LMFDB - Embedded newform 2009.4.a.k.1.5

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:	$36$
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-4.65790 q^{2} +6.35474 q^{3} +13.6960 q^{4} +11.2439 q^{5} -29.5997 q^{6} -26.5313 q^{8} +13.3827 q^{9} +O(q^{10})$	\(q-4.65790 q^{2} +6.35474 q^{3} +13.6960 q^{4} +11.2439 q^{5} -29.5997 q^{6} -26.5313 q^{8} +13.3827 q^{9} -52.3728 q^{10} -29.2745 q^{11} +87.0345 q^{12} +35.0862 q^{13} +71.4520 q^{15} +14.0122 q^{16} -46.7240 q^{17} -62.3354 q^{18} -1.76354 q^{19} +153.996 q^{20} +136.358 q^{22} -68.4389 q^{23} -168.600 q^{24} +1.42486 q^{25} -163.428 q^{26} -86.5342 q^{27} -33.0184 q^{29} -332.816 q^{30} +97.7014 q^{31} +146.983 q^{32} -186.032 q^{33} +217.636 q^{34} +183.290 q^{36} -88.2462 q^{37} +8.21436 q^{38} +222.964 q^{39} -298.315 q^{40} -41.0000 q^{41} -128.780 q^{43} -400.943 q^{44} +150.474 q^{45} +318.781 q^{46} +240.799 q^{47} +89.0438 q^{48} -6.63687 q^{50} -296.919 q^{51} +480.540 q^{52} +313.153 q^{53} +403.067 q^{54} -329.159 q^{55} -11.2068 q^{57} +153.796 q^{58} +708.283 q^{59} +978.605 q^{60} -717.140 q^{61} -455.083 q^{62} -796.730 q^{64} +394.505 q^{65} +866.517 q^{66} -767.607 q^{67} -639.932 q^{68} -434.912 q^{69} +318.806 q^{71} -355.062 q^{72} +1178.08 q^{73} +411.041 q^{74} +9.05465 q^{75} -24.1534 q^{76} -1038.54 q^{78} -239.006 q^{79} +157.551 q^{80} -911.236 q^{81} +190.974 q^{82} -553.454 q^{83} -525.360 q^{85} +599.842 q^{86} -209.823 q^{87} +776.691 q^{88} -850.686 q^{89} -700.892 q^{90} -937.339 q^{92} +620.867 q^{93} -1121.61 q^{94} -19.8290 q^{95} +934.040 q^{96} -1229.07 q^{97} -391.773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9	\( 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9} + 12 q^{10} - 140 q^{11} - 186 q^{12} + 72 q^{13} - 366 q^{15} - 15 q^{16} + 2 q^{17} - 212 q^{18} - 30 q^{19} + 334 q^{20} - 346 q^{22} - 314 q^{23} - 106 q^{24} + 570 q^{25} - 303 q^{26} + 204 q^{27} - 356 q^{29} - 357 q^{30} + 4 q^{31} - 532 q^{32} + 30 q^{33} + 364 q^{34} + 113 q^{36} - 1398 q^{37} + 264 q^{38} - 1348 q^{39} - 26 q^{40} - 1476 q^{41} - 1072 q^{43} - 1507 q^{44} + 1132 q^{45} - 1356 q^{46} + 622 q^{47} - 1724 q^{48} - 1426 q^{50} - 668 q^{51} + 877 q^{52} - 412 q^{53} + 1814 q^{54} - 1114 q^{55} - 4082 q^{57} - 1309 q^{58} + 620 q^{59} - 3724 q^{60} - 774 q^{61} - 1665 q^{62} - 3285 q^{64} - 1036 q^{65} + 1056 q^{66} - 2972 q^{67} + 1525 q^{68} - 3304 q^{69} - 3540 q^{71} - 821 q^{72} + 60 q^{73} - 2043 q^{74} - 450 q^{75} - 2171 q^{76} - 1136 q^{78} - 5190 q^{79} + 1564 q^{80} + 284 q^{81} + 205 q^{82} - 1656 q^{83} - 5064 q^{85} - 782 q^{86} + 1940 q^{87} - 4232 q^{88} + 1196 q^{89} - 8030 q^{90} - 4618 q^{92} + 698 q^{93} + 35 q^{94} - 1968 q^{95} + 7926 q^{96} - 3862 q^{97} - 5964 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9 + 12 * q^10 - 140 * q^11 - 186 * q^12 + 72 * q^13 - 366 * q^15 - 15 * q^16 + 2 * q^17 - 212 * q^18 - 30 * q^19 + 334 * q^20 - 346 * q^22 - 314 * q^23 - 106 * q^24 + 570 * q^25 - 303 * q^26 + 204 * q^27 - 356 * q^29 - 357 * q^30 + 4 * q^31 - 532 * q^32 + 30 * q^33 + 364 * q^34 + 113 * q^36 - 1398 * q^37 + 264 * q^38 - 1348 * q^39 - 26 * q^40 - 1476 * q^41 - 1072 * q^43 - 1507 * q^44 + 1132 * q^45 - 1356 * q^46 + 622 * q^47 - 1724 * q^48 - 1426 * q^50 - 668 * q^51 + 877 * q^52 - 412 * q^53 + 1814 * q^54 - 1114 * q^55 - 4082 * q^57 - 1309 * q^58 + 620 * q^59 - 3724 * q^60 - 774 * q^61 - 1665 * q^62 - 3285 * q^64 - 1036 * q^65 + 1056 * q^66 - 2972 * q^67 + 1525 * q^68 - 3304 * q^69 - 3540 * q^71 - 821 * q^72 + 60 * q^73 - 2043 * q^74 - 450 * q^75 - 2171 * q^76 - 1136 * q^78 - 5190 * q^79 + 1564 * q^80 + 284 * q^81 + 205 * q^82 - 1656 * q^83 - 5064 * q^85 - 782 * q^86 + 1940 * q^87 - 4232 * q^88 + 1196 * q^89 - 8030 * q^90 - 4618 * q^92 + 698 * q^93 + 35 * q^94 - 1968 * q^95 + 7926 * q^96 - 3862 * q^97 - 5964 * 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 $

$2$	−4.65790	−1.64681	−0.823407	−	0.567451i	$-0.807930\pi$
$2$	−4.65790	−1.64681	−0.823407	+	0.567451i	$0.807930\pi$
$3$	6.35474	1.22297	0.611485	−	0.791256i	$-0.290572\pi$
$3$	6.35474	1.22297	0.611485	+	0.791256i	$0.290572\pi$
$4$	13.6960	1.71200
$5$	11.2439	1.00568	0.502842	−	0.864379i	$-0.332288\pi$
$5$	11.2439	1.00568	0.502842	+	0.864379i	$0.332288\pi$
$6$	−29.5997	−2.01401
$7$	0	0
$7$	0	0
$8$	−26.5313	−1.17253
$9$	13.3827	0.495657
$10$	−52.3728	−1.65617
$11$	−29.2745	−0.802418	−0.401209	−	0.915987i	$-0.631410\pi$
$11$	−29.2745	−0.802418	−0.401209	+	0.915987i	$0.631410\pi$
$12$	87.0345	2.09372
$13$	35.0862	0.748551	0.374275	−	0.927318i	$-0.377892\pi$
$13$	35.0862	0.748551	0.374275	+	0.927318i	$0.377892\pi$
$14$	0	0
$15$	71.4520	1.22992
$16$	14.0122	0.218940
$17$	−46.7240	−0.666603	−0.333301	−	0.942820i	$-0.608163\pi$
$17$	−46.7240	−0.666603	−0.333301	+	0.942820i	$0.608163\pi$
$18$	−62.3354	−0.816255
$19$	−1.76354	−0.0212938	−0.0106469	−	0.999943i	$-0.503389\pi$
$19$	−1.76354	−0.0212938	−0.0106469	+	0.999943i	$0.503389\pi$
$20$	153.996	1.72173
$21$	0	0
$22$	136.358	1.32143
$23$	−68.4389	−0.620457	−0.310228	−	0.950662i	$-0.600406\pi$
$23$	−68.4389	−0.620457	−0.310228	+	0.950662i	$0.600406\pi$
$24$	−168.600	−1.43397
$25$	1.42486	0.0113989
$26$	−163.428	−1.23272
$27$	−86.5342	−0.616797
$28$	0	0
$29$	−33.0184	−0.211426	−0.105713	−	0.994397i	$-0.533713\pi$
$29$	−33.0184	−0.211426	−0.105713	+	0.994397i	$0.533713\pi$
$30$	−332.816	−2.02545
$31$	97.7014	0.566055	0.283027	−	0.959112i	$-0.408661\pi$
$31$	97.7014	0.566055	0.283027	+	0.959112i	$0.408661\pi$
$32$	146.983	0.811975
$33$	−186.032	−0.981334
$34$	217.636	1.09777
$35$	0	0
$36$	183.290	0.848564
$37$	−88.2462	−0.392097	−0.196048	−	0.980594i	$-0.562811\pi$
$37$	−88.2462	−0.392097	−0.196048	+	0.980594i	$0.562811\pi$
$38$	8.21436	0.0350670
$39$	222.964	0.915455
$40$	−298.315	−1.17919
$41$	−41.0000	−0.156174
$41$	−41.0000	−0.156174
$42$	0	0
$43$	−128.780	−0.456714	−0.228357	−	0.973577i	$-0.573335\pi$
$43$	−128.780	−0.456714	−0.228357	+	0.973577i	$0.573335\pi$
$44$	−400.943	−1.37374
$45$	150.474	0.498474
$46$	318.781	1.02178
$47$	240.799	0.747321	0.373661	−	0.927566i	$-0.378103\pi$
$47$	240.799	0.747321	0.373661	+	0.927566i	$0.378103\pi$
$48$	89.0438	0.267758
$49$	0	0
$50$	−6.63687	−0.0187719
$51$	−296.919	−0.815235
$52$	480.540	1.28152
$53$	313.153	0.811601	0.405801	−	0.913962i	$-0.366993\pi$
$53$	313.153	0.811601	0.405801	+	0.913962i	$0.366993\pi$
$54$	403.067	1.01575
$55$	−329.159	−0.806978
$56$	0	0
$57$	−11.2068	−0.0260417
$58$	153.796	0.348180
$59$	708.283	1.56289	0.781445	−	0.623974i	$-0.214483\pi$
$59$	708.283	1.56289	0.781445	+	0.623974i	$0.214483\pi$
$60$	978.605	2.10562
$61$	−717.140	−1.50525	−0.752626	−	0.658448i	$-0.771213\pi$
$61$	−717.140	−1.50525	−0.752626	+	0.658448i	$0.771213\pi$
$62$	−455.083	−0.932187
$63$	0	0
$64$	−796.730	−1.55611
$65$	394.505	0.752805
$66$	866.517	1.61607
$67$	−767.607	−1.39967	−0.699837	−	0.714303i	$-0.746744\pi$
$67$	−767.607	−1.39967	−0.699837	+	0.714303i	$0.746744\pi$
$68$	−639.932	−1.14122
$69$	−434.912	−0.758800
$70$	0	0
$71$	318.806	0.532892	0.266446	−	0.963850i	$-0.414151\pi$
$71$	318.806	0.532892	0.266446	+	0.963850i	$0.414151\pi$
$72$	−355.062	−0.581173
$73$	1178.08	1.88881	0.944407	−	0.328778i	$-0.106637\pi$
$73$	1178.08	1.88881	0.944407	+	0.328778i	$0.106637\pi$
$74$	411.041	0.645711
$75$	9.05465	0.0139405
$76$	−24.1534	−0.0364550
$77$	0	0
$78$	−1038.54	−1.50759
$79$	−239.006	−0.340384	−0.170192	−	0.985411i	$-0.554439\pi$
$79$	−239.006	−0.340384	−0.170192	+	0.985411i	$0.554439\pi$
$80$	157.551	0.220185
$81$	−911.236	−1.24998
$82$	190.974	0.257189
$83$	−553.454	−0.731921	−0.365960	−	0.930630i	$-0.619259\pi$
$83$	−553.454	−0.731921	−0.365960	+	0.930630i	$0.619259\pi$
$84$	0	0
$85$	−525.360	−0.670391
$86$	599.842	0.752123
$87$	−209.823	−0.258568
$88$	776.691	0.940859
$89$	−850.686	−1.01317	−0.506587	−	0.862189i	$-0.669093\pi$
$89$	−850.686	−1.01317	−0.506587	+	0.862189i	$0.669093\pi$
$90$	−700.892	−0.820894
$91$	0	0
$92$	−937.339	−1.06222
$93$	620.867	0.692268
$94$	−1121.61	−1.23070
$95$	−19.8290	−0.0214148
$96$	934.040	0.993022
$97$	−1229.07	−1.28652	−0.643262	−	0.765646i	$-0.722419\pi$
$97$	−1229.07	−1.28652	−0.643262	+	0.765646i	$0.722419\pi$
$98$	0	0
$99$	−391.773	−0.397724
$100$	19.5149	0.0195149
$101$	−1163.20	−1.14597	−0.572985	−	0.819566i	$-0.694215\pi$
$101$	−1163.20	−1.14597	−0.572985	+	0.819566i	$0.694215\pi$
$102$	1383.02	1.34254
$103$	−981.179	−0.938626	−0.469313	−	0.883032i	$-0.655498\pi$
$103$	−981.179	−0.938626	−0.469313	+	0.883032i	$0.655498\pi$
$104$	−930.883	−0.877698
$105$	0	0
$106$	−1458.63	−1.33656
$107$	−310.626	−0.280649	−0.140324	−	0.990106i	$-0.544815\pi$
$107$	−310.626	−0.280649	−0.140324	+	0.990106i	$0.544815\pi$
$108$	−1185.17	−1.05595
$109$	−78.0135	−0.0685536	−0.0342768	−	0.999412i	$-0.510913\pi$
$109$	−78.0135	−0.0685536	−0.0342768	+	0.999412i	$0.510913\pi$
$110$	1533.19	1.32894
$111$	−560.782	−0.479523
$112$	0	0
$113$	408.421	0.340009	0.170005	−	0.985443i	$-0.445622\pi$
$113$	408.421	0.340009	0.170005	+	0.985443i	$0.445622\pi$
$114$	52.2002	0.0428859
$115$	−769.519	−0.623983
$116$	−452.220	−0.361962
$117$	469.549	0.371024
$118$	−3299.11	−2.57379
$119$	0	0
$120$	−1895.71	−1.44212
$121$	−474.003	−0.356125
$122$	3340.36	2.47887
$123$	−260.544	−0.190996
$124$	1338.12	0.969085
$125$	−1389.46	−0.994220
$126$	0	0
$127$	164.932	0.115239	0.0576195	−	0.998339i	$-0.481649\pi$
$127$	164.932	0.115239	0.0576195	+	0.998339i	$0.481649\pi$
$128$	2535.22	1.75065
$129$	−818.361	−0.558548
$130$	−1837.56	−1.23973
$131$	−2049.85	−1.36715	−0.683574	−	0.729881i	$-0.739575\pi$
$131$	−2049.85	−1.36715	−0.683574	+	0.729881i	$0.739575\pi$
$132$	−2547.89	−1.68004
$133$	0	0
$134$	3575.43	2.30500
$135$	−972.980	−0.620302
$136$	1239.65	0.781611
$137$	−1814.88	−1.13179	−0.565895	−	0.824477i	$-0.691469\pi$
$137$	−1814.88	−1.13179	−0.565895	+	0.824477i	$0.691469\pi$
$138$	2025.77	1.24960
$139$	−258.887	−0.157975	−0.0789874	−	0.996876i	$-0.525169\pi$
$139$	−258.887	−0.157975	−0.0789874	+	0.996876i	$0.525169\pi$
$140$	0	0
$141$	1530.21	0.913952
$142$	−1484.96	−0.877574
$143$	−1027.13	−0.600650
$144$	187.521	0.108519
$145$	−371.255	−0.212628
$146$	−5487.36	−3.11053
$147$	0	0
$148$	−1208.62	−0.671269
$149$	644.321	0.354261	0.177130	−	0.984187i	$-0.443319\pi$
$149$	644.321	0.354261	0.177130	+	0.984187i	$0.443319\pi$
$150$	−42.1756	−0.0229575
$151$	1924.73	1.03730	0.518649	−	0.854987i	$-0.326435\pi$
$151$	1924.73	1.03730	0.518649	+	0.854987i	$0.326435\pi$
$152$	46.7889	0.0249676
$153$	−625.296	−0.330406
$154$	0	0
$155$	1098.54	0.569272
$156$	3053.71	1.56726
$157$	−1700.36	−0.864353	−0.432177	−	0.901789i	$-0.642254\pi$
$157$	−1700.36	−0.864353	−0.432177	+	0.901789i	$0.642254\pi$
$158$	1113.27	0.560549
$159$	1990.01	0.992565
$160$	1652.66	0.816590
$161$	0	0
$162$	4244.44	2.05849
$163$	1711.34	0.822345	0.411173	−	0.911557i	$-0.365119\pi$
$163$	1711.34	0.822345	0.411173	+	0.911557i	$0.365119\pi$
$164$	−561.536	−0.267369
$165$	−2091.72	−0.986911
$166$	2577.93	1.20534
$167$	−936.113	−0.433764	−0.216882	−	0.976198i	$-0.569589\pi$
$167$	−936.113	−0.433764	−0.216882	+	0.976198i	$0.569589\pi$
$168$	0	0
$169$	−965.959	−0.439672
$170$	2447.07	1.10401
$171$	−23.6009	−0.0105544
$172$	−1763.76	−0.781894
$173$	−2719.97	−1.19535	−0.597675	−	0.801739i	$-0.703909\pi$
$173$	−2719.97	−1.19535	−0.597675	+	0.801739i	$0.703909\pi$
$174$	977.336	0.425814
$175$	0	0
$176$	−410.200	−0.175682
$177$	4500.95	1.91137
$178$	3962.41	1.66851
$179$	2665.43	1.11298	0.556491	−	0.830854i	$-0.312147\pi$
$179$	2665.43	1.11298	0.556491	+	0.830854i	$0.312147\pi$
$180$	2060.89	0.853387
$181$	1158.70	0.475832	0.237916	−	0.971286i	$-0.423536\pi$
$181$	1158.70	0.475832	0.237916	+	0.971286i	$0.423536\pi$
$182$	0	0
$183$	−4557.24	−1.84088
$184$	1815.78	0.727504
$185$	−992.229	−0.394325
$186$	−2891.93	−1.14004
$187$	1367.82	0.534894
$188$	3297.97	1.27941
$189$	0	0
$190$	92.3613	0.0352663
$191$	297.589	0.112737	0.0563685	−	0.998410i	$-0.482048\pi$
$191$	297.589	0.112737	0.0563685	+	0.998410i	$0.482048\pi$
$192$	−5063.01	−1.90308
$193$	2332.07	0.869772	0.434886	−	0.900485i	$-0.356789\pi$
$193$	2332.07	0.869772	0.434886	+	0.900485i	$0.356789\pi$
$194$	5724.86	2.11867
$195$	2506.98	0.920658
$196$	0	0
$197$	1130.98	0.409029	0.204515	−	0.978864i	$-0.434438\pi$
$197$	1130.98	0.409029	0.204515	+	0.978864i	$0.434438\pi$
$198$	1824.84	0.654978
$199$	−3174.97	−1.13099	−0.565497	−	0.824750i	$-0.691316\pi$
$199$	−3174.97	−1.13099	−0.565497	+	0.824750i	$0.691316\pi$
$200$	−37.8035	−0.0133656
$201$	−4877.94	−1.71176
$202$	5418.08	1.88720
$203$	0	0
$204$	−4066.60	−1.39568
$205$	−460.999	−0.157061
$206$	4570.23	1.54574
$207$	−915.901	−0.307534
$208$	491.634	0.163888
$209$	51.6266	0.0170866
$210$	0	0
$211$	−3954.25	−1.29015	−0.645075	−	0.764119i	$-0.723174\pi$
$211$	−3954.25	−1.29015	−0.645075	+	0.764119i	$0.723174\pi$
$212$	4288.94	1.38946
$213$	2025.93	0.651711
$214$	1446.87	0.462176
$215$	−1447.98	−0.459310
$216$	2295.87	0.723212
$217$	0	0
$218$	363.379	0.112895
$219$	7486.37	2.30996
$220$	−4508.16	−1.38155
$221$	−1639.37	−0.498986
$222$	2612.06	0.789685
$223$	−3593.37	−1.07906	−0.539529	−	0.841967i	$-0.681398\pi$
$223$	−3593.37	−1.07906	−0.539529	+	0.841967i	$0.681398\pi$
$224$	0	0
$225$	19.0686	0.00564996
$226$	−1902.38	−0.559932
$227$	−2646.70	−0.773866	−0.386933	−	0.922108i	$-0.626465\pi$
$227$	−2646.70	−0.773866	−0.386933	+	0.922108i	$0.626465\pi$
$228$	−153.488	−0.0445834
$229$	−993.382	−0.286657	−0.143329	−	0.989675i	$-0.545781\pi$
$229$	−993.382	−0.286657	−0.143329	+	0.989675i	$0.545781\pi$
$230$	3584.34	1.02758
$231$	0	0
$232$	876.022	0.247904
$233$	−2194.66	−0.617069	−0.308534	−	0.951213i	$-0.599838\pi$
$233$	−2194.66	−0.617069	−0.308534	+	0.951213i	$0.599838\pi$
$234$	−2187.11	−0.611009
$235$	2707.51	0.751568
$236$	9700.63	2.67567
$237$	−1518.82	−0.416279
$238$	0	0
$239$	2942.63	0.796415	0.398207	−	0.917295i	$-0.369632\pi$
$239$	2942.63	0.796415	0.398207	+	0.917295i	$0.369632\pi$
$240$	1001.20	0.269279
$241$	6047.06	1.61629	0.808144	−	0.588985i	$-0.200472\pi$
$241$	6047.06	1.61629	0.808144	+	0.588985i	$0.200472\pi$
$242$	2207.86	0.586473
$243$	−3454.25	−0.911894
$244$	−9821.94	−2.57699
$245$	0	0
$246$	1213.59	0.314535
$247$	−61.8757	−0.0159395
$248$	−2592.15	−0.663716
$249$	−3517.05	−0.895118
$250$	6471.98	1.63730
$251$	−806.022	−0.202692	−0.101346	−	0.994851i	$-0.532315\pi$
$251$	−806.022	−0.202692	−0.101346	+	0.994851i	$0.532315\pi$
$252$	0	0
$253$	2003.52	0.497866
$254$	−768.236	−0.189777
$255$	−3338.52	−0.819869
$256$	−5434.94	−1.32689
$257$	−2236.08	−0.542734	−0.271367	−	0.962476i	$-0.587476\pi$
$257$	−2236.08	−0.542734	−0.271367	+	0.962476i	$0.587476\pi$
$258$	3811.84	0.919825
$259$	0	0
$260$	5403.14	1.28880
$261$	−441.877	−0.104795
$262$	9547.99	2.25144
$263$	5513.18	1.29261	0.646307	−	0.763078i	$-0.276313\pi$
$263$	5513.18	1.29261	0.646307	+	0.763078i	$0.276313\pi$
$264$	4935.67	1.15064
$265$	3521.06	0.816214
$266$	0	0
$267$	−5405.89	−1.23908
$268$	−10513.1	−2.39624
$269$	5504.99	1.24775	0.623876	−	0.781523i	$-0.285557\pi$
$269$	5504.99	1.24775	0.623876	+	0.781523i	$0.285557\pi$
$270$	4532.04	1.02152
$271$	4431.68	0.993379	0.496689	−	0.867928i	$-0.334549\pi$
$271$	4431.68	0.993379	0.496689	+	0.867928i	$0.334549\pi$
$272$	−654.706	−0.145946
$273$	0	0
$274$	8453.50	1.86385
$275$	−41.7122	−0.00914670
$276$	−5956.55	−1.29907
$277$	8803.39	1.90955	0.954773	−	0.297335i	$-0.0960979\pi$
$277$	8803.39	1.90955	0.954773	+	0.297335i	$0.0960979\pi$
$278$	1205.87	0.260155
$279$	1307.51	0.280569
$280$	0	0
$281$	−4516.21	−0.958770	−0.479385	−	0.877605i	$-0.659140\pi$
$281$	−4516.21	−0.958770	−0.479385	+	0.877605i	$0.659140\pi$
$282$	−7127.57	−1.50511
$283$	−1075.14	−0.225832	−0.112916	−	0.993605i	$-0.536019\pi$
$283$	−1075.14	−0.225832	−0.112916	+	0.993605i	$0.536019\pi$
$284$	4366.36	0.912310
$285$	−126.008	−0.0261897
$286$	4784.27	0.989160
$287$	0	0
$288$	1967.04	0.402461
$289$	−2729.86	−0.555641
$290$	1729.27	0.350159
$291$	−7810.40	−1.57338
$292$	16134.9	3.23365
$293$	−1699.41	−0.338841	−0.169421	−	0.985544i	$-0.554190\pi$
$293$	−1699.41	−0.338841	−0.169421	+	0.985544i	$0.554190\pi$
$294$	0	0
$295$	7963.85	1.57177
$296$	2341.29	0.459745
$297$	2533.25	0.494929
$298$	−3001.18	−0.583402
$299$	−2401.26	−0.464443
$300$	124.012	0.0238662
$301$	0	0
$302$	−8965.17	−1.70824
$303$	−7391.85	−1.40149
$304$	−24.7110	−0.00466208
$305$	−8063.44	−1.51381
$306$	2912.56	0.544118
$307$	1251.70	0.232699	0.116349	−	0.993208i	$-0.462881\pi$
$307$	1251.70	0.232699	0.116349	+	0.993208i	$0.462881\pi$
$308$	0	0
$309$	−6235.14	−1.14791
$310$	−5116.90	−0.937485
$311$	580.513	0.105845	0.0529226	−	0.998599i	$-0.483146\pi$
$311$	580.513	0.105845	0.0529226	+	0.998599i	$0.483146\pi$
$312$	−5915.52	−1.07340
$313$	622.539	0.112422	0.0562109	−	0.998419i	$-0.482098\pi$
$313$	622.539	0.112422	0.0562109	+	0.998419i	$0.482098\pi$
$314$	7920.10	1.42343
$315$	0	0
$316$	−3273.43	−0.582737
$317$	10683.0	1.89279	0.946397	−	0.323005i	$-0.104693\pi$
$317$	10683.0	1.89279	0.946397	+	0.323005i	$0.104693\pi$
$318$	−9269.24	−1.63457
$319$	966.598	0.169652
$320$	−8958.34	−1.56496
$321$	−1973.95	−0.343225
$322$	0	0
$323$	82.3995	0.0141945
$324$	−12480.3	−2.13997
$325$	49.9931	0.00853267
$326$	−7971.23	−1.35425
$327$	−495.756	−0.0838390
$328$	1087.78	0.183118
$329$	0	0
$330$	9743.02	1.62526
$331$	−10922.3	−1.81373	−0.906863	−	0.421425i	$-0.861530\pi$
$331$	−10922.3	−1.81373	−0.906863	+	0.421425i	$0.861530\pi$
$332$	−7580.09	−1.25305
$333$	−1180.98	−0.194346
$334$	4360.32	0.714329
$335$	−8630.88	−1.40763
$336$	0	0
$337$	−1405.88	−0.227250	−0.113625	−	0.993524i	$-0.536246\pi$
$337$	−1405.88	−0.227250	−0.113625	+	0.993524i	$0.536246\pi$
$338$	4499.34	0.724058
$339$	2595.41	0.415821
$340$	−7195.32	−1.14771
$341$	−2860.16	−0.454212
$342$	109.931	0.0173812
$343$	0	0
$344$	3416.69	0.535511
$345$	−4890.10	−0.763113
$346$	12669.3	1.96852
$347$	−1677.71	−0.259551	−0.129776	−	0.991543i	$-0.541426\pi$
$347$	−1677.71	−0.259551	−0.129776	+	0.991543i	$0.541426\pi$
$348$	−2873.74	−0.442668
$349$	3336.36	0.511723	0.255862	−	0.966713i	$-0.417641\pi$
$349$	3336.36	0.511723	0.255862	+	0.966713i	$0.417641\pi$
$350$	0	0
$351$	−3036.15	−0.461703
$352$	−4302.86	−0.651544
$353$	−11354.0	−1.71193	−0.855964	−	0.517036i	$-0.827035\pi$
$353$	−11354.0	−1.71193	−0.855964	+	0.517036i	$0.827035\pi$
$354$	−20965.0	−3.14767
$355$	3584.62	0.535920
$356$	−11651.0	−1.73455
$357$	0	0
$358$	−12415.3	−1.83287
$359$	7003.21	1.02957	0.514784	−	0.857320i	$-0.327872\pi$
$359$	7003.21	1.02957	0.514784	+	0.857320i	$0.327872\pi$
$360$	−3992.27	−0.584476
$361$	−6855.89	−0.999547
$362$	−5397.11	−0.783608
$363$	−3012.17	−0.435531
$364$	0	0
$365$	13246.2	1.89955
$366$	21227.1	3.03159
$367$	−12464.2	−1.77283	−0.886414	−	0.462893i	$-0.846811\pi$
$367$	−12464.2	−1.77283	−0.886414	+	0.462893i	$0.846811\pi$
$368$	−958.979	−0.135843
$369$	−548.692	−0.0774086
$370$	4621.70	0.649380
$371$	0	0
$372$	8503.39	1.18516
$373$	−9341.71	−1.29677	−0.648385	−	0.761312i	$-0.724555\pi$
$373$	−9341.71	−1.29677	−0.648385	+	0.761312i	$0.724555\pi$
$374$	−6371.18	−0.880871
$375$	−8829.69	−1.21590
$376$	−6388.70	−0.876256
$377$	−1158.49	−0.158263
$378$	0	0
$379$	−13030.0	−1.76599	−0.882993	−	0.469386i	$-0.844475\pi$
$379$	−13030.0	−1.76599	−0.882993	+	0.469386i	$0.844475\pi$
$380$	−271.577	−0.0366622
$381$	1048.10	0.140934
$382$	−1386.14	−0.185657
$383$	8724.52	1.16397	0.581987	−	0.813198i	$-0.302275\pi$
$383$	8724.52	1.16397	0.581987	+	0.813198i	$0.302275\pi$
$384$	16110.7	2.14100
$385$	0	0
$386$	−10862.5	−1.43235
$387$	−1723.42	−0.226374
$388$	−16833.3	−2.20253
$389$	9396.81	1.22477	0.612387	−	0.790558i	$-0.290209\pi$
$389$	9396.81	1.22477	0.612387	+	0.790558i	$0.290209\pi$
$390$	−11677.2	−1.51615
$391$	3197.74	0.413598
$392$	0	0
$393$	−13026.3	−1.67198
$394$	−5267.97	−0.673595
$395$	−2687.36	−0.342318
$396$	−5365.72	−0.680903
$397$	−6108.93	−0.772288	−0.386144	−	0.922438i	$-0.626193\pi$
$397$	−6108.93	−0.772288	−0.386144	+	0.922438i	$0.626193\pi$
$398$	14788.7	1.86254
$399$	0	0
$400$	19.9655	0.00249568
$401$	−1900.95	−0.236731	−0.118365	−	0.992970i	$-0.537765\pi$
$401$	−1900.95	−0.236731	−0.118365	+	0.992970i	$0.537765\pi$
$402$	22720.9	2.81895
$403$	3427.97	0.423721
$404$	−15931.2	−1.96190
$405$	−10245.8	−1.25709
$406$	0	0
$407$	2583.36	0.314625
$408$	7877.66	0.955888
$409$	15668.0	1.89421	0.947105	−	0.320924i	$-0.103993\pi$
$409$	15668.0	1.89421	0.947105	+	0.320924i	$0.103993\pi$
$410$	2147.29	0.258651
$411$	−11533.1	−1.38415
$412$	−13438.2	−1.60693
$413$	0	0
$414$	4266.17	0.506451
$415$	−6222.97	−0.736080
$416$	5157.08	0.607805
$417$	−1645.16	−0.193198
$418$	−240.471	−0.0281384
$419$	9342.16	1.08925	0.544623	−	0.838681i	$-0.316673\pi$
$419$	9342.16	1.08925	0.544623	+	0.838681i	$0.316673\pi$
$420$	0	0
$421$	8369.67	0.968913	0.484457	−	0.874815i	$-0.339017\pi$
$421$	8369.67	0.968913	0.484457	+	0.874815i	$0.339017\pi$
$422$	18418.5	2.12464
$423$	3222.55	0.370415
$424$	−8308.36	−0.951627
$425$	−66.5754	−0.00759855
$426$	−9436.57	−1.07325
$427$	0	0
$428$	−4254.34	−0.480470
$429$	−6527.15	−0.734578
$430$	6744.55	0.756398
$431$	−16299.8	−1.82166	−0.910829	−	0.412784i	$-0.864556\pi$
$431$	−16299.8	−1.82166	−0.910829	+	0.412784i	$0.864556\pi$
$432$	−1212.53	−0.135042
$433$	−10004.5	−1.11036	−0.555181	−	0.831730i	$-0.687351\pi$
$433$	−10004.5	−1.11036	−0.555181	+	0.831730i	$0.687351\pi$
$434$	0	0
$435$	−2359.23	−0.260038
$436$	−1068.47	−0.117364
$437$	120.694	0.0132119
$438$	−34870.7	−3.80408
$439$	3101.00	0.337136	0.168568	−	0.985690i	$-0.446086\pi$
$439$	3101.00	0.337136	0.168568	+	0.985690i	$0.446086\pi$
$440$	8733.03	0.946206
$441$	0	0
$442$	7636.01	0.821737
$443$	−5634.48	−0.604294	−0.302147	−	0.953261i	$-0.597703\pi$
$443$	−5634.48	−0.604294	−0.302147	+	0.953261i	$0.597703\pi$
$444$	−7680.46	−0.820942
$445$	−9565.01	−1.01893
$446$	16737.5	1.77701
$447$	4094.50	0.433251
$448$	0	0
$449$	−1908.77	−0.200624	−0.100312	−	0.994956i	$-0.531984\pi$
$449$	−1908.77	−0.200624	−0.100312	+	0.994956i	$0.531984\pi$
$450$	−88.8195	−0.00930443
$451$	1200.26	0.125317
$452$	5593.73	0.582095
$453$	12231.1	1.26858
$454$	12328.0	1.27441
$455$	0	0
$456$	297.331	0.0305347
$457$	−13615.6	−1.39367	−0.696837	−	0.717230i	$-0.745410\pi$
$457$	−13615.6	−1.39367	−0.696837	+	0.717230i	$0.745410\pi$
$458$	4627.07	0.472072
$459$	4043.23	0.411158
$460$	−10539.3	−1.06826
$461$	6682.56	0.675136	0.337568	−	0.941301i	$-0.390396\pi$
$461$	6682.56	0.675136	0.337568	+	0.941301i	$0.390396\pi$
$462$	0	0
$463$	−13498.4	−1.35491	−0.677456	−	0.735563i	$-0.736918\pi$
$463$	−13498.4	−1.35491	−0.677456	+	0.735563i	$0.736918\pi$
$464$	−462.660	−0.0462898
$465$	6980.96	0.696202
$466$	10222.5	1.01620
$467$	241.279	0.0239081	0.0119540	−	0.999929i	$-0.496195\pi$
$467$	241.279	0.0239081	0.0119540	+	0.999929i	$0.496195\pi$
$468$	6430.94	0.635193
$469$	0	0
$470$	−12611.3	−1.23769
$471$	−10805.3	−1.05708
$472$	−18791.7	−1.83254
$473$	3769.96	0.366476
$474$	7074.52	0.685535
$475$	−2.51280	−0.000242727 0
$476$	0	0
$477$	4190.85	0.402276
$478$	−13706.5	−1.31155
$479$	7219.18	0.688628	0.344314	−	0.938855i	$-0.388112\pi$
$479$	7219.18	0.688628	0.344314	+	0.938855i	$0.388112\pi$
$480$	10502.2	0.998666
$481$	−3096.22	−0.293504
$482$	−28166.6	−2.66173
$483$	0	0
$484$	−6491.94	−0.609686
$485$	−13819.5	−1.29384
$486$	16089.5	1.50172
$487$	−12800.6	−1.19107	−0.595534	−	0.803330i	$-0.703059\pi$
$487$	−12800.6	−1.19107	−0.595534	+	0.803330i	$0.703059\pi$
$488$	19026.7	1.76495
$489$	10875.1	1.00570
$490$	0	0
$491$	−5589.73	−0.513770	−0.256885	−	0.966442i	$-0.582696\pi$
$491$	−5589.73	−0.513770	−0.256885	+	0.966442i	$0.582696\pi$
$492$	−3568.41	−0.326985
$493$	1542.75	0.140937
$494$	288.211	0.0262494
$495$	−4405.05	−0.399985
$496$	1369.01	0.123932
$497$	0	0
$498$	16382.1	1.47409
$499$	20648.9	1.85245	0.926223	−	0.376977i	$-0.123036\pi$
$499$	20648.9	1.85245	0.926223	+	0.376977i	$0.123036\pi$
$500$	−19030.1	−1.70210
$501$	−5948.76	−0.530481
$502$	3754.36	0.333796
$503$	10500.8	0.930830	0.465415	−	0.885093i	$-0.345905\pi$
$503$	10500.8	0.930830	0.465415	+	0.885093i	$0.345905\pi$
$504$	0	0
$505$	−13078.9	−1.15248
$506$	−9332.17	−0.819892
$507$	−6138.42	−0.537706
$508$	2258.91	0.197289
$509$	13072.1	1.13833	0.569165	−	0.822224i	$-0.307267\pi$
$509$	13072.1	1.13833	0.569165	+	0.822224i	$0.307267\pi$
$510$	15550.5	1.35017
$511$	0	0
$512$	5033.65	0.434488
$513$	152.606	0.0131340
$514$	10415.4	0.893782
$515$	−11032.3	−0.943960
$516$	−11208.3	−0.956233
$517$	−7049.26	−0.599664
$518$	0	0
$519$	−17284.7	−1.46188
$520$	−10466.7	−0.882686
$521$	583.304	0.0490499	0.0245250	−	0.999699i	$-0.492193\pi$
$521$	583.304	0.0490499	0.0245250	+	0.999699i	$0.492193\pi$
$522$	2058.22	0.172578
$523$	−20513.5	−1.71509	−0.857545	−	0.514410i	$-0.828011\pi$
$523$	−20513.5	−1.71509	−0.857545	+	0.514410i	$0.828011\pi$
$524$	−28074.7	−2.34055
$525$	0	0
$526$	−25679.8	−2.12869
$527$	−4565.00	−0.377333
$528$	−2606.71	−0.214854
$529$	−7483.11	−0.615033
$530$	−16400.7	−1.34415
$531$	9478.76	0.774658
$532$	0	0
$533$	−1438.53	−0.116904
$534$	25180.1	2.04054
$535$	−3492.65	−0.282244
$536$	20365.6	1.64116
$537$	16938.1	1.36114
$538$	−25641.7	−2.05482
$539$	0	0
$540$	−13325.9	−1.06196
$541$	−17912.5	−1.42351	−0.711755	−	0.702428i	$-0.752099\pi$
$541$	−17912.5	−1.42351	−0.711755	+	0.702428i	$0.752099\pi$
$542$	−20642.3	−1.63591
$543$	7363.25	0.581929
$544$	−6867.65	−0.541265
$545$	−877.175	−0.0689432
$546$	0	0
$547$	−20781.0	−1.62437	−0.812187	−	0.583397i	$-0.801723\pi$
$547$	−20781.0	−1.62437	−0.812187	+	0.583397i	$0.801723\pi$
$548$	−24856.5	−1.93762
$549$	−9597.30	−0.746089
$550$	194.291	0.0150629
$551$	58.2291	0.00450208
$552$	11538.8	0.889716
$553$	0	0
$554$	−41005.3	−3.14467
$555$	−6305.36	−0.482248
$556$	−3545.71	−0.270452
$557$	16805.0	1.27836	0.639182	−	0.769055i	$-0.279273\pi$
$557$	16805.0	1.27836	0.639182	+	0.769055i	$0.279273\pi$
$558$	−6090.26	−0.462045
$559$	−4518.38	−0.341874
$560$	0	0
$561$	8692.16	0.654160
$562$	21036.0	1.57892
$563$	536.176	0.0401370	0.0200685	−	0.999799i	$-0.493612\pi$
$563$	536.176	0.0401370	0.0200685	+	0.999799i	$0.493612\pi$
$564$	20957.8	1.56468
$565$	4592.24	0.341942
$566$	5007.90	0.371904
$567$	0	0
$568$	−8458.34	−0.624831
$569$	19828.2	1.46088	0.730441	−	0.682976i	$-0.239315\pi$
$569$	19828.2	1.46088	0.730441	+	0.682976i	$0.239315\pi$
$570$	586.932	0.0431296
$571$	15823.3	1.15969	0.579846	−	0.814726i	$-0.303113\pi$
$571$	15823.3	1.15969	0.579846	+	0.814726i	$0.303113\pi$
$572$	−14067.6	−1.02831
$573$	1891.10	0.137874
$574$	0	0
$575$	−97.5162	−0.00707254
$576$	−10662.4	−0.771299
$577$	1319.24	0.0951832	0.0475916	−	0.998867i	$-0.484845\pi$
$577$	1319.24	0.0951832	0.0475916	+	0.998867i	$0.484845\pi$
$578$	12715.4	0.915038
$579$	14819.7	1.06371
$580$	−5084.70	−0.364019
$581$	0	0
$582$	36380.0	2.59107
$583$	−9167.40	−0.651244
$584$	−31255.9	−2.21469
$585$	5279.56	0.373133
$586$	7915.66	0.558009
$587$	−17982.6	−1.26443	−0.632217	−	0.774792i	$-0.717855\pi$
$587$	−17982.6	−1.26443	−0.632217	+	0.774792i	$0.717855\pi$
$588$	0	0
$589$	−172.300	−0.0120535
$590$	−37094.8	−2.58842
$591$	7187.06	0.500230
$592$	−1236.52	−0.0858458
$593$	−12533.4	−0.867932	−0.433966	−	0.900929i	$-0.642886\pi$
$593$	−12533.4	−0.867932	−0.433966	+	0.900929i	$0.642886\pi$
$594$	−11799.6	−0.815056
$595$	0	0
$596$	8824.62	0.606494
$597$	−20176.1	−1.38317
$598$	11184.8	0.764852
$599$	3518.73	0.240019	0.120010	−	0.992773i	$-0.461707\pi$
$599$	3518.73	0.240019	0.120010	+	0.992773i	$0.461707\pi$
$600$	−240.232	−0.0163457
$601$	−20182.2	−1.36980	−0.684900	−	0.728637i	$-0.740154\pi$
$601$	−20182.2	−1.36980	−0.684900	+	0.728637i	$0.740154\pi$
$602$	0	0
$603$	−10272.7	−0.693758
$604$	26361.0	1.77585
$605$	−5329.63	−0.358149
$606$	34430.5	2.30799
$607$	−17625.6	−1.17858	−0.589292	−	0.807920i	$-0.700593\pi$
$607$	−17625.6	−1.17858	−0.589292	+	0.807920i	$0.700593\pi$
$608$	−259.210	−0.0172901
$609$	0	0
$610$	37558.6	2.49296
$611$	8448.71	0.559408
$612$	−8564.04	−0.565655
$613$	16125.4	1.06248	0.531238	−	0.847223i	$-0.321727\pi$
$613$	16125.4	1.06248	0.531238	+	0.847223i	$0.321727\pi$
$614$	−5830.31	−0.383212
$615$	−2929.53	−0.192081
$616$	0	0
$617$	18923.0	1.23470	0.617352	−	0.786687i	$-0.288205\pi$
$617$	18923.0	1.23470	0.617352	+	0.786687i	$0.288205\pi$
$618$	29042.6	1.89040
$619$	−27703.0	−1.79883	−0.899417	−	0.437091i	$-0.856009\pi$
$619$	−27703.0	−1.79883	−0.899417	+	0.437091i	$0.856009\pi$
$620$	15045.6	0.974592
$621$	5922.31	0.382696
$622$	−2703.97	−0.174307
$623$	0	0
$624$	3124.21	0.200430
$625$	−15801.1	−1.01127
$626$	−2899.72	−0.185138
$627$	328.074	0.0208963
$628$	−23288.1	−1.47977
$629$	4123.22	0.261373
$630$	0	0
$631$	−7598.50	−0.479384	−0.239692	−	0.970849i	$-0.577047\pi$
$631$	−7598.50	−0.479384	−0.239692	+	0.970849i	$0.577047\pi$
$632$	6341.15	0.399110
$633$	−25128.2	−1.57782
$634$	−49760.2	−3.11708
$635$	1854.48	0.115894
$636$	27255.1	1.69927
$637$	0	0
$638$	−4502.31	−0.279386
$639$	4266.50	0.264132
$640$	28505.7	1.76060
$641$	16821.9	1.03654	0.518272	−	0.855216i	$-0.326576\pi$
$641$	16821.9	1.03654	0.518272	+	0.855216i	$0.326576\pi$
$642$	9194.46	0.565228
$643$	2905.25	0.178183	0.0890917	−	0.996023i	$-0.471604\pi$
$643$	2905.25	0.178183	0.0890917	+	0.996023i	$0.471604\pi$
$644$	0	0
$645$	−9201.55	−0.561722
$646$	−383.808	−0.0233757
$647$	30004.9	1.82321	0.911604	−	0.411069i	$-0.134844\pi$
$647$	30004.9	1.82321	0.911604	+	0.411069i	$0.134844\pi$
$648$	24176.3	1.46564
$649$	−20734.6	−1.25409
$650$	−232.863	−0.0140517
$651$	0	0
$652$	23438.5	1.40785
$653$	21811.4	1.30711	0.653557	−	0.756877i	$-0.273276\pi$
$653$	21811.4	1.30711	0.653557	+	0.756877i	$0.273276\pi$
$654$	2309.18	0.138067
$655$	−23048.3	−1.37492
$656$	−574.500	−0.0341927
$657$	15765.9	0.936204
$658$	0	0
$659$	2115.51	0.125051	0.0625255	−	0.998043i	$-0.480085\pi$
$659$	2115.51	0.125051	0.0625255	+	0.998043i	$0.480085\pi$
$660$	−28648.2	−1.68959
$661$	6489.15	0.381843	0.190922	−	0.981605i	$-0.438852\pi$
$661$	6489.15	0.381843	0.190922	+	0.981605i	$0.438852\pi$
$662$	50874.9	2.98687
$663$	−10417.8	−0.610245
$664$	14683.9	0.858199
$665$	0	0
$666$	5500.86	0.320051
$667$	2259.74	0.131181
$668$	−12821.0	−0.742604
$669$	−22834.9	−1.31966
$670$	40201.7	2.31810
$671$	20993.9	1.20784
$672$	0	0
$673$	27925.9	1.59950	0.799752	−	0.600331i	$-0.204964\pi$
$673$	27925.9	1.59950	0.799752	+	0.600331i	$0.204964\pi$
$674$	6548.44	0.374238
$675$	−123.299	−0.00703081
$676$	−13229.8	−0.752718
$677$	−23956.7	−1.36002	−0.680009	−	0.733204i	$-0.738024\pi$
$677$	−23956.7	−1.36002	−0.680009	+	0.733204i	$0.738024\pi$
$678$	−12089.2	−0.684780
$679$	0	0
$680$	13938.5	0.786053
$681$	−16819.1	−0.946415
$682$	13322.3	0.748004
$683$	−13520.5	−0.757461	−0.378730	−	0.925507i	$-0.623639\pi$
$683$	−13520.5	−0.757461	−0.378730	+	0.925507i	$0.623639\pi$
$684$	−323.238	−0.0180692
$685$	−20406.2	−1.13822
$686$	0	0
$687$	−6312.69	−0.350574
$688$	−1804.48	−0.0999932
$689$	10987.3	0.607525
$690$	22777.6	1.25671
$691$	−1799.25	−0.0990546	−0.0495273	−	0.998773i	$-0.515771\pi$
$691$	−1799.25	−0.0990546	−0.0495273	+	0.998773i	$0.515771\pi$
$692$	−37252.7	−2.04644
$693$	0	0
$694$	7814.60	0.427432
$695$	−2910.89	−0.158873
$696$	5566.89	0.303179
$697$	1915.69	0.104106
$698$	−15540.4	−0.842713
$699$	−13946.5	−0.754657
$700$	0	0
$701$	−14305.5	−0.770775	−0.385387	−	0.922755i	$-0.625932\pi$
$701$	−14305.5	−0.770775	−0.385387	+	0.922755i	$0.625932\pi$
$702$	14142.1	0.760340
$703$	155.625	0.00834924
$704$	23323.9	1.24865
$705$	17205.5	0.919146
$706$	52885.5	2.81923
$707$	0	0
$708$	61645.0	3.27226
$709$	3351.96	0.177554	0.0887768	−	0.996052i	$-0.471704\pi$
$709$	3351.96	0.177554	0.0887768	+	0.996052i	$0.471704\pi$
$710$	−16696.8	−0.882561
$711$	−3198.56	−0.168714
$712$	22569.8	1.18798
$713$	−6686.58	−0.351212
$714$	0	0
$715$	−11548.9	−0.604064
$716$	36505.7	1.90542
$717$	18699.7	0.973992
$718$	−32620.2	−1.69551
$719$	25194.9	1.30683	0.653415	−	0.757000i	$-0.273336\pi$
$719$	25194.9	1.30683	0.653415	+	0.757000i	$0.273336\pi$
$720$	2108.47	0.109136
$721$	0	0
$722$	31934.0	1.64607
$723$	38427.5	1.97667
$724$	15869.6	0.814624
$725$	−47.0468	−0.00241003
$726$	14030.4	0.717239
$727$	13168.0	0.671766	0.335883	−	0.941904i	$-0.390965\pi$
$727$	13168.0	0.671766	0.335883	+	0.941904i	$0.390965\pi$
$728$	0	0
$729$	2652.52	0.134762
$730$	−61699.2	−3.12821
$731$	6017.10	0.304447
$732$	−62415.9	−3.15158
$733$	22001.9	1.10868	0.554339	−	0.832291i	$-0.312971\pi$
$733$	22001.9	1.10868	0.554339	+	0.832291i	$0.312971\pi$
$734$	58057.1	2.91952
$735$	0	0
$736$	−10059.4	−0.503796
$737$	22471.3	1.12312
$738$	2555.75	0.127478
$739$	27995.4	1.39354	0.696770	−	0.717294i	$-0.254620\pi$
$739$	27995.4	1.39354	0.696770	+	0.717294i	$0.254620\pi$
$740$	−13589.6	−0.675084
$741$	−393.204	−0.0194936
$742$	0	0
$743$	8468.12	0.418123	0.209061	−	0.977903i	$-0.432959\pi$
$743$	8468.12	0.418123	0.209061	+	0.977903i	$0.432959\pi$
$744$	−16472.4	−0.811705
$745$	7244.67	0.356274
$746$	43512.7	2.13554
$747$	−7406.73	−0.362782
$748$	18733.7	0.915738
$749$	0	0
$750$	41127.8	2.00236
$751$	2867.62	0.139335	0.0696677	−	0.997570i	$-0.477806\pi$
$751$	2867.62	0.139335	0.0696677	+	0.997570i	$0.477806\pi$
$752$	3374.12	0.163619
$753$	−5122.06	−0.247886
$754$	5396.13	0.260630
$755$	21641.4	1.04319
$756$	0	0
$757$	30665.9	1.47235	0.736177	−	0.676789i	$-0.236629\pi$
$757$	30665.9	1.47235	0.736177	+	0.676789i	$0.236629\pi$
$758$	60692.6	2.90825
$759$	12731.8	0.608875
$760$	526.089	0.0251095
$761$	22689.0	1.08078	0.540391	−	0.841414i	$-0.318276\pi$
$761$	22689.0	1.08078	0.540391	+	0.841414i	$0.318276\pi$
$762$	−4881.94	−0.232092
$763$	0	0
$764$	4075.77	0.193006
$765$	−7030.75	−0.332284
$766$	−40637.9	−1.91685
$767$	24850.9	1.16990
$768$	−34537.7	−1.62275
$769$	−2519.02	−0.118125	−0.0590626	−	0.998254i	$-0.518811\pi$
$769$	−2519.02	−0.118125	−0.0590626	+	0.998254i	$0.518811\pi$
$770$	0	0
$771$	−14209.7	−0.663747
$772$	31940.0	1.48905
$773$	−11854.3	−0.551580	−0.275790	−	0.961218i	$-0.588939\pi$
$773$	−11854.3	−0.551580	−0.275790	+	0.961218i	$0.588939\pi$
$774$	8027.53	0.372795
$775$	139.211	0.00645241
$776$	32608.8	1.50849
$777$	0	0
$778$	−43769.4	−2.01698
$779$	72.3049	0.00332554
$780$	34335.5	1.57617
$781$	−9332.89	−0.427602
$782$	−14894.8	−0.681119
$783$	2857.22	0.130407
$784$	0	0
$785$	−19118.6	−0.869266
$786$	60675.0	2.75344
$787$	10032.2	0.454394	0.227197	−	0.973849i	$-0.427044\pi$
$787$	10032.2	0.454394	0.227197	+	0.973849i	$0.427044\pi$
$788$	15489.8	0.700257
$789$	35034.8	1.58083
$790$	12517.4	0.563735
$791$	0	0
$792$	10394.3	0.466343
$793$	−25161.7	−1.12676
$794$	28454.8	1.27182
$795$	22375.4	0.998206
$796$	−43484.4	−1.93626
$797$	36341.2	1.61515	0.807573	−	0.589768i	$-0.200781\pi$
$797$	36341.2	1.61515	0.807573	+	0.589768i	$0.200781\pi$
$798$	0	0
$799$	−11251.1	−0.498166
$800$	209.431	0.00925564
$801$	−11384.5	−0.502187
$802$	8854.45	0.389852
$803$	−34487.6	−1.51562
$804$	−66808.3	−2.93053
$805$	0	0
$806$	−15967.1	−0.697789
$807$	34982.8	1.52596
$808$	30861.3	1.34368
$809$	−35568.5	−1.54576	−0.772881	−	0.634551i	$-0.781185\pi$
$809$	−35568.5	−1.54576	−0.772881	+	0.634551i	$0.781185\pi$
$810$	47724.0	2.07019
$811$	46.5715	0.00201646	0.00100823	−	0.999999i	$-0.499679\pi$
$811$	46.5715	0.00201646	0.00100823	+	0.999999i	$0.499679\pi$
$812$	0	0
$813$	28162.2	1.21487
$814$	−12033.0	−0.518130
$815$	19242.1	0.827019
$816$	−4160.49	−0.178488
$817$	227.107	0.00972519
$818$	−72979.8	−3.11941
$819$	0	0
$820$	−6313.84	−0.268889
$821$	−22881.8	−0.972691	−0.486345	−	0.873767i	$-0.661670\pi$
$821$	−22881.8	−0.972691	−0.486345	+	0.873767i	$0.661670\pi$
$822$	53719.8	2.27943
$823$	−15851.0	−0.671361	−0.335681	−	0.941976i	$-0.608966\pi$
$823$	−15851.0	−0.671361	−0.335681	+	0.941976i	$0.608966\pi$
$824$	26032.0	1.10057
$825$	−265.070	−0.0111861
$826$	0	0
$827$	−16566.8	−0.696597	−0.348298	−	0.937384i	$-0.613240\pi$
$827$	−16566.8	−0.696597	−0.348298	+	0.937384i	$0.613240\pi$
$828$	−12544.2	−0.526497
$829$	−25680.9	−1.07592	−0.537958	−	0.842972i	$-0.680804\pi$
$829$	−25680.9	−1.07592	−0.537958	+	0.842972i	$0.680804\pi$
$830$	28985.9	1.21219
$831$	55943.3	2.33532
$832$	−27954.2	−1.16483
$833$	0	0
$834$	7662.98	0.318162
$835$	−10525.5	−0.436229
$836$	707.078	0.0292521
$837$	−8454.51	−0.349140
$838$	−43514.8	−1.79379
$839$	−27224.0	−1.12023	−0.560117	−	0.828413i	$-0.689244\pi$
$839$	−27224.0	−1.12023	−0.560117	+	0.828413i	$0.689244\pi$
$840$	0	0
$841$	−23298.8	−0.955299
$842$	−38985.0	−1.59562
$843$	−28699.3	−1.17255
$844$	−54157.4	−2.20874
$845$	−10861.1	−0.442171
$846$	−15010.3	−0.610005
$847$	0	0
$848$	4387.96	0.177692
$849$	−6832.25	−0.276186
$850$	310.101	0.0125134
$851$	6039.47	0.243279
$852$	27747.1	1.11573
$853$	22973.0	0.922135	0.461067	−	0.887365i	$-0.347467\pi$
$853$	22973.0	0.922135	0.461067	+	0.887365i	$0.347467\pi$
$854$	0	0
$855$	−265.366	−0.0106144
$856$	8241.33	0.329069
$857$	28185.3	1.12345	0.561723	−	0.827325i	$-0.310139\pi$
$857$	28185.3	1.12345	0.561723	+	0.827325i	$0.310139\pi$
$858$	30402.8	1.20971
$859$	13475.5	0.535249	0.267624	−	0.963523i	$-0.413761\pi$
$859$	13475.5	0.535249	0.267624	+	0.963523i	$0.413761\pi$
$860$	−19831.5	−0.786337
$861$	0	0
$862$	75922.8	2.99993
$863$	31712.8	1.25089	0.625443	−	0.780270i	$-0.284918\pi$
$863$	31712.8	1.25089	0.625443	+	0.780270i	$0.284918\pi$
$864$	−12719.1	−0.500824
$865$	−30583.0	−1.20214
$866$	46600.0	1.82856
$867$	−17347.6	−0.679533
$868$	0	0
$869$	6996.80	0.273130
$870$	10989.0	0.428234
$871$	−26932.4	−1.04773
$872$	2069.80	0.0803811
$873$	−16448.3	−0.637675
$874$	−562.182	−0.0217576
$875$	0	0
$876$	102533.	3.95466
$877$	24121.4	0.928758	0.464379	−	0.885637i	$-0.346278\pi$
$877$	24121.4	0.928758	0.464379	+	0.885637i	$0.346278\pi$
$878$	−14444.2	−0.555201
$879$	−10799.3	−0.414393
$880$	−4612.24	−0.176680
$881$	−46318.1	−1.77128	−0.885640	−	0.464372i	$-0.846280\pi$
$881$	−46318.1	−1.77128	−0.885640	+	0.464372i	$0.846280\pi$
$882$	0	0
$883$	−29185.3	−1.11230	−0.556152	−	0.831081i	$-0.687723\pi$
$883$	−29185.3	−1.11230	−0.556152	+	0.831081i	$0.687723\pi$
$884$	−22452.8	−0.854263
$885$	50608.2	1.92223
$886$	26244.8	0.995161
$887$	−19165.1	−0.725481	−0.362741	−	0.931890i	$-0.618159\pi$
$887$	−19165.1	−0.725481	−0.362741	+	0.931890i	$0.618159\pi$
$888$	14878.3	0.562255
$889$	0	0
$890$	44552.8	1.67799
$891$	26676.0	1.00301
$892$	−49214.7	−1.84734
$893$	−424.657	−0.0159133
$894$	−19071.7	−0.713483
$895$	29969.8	1.11931
$896$	0	0
$897$	−15259.4	−0.568000
$898$	8890.83	0.330391
$899$	−3225.95	−0.119679
$900$	261.163	0.00967272
$901$	−14631.8	−0.541016
$902$	−5590.66	−0.206373
$903$	0	0
$904$	−10836.0	−0.398671
$905$	13028.3	0.478537
$906$	−56971.4	−2.08912
$907$	−30859.8	−1.12975	−0.564875	−	0.825176i	$-0.691076\pi$
$907$	−30859.8	−1.12975	−0.564875	+	0.825176i	$0.691076\pi$
$908$	−36249.1	−1.32486
$909$	−15566.8	−0.568008
$910$	0	0
$911$	−9980.20	−0.362962	−0.181481	−	0.983394i	$-0.558089\pi$
$911$	−9980.20	−0.362962	−0.181481	+	0.983394i	$0.558089\pi$
$912$	−157.032	−0.00570159
$913$	16202.1	0.587306
$914$	63419.8	2.29512
$915$	−51241.1	−1.85134
$916$	−13605.3	−0.490757
$917$	0	0
$918$	−18832.9	−0.677101
$919$	−4787.15	−0.171832	−0.0859159	−	0.996302i	$-0.527382\pi$
$919$	−4787.15	−0.171832	−0.0859159	+	0.996302i	$0.527382\pi$
$920$	20416.4	0.731639
$921$	7954.26	0.284584
$922$	−31126.6	−1.11182
$923$	11185.7	0.398896
$924$	0	0
$925$	−125.739	−0.00446948
$926$	62874.2	2.23129
$927$	−13130.9	−0.465237
$928$	−4853.15	−0.171673
$929$	−38536.6	−1.36097	−0.680487	−	0.732760i	$-0.738232\pi$
$929$	−38536.6	−1.36097	−0.680487	+	0.732760i	$0.738232\pi$
$930$	−32516.6	−1.14652
$931$	0	0
$932$	−30058.0	−1.05642
$933$	3689.01	0.129446
$934$	−1123.85	−0.0393722
$935$	15379.6	0.537934
$936$	−12457.8	−0.435037
$937$	42871.0	1.49470	0.747351	−	0.664430i	$-0.231326\pi$
$937$	42871.0	1.49470	0.747351	+	0.664430i	$0.231326\pi$
$938$	0	0
$939$	3956.08	0.137488
$940$	37082.0	1.28668
$941$	8395.70	0.290852	0.145426	−	0.989369i	$-0.453545\pi$
$941$	8395.70	0.290852	0.145426	+	0.989369i	$0.453545\pi$
$942$	50330.2	1.74081
$943$	2806.00	0.0968991
$944$	9924.59	0.342180
$945$	0	0
$946$	−17560.1	−0.603517
$947$	4737.20	0.162554	0.0812768	−	0.996692i	$-0.474100\pi$
$947$	4737.20	0.162554	0.0812768	+	0.996692i	$0.474100\pi$
$948$	−20801.8	−0.712670
$949$	41334.2	1.41387
$950$	11.7044	0.000399726 0
$951$	67887.6	2.31483
$952$	0	0
$953$	23910.9	0.812751	0.406375	−	0.913706i	$-0.366793\pi$
$953$	23910.9	0.812751	0.406375	+	0.913706i	$0.366793\pi$
$954$	−19520.5	−0.662474
$955$	3346.05	0.113378
$956$	40302.3	1.36346
$957$	6142.48	0.207480
$958$	−33626.2	−1.13404
$959$	0	0
$960$	−56927.9	−1.91390
$961$	−20245.4	−0.679582
$962$	14421.9	0.483347
$963$	−4157.03	−0.139105
$964$	82820.5	2.76708
$965$	26221.5	0.874715
$966$	0	0
$967$	−29925.7	−0.995188	−0.497594	−	0.867410i	$-0.665783\pi$
$967$	−29925.7	−0.995188	−0.497594	+	0.867410i	$0.665783\pi$
$968$	12575.9	0.417568
$969$	523.627	0.0173595
$970$	64369.7	2.13071
$971$	−17165.2	−0.567308	−0.283654	−	0.958927i	$-0.591547\pi$
$971$	−17165.2	−0.567308	−0.283654	+	0.958927i	$0.591547\pi$
$972$	−47309.4	−1.56116
$973$	0	0
$974$	59623.8	1.96147
$975$	317.693	0.0104352
$976$	−10048.7	−0.329561
$977$	5747.59	0.188211	0.0941053	−	0.995562i	$-0.470001\pi$
$977$	5747.59	0.188211	0.0941053	+	0.995562i	$0.470001\pi$
$978$	−50655.1	−1.65621
$979$	24903.4	0.812989
$980$	0	0
$981$	−1044.03	−0.0339791
$982$	26036.4	0.846083
$983$	48524.5	1.57446	0.787228	−	0.616662i	$-0.211515\pi$
$983$	48524.5	1.57446	0.787228	+	0.616662i	$0.211515\pi$
$984$	6912.59	0.223948
$985$	12716.6	0.411354
$986$	−7185.98	−0.232098
$987$	0	0
$988$	−847.449	−0.0272884
$989$	8813.54	0.283371
$990$	20518.3	0.658700
$991$	23068.1	0.739437	0.369718	−	0.929144i	$-0.379454\pi$
$991$	23068.1	0.739437	0.369718	+	0.929144i	$0.379454\pi$
$992$	14360.5	0.459622
$993$	−69408.3	−2.21813
$994$	0	0
$995$	−35699.0	−1.13742
$996$	−48169.5	−1.53244
$997$	47404.1	1.50582	0.752910	−	0.658123i	$-0.228649\pi$
$997$	47404.1	1.50582	0.752910	+	0.658123i	$0.228649\pi$
$998$	−96180.3	−3.05063
$999$	7636.31	0.241844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.k.1.5		36
7.3	odd	6		287.4.e.a.247.32	yes	72
7.5	odd	6		287.4.e.a.165.32	✓	72
7.6	odd	2		2009.4.a.j.1.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.4.e.a.165.32	✓	72	7.5	odd	6
287.4.e.a.247.32	yes	72	7.3	odd	6
2009.4.a.j.1.5		36	7.6	odd	2
2009.4.a.k.1.5		36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.65790 q^{2} +6.35474 q^{3} +13.6960 q^{4} +11.2439 q^{5} -29.5997 q^{6} -26.5313 q^{8} +13.3827 q^{9} +O(q^{10})\)	\(q-4.65790 q^{2} +6.35474 q^{3} +13.6960 q^{4} +11.2439 q^{5} -29.5997 q^{6} -26.5313 q^{8} +13.3827 q^{9} -52.3728 q^{10} -29.2745 q^{11} +87.0345 q^{12} +35.0862 q^{13} +71.4520 q^{15} +14.0122 q^{16} -46.7240 q^{17} -62.3354 q^{18} -1.76354 q^{19} +153.996 q^{20} +136.358 q^{22} -68.4389 q^{23} -168.600 q^{24} +1.42486 q^{25} -163.428 q^{26} -86.5342 q^{27} -33.0184 q^{29} -332.816 q^{30} +97.7014 q^{31} +146.983 q^{32} -186.032 q^{33} +217.636 q^{34} +183.290 q^{36} -88.2462 q^{37} +8.21436 q^{38} +222.964 q^{39} -298.315 q^{40} -41.0000 q^{41} -128.780 q^{43} -400.943 q^{44} +150.474 q^{45} +318.781 q^{46} +240.799 q^{47} +89.0438 q^{48} -6.63687 q^{50} -296.919 q^{51} +480.540 q^{52} +313.153 q^{53} +403.067 q^{54} -329.159 q^{55} -11.2068 q^{57} +153.796 q^{58} +708.283 q^{59} +978.605 q^{60} -717.140 q^{61} -455.083 q^{62} -796.730 q^{64} +394.505 q^{65} +866.517 q^{66} -767.607 q^{67} -639.932 q^{68} -434.912 q^{69} +318.806 q^{71} -355.062 q^{72} +1178.08 q^{73} +411.041 q^{74} +9.05465 q^{75} -24.1534 q^{76} -1038.54 q^{78} -239.006 q^{79} +157.551 q^{80} -911.236 q^{81} +190.974 q^{82} -553.454 q^{83} -525.360 q^{85} +599.842 q^{86} -209.823 q^{87} +776.691 q^{88} -850.686 q^{89} -700.892 q^{90} -937.339 q^{92} +620.867 q^{93} -1121.61 q^{94} -19.8290 q^{95} +934.040 q^{96} -1229.07 q^{97} -391.773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9	\( 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9} + 12 q^{10} - 140 q^{11} - 186 q^{12} + 72 q^{13} - 366 q^{15} - 15 q^{16} + 2 q^{17} - 212 q^{18} - 30 q^{19} + 334 q^{20} - 346 q^{22} - 314 q^{23} - 106 q^{24} + 570 q^{25} - 303 q^{26} + 204 q^{27} - 356 q^{29} - 357 q^{30} + 4 q^{31} - 532 q^{32} + 30 q^{33} + 364 q^{34} + 113 q^{36} - 1398 q^{37} + 264 q^{38} - 1348 q^{39} - 26 q^{40} - 1476 q^{41} - 1072 q^{43} - 1507 q^{44} + 1132 q^{45} - 1356 q^{46} + 622 q^{47} - 1724 q^{48} - 1426 q^{50} - 668 q^{51} + 877 q^{52} - 412 q^{53} + 1814 q^{54} - 1114 q^{55} - 4082 q^{57} - 1309 q^{58} + 620 q^{59} - 3724 q^{60} - 774 q^{61} - 1665 q^{62} - 3285 q^{64} - 1036 q^{65} + 1056 q^{66} - 2972 q^{67} + 1525 q^{68} - 3304 q^{69} - 3540 q^{71} - 821 q^{72} + 60 q^{73} - 2043 q^{74} - 450 q^{75} - 2171 q^{76} - 1136 q^{78} - 5190 q^{79} + 1564 q^{80} + 284 q^{81} + 205 q^{82} - 1656 q^{83} - 5064 q^{85} - 782 q^{86} + 1940 q^{87} - 4232 q^{88} + 1196 q^{89} - 8030 q^{90} - 4618 q^{92} + 698 q^{93} + 35 q^{94} - 1968 q^{95} + 7926 q^{96} - 3862 q^{97} - 5964 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9 + 12 * q^10 - 140 * q^11 - 186 * q^12 + 72 * q^13 - 366 * q^15 - 15 * q^16 + 2 * q^17 - 212 * q^18 - 30 * q^19 + 334 * q^20 - 346 * q^22 - 314 * q^23 - 106 * q^24 + 570 * q^25 - 303 * q^26 + 204 * q^27 - 356 * q^29 - 357 * q^30 + 4 * q^31 - 532 * q^32 + 30 * q^33 + 364 * q^34 + 113 * q^36 - 1398 * q^37 + 264 * q^38 - 1348 * q^39 - 26 * q^40 - 1476 * q^41 - 1072 * q^43 - 1507 * q^44 + 1132 * q^45 - 1356 * q^46 + 622 * q^47 - 1724 * q^48 - 1426 * q^50 - 668 * q^51 + 877 * q^52 - 412 * q^53 + 1814 * q^54 - 1114 * q^55 - 4082 * q^57 - 1309 * q^58 + 620 * q^59 - 3724 * q^60 - 774 * q^61 - 1665 * q^62 - 3285 * q^64 - 1036 * q^65 + 1056 * q^66 - 2972 * q^67 + 1525 * q^68 - 3304 * q^69 - 3540 * q^71 - 821 * q^72 + 60 * q^73 - 2043 * q^74 - 450 * q^75 - 2171 * q^76 - 1136 * q^78 - 5190 * q^79 + 1564 * q^80 + 284 * q^81 + 205 * q^82 - 1656 * q^83 - 5064 * q^85 - 782 * q^86 + 1940 * q^87 - 4232 * q^88 + 1196 * q^89 - 8030 * q^90 - 4618 * q^92 + 698 * q^93 + 35 * q^94 - 1968 * q^95 + 7926 * q^96 - 3862 * q^97 - 5964 * q^99

Introduction

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