LMFDB - Embedded newform 2009.4.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,4,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2009.a (trivial)

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:	yes
Analytic conductor:	$118.534837202$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.18542 q^{2} -5.95392 q^{3} +18.8886 q^{4} +18.5974 q^{5} +30.8736 q^{6} -56.4620 q^{8} +8.44915 q^{9} +O(q^{10})$	\(q-5.18542 q^{2} -5.95392 q^{3} +18.8886 q^{4} +18.5974 q^{5} +30.8736 q^{6} -56.4620 q^{8} +8.44915 q^{9} -96.4352 q^{10} -4.03513 q^{11} -112.461 q^{12} -3.74460 q^{13} -110.727 q^{15} +141.670 q^{16} -31.7720 q^{17} -43.8124 q^{18} -128.465 q^{19} +351.278 q^{20} +20.9238 q^{22} -83.0637 q^{23} +336.170 q^{24} +220.862 q^{25} +19.4173 q^{26} +110.450 q^{27} +101.320 q^{29} +574.167 q^{30} -19.6339 q^{31} -282.925 q^{32} +24.0248 q^{33} +164.751 q^{34} +159.593 q^{36} +408.911 q^{37} +666.146 q^{38} +22.2951 q^{39} -1050.04 q^{40} +41.0000 q^{41} -86.2241 q^{43} -76.2179 q^{44} +157.132 q^{45} +430.720 q^{46} +389.553 q^{47} -843.493 q^{48} -1145.26 q^{50} +189.168 q^{51} -70.7303 q^{52} -568.450 q^{53} -572.731 q^{54} -75.0427 q^{55} +764.871 q^{57} -525.389 q^{58} -253.788 q^{59} -2091.48 q^{60} +483.847 q^{61} +101.810 q^{62} +333.721 q^{64} -69.6397 q^{65} -124.579 q^{66} -751.280 q^{67} -600.129 q^{68} +494.554 q^{69} -287.176 q^{71} -477.055 q^{72} +508.841 q^{73} -2120.38 q^{74} -1315.00 q^{75} -2426.53 q^{76} -115.609 q^{78} +265.771 q^{79} +2634.69 q^{80} -885.739 q^{81} -212.602 q^{82} +847.241 q^{83} -590.876 q^{85} +447.108 q^{86} -603.254 q^{87} +227.831 q^{88} +962.744 q^{89} -814.795 q^{90} -1568.96 q^{92} +116.899 q^{93} -2020.00 q^{94} -2389.11 q^{95} +1684.51 q^{96} -408.253 q^{97} -34.0934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 2 q^{2} - 24 q^{3} + 230 q^{4} - 40 q^{5} - 72 q^{6} - 18 q^{8} + 572 q^{9}+O(q^{10}) $ 60 * q + 2 * q^2 - 24 * q^3 + 230 * q^4 - 40 * q^5 - 72 * q^6 - 18 * q^8 + 572 * q^9	\( 60 q + 2 q^{2} - 24 q^{3} + 230 q^{4} - 40 q^{5} - 72 q^{6} - 18 q^{8} + 572 q^{9} - 160 q^{10} - 100 q^{11} - 646 q^{12} - 156 q^{13} + 64 q^{15} + 1294 q^{16} - 136 q^{17} + 106 q^{18} - 848 q^{19} - 480 q^{20} - 236 q^{22} - 268 q^{23} - 864 q^{24} + 1500 q^{25} - 1150 q^{26} - 864 q^{27} - 276 q^{29} + 20 q^{30} - 2480 q^{31} + 18 q^{32} - 752 q^{33} - 1632 q^{34} + 2638 q^{36} + 152 q^{37} - 456 q^{38} - 448 q^{39} - 1972 q^{40} + 2460 q^{41} - 380 q^{43} - 560 q^{44} - 1800 q^{45} - 136 q^{46} - 1668 q^{47} - 5360 q^{48} - 430 q^{50} - 680 q^{51} - 1872 q^{52} - 1012 q^{53} - 1318 q^{54} - 6144 q^{55} + 1112 q^{57} - 596 q^{58} - 1888 q^{59} + 2284 q^{60} - 3176 q^{61} - 3440 q^{62} + 7210 q^{64} - 664 q^{65} - 2112 q^{66} + 660 q^{67} + 312 q^{68} - 7528 q^{69} - 2168 q^{71} - 1004 q^{72} - 3504 q^{73} + 286 q^{74} - 3112 q^{75} - 9008 q^{76} + 570 q^{78} + 1872 q^{79} - 4480 q^{80} + 3796 q^{81} + 82 q^{82} - 4600 q^{83} + 72 q^{85} - 816 q^{86} - 3480 q^{87} - 4884 q^{88} - 2600 q^{89} - 4320 q^{90} - 2810 q^{92} + 3376 q^{93} - 7610 q^{94} - 5672 q^{95} - 7294 q^{96} - 8648 q^{97} - 7620 q^{99}+O(q^{100}) \) 60 * q + 2 * q^2 - 24 * q^3 + 230 * q^4 - 40 * q^5 - 72 * q^6 - 18 * q^8 + 572 * q^9 - 160 * q^10 - 100 * q^11 - 646 * q^12 - 156 * q^13 + 64 * q^15 + 1294 * q^16 - 136 * q^17 + 106 * q^18 - 848 * q^19 - 480 * q^20 - 236 * q^22 - 268 * q^23 - 864 * q^24 + 1500 * q^25 - 1150 * q^26 - 864 * q^27 - 276 * q^29 + 20 * q^30 - 2480 * q^31 + 18 * q^32 - 752 * q^33 - 1632 * q^34 + 2638 * q^36 + 152 * q^37 - 456 * q^38 - 448 * q^39 - 1972 * q^40 + 2460 * q^41 - 380 * q^43 - 560 * q^44 - 1800 * q^45 - 136 * q^46 - 1668 * q^47 - 5360 * q^48 - 430 * q^50 - 680 * q^51 - 1872 * q^52 - 1012 * q^53 - 1318 * q^54 - 6144 * q^55 + 1112 * q^57 - 596 * q^58 - 1888 * q^59 + 2284 * q^60 - 3176 * q^61 - 3440 * q^62 + 7210 * q^64 - 664 * q^65 - 2112 * q^66 + 660 * q^67 + 312 * q^68 - 7528 * q^69 - 2168 * q^71 - 1004 * q^72 - 3504 * q^73 + 286 * q^74 - 3112 * q^75 - 9008 * q^76 + 570 * q^78 + 1872 * q^79 - 4480 * q^80 + 3796 * q^81 + 82 * q^82 - 4600 * q^83 + 72 * q^85 - 816 * q^86 - 3480 * q^87 - 4884 * q^88 - 2600 * q^89 - 4320 * q^90 - 2810 * q^92 + 3376 * q^93 - 7610 * q^94 - 5672 * q^95 - 7294 * q^96 - 8648 * q^97 - 7620 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−5.18542	−1.83332	−0.916662	−	0.399664i	$-0.869127\pi$
$2$	−5.18542	−1.83332	−0.916662	+	0.399664i	$0.869127\pi$
$3$	−5.95392	−1.14583	−0.572916	−	0.819614i	$-0.694188\pi$
$3$	−5.95392	−1.14583	−0.572916	+	0.819614i	$0.694188\pi$
$4$	18.8886	2.36107
$5$	18.5974	1.66340	0.831700	−	0.555226i	$-0.187368\pi$
$5$	18.5974	1.66340	0.831700	+	0.555226i	$0.187368\pi$
$6$	30.8736	2.10068
$7$	0	0
$7$	0	0
$8$	−56.4620	−2.49529
$9$	8.44915	0.312931
$10$	−96.4352	−3.04955
$11$	−4.03513	−0.110603	−0.0553016	−	0.998470i	$-0.517612\pi$
$11$	−4.03513	−0.110603	−0.0553016	+	0.998470i	$0.517612\pi$
$12$	−112.461	−2.70540
$13$	−3.74460	−0.0798897	−0.0399448	−	0.999202i	$-0.512718\pi$
$13$	−3.74460	−0.0798897	−0.0399448	+	0.999202i	$0.512718\pi$
$14$	0	0
$15$	−110.727	−1.90598
$16$	141.670	2.21360
$17$	−31.7720	−0.453285	−0.226643	−	0.973978i	$-0.572775\pi$
$17$	−31.7720	−0.453285	−0.226643	+	0.973978i	$0.572775\pi$
$18$	−43.8124	−0.573704
$19$	−128.465	−1.55115	−0.775577	−	0.631253i	$-0.782541\pi$
$19$	−128.465	−1.55115	−0.775577	+	0.631253i	$0.782541\pi$
$20$	351.278	3.92741
$21$	0	0
$22$	20.9238	0.202772
$23$	−83.0637	−0.753042	−0.376521	−	0.926408i	$-0.622880\pi$
$23$	−83.0637	−0.753042	−0.376521	+	0.926408i	$0.622880\pi$
$24$	336.170	2.85918
$25$	220.862	1.76690
$26$	19.4173	0.146464
$27$	110.450	0.787265
$28$	0	0
$29$	101.320	0.648784	0.324392	−	0.945923i	$-0.394840\pi$
$29$	101.320	0.648784	0.324392	+	0.945923i	$0.394840\pi$
$30$	574.167	3.49427
$31$	−19.6339	−0.113753	−0.0568767	−	0.998381i	$-0.518114\pi$
$31$	−19.6339	−0.113753	−0.0568767	+	0.998381i	$0.518114\pi$
$32$	−282.925	−1.56295
$33$	24.0248	0.126733
$34$	164.751	0.831019
$35$	0	0
$36$	159.593	0.738854
$37$	408.911	1.81688	0.908440	−	0.418015i	$-0.137274\pi$
$37$	408.911	1.81688	0.908440	+	0.418015i	$0.137274\pi$
$38$	666.146	2.84377
$39$	22.2951	0.0915402
$40$	−1050.04	−4.15066
$41$	41.0000	0.156174
$41$	41.0000	0.156174
$42$	0	0
$43$	−86.2241	−0.305792	−0.152896	−	0.988242i	$-0.548860\pi$
$43$	−86.2241	−0.305792	−0.152896	+	0.988242i	$0.548860\pi$
$44$	−76.2179	−0.261143
$45$	157.132	0.520530
$46$	430.720	1.38057
$47$	389.553	1.20898	0.604491	−	0.796612i	$-0.293376\pi$
$47$	389.553	1.20898	0.604491	+	0.796612i	$0.293376\pi$
$48$	−843.493	−2.53641
$49$	0	0
$50$	−1145.26	−3.23929
$51$	189.168	0.519389
$52$	−70.7303	−0.188625
$53$	−568.450	−1.47326	−0.736629	−	0.676297i	$-0.763583\pi$
$53$	−568.450	−1.47326	−0.736629	+	0.676297i	$0.763583\pi$
$54$	−572.731	−1.44331
$55$	−75.0427	−0.183977
$56$	0	0
$57$	764.871	1.77736
$58$	−525.389	−1.18943
$59$	−253.788	−0.560006	−0.280003	−	0.959999i	$-0.590335\pi$
$59$	−253.788	−0.560006	−0.280003	+	0.959999i	$0.590335\pi$
$60$	−2091.48	−4.50015
$61$	483.847	1.01558	0.507789	−	0.861481i	$-0.330463\pi$
$61$	483.847	1.01558	0.507789	+	0.861481i	$0.330463\pi$
$62$	101.810	0.208547
$63$	0	0
$64$	333.721	0.651798
$65$	−69.6397	−0.132888
$66$	−124.579	−0.232342
$67$	−751.280	−1.36990	−0.684951	−	0.728589i	$-0.740177\pi$
$67$	−751.280	−1.36990	−0.684951	+	0.728589i	$0.740177\pi$
$68$	−600.129	−1.07024
$69$	494.554	0.862860
$70$	0	0
$71$	−287.176	−0.480021	−0.240011	−	0.970770i	$-0.577151\pi$
$71$	−287.176	−0.480021	−0.240011	+	0.970770i	$0.577151\pi$
$72$	−477.055	−0.780855
$73$	508.841	0.815827	0.407913	−	0.913021i	$-0.366257\pi$
$73$	508.841	0.815827	0.407913	+	0.913021i	$0.366257\pi$
$74$	−2120.38	−3.33093
$75$	−1315.00	−2.02457
$76$	−2426.53	−3.66239
$77$	0	0
$78$	−115.609	−0.167823
$79$	265.771	0.378502	0.189251	−	0.981929i	$-0.439394\pi$
$79$	265.771	0.378502	0.189251	+	0.981929i	$0.439394\pi$
$80$	2634.69	3.68210
$81$	−885.739	−1.21501
$82$	−212.602	−0.286317
$83$	847.241	1.12044	0.560221	−	0.828343i	$-0.310716\pi$
$83$	847.241	1.12044	0.560221	+	0.828343i	$0.310716\pi$
$84$	0	0
$85$	−590.876	−0.753995
$86$	447.108	0.560616
$87$	−603.254	−0.743397
$88$	227.831	0.275987
$89$	962.744	1.14664	0.573319	−	0.819333i	$-0.305656\pi$
$89$	962.744	1.14664	0.573319	+	0.819333i	$0.305656\pi$
$90$	−814.795	−0.954300
$91$	0	0
$92$	−1568.96	−1.77799
$93$	116.899	0.130342
$94$	−2020.00	−2.21646
$95$	−2389.11	−2.58019
$96$	1684.51	1.79088
$97$	−408.253	−0.427338	−0.213669	−	0.976906i	$-0.568541\pi$
$97$	−408.253	−0.427338	−0.213669	+	0.976906i	$0.568541\pi$
$98$	0	0
$99$	−34.0934	−0.0346112
$100$	4171.78	4.17178
$101$	−1749.19	−1.72328	−0.861640	−	0.507521i	$-0.830562\pi$
$101$	−1749.19	−1.72328	−0.861640	+	0.507521i	$0.830562\pi$
$102$	−980.917	−0.952208
$103$	508.160	0.486121	0.243061	−	0.970011i	$-0.421849\pi$
$103$	508.160	0.486121	0.243061	+	0.970011i	$0.421849\pi$
$104$	211.428	0.199348
$105$	0	0
$106$	2947.65	2.70096
$107$	1201.32	1.08538	0.542691	−	0.839932i	$-0.317405\pi$
$107$	1201.32	1.08538	0.542691	+	0.839932i	$0.317405\pi$
$108$	2086.25	1.85879
$109$	1072.99	0.942879	0.471440	−	0.881898i	$-0.343734\pi$
$109$	1072.99	0.942879	0.471440	+	0.881898i	$0.343734\pi$
$110$	389.128	0.337290
$111$	−2434.62	−2.08184
$112$	0	0
$113$	−1166.17	−0.970831	−0.485416	−	0.874284i	$-0.661332\pi$
$113$	−1166.17	−0.970831	−0.485416	+	0.874284i	$0.661332\pi$
$114$	−3966.18	−3.25848
$115$	−1544.77	−1.25261
$116$	1913.80	1.53183
$117$	−31.6387	−0.0250000
$118$	1316.00	1.02667
$119$	0	0
$120$	6251.88	4.75596
$121$	−1314.72	−0.987767
$122$	−2508.95	−1.86188
$123$	−244.111	−0.178949
$124$	−370.857	−0.268580
$125$	1782.78	1.27566
$126$	0	0
$127$	34.0939	0.0238216	0.0119108	−	0.999929i	$-0.496209\pi$
$127$	34.0939	0.0238216	0.0119108	+	0.999929i	$0.496209\pi$
$128$	532.915	0.367996
$129$	513.371	0.350386
$130$	361.111	0.243627
$131$	−2385.17	−1.59079	−0.795395	−	0.606091i	$-0.792737\pi$
$131$	−2385.17	−1.59079	−0.795395	+	0.606091i	$0.792737\pi$
$132$	453.795	0.299226
$133$	0	0
$134$	3895.70	2.51147
$135$	2054.08	1.30954
$136$	1793.91	1.13108
$137$	1977.98	1.23351	0.616753	−	0.787157i	$-0.288448\pi$
$137$	1977.98	1.23351	0.616753	+	0.787157i	$0.288448\pi$
$138$	−2564.47	−1.58190
$139$	−216.725	−0.132248	−0.0661238	−	0.997811i	$-0.521063\pi$
$139$	−216.725	−0.132248	−0.0661238	+	0.997811i	$0.521063\pi$
$140$	0	0
$141$	−2319.37	−1.38529
$142$	1489.13	0.880034
$143$	15.1099	0.00883606
$144$	1196.99	0.692705
$145$	1884.29	1.07919
$146$	−2638.56	−1.49567
$147$	0	0
$148$	7723.76	4.28979
$149$	2732.73	1.50251	0.751256	−	0.660011i	$-0.229448\pi$
$149$	2732.73	1.50251	0.751256	+	0.660011i	$0.229448\pi$
$150$	6818.80	3.71169
$151$	−36.3955	−0.0196147	−0.00980736	−	0.999952i	$-0.503122\pi$
$151$	−36.3955	−0.0196147	−0.00980736	+	0.999952i	$0.503122\pi$
$152$	7253.39	3.87058
$153$	−268.447	−0.141847
$154$	0	0
$155$	−365.139	−0.189217
$156$	421.122	0.216133
$157$	−3070.94	−1.56107	−0.780534	−	0.625114i	$-0.785053\pi$
$157$	−3070.94	−1.56107	−0.780534	+	0.625114i	$0.785053\pi$
$158$	−1378.14	−0.693916
$159$	3384.51	1.68811
$160$	−5261.65	−2.59981
$161$	0	0
$162$	4592.93	2.22750
$163$	2322.66	1.11610	0.558051	−	0.829807i	$-0.311549\pi$
$163$	2322.66	1.11610	0.558051	+	0.829807i	$0.311549\pi$
$164$	774.432	0.368738
$165$	446.798	0.210807
$166$	−4393.30	−2.05413
$167$	−2980.08	−1.38087	−0.690436	−	0.723394i	$-0.742581\pi$
$167$	−2980.08	−1.38087	−0.690436	+	0.723394i	$0.742581\pi$
$168$	0	0
$169$	−2182.98	−0.993618
$170$	3063.94	1.38232
$171$	−1085.42	−0.485405
$172$	−1628.65	−0.721998
$173$	3511.33	1.54313	0.771565	−	0.636151i	$-0.219475\pi$
$173$	3511.33	1.54313	0.771565	+	0.636151i	$0.219475\pi$
$174$	3128.12	1.36289
$175$	0	0
$176$	−571.657	−0.244831
$177$	1511.03	0.641673
$178$	−4992.24	−2.10216
$179$	353.920	0.147783	0.0738917	−	0.997266i	$-0.476458\pi$
$179$	353.920	0.147783	0.0738917	+	0.997266i	$0.476458\pi$
$180$	2968.00	1.22901
$181$	1779.31	0.730690	0.365345	−	0.930872i	$-0.380951\pi$
$181$	1779.31	0.730690	0.365345	+	0.930872i	$0.380951\pi$
$182$	0	0
$183$	−2880.79	−1.16368
$184$	4689.94	1.87906
$185$	7604.67	3.02220
$186$	−606.169	−0.238959
$187$	128.204	0.0501349
$188$	7358.11	2.85450
$189$	0	0
$190$	12388.6	4.73032
$191$	−2713.98	−1.02815	−0.514075	−	0.857745i	$-0.671865\pi$
$191$	−2713.98	−1.02815	−0.514075	+	0.857745i	$0.671865\pi$
$192$	−1986.94	−0.746851
$193$	−101.366	−0.0378056	−0.0189028	−	0.999821i	$-0.506017\pi$
$193$	−101.366	−0.0378056	−0.0189028	+	0.999821i	$0.506017\pi$
$194$	2116.96	0.783449
$195$	414.629	0.152268
$196$	0	0
$197$	2746.71	0.993374	0.496687	−	0.867930i	$-0.334550\pi$
$197$	2746.71	0.993374	0.496687	+	0.867930i	$0.334550\pi$
$198$	176.789	0.0634536
$199$	−5356.21	−1.90800	−0.953998	−	0.299812i	$-0.903076\pi$
$199$	−5356.21	−1.90800	−0.953998	+	0.299812i	$0.903076\pi$
$200$	−12470.3	−4.40892
$201$	4473.06	1.56968
$202$	9070.30	3.15933
$203$	0	0
$204$	3573.12	1.22632
$205$	762.492	0.259779
$206$	−2635.02	−0.891217
$207$	−701.817	−0.235651
$208$	−530.499	−0.176844
$209$	518.373	0.171563
$210$	0	0
$211$	−2288.45	−0.746650	−0.373325	−	0.927701i	$-0.621782\pi$
$211$	−2288.45	−0.746650	−0.373325	+	0.927701i	$0.621782\pi$
$212$	−10737.2	−3.47847
$213$	1709.82	0.550024
$214$	−6229.35	−1.98986
$215$	−1603.54	−0.508654
$216$	−6236.24	−1.96446
$217$	0	0
$218$	−5563.91	−1.72860
$219$	−3029.60	−0.934801
$220$	−1417.45	−0.434384
$221$	118.974	0.0362128
$222$	12624.6	3.81669
$223$	4420.85	1.32754	0.663772	−	0.747935i	$-0.268955\pi$
$223$	4420.85	1.32754	0.663772	+	0.747935i	$0.268955\pi$
$224$	0	0
$225$	1866.10	0.552918
$226$	6047.08	1.77985
$227$	−706.484	−0.206568	−0.103284	−	0.994652i	$-0.532935\pi$
$227$	−706.484	−0.206568	−0.103284	+	0.994652i	$0.532935\pi$
$228$	14447.3	4.19648
$229$	−3728.02	−1.07578	−0.537892	−	0.843014i	$-0.680779\pi$
$229$	−3728.02	−1.07578	−0.537892	+	0.843014i	$0.680779\pi$
$230$	8010.26	2.29644
$231$	0	0
$232$	−5720.75	−1.61890
$233$	−4879.59	−1.37199	−0.685993	−	0.727608i	$-0.740632\pi$
$233$	−4879.59	−1.37199	−0.685993	+	0.727608i	$0.740632\pi$
$234$	164.060	0.0458331
$235$	7244.66	2.01102
$236$	−4793.69	−1.32222
$237$	−1582.38	−0.433699
$238$	0	0
$239$	5274.56	1.42754	0.713772	−	0.700379i	$-0.246985\pi$
$239$	5274.56	1.42754	0.713772	+	0.700379i	$0.246985\pi$
$240$	−15686.8	−4.21907
$241$	2846.20	0.760747	0.380373	−	0.924833i	$-0.375795\pi$
$241$	2846.20	0.760747	0.380373	+	0.924833i	$0.375795\pi$
$242$	6817.37	1.81090
$243$	2291.46	0.604927
$244$	9139.19	2.39786
$245$	0	0
$246$	1265.82	0.328071
$247$	481.051	0.123921
$248$	1108.57	0.283848
$249$	−5044.40	−1.28384
$250$	−9244.48	−2.33869
$251$	3756.76	0.944720	0.472360	−	0.881406i	$-0.343402\pi$
$251$	3756.76	0.944720	0.472360	+	0.881406i	$0.343402\pi$
$252$	0	0
$253$	335.172	0.0832890
$254$	−176.791	−0.0436727
$255$	3518.03	0.863951
$256$	−5433.15	−1.32645
$257$	−3947.60	−0.958149	−0.479074	−	0.877774i	$-0.659028\pi$
$257$	−3947.60	−0.958149	−0.479074	+	0.877774i	$0.659028\pi$
$258$	−2662.05	−0.642371
$259$	0	0
$260$	−1315.40	−0.313759
$261$	856.071	0.203025
$262$	12368.1	2.91643
$263$	2595.19	0.608465	0.304232	−	0.952598i	$-0.401600\pi$
$263$	2595.19	0.608465	0.304232	+	0.952598i	$0.401600\pi$
$264$	−1356.49	−0.316235
$265$	−10571.7	−2.45062
$266$	0	0
$267$	−5732.10	−1.31385
$268$	−14190.6	−3.23444
$269$	−6897.69	−1.56342	−0.781709	−	0.623643i	$-0.785652\pi$
$269$	−6897.69	−1.56342	−0.781709	+	0.623643i	$0.785652\pi$
$270$	−10651.3	−2.40080
$271$	−5293.20	−1.18649	−0.593245	−	0.805022i	$-0.702154\pi$
$271$	−5293.20	−1.18649	−0.593245	+	0.805022i	$0.702154\pi$
$272$	−4501.16	−1.00339
$273$	0	0
$274$	−10256.7	−2.26141
$275$	−891.206	−0.195425
$276$	9341.44	2.03728
$277$	6488.00	1.40731	0.703657	−	0.710539i	$-0.251549\pi$
$277$	6488.00	1.40731	0.703657	+	0.710539i	$0.251549\pi$
$278$	1123.81	0.242452
$279$	−165.890	−0.0355970
$280$	0	0
$281$	2111.22	0.448201	0.224101	−	0.974566i	$-0.428056\pi$
$281$	2111.22	0.448201	0.224101	+	0.974566i	$0.428056\pi$
$282$	12026.9	2.53969
$283$	−8248.54	−1.73260	−0.866298	−	0.499528i	$-0.833507\pi$
$283$	−8248.54	−1.73260	−0.866298	+	0.499528i	$0.833507\pi$
$284$	−5424.35	−1.13337
$285$	14224.6	2.95646
$286$	−78.3514	−0.0161994
$287$	0	0
$288$	−2390.47	−0.489097
$289$	−3903.54	−0.794532
$290$	−9770.86	−1.97850
$291$	2430.70	0.489658
$292$	9611.29	1.92623
$293$	3806.99	0.759066	0.379533	−	0.925178i	$-0.376085\pi$
$293$	3806.99	0.759066	0.379533	+	0.925178i	$0.376085\pi$
$294$	0	0
$295$	−4719.78	−0.931513
$296$	−23087.9	−4.53364
$297$	−445.681	−0.0870741
$298$	−14170.4	−2.75459
$299$	311.040	0.0601603
$300$	−24838.4	−4.78015
$301$	0	0
$302$	188.726	0.0359601
$303$	10414.6	1.97459
$304$	−18199.7	−3.43363
$305$	8998.28	1.68931
$306$	1392.01	0.260052
$307$	−7743.96	−1.43964	−0.719822	−	0.694158i	$-0.755777\pi$
$307$	−7743.96	−1.43964	−0.719822	+	0.694158i	$0.755777\pi$
$308$	0	0
$309$	−3025.54	−0.557013
$310$	1893.40	0.346896
$311$	−7633.71	−1.39186	−0.695930	−	0.718110i	$-0.745007\pi$
$311$	−7633.71	−1.39186	−0.695930	+	0.718110i	$0.745007\pi$
$312$	−1258.82	−0.228419
$313$	7676.73	1.38631	0.693154	−	0.720789i	$-0.256221\pi$
$313$	7676.73	1.38631	0.693154	+	0.720789i	$0.256221\pi$
$314$	15924.1	2.86194
$315$	0	0
$316$	5020.05	0.893671
$317$	−4729.93	−0.838042	−0.419021	−	0.907977i	$-0.637627\pi$
$317$	−4729.93	−0.838042	−0.419021	+	0.907977i	$0.637627\pi$
$318$	−17550.1	−3.09484
$319$	−408.841	−0.0717576
$320$	6206.32	1.08420
$321$	−7152.56	−1.24367
$322$	0	0
$323$	4081.60	0.703115
$324$	−16730.4	−2.86872
$325$	−827.041	−0.141157
$326$	−12044.0	−2.04618
$327$	−6388.50	−1.08038
$328$	−2314.94	−0.389699
$329$	0	0
$330$	−2316.84	−0.386478
$331$	−5181.92	−0.860496	−0.430248	−	0.902711i	$-0.641574\pi$
$331$	−5181.92	−0.860496	−0.430248	+	0.902711i	$0.641574\pi$
$332$	16003.2	2.64545
$333$	3454.95	0.568559
$334$	15453.0	2.53158
$335$	−13971.8	−2.27870
$336$	0	0
$337$	−6912.57	−1.11736	−0.558682	−	0.829382i	$-0.688693\pi$
$337$	−6912.57	−1.11736	−0.558682	+	0.829382i	$0.688693\pi$
$338$	11319.7	1.82162
$339$	6943.27	1.11241
$340$	−11160.8	−1.78024
$341$	79.2253	0.0125815
$342$	5628.37	0.889904
$343$	0	0
$344$	4868.38	0.763040
$345$	9197.41	1.43528
$346$	−18207.7	−2.82905
$347$	−7608.47	−1.17707	−0.588536	−	0.808471i	$-0.700295\pi$
$347$	−7608.47	−1.17707	−0.588536	+	0.808471i	$0.700295\pi$
$348$	−11394.6	−1.75522
$349$	−4171.81	−0.639862	−0.319931	−	0.947441i	$-0.603660\pi$
$349$	−4171.81	−0.639862	−0.319931	+	0.947441i	$0.603660\pi$
$350$	0	0
$351$	−413.592	−0.0628944
$352$	1141.64	0.172868
$353$	9936.52	1.49821	0.749104	−	0.662452i	$-0.230484\pi$
$353$	9936.52	1.49821	0.749104	+	0.662452i	$0.230484\pi$
$354$	−7835.34	−1.17639
$355$	−5340.71	−0.798467
$356$	18184.9	2.70730
$357$	0	0
$358$	−1835.22	−0.270935
$359$	−1119.05	−0.164516	−0.0822580	−	0.996611i	$-0.526213\pi$
$359$	−1119.05	−0.164516	−0.0822580	+	0.996611i	$0.526213\pi$
$360$	−8871.98	−1.29887
$361$	9644.29	1.40608
$362$	−9226.46	−1.33959
$363$	7827.72	1.13182
$364$	0	0
$365$	9463.11	1.35705
$366$	14938.1	2.13341
$367$	−8461.91	−1.20356	−0.601782	−	0.798660i	$-0.705543\pi$
$367$	−8461.91	−1.20356	−0.601782	+	0.798660i	$0.705543\pi$
$368$	−11767.7	−1.66693
$369$	346.415	0.0488717
$370$	−39433.4	−5.54067
$371$	0	0
$372$	2208.05	0.307748
$373$	10482.8	1.45517	0.727585	−	0.686017i	$-0.240643\pi$
$373$	10482.8	1.45517	0.727585	+	0.686017i	$0.240643\pi$
$374$	−664.793	−0.0919134
$375$	−10614.5	−1.46169
$376$	−21994.9	−3.01676
$377$	−379.405	−0.0518311
$378$	0	0
$379$	−9175.00	−1.24350	−0.621752	−	0.783214i	$-0.713579\pi$
$379$	−9175.00	−1.24350	−0.621752	+	0.783214i	$0.713579\pi$
$380$	−45127.0	−6.09202
$381$	−202.992	−0.0272956
$382$	14073.1	1.88493
$383$	−2022.49	−0.269829	−0.134915	−	0.990857i	$-0.543076\pi$
$383$	−2022.49	−0.269829	−0.134915	+	0.990857i	$0.543076\pi$
$384$	−3172.93	−0.421661
$385$	0	0
$386$	525.626	0.0693099
$387$	−728.520	−0.0956919
$388$	−7711.32	−1.00898
$389$	−5635.73	−0.734557	−0.367279	−	0.930111i	$-0.619710\pi$
$389$	−5635.73	−0.734557	−0.367279	+	0.930111i	$0.619710\pi$
$390$	−2150.03	−0.279156
$391$	2639.10	0.341343
$392$	0	0
$393$	14201.1	1.82278
$394$	−14242.8	−1.82118
$395$	4942.65	0.629599
$396$	−643.976	−0.0817197
$397$	−5750.29	−0.726949	−0.363475	−	0.931604i	$-0.618410\pi$
$397$	−5750.29	−0.726949	−0.363475	+	0.931604i	$0.618410\pi$
$398$	27774.2	3.49797
$399$	0	0
$400$	31289.6	3.91120
$401$	6810.73	0.848159	0.424080	−	0.905625i	$-0.360598\pi$
$401$	6810.73	0.848159	0.424080	+	0.905625i	$0.360598\pi$
$402$	−23194.7	−2.87773
$403$	73.5212	0.00908772
$404$	−33039.8	−4.06879
$405$	−16472.4	−2.02104
$406$	0	0
$407$	−1650.01	−0.200953
$408$	−10680.8	−1.29603
$409$	−4655.79	−0.562870	−0.281435	−	0.959580i	$-0.590810\pi$
$409$	−4655.79	−0.562870	−0.281435	+	0.959580i	$0.590810\pi$
$410$	−3953.84	−0.476259
$411$	−11776.7	−1.41339
$412$	9598.43	1.14777
$413$	0	0
$414$	3639.22	0.432024
$415$	15756.4	1.86374
$416$	1059.44	0.124864
$417$	1290.37	0.151533
$418$	−2687.98	−0.314530
$419$	650.854	0.0758862	0.0379431	−	0.999280i	$-0.487919\pi$
$419$	650.854	0.0758862	0.0379431	+	0.999280i	$0.487919\pi$
$420$	0	0
$421$	10297.3	1.19206	0.596032	−	0.802961i	$-0.296743\pi$
$421$	10297.3	1.19206	0.596032	+	0.802961i	$0.296743\pi$
$422$	11866.6	1.36885
$423$	3291.39	0.378329
$424$	32095.8	3.67620
$425$	−7017.24	−0.800909
$426$	−8866.14	−1.00837
$427$	0	0
$428$	22691.2	2.56267
$429$	−89.9633	−0.0101246
$430$	8315.04	0.932528
$431$	4390.71	0.490703	0.245351	−	0.969434i	$-0.421097\pi$
$431$	4390.71	0.490703	0.245351	+	0.969434i	$0.421097\pi$
$432$	15647.5	1.74269
$433$	−9442.26	−1.04796	−0.523979	−	0.851731i	$-0.675553\pi$
$433$	−9442.26	−1.04796	−0.523979	+	0.851731i	$0.675553\pi$
$434$	0	0
$435$	−11218.9	−1.23657
$436$	20267.3	2.22621
$437$	10670.8	1.16808
$438$	15709.7	1.71379
$439$	2478.22	0.269429	0.134714	−	0.990884i	$-0.456988\pi$
$439$	2478.22	0.269429	0.134714	+	0.990884i	$0.456988\pi$
$440$	4237.06	0.459077
$441$	0	0
$442$	−616.929	−0.0663898
$443$	14399.3	1.54432	0.772160	−	0.635428i	$-0.219176\pi$
$443$	14399.3	1.54432	0.772160	+	0.635428i	$0.219176\pi$
$444$	−45986.6	−4.91538
$445$	17904.5	1.90732
$446$	−22924.0	−2.43382
$447$	−16270.5	−1.72163
$448$	0	0
$449$	8081.74	0.849445	0.424722	−	0.905324i	$-0.360372\pi$
$449$	8081.74	0.849445	0.424722	+	0.905324i	$0.360372\pi$
$450$	−9676.50	−1.01368
$451$	−165.440	−0.0172733
$452$	−22027.3	−2.29221
$453$	216.696	0.0224752
$454$	3663.42	0.378706
$455$	0	0
$456$	−43186.1	−4.43503
$457$	5090.29	0.521036	0.260518	−	0.965469i	$-0.416107\pi$
$457$	5090.29	0.521036	0.260518	+	0.965469i	$0.416107\pi$
$458$	19331.4	1.97226
$459$	−3509.23	−0.356856
$460$	−29178.5	−2.95751
$461$	−12568.7	−1.26982	−0.634908	−	0.772588i	$-0.718962\pi$
$461$	−12568.7	−1.26982	−0.634908	+	0.772588i	$0.718962\pi$
$462$	0	0
$463$	14806.2	1.48618	0.743089	−	0.669192i	$-0.233360\pi$
$463$	14806.2	1.48618	0.743089	+	0.669192i	$0.233360\pi$
$464$	14354.1	1.43615
$465$	2174.01	0.216811
$466$	25302.7	2.51529
$467$	5975.61	0.592116	0.296058	−	0.955170i	$-0.404328\pi$
$467$	5975.61	0.592116	0.296058	+	0.955170i	$0.404328\pi$
$468$	−597.611	−0.0590268
$469$	0	0
$470$	−37566.6	−3.68685
$471$	18284.1	1.78872
$472$	14329.4	1.39738
$473$	347.925	0.0338216
$474$	8205.32	0.795111
$475$	−28373.1	−2.74073
$476$	0	0
$477$	−4802.92	−0.461029
$478$	−27350.8	−2.61715
$479$	10662.8	1.01711	0.508554	−	0.861030i	$-0.330180\pi$
$479$	10662.8	1.01711	0.508554	+	0.861030i	$0.330180\pi$
$480$	31327.4	2.97895
$481$	−1531.21	−0.145150
$482$	−14758.8	−1.39470
$483$	0	0
$484$	−24833.2	−2.33219
$485$	−7592.43	−0.710834
$486$	−11882.2	−1.10903
$487$	−9431.84	−0.877613	−0.438806	−	0.898582i	$-0.644599\pi$
$487$	−9431.84	−0.877613	−0.438806	+	0.898582i	$0.644599\pi$
$488$	−27318.9	−2.53416
$489$	−13828.9	−1.27887
$490$	0	0
$491$	−2780.73	−0.255586	−0.127793	−	0.991801i	$-0.540789\pi$
$491$	−2780.73	−0.255586	−0.127793	+	0.991801i	$0.540789\pi$
$492$	−4610.91	−0.422512
$493$	−3219.16	−0.294084
$494$	−2494.45	−0.227188
$495$	−634.047	−0.0575723
$496$	−2781.54	−0.251804
$497$	0	0
$498$	26157.3	2.35369
$499$	3038.65	0.272602	0.136301	−	0.990667i	$-0.456479\pi$
$499$	3038.65	0.272602	0.136301	+	0.990667i	$0.456479\pi$
$500$	33674.3	3.01192
$501$	17743.2	1.58225
$502$	−19480.4	−1.73198
$503$	8505.89	0.753994	0.376997	−	0.926215i	$-0.376957\pi$
$503$	8505.89	0.753994	0.376997	+	0.926215i	$0.376957\pi$
$504$	0	0
$505$	−32530.4	−2.86650
$506$	−1738.01	−0.152696
$507$	12997.3	1.13852
$508$	643.986	0.0562446
$509$	−3062.99	−0.266728	−0.133364	−	0.991067i	$-0.542578\pi$
$509$	−3062.99	−0.266728	−0.133364	+	0.991067i	$0.542578\pi$
$510$	−18242.5	−1.58390
$511$	0	0
$512$	23909.9	2.06382
$513$	−14189.0	−1.22117
$514$	20470.0	1.75660
$515$	9450.44	0.808613
$516$	9696.87	0.827288
$517$	−1571.90	−0.133717
$518$	0	0
$519$	−20906.2	−1.76817
$520$	3932.00	0.331595
$521$	7247.81	0.609467	0.304734	−	0.952438i	$-0.401433\pi$
$521$	7247.81	0.609467	0.304734	+	0.952438i	$0.401433\pi$
$522$	−4439.09	−0.372210
$523$	11947.4	0.998900	0.499450	−	0.866343i	$-0.333536\pi$
$523$	11947.4	0.998900	0.499450	+	0.866343i	$0.333536\pi$
$524$	−45052.6	−3.75597
$525$	0	0
$526$	−13457.2	−1.11551
$527$	623.809	0.0515627
$528$	3403.60	0.280536
$529$	−5267.42	−0.432927
$530$	54818.6	4.49277
$531$	−2144.29	−0.175243
$532$	0	0
$533$	−153.529	−0.0124767
$534$	29723.4	2.40872
$535$	22341.4	1.80542
$536$	42418.8	3.41830
$537$	−2107.21	−0.169335
$538$	35767.4	2.86625
$539$	0	0
$540$	38798.8	3.09191
$541$	−11338.6	−0.901077	−0.450538	−	0.892757i	$-0.648768\pi$
$541$	−11338.6	−0.901077	−0.450538	+	0.892757i	$0.648768\pi$
$542$	27447.5	2.17522
$543$	−10593.9	−0.837248
$544$	8989.09	0.708463
$545$	19954.8	1.56838
$546$	0	0
$547$	−573.499	−0.0448282	−0.0224141	−	0.999749i	$-0.507135\pi$
$547$	−573.499	−0.0448282	−0.0224141	+	0.999749i	$0.507135\pi$
$548$	37361.3	2.91240
$549$	4088.09	0.317806
$550$	4621.28	0.358276
$551$	−13016.1	−1.00636
$552$	−27923.5	−2.15309
$553$	0	0
$554$	−33643.0	−2.58006
$555$	−45277.6	−3.46293
$556$	−4093.64	−0.312246
$557$	−3593.36	−0.273350	−0.136675	−	0.990616i	$-0.543642\pi$
$557$	−3593.36	−0.273350	−0.136675	+	0.990616i	$0.543642\pi$
$558$	860.208	0.0652608
$559$	322.875	0.0244296
$560$	0	0
$561$	−763.317	−0.0574461
$562$	−10947.5	−0.821698
$563$	−9439.58	−0.706627	−0.353314	−	0.935505i	$-0.614945\pi$
$563$	−9439.58	−0.706627	−0.353314	+	0.935505i	$0.614945\pi$
$564$	−43809.6	−3.27077
$565$	−21687.7	−1.61488
$566$	42772.1	3.17641
$567$	0	0
$568$	16214.5	1.19779
$569$	5475.76	0.403437	0.201719	−	0.979444i	$-0.435347\pi$
$569$	5475.76	0.403437	0.201719	+	0.979444i	$0.435347\pi$
$570$	−73760.5	−5.42015
$571$	3092.25	0.226632	0.113316	−	0.993559i	$-0.463853\pi$
$571$	3092.25	0.226632	0.113316	+	0.993559i	$0.463853\pi$
$572$	285.406	0.0208626
$573$	16158.8	1.17809
$574$	0	0
$575$	−18345.6	−1.33055
$576$	2819.65	0.203968
$577$	−17554.0	−1.26652	−0.633261	−	0.773938i	$-0.718284\pi$
$577$	−17554.0	−1.26652	−0.633261	+	0.773938i	$0.718284\pi$
$578$	20241.5	1.45663
$579$	603.525	0.0433189
$580$	35591.7	2.54804
$581$	0	0
$582$	−12604.2	−0.897701
$583$	2293.77	0.162947
$584$	−28730.2	−2.03572
$585$	−588.397	−0.0415850
$586$	−19740.8	−1.39161
$587$	13898.4	0.977254	0.488627	−	0.872493i	$-0.337498\pi$
$587$	13898.4	0.977254	0.488627	+	0.872493i	$0.337498\pi$
$588$	0	0
$589$	2522.27	0.176449
$590$	24474.1	1.70777
$591$	−16353.7	−1.13824
$592$	57930.6	4.02184
$593$	−12052.8	−0.834652	−0.417326	−	0.908757i	$-0.637033\pi$
$593$	−12052.8	−0.834652	−0.417326	+	0.908757i	$0.637033\pi$
$594$	2311.04	0.159635
$595$	0	0
$596$	51617.5	3.54754
$597$	31890.4	2.18624
$598$	−1612.88	−0.110293
$599$	6857.09	0.467735	0.233867	−	0.972269i	$-0.424862\pi$
$599$	6857.09	0.467735	0.233867	+	0.972269i	$0.424862\pi$
$600$	74247.2	5.05188
$601$	808.455	0.0548712	0.0274356	−	0.999624i	$-0.491266\pi$
$601$	808.455	0.0548712	0.0274356	+	0.999624i	$0.491266\pi$
$602$	0	0
$603$	−6347.68	−0.428686
$604$	−687.460	−0.0463118
$605$	−24450.3	−1.64305
$606$	−54003.8	−3.62006
$607$	−8142.15	−0.544448	−0.272224	−	0.962234i	$-0.587759\pi$
$607$	−8142.15	−0.544448	−0.272224	+	0.962234i	$0.587759\pi$
$608$	36345.9	2.42438
$609$	0	0
$610$	−46659.9	−3.09705
$611$	−1458.72	−0.0965852
$612$	−5070.58	−0.334912
$613$	16917.8	1.11469	0.557345	−	0.830281i	$-0.311820\pi$
$613$	16917.8	1.11469	0.557345	+	0.830281i	$0.311820\pi$
$614$	40155.7	2.63933
$615$	−4539.82	−0.297663
$616$	0	0
$617$	3722.98	0.242920	0.121460	−	0.992596i	$-0.461242\pi$
$617$	3722.98	0.242920	0.121460	+	0.992596i	$0.461242\pi$
$618$	15688.7	1.02119
$619$	−9017.81	−0.585551	−0.292776	−	0.956181i	$-0.594579\pi$
$619$	−9017.81	−0.585551	−0.292776	+	0.956181i	$0.594579\pi$
$620$	−6896.96	−0.446756
$621$	−9174.41	−0.592844
$622$	39584.0	2.55173
$623$	0	0
$624$	3158.55	0.202633
$625$	5547.31	0.355028
$626$	−39807.1	−2.54155
$627$	−3086.35	−0.196582
$628$	−58005.7	−3.68580
$629$	−12991.9	−0.823566
$630$	0	0
$631$	−27100.2	−1.70973	−0.854866	−	0.518849i	$-0.826361\pi$
$631$	−27100.2	−1.70973	−0.854866	+	0.518849i	$0.826361\pi$
$632$	−15006.0	−0.944471
$633$	13625.2	0.855535
$634$	24526.7	1.53640
$635$	634.057	0.0396249
$636$	63928.6	3.98574
$637$	0	0
$638$	2120.01	0.131555
$639$	−2426.39	−0.150214
$640$	9910.81	0.612124
$641$	−6294.72	−0.387873	−0.193936	−	0.981014i	$-0.562126\pi$
$641$	−6294.72	−0.387873	−0.193936	+	0.981014i	$0.562126\pi$
$642$	37089.0	2.28004
$643$	−24738.6	−1.51726	−0.758628	−	0.651524i	$-0.774130\pi$
$643$	−24738.6	−1.51726	−0.758628	+	0.651524i	$0.774130\pi$
$644$	0	0
$645$	9547.36	0.582832
$646$	−21164.8	−1.28904
$647$	27673.5	1.68154	0.840770	−	0.541393i	$-0.182103\pi$
$647$	27673.5	1.68154	0.840770	+	0.541393i	$0.182103\pi$
$648$	50010.6	3.03179
$649$	1024.07	0.0619385
$650$	4288.55	0.258786
$651$	0	0
$652$	43871.7	2.63520
$653$	−31377.6	−1.88040	−0.940201	−	0.340621i	$-0.889363\pi$
$653$	−31377.6	−1.88040	−0.940201	+	0.340621i	$0.889363\pi$
$654$	33127.1	1.98069
$655$	−44357.9	−2.64612
$656$	5808.48	0.345706
$657$	4299.27	0.255298
$658$	0	0
$659$	21503.3	1.27109	0.635547	−	0.772062i	$-0.280774\pi$
$659$	21503.3	1.27109	0.635547	+	0.772062i	$0.280774\pi$
$660$	8439.39	0.497732
$661$	−10893.6	−0.641015	−0.320507	−	0.947246i	$-0.603853\pi$
$661$	−10893.6	−0.641015	−0.320507	+	0.947246i	$0.603853\pi$
$662$	26870.5	1.57757
$663$	−708.360	−0.0414938
$664$	−47836.9	−2.79583
$665$	0	0
$666$	−17915.4	−1.04235
$667$	−8416.05	−0.488562
$668$	−56289.5	−3.26034
$669$	−26321.4	−1.52114
$670$	72449.8	4.17758
$671$	−1952.38	−0.112326
$672$	0	0
$673$	9244.77	0.529509	0.264755	−	0.964316i	$-0.414709\pi$
$673$	9244.77	0.529509	0.264755	+	0.964316i	$0.414709\pi$
$674$	35844.6	2.04849
$675$	24394.3	1.39102
$676$	−41233.4	−2.34601
$677$	15402.0	0.874368	0.437184	−	0.899372i	$-0.355976\pi$
$677$	15402.0	0.874368	0.437184	+	0.899372i	$0.355976\pi$
$678$	−36003.8	−2.03941
$679$	0	0
$680$	33362.0	1.88144
$681$	4206.35	0.236692
$682$	−410.816	−0.0230659
$683$	−9951.28	−0.557504	−0.278752	−	0.960363i	$-0.589921\pi$
$683$	−9951.28	−0.557504	−0.278752	+	0.960363i	$0.589921\pi$
$684$	−20502.1	−1.14608
$685$	36785.2	2.05181
$686$	0	0
$687$	22196.3	1.23267
$688$	−12215.4	−0.676901
$689$	2128.62	0.117698
$690$	−47692.5	−2.63133
$691$	−29824.9	−1.64196	−0.820980	−	0.570957i	$-0.806572\pi$
$691$	−29824.9	−1.64196	−0.820980	+	0.570957i	$0.806572\pi$
$692$	66324.1	3.64344
$693$	0	0
$694$	39453.1	2.15795
$695$	−4030.52	−0.219980
$696$	34060.9	1.85499
$697$	−1302.65	−0.0707913
$698$	21632.6	1.17307
$699$	29052.7	1.57206
$700$	0	0
$701$	−16799.2	−0.905129	−0.452564	−	0.891732i	$-0.649491\pi$
$701$	−16799.2	−0.905129	−0.452564	+	0.891732i	$0.649491\pi$
$702$	2144.65	0.115306
$703$	−52530.8	−2.81826
$704$	−1346.60	−0.0720910
$705$	−43134.1	−2.30429
$706$	−51525.1	−2.74670
$707$	0	0
$708$	28541.3	1.51504
$709$	−4049.51	−0.214503	−0.107251	−	0.994232i	$-0.534205\pi$
$709$	−4049.51	−0.214503	−0.107251	+	0.994232i	$0.534205\pi$
$710$	27693.9	1.46385
$711$	2245.54	0.118445
$712$	−54358.4	−2.86119
$713$	1630.86	0.0856611
$714$	0	0
$715$	281.005	0.0146979
$716$	6685.05	0.348927
$717$	−31404.3	−1.63572
$718$	5802.75	0.301611
$719$	−31903.3	−1.65479	−0.827393	−	0.561623i	$-0.810177\pi$
$719$	−31903.3	−1.65479	−0.827393	+	0.561623i	$0.810177\pi$
$720$	22260.9	1.15224
$721$	0	0
$722$	−50009.7	−2.57780
$723$	−16946.1	−0.871688
$724$	33608.6	1.72521
$725$	22377.8	1.14633
$726$	−40590.0	−2.07498
$727$	−2061.40	−0.105162	−0.0525811	−	0.998617i	$-0.516745\pi$
$727$	−2061.40	−0.105162	−0.0525811	+	0.998617i	$0.516745\pi$
$728$	0	0
$729$	10271.8	0.521861
$730$	−49070.2	−2.48790
$731$	2739.52	0.138611
$732$	−54414.0	−2.74754
$733$	−2710.14	−0.136564	−0.0682818	−	0.997666i	$-0.521752\pi$
$733$	−2710.14	−0.136564	−0.0682818	+	0.997666i	$0.521752\pi$
$734$	43878.6	2.20652
$735$	0	0
$736$	23500.8	1.17697
$737$	3031.51	0.151516
$738$	−1796.31	−0.0895976
$739$	−19467.1	−0.969025	−0.484513	−	0.874784i	$-0.661003\pi$
$739$	−19467.1	−0.969025	−0.484513	+	0.874784i	$0.661003\pi$
$740$	143642.	7.13563
$741$	−2864.14	−0.141993
$742$	0	0
$743$	21733.3	1.07310	0.536552	−	0.843867i	$-0.319727\pi$
$743$	21733.3	1.07310	0.536552	+	0.843867i	$0.319727\pi$
$744$	−6600.33	−0.325242
$745$	50821.7	2.49928
$746$	−54357.7	−2.66780
$747$	7158.46	0.350622
$748$	2421.60	0.118372
$749$	0	0
$750$	55040.9	2.67975
$751$	8501.26	0.413070	0.206535	−	0.978439i	$-0.433781\pi$
$751$	8501.26	0.413070	0.206535	+	0.978439i	$0.433781\pi$
$752$	55188.1	2.67620
$753$	−22367.5	−1.08249
$754$	1967.37	0.0950232
$755$	−676.860	−0.0326271
$756$	0	0
$757$	−38910.2	−1.86818	−0.934092	−	0.357032i	$-0.883789\pi$
$757$	−38910.2	−1.86818	−0.934092	+	0.357032i	$0.883789\pi$
$758$	47576.3	2.27975
$759$	−1995.59	−0.0954352
$760$	134894.	6.43832
$761$	−2089.08	−0.0995125	−0.0497562	−	0.998761i	$-0.515844\pi$
$761$	−2089.08	−0.0995125	−0.0497562	+	0.998761i	$0.515844\pi$
$762$	1052.60	0.0500416
$763$	0	0
$764$	−51263.3	−2.42754
$765$	−4992.40	−0.235949
$766$	10487.5	0.494684
$767$	950.334	0.0447387
$768$	32348.5	1.51989
$769$	−34980.5	−1.64035	−0.820175	−	0.572113i	$-0.806124\pi$
$769$	−34980.5	−1.64035	−0.820175	+	0.572113i	$0.806124\pi$
$770$	0	0
$771$	23503.7	1.09788
$772$	−1914.66	−0.0892619
$773$	−26234.1	−1.22067	−0.610333	−	0.792145i	$-0.708965\pi$
$773$	−26234.1	−1.22067	−0.610333	+	0.792145i	$0.708965\pi$
$774$	3777.69	0.175434
$775$	−4336.39	−0.200990
$776$	23050.8	1.06633
$777$	0	0
$778$	29223.6	1.34668
$779$	−5267.07	−0.242250
$780$	7831.77	0.359516
$781$	1158.79	0.0530919
$782$	−13684.9	−0.625792
$783$	11190.9	0.510765
$784$	0	0
$785$	−57111.4	−2.59668
$786$	−73638.8	−3.34174
$787$	−25461.5	−1.15325	−0.576624	−	0.817010i	$-0.695630\pi$
$787$	−25461.5	−1.15325	−0.576624	+	0.817010i	$0.695630\pi$
$788$	51881.4	2.34543
$789$	−15451.6	−0.697199
$790$	−25629.7	−1.15426
$791$	0	0
$792$	1924.98	0.0863651
$793$	−1811.81	−0.0811342
$794$	29817.7	1.33273
$795$	62942.9	2.80799
$796$	−101171.	−4.50492
$797$	−35392.1	−1.57297	−0.786483	−	0.617612i	$-0.788100\pi$
$797$	−35392.1	−1.57297	−0.786483	+	0.617612i	$0.788100\pi$
$798$	0	0
$799$	−12376.9	−0.548014
$800$	−62487.3	−2.76158
$801$	8134.37	0.358819
$802$	−35316.5	−1.55495
$803$	−2053.24	−0.0902331
$804$	84489.8	3.70613
$805$	0	0
$806$	−381.238	−0.0166607
$807$	41068.3	1.79142
$808$	98762.9	4.30008
$809$	−10434.5	−0.453470	−0.226735	−	0.973956i	$-0.572805\pi$
$809$	−10434.5	−0.453470	−0.226735	+	0.973956i	$0.572805\pi$
$810$	85416.4	3.70522
$811$	13361.1	0.578510	0.289255	−	0.957252i	$-0.406592\pi$
$811$	13361.1	0.578510	0.289255	+	0.957252i	$0.406592\pi$
$812$	0	0
$813$	31515.3	1.35952
$814$	8555.99	0.368412
$815$	43195.3	1.85652
$816$	26799.5	1.14972
$817$	11076.8	0.474330
$818$	24142.2	1.03192
$819$	0	0
$820$	14402.4	0.613358
$821$	34916.8	1.48429	0.742146	−	0.670238i	$-0.233808\pi$
$821$	34916.8	1.48429	0.742146	+	0.670238i	$0.233808\pi$
$822$	61067.3	2.59120
$823$	1480.10	0.0626890	0.0313445	−	0.999509i	$-0.490021\pi$
$823$	1480.10	0.0626890	0.0313445	+	0.999509i	$0.490021\pi$
$824$	−28691.7	−1.21301
$825$	5306.17	0.223924
$826$	0	0
$827$	38330.1	1.61169	0.805845	−	0.592126i	$-0.201711\pi$
$827$	38330.1	1.61169	0.805845	+	0.592126i	$0.201711\pi$
$828$	−13256.3	−0.556389
$829$	−19823.1	−0.830499	−0.415250	−	0.909708i	$-0.636306\pi$
$829$	−19823.1	−0.830499	−0.415250	+	0.909708i	$0.636306\pi$
$830$	−81703.8	−3.41684
$831$	−38629.0	−1.61255
$832$	−1249.65	−0.0520719
$833$	0	0
$834$	−6691.09	−0.277810
$835$	−55421.6	−2.29694
$836$	9791.34	0.405072
$837$	−2168.57	−0.0895540
$838$	−3374.95	−0.139124
$839$	−20810.5	−0.856328	−0.428164	−	0.903701i	$-0.640839\pi$
$839$	−20810.5	−0.856328	−0.428164	+	0.903701i	$0.640839\pi$
$840$	0	0
$841$	−14123.2	−0.579080
$842$	−53395.7	−2.18544
$843$	−12570.0	−0.513563
$844$	−43225.5	−1.76290
$845$	−40597.6	−1.65278
$846$	−17067.3	−0.693599
$847$	0	0
$848$	−80532.5	−3.26120
$849$	49111.1	1.98526
$850$	36387.4	1.46832
$851$	−33965.7	−1.36819
$852$	32296.1	1.29865
$853$	7.14093	0.000286636 0	0.000143318	−	1.00000i	$-0.499954\pi$
$853$	7.14093	0.000286636 0	0.000143318		1.00000i	$0.499954\pi$
$854$	0	0
$855$	−20186.0	−0.807422
$856$	−67828.8	−2.70834
$857$	−5855.40	−0.233392	−0.116696	−	0.993168i	$-0.537230\pi$
$857$	−5855.40	−0.233392	−0.116696	+	0.993168i	$0.537230\pi$
$858$	466.498	0.0185617
$859$	1149.27	0.0456492	0.0228246	−	0.999739i	$-0.492734\pi$
$859$	1149.27	0.0456492	0.0228246	+	0.999739i	$0.492734\pi$
$860$	−30288.7	−1.20097
$861$	0	0
$862$	−22767.7	−0.899617
$863$	25842.6	1.01934	0.509672	−	0.860369i	$-0.329767\pi$
$863$	25842.6	1.01934	0.509672	+	0.860369i	$0.329767\pi$
$864$	−31249.1	−1.23046
$865$	65301.5	2.56684
$866$	48962.1	1.92125
$867$	23241.3	0.910401
$868$	0	0
$869$	−1072.42	−0.0418635
$870$	58174.9	2.26703
$871$	2813.25	0.109441
$872$	−60583.2	−2.35276
$873$	−3449.39	−0.133728
$874$	−55332.5	−2.14148
$875$	0	0
$876$	−57224.9	−2.20713
$877$	28179.6	1.08501	0.542507	−	0.840051i	$-0.317475\pi$
$877$	28179.6	1.08501	0.542507	+	0.840051i	$0.317475\pi$
$878$	−12850.6	−0.493950
$879$	−22666.5	−0.869763
$880$	−10631.3	−0.407252
$881$	−46830.8	−1.79088	−0.895442	−	0.445178i	$-0.853141\pi$
$881$	−46830.8	−1.79088	−0.895442	+	0.445178i	$0.853141\pi$
$882$	0	0
$883$	21861.4	0.833178	0.416589	−	0.909095i	$-0.363226\pi$
$883$	21861.4	0.833178	0.416589	+	0.909095i	$0.363226\pi$
$884$	2247.25	0.0855012
$885$	28101.2	1.06736
$886$	−74666.7	−2.83124
$887$	−12086.9	−0.457539	−0.228769	−	0.973481i	$-0.573470\pi$
$887$	−12086.9	−0.457539	−0.228769	+	0.973481i	$0.573470\pi$
$888$	137464.	5.19479
$889$	0	0
$890$	−92842.4	−3.49673
$891$	3574.07	0.134384
$892$	83503.7	3.13443
$893$	−50044.0	−1.87532
$894$	84369.3	3.15630
$895$	6581.98	0.245823
$896$	0	0
$897$	−1851.91	−0.0689336
$898$	−41907.2	−1.55731
$899$	−1989.32	−0.0738013
$900$	35247.9	1.30548
$901$	18060.8	0.667806
$902$	857.877	0.0316676
$903$	0	0
$904$	65844.2	2.42251
$905$	33090.4	1.21543
$906$	−1123.66	−0.0412043
$907$	−49395.1	−1.80831	−0.904155	−	0.427205i	$-0.859498\pi$
$907$	−49395.1	−1.80831	−0.904155	+	0.427205i	$0.859498\pi$
$908$	−13344.5	−0.487723
$909$	−14779.2	−0.539268
$910$	0	0
$911$	−15571.8	−0.566320	−0.283160	−	0.959073i	$-0.591383\pi$
$911$	−15571.8	−0.566320	−0.283160	+	0.959073i	$0.591383\pi$
$912$	108359.	3.93437
$913$	−3418.72	−0.123925
$914$	−26395.3	−0.955228
$915$	−53575.0	−1.93567
$916$	−70417.1	−2.54001
$917$	0	0
$918$	18196.8	0.654232
$919$	−34128.6	−1.22502	−0.612512	−	0.790461i	$-0.709841\pi$
$919$	−34128.6	−1.22502	−0.612512	+	0.790461i	$0.709841\pi$
$920$	87220.5	3.12563
$921$	46106.9	1.64959
$922$	65174.2	2.32798
$923$	1075.36	0.0383487
$924$	0	0
$925$	90313.0	3.21024
$926$	−76776.2	−2.72465
$927$	4293.52	0.152123
$928$	−28666.0	−1.01402
$929$	32981.6	1.16479	0.582396	−	0.812905i	$-0.302115\pi$
$929$	32981.6	1.16479	0.582396	+	0.812905i	$0.302115\pi$
$930$	−11273.1	−0.397485
$931$	0	0
$932$	−92168.6	−3.23936
$933$	45450.5	1.59484
$934$	−30986.1	−1.08554
$935$	2384.26	0.0833943
$936$	1786.38	0.0623822
$937$	26741.8	0.932355	0.466178	−	0.884691i	$-0.345631\pi$
$937$	26741.8	0.932355	0.466178	+	0.884691i	$0.345631\pi$
$938$	0	0
$939$	−45706.6	−1.58848
$940$	136842.	4.74817
$941$	−15863.0	−0.549542	−0.274771	−	0.961510i	$-0.588602\pi$
$941$	−15863.0	−0.549542	−0.274771	+	0.961510i	$0.588602\pi$
$942$	−94810.9	−3.27930
$943$	−3405.61	−0.117605
$944$	−35954.2	−1.23963
$945$	0	0
$946$	−1804.14	−0.0620059
$947$	8387.53	0.287812	0.143906	−	0.989591i	$-0.454034\pi$
$947$	8387.53	0.287812	0.143906	+	0.989591i	$0.454034\pi$
$948$	−29889.0	−1.02400
$949$	−1905.41	−0.0651761
$950$	147126.	5.02464
$951$	28161.6	0.960256
$952$	0	0
$953$	−35820.4	−1.21756	−0.608782	−	0.793338i	$-0.708341\pi$
$953$	−35820.4	−1.21756	−0.608782	+	0.793338i	$0.708341\pi$
$954$	24905.2	0.845214
$955$	−50472.9	−1.71022
$956$	99629.0	3.37054
$957$	2434.20	0.0822222
$958$	−55291.0	−1.86469
$959$	0	0
$960$	−36951.9	−1.24231
$961$	−29405.5	−0.987060
$962$	7939.97	0.266107
$963$	10150.1	0.339650
$964$	53760.8	1.79618
$965$	−1885.14	−0.0628859
$966$	0	0
$967$	−2618.25	−0.0870707	−0.0435353	−	0.999052i	$-0.513862\pi$
$967$	−2618.25	−0.0870707	−0.0435353	+	0.999052i	$0.513862\pi$
$968$	74231.5	2.46476
$969$	−24301.5	−0.805652
$970$	39369.9	1.30319
$971$	−22029.8	−0.728085	−0.364042	−	0.931382i	$-0.618604\pi$
$971$	−22029.8	−0.728085	−0.364042	+	0.931382i	$0.618604\pi$
$972$	43282.5	1.42828
$973$	0	0
$974$	48908.1	1.60895
$975$	4924.13	0.161742
$976$	68546.7	2.24808
$977$	27815.2	0.910835	0.455418	−	0.890278i	$-0.349490\pi$
$977$	27815.2	0.910835	0.455418	+	0.890278i	$0.349490\pi$
$978$	71708.7	2.34457
$979$	−3884.79	−0.126822
$980$	0	0
$981$	9065.86	0.295057
$982$	14419.3	0.468571
$983$	53.8574	0.00174749	0.000873746	−	1.00000i	$-0.499722\pi$
$983$	53.8574	0.00174749	0.000873746		1.00000i	$0.499722\pi$
$984$	13783.0	0.446529
$985$	51081.5	1.65238
$986$	16692.7	0.539152
$987$	0	0
$988$	9086.37	0.292587
$989$	7162.09	0.230274
$990$	3287.80	0.105549
$991$	19959.6	0.639795	0.319897	−	0.947452i	$-0.396352\pi$
$991$	19959.6	0.639795	0.319897	+	0.947452i	$0.396352\pi$
$992$	5554.91	0.177791
$993$	30852.7	0.985984
$994$	0	0
$995$	−99611.3	−3.17376
$996$	−95281.7	−3.03124
$997$	7778.61	0.247092	0.123546	−	0.992339i	$-0.460573\pi$
$997$	7778.61	0.247092	0.123546	+	0.992339i	$0.460573\pi$
$998$	−15756.7	−0.499768
$999$	45164.3	1.43037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.n.1.4	✓	60
7.6	odd	2		2009.4.a.o.1.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.4.a.n.1.4	✓	60	1.1	even	1	trivial
2009.4.a.o.1.4	yes	60	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q-5.18542 q^{2} -5.95392 q^{3} +18.8886 q^{4} +18.5974 q^{5} +30.8736 q^{6} -56.4620 q^{8} +8.44915 q^{9} +O(q^{10})\)	\(q-5.18542 q^{2} -5.95392 q^{3} +18.8886 q^{4} +18.5974 q^{5} +30.8736 q^{6} -56.4620 q^{8} +8.44915 q^{9} -96.4352 q^{10} -4.03513 q^{11} -112.461 q^{12} -3.74460 q^{13} -110.727 q^{15} +141.670 q^{16} -31.7720 q^{17} -43.8124 q^{18} -128.465 q^{19} +351.278 q^{20} +20.9238 q^{22} -83.0637 q^{23} +336.170 q^{24} +220.862 q^{25} +19.4173 q^{26} +110.450 q^{27} +101.320 q^{29} +574.167 q^{30} -19.6339 q^{31} -282.925 q^{32} +24.0248 q^{33} +164.751 q^{34} +159.593 q^{36} +408.911 q^{37} +666.146 q^{38} +22.2951 q^{39} -1050.04 q^{40} +41.0000 q^{41} -86.2241 q^{43} -76.2179 q^{44} +157.132 q^{45} +430.720 q^{46} +389.553 q^{47} -843.493 q^{48} -1145.26 q^{50} +189.168 q^{51} -70.7303 q^{52} -568.450 q^{53} -572.731 q^{54} -75.0427 q^{55} +764.871 q^{57} -525.389 q^{58} -253.788 q^{59} -2091.48 q^{60} +483.847 q^{61} +101.810 q^{62} +333.721 q^{64} -69.6397 q^{65} -124.579 q^{66} -751.280 q^{67} -600.129 q^{68} +494.554 q^{69} -287.176 q^{71} -477.055 q^{72} +508.841 q^{73} -2120.38 q^{74} -1315.00 q^{75} -2426.53 q^{76} -115.609 q^{78} +265.771 q^{79} +2634.69 q^{80} -885.739 q^{81} -212.602 q^{82} +847.241 q^{83} -590.876 q^{85} +447.108 q^{86} -603.254 q^{87} +227.831 q^{88} +962.744 q^{89} -814.795 q^{90} -1568.96 q^{92} +116.899 q^{93} -2020.00 q^{94} -2389.11 q^{95} +1684.51 q^{96} -408.253 q^{97} -34.0934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 2 q^{2} - 24 q^{3} + 230 q^{4} - 40 q^{5} - 72 q^{6} - 18 q^{8} + 572 q^{9}+O(q^{10}) \) 60 * q + 2 * q^2 - 24 * q^3 + 230 * q^4 - 40 * q^5 - 72 * q^6 - 18 * q^8 + 572 * q^9	\( 60 q + 2 q^{2} - 24 q^{3} + 230 q^{4} - 40 q^{5} - 72 q^{6} - 18 q^{8} + 572 q^{9} - 160 q^{10} - 100 q^{11} - 646 q^{12} - 156 q^{13} + 64 q^{15} + 1294 q^{16} - 136 q^{17} + 106 q^{18} - 848 q^{19} - 480 q^{20} - 236 q^{22} - 268 q^{23} - 864 q^{24} + 1500 q^{25} - 1150 q^{26} - 864 q^{27} - 276 q^{29} + 20 q^{30} - 2480 q^{31} + 18 q^{32} - 752 q^{33} - 1632 q^{34} + 2638 q^{36} + 152 q^{37} - 456 q^{38} - 448 q^{39} - 1972 q^{40} + 2460 q^{41} - 380 q^{43} - 560 q^{44} - 1800 q^{45} - 136 q^{46} - 1668 q^{47} - 5360 q^{48} - 430 q^{50} - 680 q^{51} - 1872 q^{52} - 1012 q^{53} - 1318 q^{54} - 6144 q^{55} + 1112 q^{57} - 596 q^{58} - 1888 q^{59} + 2284 q^{60} - 3176 q^{61} - 3440 q^{62} + 7210 q^{64} - 664 q^{65} - 2112 q^{66} + 660 q^{67} + 312 q^{68} - 7528 q^{69} - 2168 q^{71} - 1004 q^{72} - 3504 q^{73} + 286 q^{74} - 3112 q^{75} - 9008 q^{76} + 570 q^{78} + 1872 q^{79} - 4480 q^{80} + 3796 q^{81} + 82 q^{82} - 4600 q^{83} + 72 q^{85} - 816 q^{86} - 3480 q^{87} - 4884 q^{88} - 2600 q^{89} - 4320 q^{90} - 2810 q^{92} + 3376 q^{93} - 7610 q^{94} - 5672 q^{95} - 7294 q^{96} - 8648 q^{97} - 7620 q^{99}+O(q^{100}) \) 60 * q + 2 * q^2 - 24 * q^3 + 230 * q^4 - 40 * q^5 - 72 * q^6 - 18 * q^8 + 572 * q^9 - 160 * q^10 - 100 * q^11 - 646 * q^12 - 156 * q^13 + 64 * q^15 + 1294 * q^16 - 136 * q^17 + 106 * q^18 - 848 * q^19 - 480 * q^20 - 236 * q^22 - 268 * q^23 - 864 * q^24 + 1500 * q^25 - 1150 * q^26 - 864 * q^27 - 276 * q^29 + 20 * q^30 - 2480 * q^31 + 18 * q^32 - 752 * q^33 - 1632 * q^34 + 2638 * q^36 + 152 * q^37 - 456 * q^38 - 448 * q^39 - 1972 * q^40 + 2460 * q^41 - 380 * q^43 - 560 * q^44 - 1800 * q^45 - 136 * q^46 - 1668 * q^47 - 5360 * q^48 - 430 * q^50 - 680 * q^51 - 1872 * q^52 - 1012 * q^53 - 1318 * q^54 - 6144 * q^55 + 1112 * q^57 - 596 * q^58 - 1888 * q^59 + 2284 * q^60 - 3176 * q^61 - 3440 * q^62 + 7210 * q^64 - 664 * q^65 - 2112 * q^66 + 660 * q^67 + 312 * q^68 - 7528 * q^69 - 2168 * q^71 - 1004 * q^72 - 3504 * q^73 + 286 * q^74 - 3112 * q^75 - 9008 * q^76 + 570 * q^78 + 1872 * q^79 - 4480 * q^80 + 3796 * q^81 + 82 * q^82 - 4600 * q^83 + 72 * q^85 - 816 * q^86 - 3480 * q^87 - 4884 * q^88 - 2600 * q^89 - 4320 * q^90 - 2810 * q^92 + 3376 * q^93 - 7610 * q^94 - 5672 * q^95 - 7294 * q^96 - 8648 * q^97 - 7620 * q^99

Introduction

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