.141212i
$681$	3.82918e6			0.316401
$682$			687116.i			0.0565678i
$683$			2.37020e7i			1.94416i	0.234640	+	0.972082i	$0.424609\pi$
$683$			2.37020e7i			1.94416i	−0.234640	+	0.972082i	$0.575391\pi$
$684$	−2.53644e6			−0.207293
$685$	4.58972e6	+	1.05520e7i	0.373731	+	0.859231i
$686$	−2.70134e6			−0.219164
$687$		−	1.18651e7i		−	0.959137i
$688$			1.38300e7i			1.11391i
$689$	−9.93651e6			−0.797418
$690$	5.56002e6	+	1.27828e7i	0.444583	+	1.02212i
$691$	−1.32012e7			−1.05176			−0.525881	−	0.850558i	$-0.676264\pi$
$691$	−1.32012e7			−1.05176			−0.525881	+	0.850558i	$0.676264\pi$
$692$			1.02336e7i			0.812387i
$693$		−	1.74911e6i		−	0.138352i
$694$	3.44278e7			2.71338
$695$	2.22969e6	−	969826.i	0.175098	−	0.0761608i
$696$	1.91788e6			0.150071
$697$		−	2.37102e6i		−	0.184865i
$698$			4.38604e6i			0.340749i
$699$	2.88056e6			0.222989
$700$	−1.69447e7	−	1.57933e7i	−1.30704	−	1.21823i
$701$	9.76550e6			0.750584			0.375292	−	0.926907i	$-0.377542\pi$
$701$	9.76550e6			0.750584			0.375292	+	0.926907i	$0.377542\pi$
$702$		−	2.26286e6i		−	0.173306i
$703$			9.74392e6i			0.743610i
$704$	5.87080e6			0.446442
$705$	−9.61267e6	+	4.18113e6i	−0.728402	+	0.316826i
$706$	−6.19677e6			−0.467900
$707$			9.16884e6i			0.689868i
$708$		−	2.90067e6i		−	0.217478i
$709$	6.77780e6			0.506376			0.253188	−	0.967417i	$-0.418521\pi$
$709$	6.77780e6			0.506376			0.253188	+	0.967417i	$0.418521\pi$
$710$	1.19840e7	+	2.75520e7i	0.892190	+	2.05120i
$711$	−1.40242e6			−0.104041
$712$			1.05985e7i			0.783506i
$713$		−	2.13963e6i		−	0.157621i
$714$	−1.28642e7			−0.944361
$715$	−976604.	−	2.24527e6i	−0.0714420	−	0.164249i
$716$	1.25576e7			0.915429
$717$			1.12980e7i			0.820739i
$718$		−	3.37302e6i		−	0.244179i
$719$	9.77686e6			0.705305			0.352653	−	0.935754i	$-0.385280\pi$
$719$	9.77686e6			0.705305			0.352653	+	0.935754i	$0.385280\pi$
$720$	−2.60756e6	+	1.13418e6i	−0.187457	+	0.0815365i
$721$	−1.69360e7			−1.21331
$722$		−	1.63589e7i		−	1.16791i
$723$			9.70317e6i			0.690348i
$724$	1.93291e7			1.37046
$725$	−5.55327e6	+	5.95812e6i	−0.392377	+	0.420983i
$726$	1.12995e6			0.0795642
$727$		−	1.13969e7i		−	0.799745i	−0.916571	−	0.399873i	$-0.869054\pi$
$727$		−	1.13969e7i		−	0.799745i	0.916571	−	0.399873i	$-0.130946\pi$
$728$			5.28176e6i			0.369360i
$729$	−531441.			−0.0370370
$730$	−3.03096e7	+	1.31835e7i	−2.10510	+	0.915636i
$731$	2.05694e7			1.42373
$732$			1.43802e7i			0.991946i
$733$			6.58492e6i			0.452679i	0.974048	+	0.226340i	$0.0726759\pi$
$733$			6.58492e6i			0.452679i	−0.974048	+	0.226340i	$0.927324\pi$
$734$	2.46605e7			1.68951
$735$	−3.01851e6	−	6.93973e6i	−0.206098	−	0.473832i
$736$	−2.58529e7			−1.75920
$737$			4.29808e6i			0.291478i
$738$			1.76327e6i			0.119173i
$739$	1.51924e7			1.02333			0.511664	−	0.859186i	$-0.329029\pi$
$739$	1.51924e7			1.02333			0.511664	+	0.859186i	$0.329029\pi$
$740$	−1.19691e7	−	2.75177e7i	−0.803494	−	1.84728i
$741$	−2.45616e6			−0.164328
$742$		−	4.20090e7i		−	2.80112i
$743$			6.92543e6i			0.460230i	0.973163	+	0.230115i	$0.0739102\pi$
$743$			6.92543e6i			0.460230i	−0.973163	+	0.230115i	$0.926090\pi$
$744$	−487292.			−0.0322743
$745$	1.12447e7	−	4.89100e6i	0.742261	−	0.322854i
$746$	3.31030e7			2.17781
$747$		−	7.21045e6i		−	0.472782i
$748$		−	4.69401e6i		−	0.306754i
$749$	9.32156e6			0.607133
$750$	−4.49573e6	+	1.27106e7i	−0.291842	+	0.825114i
$751$	−1.53073e7			−0.990370			−0.495185	−	0.868788i	$-0.664900\pi$
$751$	−1.53073e7			−0.990370			−0.495185	+	0.868788i	$0.664900\pi$
$752$		−	1.30843e7i		−	0.843737i
$753$			8.26898e6i			0.531452i
$754$	8.09024e6			0.518242
$755$	1.68797e6	−	734201.i	0.107770	−	0.0468757i
$756$	5.40361e6			0.343858
$757$			9.00842e6i			0.571359i	0.958325	+	0.285679i	$0.0922193\pi$
$757$			9.00842e6i			0.571359i	−0.958325	+	0.285679i	$0.907781\pi$
$758$			1.40080e7i			0.885531i
$759$	−3.51857e6			−0.221698
$760$	−1.37444e6	−	3.15993e6i	−0.0863162	−	0.198446i
$761$	1.62103e7			1.01468			0.507339	−	0.861746i	$-0.330629\pi$
$761$	1.62103e7			1.01468			0.507339	+	0.861746i	$0.330629\pi$
$762$			1.84367e6i			0.115026i
$763$		−	2.47265e7i		−	1.53763i
$764$	−1.22187e7			−0.757343
$765$	1.68687e6	+	3.87822e6i	0.104215	+	0.239596i
$766$	3.31740e7			2.04280
$767$		−	2.80886e6i		−	0.172402i
$768$		−	1.62404e6i		−	0.0993558i
$769$	−1.67909e7			−1.02390			−0.511950	−	0.859015i	$-0.671077\pi$
$769$	−1.67909e7			−1.02390			−0.511950	+	0.859015i	$0.671077\pi$
$770$	9.49243e6	−	4.12883e6i	0.576966	−	0.250957i
$771$	7.17619e6			0.434768
$772$		−	1.16516e7i		−	0.703629i
$773$		−	1.62605e7i		−	0.978780i	−0.872065	−	0.489390i	$-0.837219\pi$
$773$		−	1.62605e7i		−	0.978780i	0.872065	−	0.489390i	$-0.162781\pi$
$774$	−1.52969e7			−0.917806
$775$	1.41097e6	−	1.51383e6i	0.0843844	−	0.0905364i
$776$	−1.11794e7			−0.666445

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+8.57523i q^{2} -9.00000i q^{3} -41.5346 q^{4} +(-51.2624 + 22.2971i) q^{5} +77.1771 q^{6} +178.462i q^{7} -81.7612i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q+8.57523i q^{2} -9.00000i q^{3} -41.5346 q^{4} +(-51.2624 + 22.2971i) q^{5} +77.1771 q^{6} +178.462i q^{7} -81.7612i q^{8} -81.0000 q^{9} +(-191.203 - 439.587i) q^{10} +121.000 q^{11} +373.811i q^{12} +361.980i q^{13} -1530.36 q^{14} +(200.674 + 461.362i) q^{15} -627.985 q^{16} +934.004i q^{17} -694.594i q^{18} -753.929 q^{19} +(2129.16 - 926.102i) q^{20} +1606.16 q^{21} +1037.60i q^{22} -3231.01i q^{23} -735.851 q^{24} +(2130.68 - 2286.01i) q^{25} -3104.06 q^{26} +729.000i q^{27} -7412.36i q^{28} -2606.34 q^{29} +(-3956.29 + 1720.83i) q^{30} +662.215 q^{31} -8001.48i q^{32} -1089.00i q^{33} -8009.30 q^{34} +(-3979.20 - 9148.42i) q^{35} +3364.30 q^{36} -12924.2i q^{37} -6465.11i q^{38} +3257.82 q^{39} +(1823.04 + 4191.28i) q^{40} -2538.56 q^{41} +13773.2i q^{42} -22022.8i q^{43} -5025.68 q^{44} +(4152.26 - 1806.07i) q^{45} +27706.7 q^{46} +20835.4i q^{47} +5651.87i q^{48} -15041.8 q^{49} +(19603.1 + 18271.0i) q^{50} +8406.03 q^{51} -15034.7i q^{52} +27450.5i q^{53} -6251.34 q^{54} +(-6202.76 + 2697.95i) q^{55} +14591.3 q^{56} +6785.36i q^{57} -22350.0i q^{58} -7759.71 q^{59} +(-8334.92 - 19162.5i) q^{60} +38469.2 q^{61} +5678.65i q^{62} -14455.5i q^{63} +48519.0 q^{64} +(-8071.11 - 18556.0i) q^{65} +9338.43 q^{66} +35521.3i q^{67} -38793.4i q^{68} -29079.1 q^{69} +(78449.8 - 34122.5i) q^{70} -62677.1 q^{71} +6622.66i q^{72} -68950.2i q^{73} +110828. q^{74} +(-20574.1 - 19176.1i) q^{75} +31314.1 q^{76} +21594.0i q^{77} +27936.5i q^{78} +17313.8 q^{79} +(32192.1 - 14002.3i) q^{80} +6561.00 q^{81} -21768.7i q^{82} +89017.9i q^{83} -66711.2 q^{84} +(-20825.6 - 47879.3i) q^{85} +188850. q^{86} +23457.1i q^{87} -9893.11i q^{88} -129627. q^{89} +(15487.4 + 35606.6i) q^{90} -64599.8 q^{91} +134199. i q^{92} -5959.94i q^{93} -178668. q^{94} +(38648.2 - 16810.4i) q^{95} -72013.3 q^{96} -136732. i q^{97} -128987. i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Introduction

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