LMFDB - Embedded newform 2009.4.a.o.1.17

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:	$0$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.67118 q^{2} +8.92227 q^{3} -0.864788 q^{4} +15.7867 q^{5} -23.8330 q^{6} +23.6795 q^{8} +52.6070 q^{9} +O(q^{10})$	\(q-2.67118 q^{2} +8.92227 q^{3} -0.864788 q^{4} +15.7867 q^{5} -23.8330 q^{6} +23.6795 q^{8} +52.6070 q^{9} -42.1690 q^{10} +19.8220 q^{11} -7.71587 q^{12} +3.90745 q^{13} +140.853 q^{15} -56.3338 q^{16} +119.529 q^{17} -140.523 q^{18} +34.1893 q^{19} -13.6521 q^{20} -52.9483 q^{22} -22.9786 q^{23} +211.275 q^{24} +124.219 q^{25} -10.4375 q^{26} +228.472 q^{27} +18.4620 q^{29} -376.244 q^{30} +209.964 q^{31} -38.9578 q^{32} +176.858 q^{33} -319.284 q^{34} -45.4939 q^{36} +132.034 q^{37} -91.3259 q^{38} +34.8634 q^{39} +373.820 q^{40} -41.0000 q^{41} -345.326 q^{43} -17.1419 q^{44} +830.488 q^{45} +61.3800 q^{46} +14.9809 q^{47} -502.626 q^{48} -331.810 q^{50} +1066.47 q^{51} -3.37912 q^{52} -313.097 q^{53} -610.291 q^{54} +312.924 q^{55} +305.046 q^{57} -49.3153 q^{58} +324.189 q^{59} -121.808 q^{60} +42.6849 q^{61} -560.852 q^{62} +554.734 q^{64} +61.6856 q^{65} -472.419 q^{66} -100.079 q^{67} -103.367 q^{68} -205.021 q^{69} +845.052 q^{71} +1245.70 q^{72} -1061.34 q^{73} -352.687 q^{74} +1108.31 q^{75} -29.5665 q^{76} -93.1264 q^{78} -982.964 q^{79} -889.323 q^{80} +618.105 q^{81} +109.518 q^{82} -1045.53 q^{83} +1886.97 q^{85} +922.427 q^{86} +164.723 q^{87} +469.375 q^{88} +1417.41 q^{89} -2218.39 q^{90} +19.8716 q^{92} +1873.36 q^{93} -40.0167 q^{94} +539.735 q^{95} -347.592 q^{96} -704.691 q^{97} +1042.78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67118	−0.944405	−0.472203	−	0.881490i	$-0.656541\pi$
$2$	−2.67118	−0.944405	−0.472203	+	0.881490i	$0.656541\pi$
$3$	8.92227	1.71709	0.858546	−	0.512736i	$-0.171368\pi$
$3$	8.92227	1.71709	0.858546	+	0.512736i	$0.171368\pi$
$4$	−0.864788	−0.108098
$5$	15.7867	1.41200	0.706001	−	0.708211i	$-0.250497\pi$
$5$	15.7867	1.41200	0.706001	+	0.708211i	$0.250497\pi$
$6$	−23.8330	−1.62163
$7$	0	0
$7$	0	0
$8$	23.6795	1.04649
$9$	52.6070	1.94841
$10$	−42.1690	−1.33350
$11$	19.8220	0.543324	0.271662	−	0.962393i	$-0.412427\pi$
$11$	19.8220	0.543324	0.271662	+	0.962393i	$0.412427\pi$
$12$	−7.71587	−0.185615
$13$	3.90745	0.0833640	0.0416820	−	0.999131i	$-0.486728\pi$
$13$	3.90745	0.0833640	0.0416820	+	0.999131i	$0.486728\pi$
$14$	0	0
$15$	140.853	2.42454
$16$	−56.3338	−0.880216
$17$	119.529	1.70530	0.852650	−	0.522482i	$-0.174994\pi$
$17$	119.529	1.70530	0.852650	+	0.522482i	$0.174994\pi$
$18$	−140.523	−1.84009
$19$	34.1893	0.412819	0.206410	−	0.978466i	$-0.433822\pi$
$19$	34.1893	0.412819	0.206410	+	0.978466i	$0.433822\pi$
$20$	−13.6521	−0.152635
$21$	0	0
$22$	−52.9483	−0.513119
$23$	−22.9786	−0.208320	−0.104160	−	0.994561i	$-0.533215\pi$
$23$	−22.9786	−0.208320	−0.104160	+	0.994561i	$0.533215\pi$
$24$	211.275	1.79693
$25$	124.219	0.993749
$26$	−10.4375	−0.0787294
$27$	228.472	1.62850
$28$	0	0
$29$	18.4620	0.118217	0.0591087	−	0.998252i	$-0.481174\pi$
$29$	18.4620	0.118217	0.0591087	+	0.998252i	$0.481174\pi$
$30$	−376.244	−2.28975
$31$	209.964	1.21647	0.608236	−	0.793756i	$-0.291877\pi$
$31$	209.964	1.21647	0.608236	+	0.793756i	$0.291877\pi$
$32$	−38.9578	−0.215213
$33$	176.858	0.932938
$34$	−319.284	−1.61049
$35$	0	0
$36$	−45.4939	−0.210620
$37$	132.034	0.586656	0.293328	−	0.956012i	$-0.405237\pi$
$37$	132.034	0.586656	0.293328	+	0.956012i	$0.405237\pi$
$38$	−91.3259	−0.389869
$39$	34.8634	0.143144
$40$	373.820	1.47765
$41$	−41.0000	−0.156174
$41$	−41.0000	−0.156174
$42$	0	0
$43$	−345.326	−1.22469	−0.612345	−	0.790591i	$-0.709774\pi$
$43$	−345.326	−1.22469	−0.612345	+	0.790591i	$0.709774\pi$
$44$	−17.1419	−0.0587326
$45$	830.488	2.75115
$46$	61.3800	0.196739
$47$	14.9809	0.0464933	0.0232467	−	0.999730i	$-0.492600\pi$
$47$	14.9809	0.0464933	0.0232467	+	0.999730i	$0.492600\pi$
$48$	−502.626	−1.51141
$49$	0	0
$50$	−331.810	−0.938502
$51$	1066.47	2.92816
$52$	−3.37912	−0.00901153
$53$	−313.097	−0.811457	−0.405728	−	0.913994i	$-0.632982\pi$
$53$	−313.097	−0.811457	−0.405728	+	0.913994i	$0.632982\pi$
$54$	−610.291	−1.53797
$55$	312.924	0.767175
$56$	0	0
$57$	305.046	0.708849
$58$	−49.3153	−0.111645
$59$	324.189	0.715352	0.357676	−	0.933846i	$-0.383569\pi$
$59$	324.189	0.715352	0.357676	+	0.933846i	$0.383569\pi$
$60$	−121.808	−0.262089
$61$	42.6849	0.0895941	0.0447970	−	0.998996i	$-0.485736\pi$
$61$	42.6849	0.0895941	0.0447970	+	0.998996i	$0.485736\pi$
$62$	−560.852	−1.14884
$63$	0	0
$64$	554.734	1.08346
$65$	61.6856	0.117710
$66$	−472.419	−0.881072
$67$	−100.079	−0.182487	−0.0912435	−	0.995829i	$-0.529084\pi$
$67$	−100.079	−0.182487	−0.0912435	+	0.995829i	$0.529084\pi$
$68$	−103.367	−0.184340
$69$	−205.021	−0.357705
$70$	0	0
$71$	845.052	1.41252	0.706262	−	0.707951i	$-0.250380\pi$
$71$	845.052	1.41252	0.706262	+	0.707951i	$0.250380\pi$
$72$	1245.70	2.03900
$73$	−1061.34	−1.70165	−0.850825	−	0.525449i	$-0.823897\pi$
$73$	−1061.34	−1.70165	−0.850825	+	0.525449i	$0.823897\pi$
$74$	−352.687	−0.554041
$75$	1108.31	1.70636
$76$	−29.5665	−0.0446252
$77$	0	0
$78$	−93.1264	−0.135186
$79$	−982.964	−1.39990	−0.699950	−	0.714192i	$-0.746794\pi$
$79$	−982.964	−1.39990	−0.699950	+	0.714192i	$0.746794\pi$
$80$	−889.323	−1.24287
$81$	618.105	0.847881
$82$	109.518	0.147491
$83$	−1045.53	−1.38268	−0.691338	−	0.722531i	$-0.742978\pi$
$83$	−1045.53	−1.38268	−0.691338	+	0.722531i	$0.742978\pi$
$84$	0	0
$85$	1886.97	2.40789
$86$	922.427	1.15660
$87$	164.723	0.202990
$88$	469.375	0.568586
$89$	1417.41	1.68815	0.844076	−	0.536223i	$-0.180149\pi$
$89$	1417.41	1.68815	0.844076	+	0.536223i	$0.180149\pi$
$90$	−2218.39	−2.59820
$91$	0	0
$92$	19.8716	0.0225191
$93$	1873.36	2.08880
$94$	−40.0167	−0.0439085
$95$	539.735	0.582902
$96$	−347.592	−0.369541
$97$	−704.691	−0.737634	−0.368817	−	0.929502i	$-0.620237\pi$
$97$	−704.691	−0.737634	−0.368817	+	0.929502i	$0.620237\pi$
$98$	0	0
$99$	1042.78	1.05862
$100$	−107.423	−0.107423
$101$	305.341	0.300817	0.150409	−	0.988624i	$-0.451941\pi$
$101$	305.341	0.300817	0.150409	+	0.988624i	$0.451941\pi$
$102$	−2848.74	−2.76537
$103$	−1691.62	−1.61826	−0.809129	−	0.587631i	$-0.800061\pi$
$103$	−1691.62	−1.61826	−0.809129	+	0.587631i	$0.800061\pi$
$104$	92.5264	0.0872400
$105$	0	0
$106$	836.339	0.766344
$107$	1062.68	0.960120	0.480060	−	0.877236i	$-0.340615\pi$
$107$	1062.68	0.960120	0.480060	+	0.877236i	$0.340615\pi$
$108$	−197.580	−0.176039
$109$	−283.596	−0.249207	−0.124603	−	0.992207i	$-0.539766\pi$
$109$	−283.596	−0.249207	−0.124603	+	0.992207i	$0.539766\pi$
$110$	−835.876	−0.724524
$111$	1178.04	1.00734
$112$	0	0
$113$	1984.18	1.65183	0.825913	−	0.563798i	$-0.190660\pi$
$113$	1984.18	1.65183	0.825913	+	0.563798i	$0.190660\pi$
$114$	−814.835	−0.669441
$115$	−362.755	−0.294149
$116$	−15.9657	−0.0127791
$117$	205.559	0.162427
$118$	−865.967	−0.675583
$119$	0	0
$120$	3335.32	2.53726
$121$	−938.087	−0.704799
$122$	−114.019	−0.0846131
$123$	−365.813	−0.268165
$124$	−181.574	−0.131499
$125$	−12.3358	−0.00882677
$126$	0	0
$127$	21.1675	0.0147898	0.00739492	−	0.999973i	$-0.497646\pi$
$127$	21.1675	0.0147898	0.00739492	+	0.999973i	$0.497646\pi$
$128$	−1170.13	−0.808017
$129$	−3081.09	−2.10291
$130$	−164.774	−0.111166
$131$	−94.3138	−0.0629025	−0.0314513	−	0.999505i	$-0.510013\pi$
$131$	−94.3138	−0.0629025	−0.0314513	+	0.999505i	$0.510013\pi$
$132$	−152.944	−0.100849
$133$	0	0
$134$	267.330	0.172342
$135$	3606.82	2.29945
$136$	2830.39	1.78459
$137$	−2579.68	−1.60874	−0.804369	−	0.594130i	$-0.797496\pi$
$137$	−2579.68	−1.60874	−0.804369	+	0.594130i	$0.797496\pi$
$138$	547.649	0.337819
$139$	1463.79	0.893214	0.446607	−	0.894730i	$-0.352632\pi$
$139$	1463.79	0.893214	0.446607	+	0.894730i	$0.352632\pi$
$140$	0	0
$141$	133.664	0.0798333
$142$	−2257.29	−1.33399
$143$	77.4537	0.0452937
$144$	−2963.55	−1.71502
$145$	291.453	0.166923
$146$	2835.03	1.60705
$147$	0	0
$148$	−114.182	−0.0634166
$149$	2480.82	1.36400	0.682001	−	0.731351i	$-0.261110\pi$
$149$	2480.82	1.36400	0.682001	+	0.731351i	$0.261110\pi$
$150$	−2960.50	−1.61149
$151$	−252.160	−0.135897	−0.0679487	−	0.997689i	$-0.521645\pi$
$151$	−252.160	−0.135897	−0.0679487	+	0.997689i	$0.521645\pi$
$152$	809.585	0.432013
$153$	6288.07	3.32262
$154$	0	0
$155$	3314.63	1.71766
$156$	−30.1494	−0.0154736
$157$	−3507.03	−1.78275	−0.891373	−	0.453271i	$-0.850257\pi$
$157$	−3507.03	−1.78275	−0.891373	+	0.453271i	$0.850257\pi$
$158$	2625.68	1.32207
$159$	−2793.54	−1.39335
$160$	−615.013	−0.303881
$161$	0	0
$162$	−1651.07	−0.800743
$163$	−69.8231	−0.0335520	−0.0167760	−	0.999859i	$-0.505340\pi$
$163$	−69.8231	−0.0335520	−0.0167760	+	0.999859i	$0.505340\pi$
$164$	35.4563	0.0168821
$165$	2791.99	1.31731
$166$	2792.81	1.30581
$167$	1610.18	0.746105	0.373053	−	0.927810i	$-0.378311\pi$
$167$	1610.18	0.746105	0.373053	+	0.927810i	$0.378311\pi$
$168$	0	0
$169$	−2181.73	−0.993050
$170$	−5040.43	−2.27402
$171$	1798.60	0.804340
$172$	298.633	0.132387
$173$	295.453	0.129843	0.0649216	−	0.997890i	$-0.479320\pi$
$173$	295.453	0.129843	0.0649216	+	0.997890i	$0.479320\pi$
$174$	−440.005	−0.191705
$175$	0	0
$176$	−1116.65	−0.478243
$177$	2892.50	1.22833
$178$	−3786.17	−1.59430
$179$	3817.66	1.59411	0.797053	−	0.603909i	$-0.206391\pi$
$179$	3817.66	1.59411	0.797053	+	0.603909i	$0.206391\pi$
$180$	−718.196	−0.297395
$181$	2916.48	1.19768	0.598841	−	0.800868i	$-0.295628\pi$
$181$	2916.48	1.19768	0.598841	+	0.800868i	$0.295628\pi$
$182$	0	0
$183$	380.846	0.153841
$184$	−544.121	−0.218006
$185$	2084.38	0.828360
$186$	−5004.08	−1.97267
$187$	2369.31	0.926531
$188$	−12.9553	−0.00502586
$189$	0	0
$190$	−1441.73	−0.550495
$191$	1445.93	0.547770	0.273885	−	0.961762i	$-0.411691\pi$
$191$	1445.93	0.547770	0.273885	+	0.961762i	$0.411691\pi$
$192$	4949.49	1.86041
$193$	−2773.06	−1.03424	−0.517122	−	0.855912i	$-0.672997\pi$
$193$	−2773.06	−1.03424	−0.517122	+	0.855912i	$0.672997\pi$
$194$	1882.36	0.696625
$195$	550.376	0.202119
$196$	0	0
$197$	−2379.06	−0.860409	−0.430205	−	0.902731i	$-0.641559\pi$
$197$	−2379.06	−0.860409	−0.430205	+	0.902731i	$0.641559\pi$
$198$	−2785.45	−0.999763
$199$	−3958.72	−1.41018	−0.705092	−	0.709116i	$-0.749094\pi$
$199$	−3958.72	−1.41018	−0.705092	+	0.709116i	$0.749094\pi$
$200$	2941.43	1.03995
$201$	−892.935	−0.313347
$202$	−815.621	−0.284093
$203$	0	0
$204$	−922.273	−0.316529
$205$	−647.253	−0.220518
$206$	4518.63	1.52829
$207$	−1208.83	−0.405893
$208$	−220.122	−0.0733784
$209$	677.702	0.224295
$210$	0	0
$211$	558.570	0.182244	0.0911222	−	0.995840i	$-0.470955\pi$
$211$	558.570	0.182244	0.0911222	+	0.995840i	$0.470955\pi$
$212$	270.763	0.0877172
$213$	7539.78	2.42543
$214$	−2838.60	−0.906743
$215$	−5451.54	−1.72926
$216$	5410.10	1.70422
$217$	0	0
$218$	757.536	0.235352
$219$	−9469.57	−2.92189
$220$	−270.613	−0.0829305
$221$	467.055	0.142161
$222$	−3146.77	−0.951340
$223$	−4706.39	−1.41329	−0.706645	−	0.707569i	$-0.749792\pi$
$223$	−4706.39	−1.41329	−0.706645	+	0.707569i	$0.749792\pi$
$224$	0	0
$225$	6534.76	1.93623
$226$	−5300.12	−1.55999
$227$	−3331.69	−0.974149	−0.487075	−	0.873360i	$-0.661936\pi$
$227$	−3331.69	−0.974149	−0.487075	+	0.873360i	$0.661936\pi$
$228$	−263.801	−0.0766255
$229$	4561.75	1.31637	0.658185	−	0.752856i	$-0.271325\pi$
$229$	4561.75	1.31637	0.658185	+	0.752856i	$0.271325\pi$
$230$	968.985	0.277796
$231$	0	0
$232$	437.170	0.123714
$233$	3847.65	1.08184	0.540918	−	0.841075i	$-0.318077\pi$
$233$	3847.65	1.08184	0.540918	+	0.841075i	$0.318077\pi$
$234$	−549.086	−0.153397
$235$	236.498	0.0656486
$236$	−280.355	−0.0773285
$237$	−8770.27	−2.40376
$238$	0	0
$239$	−1525.11	−0.412765	−0.206383	−	0.978471i	$-0.566169\pi$
$239$	−1525.11	−0.412765	−0.206383	+	0.978471i	$0.566169\pi$
$240$	−7934.78	−2.13412
$241$	−5206.19	−1.39154	−0.695769	−	0.718266i	$-0.744936\pi$
$241$	−5206.19	−1.39154	−0.695769	+	0.718266i	$0.744936\pi$
$242$	2505.80	0.665616
$243$	−653.853	−0.172612
$244$	−36.9134	−0.00968498
$245$	0	0
$246$	977.154	0.253256
$247$	133.593	0.0344143
$248$	4971.84	1.27303
$249$	−9328.53	−2.37418
$250$	32.9511	0.00833605
$251$	440.142	0.110683	0.0553417	−	0.998467i	$-0.482375\pi$
$251$	440.142	0.110683	0.0553417	+	0.998467i	$0.482375\pi$
$252$	0	0
$253$	−455.483	−0.113186
$254$	−56.5422	−0.0139676
$255$	16836.0	4.13456
$256$	−1312.23	−0.320369
$257$	−3623.97	−0.879600	−0.439800	−	0.898096i	$-0.644951\pi$
$257$	−3623.97	−0.879600	−0.439800	+	0.898096i	$0.644951\pi$
$258$	8230.15	1.98599
$259$	0	0
$260$	−53.3450	−0.0127243
$261$	971.229	0.230336
$262$	251.929	0.0594055
$263$	−4268.77	−1.00085	−0.500425	−	0.865780i	$-0.666823\pi$
$263$	−4268.77	−1.00085	−0.500425	+	0.865780i	$0.666823\pi$
$264$	4187.89	0.976314
$265$	−4942.76	−1.14578
$266$	0	0
$267$	12646.6	2.89871
$268$	86.5473	0.0197266
$269$	−2497.34	−0.566042	−0.283021	−	0.959114i	$-0.591337\pi$
$269$	−2497.34	−0.566042	−0.283021	+	0.959114i	$0.591337\pi$
$270$	−9634.46	−2.17161
$271$	−2161.21	−0.484443	−0.242221	−	0.970221i	$-0.577876\pi$
$271$	−2161.21	−0.484443	−0.242221	+	0.970221i	$0.577876\pi$
$272$	−6733.54	−1.50103
$273$	0	0
$274$	6890.80	1.51930
$275$	2462.27	0.539928
$276$	177.300	0.0386674
$277$	2890.73	0.627030	0.313515	−	0.949583i	$-0.398493\pi$
$277$	2890.73	0.627030	0.313515	+	0.949583i	$0.398493\pi$
$278$	−3910.04	−0.843556
$279$	11045.6	2.37018
$280$	0	0
$281$	5331.87	1.13193	0.565965	−	0.824429i	$-0.308504\pi$
$281$	5331.87	1.13193	0.565965	+	0.824429i	$0.308504\pi$
$282$	−357.040	−0.0753950
$283$	63.3063	0.0132974	0.00664871	−	0.999978i	$-0.497884\pi$
$283$	63.3063	0.0132974	0.00664871	+	0.999978i	$0.497884\pi$
$284$	−730.790	−0.152692
$285$	4815.66	1.00090
$286$	−206.893	−0.0427756
$287$	0	0
$288$	−2049.45	−0.419323
$289$	9374.25	1.90805
$290$	−778.524	−0.157643
$291$	−6287.44	−1.26659
$292$	917.834	0.183946
$293$	−215.623	−0.0429926	−0.0214963	−	0.999769i	$-0.506843\pi$
$293$	−215.623	−0.0429926	−0.0214963	+	0.999769i	$0.506843\pi$
$294$	0	0
$295$	5117.86	1.01008
$296$	3126.50	0.613932
$297$	4528.79	0.884804
$298$	−6626.71	−1.28817
$299$	−89.7878	−0.0173664
$300$	−958.455	−0.184455
$301$	0	0
$302$	673.566	0.128342
$303$	2724.33	0.516531
$304$	−1926.02	−0.363370
$305$	673.851	0.126507
$306$	−16796.6	−3.13790
$307$	2041.58	0.379542	0.189771	−	0.981828i	$-0.439225\pi$
$307$	2041.58	0.379542	0.189771	+	0.981828i	$0.439225\pi$
$308$	0	0
$309$	−15093.1	−2.77870
$310$	−8853.98	−1.62217
$311$	2832.51	0.516454	0.258227	−	0.966084i	$-0.416862\pi$
$311$	2832.51	0.516454	0.258227	+	0.966084i	$0.416862\pi$
$312$	825.546	0.149799
$313$	−4093.54	−0.739234	−0.369617	−	0.929184i	$-0.620511\pi$
$313$	−4093.54	−0.739234	−0.369617	+	0.929184i	$0.620511\pi$
$314$	9367.90	1.68363
$315$	0	0
$316$	850.055	0.151327
$317$	−3254.53	−0.576633	−0.288317	−	0.957535i	$-0.593096\pi$
$317$	−3254.53	−0.576633	−0.288317	+	0.957535i	$0.593096\pi$
$318$	7462.05	1.31588
$319$	365.954	0.0642304
$320$	8757.40	1.52985
$321$	9481.49	1.64862
$322$	0	0
$323$	4086.62	0.703981
$324$	−534.530	−0.0916546
$325$	485.378	0.0828429
$326$	186.510	0.0316866
$327$	−2530.32	−0.427911
$328$	−970.858	−0.163435
$329$	0	0
$330$	−7457.92	−1.24408
$331$	−6184.69	−1.02701	−0.513506	−	0.858086i	$-0.671654\pi$
$331$	−6184.69	−1.02701	−0.513506	+	0.858086i	$0.671654\pi$
$332$	904.164	0.149465
$333$	6945.92	1.14304
$334$	−4301.09	−0.704626
$335$	−1579.92	−0.257672
$336$	0	0
$337$	−8459.94	−1.36748	−0.683742	−	0.729724i	$-0.739649\pi$
$337$	−8459.94	−1.36748	−0.683742	+	0.729724i	$0.739649\pi$
$338$	5827.80	0.937842
$339$	17703.4	2.83634
$340$	−1631.83	−0.260289
$341$	4161.92	0.660939
$342$	−4804.38	−0.759623
$343$	0	0
$344$	−8177.12	−1.28163
$345$	−3236.60	−0.505081
$346$	−789.209	−0.122625
$347$	11534.9	1.78452	0.892260	−	0.451522i	$-0.149119\pi$
$347$	11534.9	1.78452	0.892260	+	0.451522i	$0.149119\pi$
$348$	−142.450	−0.0219429
$349$	1223.66	0.187682	0.0938412	−	0.995587i	$-0.470085\pi$
$349$	1223.66	0.187682	0.0938412	+	0.995587i	$0.470085\pi$
$350$	0	0
$351$	892.745	0.135758
$352$	−772.222	−0.116931
$353$	−2357.16	−0.355408	−0.177704	−	0.984084i	$-0.556867\pi$
$353$	−2357.16	−0.355408	−0.177704	+	0.984084i	$0.556867\pi$
$354$	−7726.40	−1.16004
$355$	13340.5	1.99449
$356$	−1225.76	−0.182487
$357$	0	0
$358$	−10197.7	−1.50548
$359$	607.048	0.0892444	0.0446222	−	0.999004i	$-0.485792\pi$
$359$	607.048	0.0892444	0.0446222	+	0.999004i	$0.485792\pi$
$360$	19665.5	2.87907
$361$	−5690.09	−0.829580
$362$	−7790.46	−1.13110
$363$	−8369.87	−1.21020
$364$	0	0
$365$	−16755.0	−2.40273
$366$	−1017.31	−0.145289
$367$	1076.60	0.153129	0.0765643	−	0.997065i	$-0.475605\pi$
$367$	1076.60	0.153129	0.0765643	+	0.997065i	$0.475605\pi$
$368$	1294.47	0.183367
$369$	−2156.89	−0.304290
$370$	−5567.75	−0.782307
$371$	0	0
$372$	−1620.06	−0.225796
$373$	9489.45	1.31728	0.658640	−	0.752458i	$-0.271132\pi$
$373$	9489.45	1.31728	0.658640	+	0.752458i	$0.271132\pi$
$374$	−6328.87	−0.875021
$375$	−110.063	−0.0151564
$376$	354.739	0.0486550
$377$	72.1394	0.00985508
$378$	0	0
$379$	12809.8	1.73614	0.868070	−	0.496442i	$-0.165360\pi$
$379$	12809.8	1.73614	0.868070	+	0.496442i	$0.165360\pi$
$380$	−466.756	−0.0630108
$381$	188.862	0.0253955
$382$	−3862.35	−0.517317
$383$	1575.44	0.210186	0.105093	−	0.994462i	$-0.466486\pi$
$383$	1575.44	0.210186	0.105093	+	0.994462i	$0.466486\pi$
$384$	−10440.2	−1.38744
$385$	0	0
$386$	7407.34	0.976745
$387$	−18166.5	−2.38619
$388$	609.408	0.0797371
$389$	8182.97	1.06656	0.533281	−	0.845938i	$-0.320959\pi$
$389$	8182.97	1.06656	0.533281	+	0.845938i	$0.320959\pi$
$390$	−1470.15	−0.190882
$391$	−2746.61	−0.355249
$392$	0	0
$393$	−841.493	−0.108009
$394$	6354.89	0.812575
$395$	−15517.7	−1.97666
$396$	−901.781	−0.114435
$397$	−13942.1	−1.76255	−0.881275	−	0.472604i	$-0.843314\pi$
$397$	−13942.1	−1.76255	−0.881275	+	0.472604i	$0.843314\pi$
$398$	10574.5	1.33178
$399$	0	0
$400$	−6997.71	−0.874714
$401$	314.194	0.0391274	0.0195637	−	0.999809i	$-0.493772\pi$
$401$	314.194	0.0391274	0.0195637	+	0.999809i	$0.493772\pi$
$402$	2385.19	0.295927
$403$	820.425	0.101410
$404$	−264.055	−0.0325179
$405$	9757.81	1.19721
$406$	0	0
$407$	2617.19	0.318745
$408$	25253.5	3.06430
$409$	−2103.88	−0.254352	−0.127176	−	0.991880i	$-0.540591\pi$
$409$	−2103.88	−0.254352	−0.127176	+	0.991880i	$0.540591\pi$
$410$	1728.93	0.208258
$411$	−23016.6	−2.76235
$412$	1462.90	0.174931
$413$	0	0
$414$	3229.02	0.383327
$415$	−16505.5	−1.95234
$416$	−152.226	−0.0179410
$417$	13060.3	1.53373
$418$	−1810.27	−0.211825
$419$	−4814.90	−0.561392	−0.280696	−	0.959797i	$-0.590565\pi$
$419$	−4814.90	−0.561392	−0.280696	+	0.959797i	$0.590565\pi$
$420$	0	0
$421$	10215.3	1.18257	0.591284	−	0.806463i	$-0.298621\pi$
$421$	10215.3	1.18257	0.591284	+	0.806463i	$0.298621\pi$
$422$	−1492.04	−0.172113
$423$	788.099	0.0905879
$424$	−7413.97	−0.849185
$425$	14847.8	1.69464
$426$	−20140.1	−2.29059
$427$	0	0
$428$	−918.990	−0.103788
$429$	691.063	0.0777735
$430$	14562.0	1.63313
$431$	5076.73	0.567373	0.283686	−	0.958917i	$-0.408443\pi$
$431$	5076.73	0.567373	0.283686	+	0.958917i	$0.408443\pi$
$432$	−12870.7	−1.43343
$433$	14738.5	1.63577	0.817885	−	0.575381i	$-0.195146\pi$
$433$	14738.5	1.63577	0.817885	+	0.575381i	$0.195146\pi$
$434$	0	0
$435$	2600.43	0.286623
$436$	245.250	0.0269389
$437$	−785.623	−0.0859987
$438$	25294.9	2.75945
$439$	16131.3	1.75377	0.876887	−	0.480696i	$-0.159616\pi$
$439$	16131.3	1.75377	0.876887	+	0.480696i	$0.159616\pi$
$440$	7409.87	0.802844
$441$	0	0
$442$	−1247.59	−0.134257
$443$	−924.188	−0.0991185	−0.0495593	−	0.998771i	$-0.515782\pi$
$443$	−924.188	−0.0991185	−0.0495593	+	0.998771i	$0.515782\pi$
$444$	−1018.76	−0.108892
$445$	22376.2	2.38367
$446$	12571.6	1.33472
$447$	22134.5	2.34212
$448$	0	0
$449$	11074.0	1.16395	0.581975	−	0.813207i	$-0.302280\pi$
$449$	11074.0	1.16395	0.581975	+	0.813207i	$0.302280\pi$
$450$	−17455.5	−1.82858
$451$	−812.704	−0.0848530
$452$	−1715.90	−0.178560
$453$	−2249.84	−0.233348
$454$	8899.54	0.919992
$455$	0	0
$456$	7223.34	0.741806
$457$	−8502.52	−0.870309	−0.435154	−	0.900356i	$-0.643306\pi$
$457$	−8502.52	−0.870309	−0.435154	+	0.900356i	$0.643306\pi$
$458$	−12185.3	−1.24319
$459$	27309.1	2.77708
$460$	313.706	0.0317970
$461$	15744.0	1.59061	0.795305	−	0.606209i	$-0.207310\pi$
$461$	15744.0	1.59061	0.795305	+	0.606209i	$0.207310\pi$
$462$	0	0
$463$	−3980.86	−0.399581	−0.199791	−	0.979839i	$-0.564026\pi$
$463$	−3980.86	−0.399581	−0.199791	+	0.979839i	$0.564026\pi$
$464$	−1040.03	−0.104057
$465$	29574.0	2.94938
$466$	−10277.8	−1.02169
$467$	3179.09	0.315013	0.157506	−	0.987518i	$-0.449655\pi$
$467$	3179.09	0.315013	0.157506	+	0.987518i	$0.449655\pi$
$468$	−177.765	−0.0175581
$469$	0	0
$470$	−631.729	−0.0619989
$471$	−31290.6	−3.06114
$472$	7676.62	0.748612
$473$	−6845.06	−0.665404
$474$	23427.0	2.27012
$475$	4246.95	0.410239
$476$	0	0
$477$	−16471.1	−1.58105
$478$	4073.84	0.389818
$479$	−1882.66	−0.179585	−0.0897923	−	0.995961i	$-0.528620\pi$
$479$	−1882.66	−0.179585	−0.0897923	+	0.995961i	$0.528620\pi$
$480$	−5487.31	−0.521793
$481$	515.917	0.0489060
$482$	13906.7	1.31418
$483$	0	0
$484$	811.246	0.0761877
$485$	−11124.7	−1.04154
$486$	1746.56	0.163016
$487$	−1768.29	−0.164536	−0.0822680	−	0.996610i	$-0.526216\pi$
$487$	−1768.29	−0.164536	−0.0822680	+	0.996610i	$0.526216\pi$
$488$	1010.75	0.0937597
$489$	−622.981	−0.0576118
$490$	0	0
$491$	14415.9	1.32501	0.662507	−	0.749056i	$-0.269492\pi$
$491$	14415.9	1.32501	0.662507	+	0.749056i	$0.269492\pi$
$492$	316.351	0.0289882
$493$	2206.75	0.201596
$494$	−356.852	−0.0325010
$495$	16462.0	1.49477
$496$	−11828.1	−1.07076
$497$	0	0
$498$	24918.2	2.24219
$499$	21785.9	1.95445	0.977226	−	0.212199i	$-0.0680626\pi$
$499$	21785.9	1.95445	0.977226	+	0.212199i	$0.0680626\pi$
$500$	10.6678	0.000954161 0
$501$	14366.5	1.28113
$502$	−1175.70	−0.104530
$503$	16083.2	1.42568	0.712838	−	0.701329i	$-0.247410\pi$
$503$	16083.2	1.42568	0.712838	+	0.701329i	$0.247410\pi$
$504$	0	0
$505$	4820.31	0.424755
$506$	1216.68	0.106893
$507$	−19466.0	−1.70516
$508$	−18.3054	−0.00159876
$509$	15535.4	1.35283	0.676417	−	0.736519i	$-0.263532\pi$
$509$	15535.4	1.35283	0.676417	+	0.736519i	$0.263532\pi$
$510$	−44972.1	−3.90470
$511$	0	0
$512$	12866.3	1.11058
$513$	7811.32	0.672277
$514$	9680.29	0.830699
$515$	−26705.1	−2.28498
$516$	2664.49	0.227321
$517$	296.952	0.0252610
$518$	0	0
$519$	2636.11	0.222953
$520$	1460.68	0.123183
$521$	−7867.32	−0.661561	−0.330781	−	0.943708i	$-0.607312\pi$
$521$	−7867.32	−0.661561	−0.330781	+	0.943708i	$0.607312\pi$
$522$	−2594.33	−0.217530
$523$	20673.1	1.72844	0.864220	−	0.503115i	$-0.167813\pi$
$523$	20673.1	1.72844	0.864220	+	0.503115i	$0.167813\pi$
$524$	81.5614	0.00679967
$525$	0	0
$526$	11402.7	0.945209
$527$	25096.9	2.07445
$528$	−9963.07	−0.821187
$529$	−11639.0	−0.956603
$530$	13203.0	1.08208
$531$	17054.6	1.39380
$532$	0	0
$533$	−160.206	−0.0130193
$534$	−33781.2	−2.73756
$535$	16776.1	1.35569
$536$	−2369.82	−0.190972
$537$	34062.2	2.73723
$538$	6670.84	0.534573
$539$	0	0
$540$	−3119.13	−0.248567
$541$	7856.44	0.624352	0.312176	−	0.950024i	$-0.398942\pi$
$541$	7856.44	0.624352	0.312176	+	0.950024i	$0.398942\pi$
$542$	5772.98	0.457510
$543$	26021.7	2.05653
$544$	−4656.59	−0.367003
$545$	−4477.03	−0.351881
$546$	0	0
$547$	−7878.61	−0.615841	−0.307921	−	0.951412i	$-0.599633\pi$
$547$	−7878.61	−0.615841	−0.307921	+	0.951412i	$0.599633\pi$
$548$	2230.88	0.173902
$549$	2245.52	0.174566
$550$	−6577.16	−0.509911
$551$	631.203	0.0488025
$552$	−4854.79	−0.374337
$553$	0	0
$554$	−7721.67	−0.592170
$555$	18597.4	1.42237
$556$	−1265.86	−0.0965550
$557$	17434.0	1.32622	0.663109	−	0.748523i	$-0.269236\pi$
$557$	17434.0	1.32622	0.663109	+	0.748523i	$0.269236\pi$
$558$	−29504.7	−2.23841
$559$	−1349.34	−0.102095
$560$	0	0
$561$	21139.7	1.59094
$562$	−14242.4	−1.06900
$563$	−12238.5	−0.916151	−0.458075	−	0.888913i	$-0.651461\pi$
$563$	−12238.5	−0.916151	−0.458075	+	0.888913i	$0.651461\pi$
$564$	−115.591	−0.00862986
$565$	31323.6	2.33238
$566$	−169.103	−0.0125582
$567$	0	0
$568$	20010.4	1.47820
$569$	−5802.00	−0.427473	−0.213737	−	0.976891i	$-0.568563\pi$
$569$	−5802.00	−0.427473	−0.213737	+	0.976891i	$0.568563\pi$
$570$	−12863.5	−0.945252
$571$	−15431.6	−1.13098	−0.565492	−	0.824754i	$-0.691314\pi$
$571$	−15431.6	−1.13098	−0.565492	+	0.824754i	$0.691314\pi$
$572$	−66.9810	−0.00489618
$573$	12901.0	0.940572
$574$	0	0
$575$	−2854.37	−0.207018
$576$	29182.9	2.11103
$577$	338.577	0.0244283	0.0122142	−	0.999925i	$-0.496112\pi$
$577$	338.577	0.0244283	0.0122142	+	0.999925i	$0.496112\pi$
$578$	−25040.3	−1.80197
$579$	−24742.0	−1.77589
$580$	−252.045	−0.0180442
$581$	0	0
$582$	16794.9	1.19617
$583$	−6206.22	−0.440884
$584$	−25132.0	−1.78077
$585$	3245.09	0.229347
$586$	575.969	0.0406025
$587$	−13979.8	−0.982980	−0.491490	−	0.870883i	$-0.663548\pi$
$587$	−13979.8	−0.982980	−0.491490	+	0.870883i	$0.663548\pi$
$588$	0	0
$589$	7178.53	0.502184
$590$	−13670.7	−0.953924
$591$	−21226.6	−1.47740
$592$	−7437.99	−0.516384
$593$	−10112.8	−0.700309	−0.350155	−	0.936692i	$-0.613871\pi$
$593$	−10112.8	−0.700309	−0.350155	+	0.936692i	$0.613871\pi$
$594$	−12097.2	−0.835614
$595$	0	0
$596$	−2145.38	−0.147447
$597$	−35320.8	−2.42142
$598$	239.840	0.0164009
$599$	18061.2	1.23199	0.615993	−	0.787751i	$-0.288755\pi$
$599$	18061.2	1.23199	0.615993	+	0.787751i	$0.288755\pi$
$600$	26244.2	1.78569
$601$	2319.70	0.157442	0.0787209	−	0.996897i	$-0.474916\pi$
$601$	2319.70	0.157442	0.0787209	+	0.996897i	$0.474916\pi$
$602$	0	0
$603$	−5264.87	−0.355559
$604$	218.065	0.0146903
$605$	−14809.3	−0.995177
$606$	−7277.19	−0.487815
$607$	−5708.68	−0.381727	−0.190863	−	0.981617i	$-0.561129\pi$
$607$	−5708.68	−0.381727	−0.190863	+	0.981617i	$0.561129\pi$
$608$	−1331.94	−0.0888442
$609$	0	0
$610$	−1799.98	−0.119474
$611$	58.5371	0.00387587
$612$	−5437.85	−0.359170
$613$	−7710.14	−0.508009	−0.254004	−	0.967203i	$-0.581748\pi$
$613$	−7710.14	−0.508009	−0.254004	+	0.967203i	$0.581748\pi$
$614$	−5453.44	−0.358442
$615$	−5774.97	−0.378649
$616$	0	0
$617$	−27235.5	−1.77708	−0.888542	−	0.458794i	$-0.848281\pi$
$617$	−27235.5	−1.77708	−0.888542	+	0.458794i	$0.848281\pi$
$618$	40316.5	2.62422
$619$	12719.4	0.825909	0.412954	−	0.910752i	$-0.364497\pi$
$619$	12719.4	0.825909	0.412954	+	0.910752i	$0.364497\pi$
$620$	−2866.45	−0.185677
$621$	−5249.97	−0.339250
$622$	−7566.16	−0.487742
$623$	0	0
$624$	−1963.99	−0.125997
$625$	−15722.1	−1.00621
$626$	10934.6	0.698137
$627$	6046.64	0.385135
$628$	3032.83	0.192712
$629$	15781.9	1.00042
$630$	0	0
$631$	−2170.58	−0.136941	−0.0684703	−	0.997653i	$-0.521812\pi$
$631$	−2170.58	−0.136941	−0.0684703	+	0.997653i	$0.521812\pi$
$632$	−23276.1	−1.46499
$633$	4983.72	0.312930
$634$	8693.45	0.544575
$635$	334.164	0.0208833
$636$	2415.82	0.150619
$637$	0	0
$638$	−977.531	−0.0606596
$639$	44455.6	2.75217
$640$	−18472.5	−1.14092
$641$	−1444.44	−0.0890045	−0.0445023	−	0.999009i	$-0.514170\pi$
$641$	−1444.44	−0.0890045	−0.0445023	+	0.999009i	$0.514170\pi$
$642$	−25326.8	−1.55696
$643$	29564.0	1.81321	0.906603	−	0.421986i	$-0.138667\pi$
$643$	29564.0	1.81321	0.906603	+	0.421986i	$0.138667\pi$
$644$	0	0
$645$	−48640.1	−2.96931
$646$	−10916.1	−0.664843
$647$	−25912.4	−1.57453	−0.787266	−	0.616614i	$-0.788504\pi$
$647$	−25912.4	−1.57453	−0.787266	+	0.616614i	$0.788504\pi$
$648$	14636.4	0.887302
$649$	6426.08	0.388668
$650$	−1296.53	−0.0782373
$651$	0	0
$652$	60.3822	0.00362692
$653$	18943.4	1.13524	0.567622	−	0.823289i	$-0.307864\pi$
$653$	18943.4	1.13524	0.567622	+	0.823289i	$0.307864\pi$
$654$	6758.94	0.404122
$655$	−1488.90	−0.0888185
$656$	2309.69	0.137467
$657$	−55833.9	−3.31551
$658$	0	0
$659$	−16360.2	−0.967078	−0.483539	−	0.875323i	$-0.660649\pi$
$659$	−16360.2	−0.967078	−0.483539	+	0.875323i	$0.660649\pi$
$660$	−2414.48	−0.142399
$661$	−33490.7	−1.97071	−0.985354	−	0.170524i	$-0.945454\pi$
$661$	−33490.7	−1.97071	−0.985354	+	0.170524i	$0.945454\pi$
$662$	16520.4	0.969916
$663$	4167.19	0.244103
$664$	−24757.7	−1.44696
$665$	0	0
$666$	−18553.8	−1.07950
$667$	−424.231	−0.0246271
$668$	−1392.47	−0.0806529
$669$	−41991.7	−2.42675
$670$	4220.25	0.243347
$671$	846.101	0.0486786
$672$	0	0
$673$	606.458	0.0347359	0.0173679	−	0.999849i	$-0.494471\pi$
$673$	606.458	0.0347359	0.0173679	+	0.999849i	$0.494471\pi$
$674$	22598.0	1.29146
$675$	28380.5	1.61832
$676$	1886.74	0.107347
$677$	6256.83	0.355199	0.177599	−	0.984103i	$-0.443167\pi$
$677$	6256.83	0.355199	0.177599	+	0.984103i	$0.443167\pi$
$678$	−47289.1	−2.67865
$679$	0	0
$680$	44682.4	2.51984
$681$	−29726.2	−1.67270
$682$	−11117.2	−0.624195
$683$	18110.1	1.01459	0.507294	−	0.861773i	$-0.330646\pi$
$683$	18110.1	1.01459	0.507294	+	0.861773i	$0.330646\pi$
$684$	−1555.40	−0.0869479
$685$	−40724.6	−2.27154
$686$	0	0
$687$	40701.1	2.26033
$688$	19453.5	1.07799
$689$	−1223.41	−0.0676463
$690$	8645.55	0.477001
$691$	29254.5	1.61055	0.805277	−	0.592898i	$-0.202016\pi$
$691$	29254.5	1.61055	0.805277	+	0.592898i	$0.202016\pi$
$692$	−255.504	−0.0140359
$693$	0	0
$694$	−30811.9	−1.68531
$695$	23108.3	1.26122
$696$	3900.55	0.212428
$697$	−4900.70	−0.266323
$698$	−3268.62	−0.177248
$699$	34329.8	1.85761
$700$	0	0
$701$	3632.36	0.195709	0.0978547	−	0.995201i	$-0.468802\pi$
$701$	3632.36	0.195709	0.0978547	+	0.995201i	$0.468802\pi$
$702$	−2384.68	−0.128211
$703$	4514.16	0.242183
$704$	10996.0	0.588673
$705$	2110.10	0.112725
$706$	6296.40	0.335649
$707$	0	0
$708$	−2501.40	−0.132780
$709$	20658.4	1.09428	0.547139	−	0.837042i	$-0.315717\pi$
$709$	20658.4	1.09428	0.547139	+	0.837042i	$0.315717\pi$
$710$	−35635.0	−1.88360
$711$	−51710.8	−2.72757
$712$	33563.6	1.76664
$713$	−4824.68	−0.253416
$714$	0	0
$715$	1222.73	0.0639548
$716$	−3301.46	−0.172321
$717$	−13607.4	−0.708756
$718$	−1621.53	−0.0842829
$719$	5881.69	0.305077	0.152538	−	0.988298i	$-0.451255\pi$
$719$	5881.69	0.305077	0.152538	+	0.988298i	$0.451255\pi$
$720$	−46784.6	−2.42161
$721$	0	0
$722$	15199.3	0.783460
$723$	−46451.1	−2.38940
$724$	−2522.14	−0.129468
$725$	2293.32	0.117478
$726$	22357.4	1.14292
$727$	25428.3	1.29722	0.648612	−	0.761119i	$-0.275350\pi$
$727$	25428.3	1.29722	0.648612	+	0.761119i	$0.275350\pi$
$728$	0	0
$729$	−22522.7	−1.14427
$730$	44755.7	2.26915
$731$	−41276.5	−2.08846
$732$	−329.351	−0.0166300
$733$	−32056.1	−1.61531	−0.807653	−	0.589658i	$-0.799263\pi$
$733$	−32056.1	−1.61531	−0.807653	+	0.589658i	$0.799263\pi$
$734$	−2875.80	−0.144615
$735$	0	0
$736$	895.195	0.0448333
$737$	−1983.77	−0.0991496
$738$	5761.43	0.287373
$739$	−29413.3	−1.46412	−0.732062	−	0.681238i	$-0.761442\pi$
$739$	−29413.3	−1.46412	−0.732062	+	0.681238i	$0.761442\pi$
$740$	−1802.54	−0.0895444
$741$	1191.95	0.0590925
$742$	0	0
$743$	−11987.7	−0.591904	−0.295952	−	0.955203i	$-0.595637\pi$
$743$	−11987.7	−0.591904	−0.295952	+	0.955203i	$0.595637\pi$
$744$	44360.1	2.18591
$745$	39163.8	1.92597
$746$	−25348.1	−1.24405
$747$	−55002.3	−2.69401
$748$	−2048.95	−0.100157
$749$	0	0
$750$	293.999	0.0143138
$751$	−23901.3	−1.16135	−0.580674	−	0.814136i	$-0.697211\pi$
$751$	−23901.3	−1.16135	−0.580674	+	0.814136i	$0.697211\pi$
$752$	−843.930	−0.0409242
$753$	3927.07	0.190054
$754$	−192.697	−0.00930719
$755$	−3980.77	−0.191887
$756$	0	0
$757$	1111.50	0.0533660	0.0266830	−	0.999644i	$-0.491506\pi$
$757$	1111.50	0.0533660	0.0266830	+	0.999644i	$0.491506\pi$
$758$	−34217.4	−1.63962
$759$	−4063.94	−0.194350
$760$	12780.6	0.610003
$761$	−16808.3	−0.800655	−0.400328	−	0.916372i	$-0.631104\pi$
$761$	−16808.3	−0.800655	−0.400328	+	0.916372i	$0.631104\pi$
$762$	−504.485	−0.0239837
$763$	0	0
$764$	−1250.43	−0.0592131
$765$	99267.7	4.69154
$766$	−4208.29	−0.198501
$767$	1266.75	0.0596347
$768$	−11708.1	−0.550104
$769$	−38716.8	−1.81556	−0.907778	−	0.419452i	$-0.862222\pi$
$769$	−38716.8	−1.81556	−0.907778	+	0.419452i	$0.862222\pi$
$770$	0	0
$771$	−32334.1	−1.51035
$772$	2398.11	0.111800
$773$	−18686.8	−0.869491	−0.434745	−	0.900553i	$-0.643162\pi$
$773$	−18686.8	−0.869491	−0.434745	+	0.900553i	$0.643162\pi$
$774$	48526.1	2.25353
$775$	26081.4	1.20887
$776$	−16686.7	−0.771930
$777$	0	0
$778$	−21858.2	−1.00727
$779$	−1401.76	−0.0644716
$780$	−475.959	−0.0218488
$781$	16750.6	0.767459
$782$	7336.71	0.335499
$783$	4218.06	0.192517
$784$	0	0
$785$	−55364.2	−2.51724
$786$	2247.78	0.102005
$787$	−34640.8	−1.56901	−0.784505	−	0.620123i	$-0.787083\pi$
$787$	−34640.8	−1.56901	−0.784505	+	0.620123i	$0.787083\pi$
$788$	2057.38	0.0930090
$789$	−38087.2	−1.71855
$790$	41450.6	1.86677
$791$	0	0
$792$	24692.4	1.10784
$793$	166.789	0.00746892
$794$	37241.8	1.66456
$795$	−44100.6	−1.96741
$796$	3423.46	0.152439
$797$	−30521.1	−1.35648	−0.678238	−	0.734842i	$-0.737256\pi$
$797$	−30521.1	−1.35648	−0.678238	+	0.734842i	$0.737256\pi$
$798$	0	0
$799$	1790.65	0.0792851
$800$	−4839.28	−0.213868
$801$	74565.8	3.28921
$802$	−839.269	−0.0369521
$803$	−21037.9	−0.924548
$804$	772.199	0.0338723
$805$	0	0
$806$	−2191.50	−0.0957722
$807$	−22281.9	−0.971947
$808$	7230.31	0.314804
$809$	−11025.9	−0.479171	−0.239585	−	0.970875i	$-0.577011\pi$
$809$	−11025.9	−0.479171	−0.239585	+	0.970875i	$0.577011\pi$
$810$	−26064.9	−1.13065
$811$	−5433.27	−0.235250	−0.117625	−	0.993058i	$-0.537528\pi$
$811$	−5433.27	−0.235250	−0.117625	+	0.993058i	$0.537528\pi$
$812$	0	0
$813$	−19282.9	−0.831833
$814$	−6990.98	−0.301024
$815$	−1102.27	−0.0473754
$816$	−60078.5	−2.57741
$817$	−11806.4	−0.505576
$818$	5619.84	0.240211
$819$	0	0
$820$	559.737	0.0238376
$821$	−30159.3	−1.28206	−0.641028	−	0.767518i	$-0.721492\pi$
$821$	−30159.3	−1.28206	−0.641028	+	0.767518i	$0.721492\pi$
$822$	61481.6	2.60878
$823$	15006.0	0.635571	0.317785	−	0.948163i	$-0.397061\pi$
$823$	15006.0	0.635571	0.317785	+	0.948163i	$0.397061\pi$
$824$	−40056.7	−1.69350
$825$	21969.0	0.927106
$826$	0	0
$827$	34352.0	1.44442	0.722210	−	0.691673i	$-0.243126\pi$
$827$	34352.0	1.44442	0.722210	+	0.691673i	$0.243126\pi$
$828$	1045.39	0.0438764
$829$	8110.14	0.339779	0.169890	−	0.985463i	$-0.445659\pi$
$829$	8110.14	0.339779	0.169890	+	0.985463i	$0.445659\pi$
$830$	44089.1	1.84380
$831$	25791.9	1.07667
$832$	2167.60	0.0903220
$833$	0	0
$834$	−34886.4	−1.44846
$835$	25419.4	1.05350
$836$	−586.069	−0.0242459
$837$	47971.0	1.98103
$838$	12861.5	0.530182
$839$	47218.0	1.94297	0.971483	−	0.237111i	$-0.0762005\pi$
$839$	47218.0	1.94297	0.971483	+	0.237111i	$0.0762005\pi$
$840$	0	0
$841$	−24048.2	−0.986025
$842$	−27286.8	−1.11682
$843$	47572.4	1.94363
$844$	−483.045	−0.0197003
$845$	−34442.3	−1.40219
$846$	−2105.15	−0.0855517
$847$	0	0
$848$	17638.0	0.714257
$849$	564.836	0.0228329
$850$	−39661.1	−1.60043
$851$	−3033.96	−0.122212
$852$	−6520.31	−0.262186
$853$	−34101.8	−1.36884	−0.684421	−	0.729087i	$-0.739945\pi$
$853$	−34101.8	−1.36884	−0.684421	+	0.729087i	$0.739945\pi$
$854$	0	0
$855$	28393.8	1.13573
$856$	25163.6	1.00476
$857$	−29167.9	−1.16261	−0.581305	−	0.813686i	$-0.697458\pi$
$857$	−29167.9	−1.16261	−0.581305	+	0.813686i	$0.697458\pi$
$858$	−1845.95	−0.0734497
$859$	33695.5	1.33839	0.669194	−	0.743088i	$-0.266639\pi$
$859$	33695.5	1.33839	0.669194	+	0.743088i	$0.266639\pi$
$860$	4714.42	0.186931
$861$	0	0
$862$	−13560.9	−0.535830
$863$	6282.92	0.247825	0.123913	−	0.992293i	$-0.460456\pi$
$863$	6282.92	0.247825	0.123913	+	0.992293i	$0.460456\pi$
$864$	−8900.77	−0.350475
$865$	4664.21	0.183339
$866$	−39369.3	−1.54483
$867$	83639.6	3.27630
$868$	0	0
$869$	−19484.4	−0.760600
$870$	−6946.21	−0.270688
$871$	−391.055	−0.0152129
$872$	−6715.40	−0.260794
$873$	−37071.6	−1.43721
$874$	2098.54	0.0812176
$875$	0	0
$876$	8189.17	0.315852
$877$	−30764.3	−1.18453	−0.592267	−	0.805741i	$-0.701767\pi$
$877$	−30764.3	−1.18453	−0.592267	+	0.805741i	$0.701767\pi$
$878$	−43089.8	−1.65627
$879$	−1923.85	−0.0738223
$880$	−17628.2	−0.675280
$881$	−35532.5	−1.35882	−0.679410	−	0.733759i	$-0.737764\pi$
$881$	−35532.5	−1.35882	−0.679410	+	0.733759i	$0.737764\pi$
$882$	0	0
$883$	−20864.9	−0.795199	−0.397600	−	0.917559i	$-0.630157\pi$
$883$	−20864.9	−0.795199	−0.397600	+	0.917559i	$0.630157\pi$
$884$	−403.904	−0.0153674
$885$	45662.9	1.73440
$886$	2468.67	0.0936081
$887$	42008.9	1.59022	0.795108	−	0.606468i	$-0.207414\pi$
$887$	42008.9	1.59022	0.795108	+	0.606468i	$0.207414\pi$
$888$	27895.5	1.05418
$889$	0	0
$890$	−59771.0	−2.25115
$891$	12252.1	0.460674
$892$	4070.03	0.152774
$893$	512.186	0.0191933
$894$	−59125.3	−2.21191
$895$	60268.0	2.25088
$896$	0	0
$897$	−801.111	−0.0298198
$898$	−29580.6	−1.09924
$899$	3876.36	0.143808
$900$	−5651.18	−0.209303
$901$	−37424.3	−1.38378
$902$	2170.88	0.0801357
$903$	0	0
$904$	46984.4	1.72863
$905$	46041.5	1.69113
$906$	6009.74	0.220375
$907$	2948.04	0.107925	0.0539626	−	0.998543i	$-0.482815\pi$
$907$	2948.04	0.107925	0.0539626	+	0.998543i	$0.482815\pi$
$908$	2881.20	0.105304
$909$	16063.1	0.586114
$910$	0	0
$911$	−21113.0	−0.767845	−0.383922	−	0.923365i	$-0.625427\pi$
$911$	−21113.0	−0.767845	−0.383922	+	0.923365i	$0.625427\pi$
$912$	−17184.4	−0.623940
$913$	−20724.6	−0.751242
$914$	22711.8	0.821924
$915$	6012.29	0.217224
$916$	−3944.94	−0.142298
$917$	0	0
$918$	−72947.7	−2.62269
$919$	−36238.2	−1.30075	−0.650375	−	0.759613i	$-0.725388\pi$
$919$	−36238.2	−1.30075	−0.650375	+	0.759613i	$0.725388\pi$
$920$	−8589.85	−0.307825
$921$	18215.6	0.651709
$922$	−42055.1	−1.50218
$923$	3302.00	0.117754
$924$	0	0
$925$	16401.1	0.582989
$926$	10633.6	0.377367
$927$	−88991.2	−3.15302
$928$	−719.238	−0.0254420
$929$	49213.7	1.73805	0.869026	−	0.494767i	$-0.164746\pi$
$929$	49213.7	1.73805	0.869026	+	0.494767i	$0.164746\pi$
$930$	−78997.7	−2.78541
$931$	0	0
$932$	−3327.40	−0.116945
$933$	25272.5	0.886799
$934$	−8491.94	−0.297500
$935$	37403.5	1.30826
$936$	4867.53	0.169979
$937$	15259.1	0.532009	0.266005	−	0.963972i	$-0.414296\pi$
$937$	15259.1	0.532009	0.266005	+	0.963972i	$0.414296\pi$
$938$	0	0
$939$	−36523.7	−1.26933
$940$	−204.521	−0.00709652
$941$	28570.8	0.989779	0.494889	−	0.868956i	$-0.335209\pi$
$941$	28570.8	0.989779	0.494889	+	0.868956i	$0.335209\pi$
$942$	83583.0	2.89096
$943$	942.123	0.0325342
$944$	−18262.8	−0.629665
$945$	0	0
$946$	18284.4	0.628411
$947$	−42243.7	−1.44956	−0.724782	−	0.688978i	$-0.758059\pi$
$947$	−42243.7	−1.44956	−0.724782	+	0.688978i	$0.758059\pi$
$948$	7584.43	0.259843
$949$	−4147.14	−0.141856
$950$	−11344.4	−0.387432
$951$	−29037.8	−0.990132
$952$	0	0
$953$	46676.4	1.58656	0.793282	−	0.608855i	$-0.208371\pi$
$953$	46676.4	1.58656	0.793282	+	0.608855i	$0.208371\pi$
$954$	43997.3	1.49315
$955$	22826.5	0.773453
$956$	1318.89	0.0446193
$957$	3265.14	0.110290
$958$	5028.93	0.169601
$959$	0	0
$960$	78135.9	2.62690
$961$	14293.9	0.479806
$962$	−1378.11	−0.0461871
$963$	55904.2	1.87070
$964$	4502.25	0.150423
$965$	−43777.3	−1.46035
$966$	0	0
$967$	−35614.1	−1.18436	−0.592178	−	0.805807i	$-0.701732\pi$
$967$	−35614.1	−1.18436	−0.592178	+	0.805807i	$0.701732\pi$
$968$	−22213.4	−0.737568
$969$	36462.0	1.20880
$970$	29716.1	0.983636
$971$	−28928.4	−0.956083	−0.478042	−	0.878337i	$-0.658653\pi$
$971$	−28928.4	−0.956083	−0.478042	+	0.878337i	$0.658653\pi$
$972$	565.444	0.0186591
$973$	0	0
$974$	4723.43	0.155389
$975$	4330.68	0.142249
$976$	−2404.60	−0.0788621
$977$	20005.8	0.655109	0.327554	−	0.944832i	$-0.393776\pi$
$977$	20005.8	0.655109	0.327554	+	0.944832i	$0.393776\pi$
$978$	1664.10	0.0544089
$979$	28096.0	0.917215
$980$	0	0
$981$	−14919.1	−0.485556
$982$	−38507.6	−1.25135
$983$	55656.8	1.80588	0.902938	−	0.429770i	$-0.141405\pi$
$983$	55656.8	1.80588	0.902938	+	0.429770i	$0.141405\pi$
$984$	−8662.26	−0.280633
$985$	−37557.3	−1.21490
$986$	−5894.63	−0.190389
$987$	0	0
$988$	−115.530	−0.00372013
$989$	7935.10	0.255128
$990$	−43972.9	−1.41167
$991$	−48428.3	−1.55235	−0.776173	−	0.630520i	$-0.782842\pi$
$991$	−48428.3	−1.55235	−0.776173	+	0.630520i	$0.782842\pi$
$992$	−8179.73	−0.261801
$993$	−55181.5	−1.76348
$994$	0	0
$995$	−62495.0	−1.99118
$996$	8067.20	0.256646
$997$	−15136.2	−0.480811	−0.240405	−	0.970673i	$-0.577280\pi$
$997$	−15136.2	−0.480811	−0.240405	+	0.970673i	$0.577280\pi$
$998$	−58194.2	−1.84580
$999$	30166.2	0.955370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.o.1.17	yes	60
7.6	odd	2		2009.4.a.n.1.17	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.4.a.n.1.17	✓	60	7.6	odd	2
2009.4.a.o.1.17	yes	60	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)

\(f(q)\)	\(=\)	\(q-2.67118 q^{2} +8.92227 q^{3} -0.864788 q^{4} +15.7867 q^{5} -23.8330 q^{6} +23.6795 q^{8} +52.6070 q^{9} +O(q^{10})\)	\(q-2.67118 q^{2} +8.92227 q^{3} -0.864788 q^{4} +15.7867 q^{5} -23.8330 q^{6} +23.6795 q^{8} +52.6070 q^{9} -42.1690 q^{10} +19.8220 q^{11} -7.71587 q^{12} +3.90745 q^{13} +140.853 q^{15} -56.3338 q^{16} +119.529 q^{17} -140.523 q^{18} +34.1893 q^{19} -13.6521 q^{20} -52.9483 q^{22} -22.9786 q^{23} +211.275 q^{24} +124.219 q^{25} -10.4375 q^{26} +228.472 q^{27} +18.4620 q^{29} -376.244 q^{30} +209.964 q^{31} -38.9578 q^{32} +176.858 q^{33} -319.284 q^{34} -45.4939 q^{36} +132.034 q^{37} -91.3259 q^{38} +34.8634 q^{39} +373.820 q^{40} -41.0000 q^{41} -345.326 q^{43} -17.1419 q^{44} +830.488 q^{45} +61.3800 q^{46} +14.9809 q^{47} -502.626 q^{48} -331.810 q^{50} +1066.47 q^{51} -3.37912 q^{52} -313.097 q^{53} -610.291 q^{54} +312.924 q^{55} +305.046 q^{57} -49.3153 q^{58} +324.189 q^{59} -121.808 q^{60} +42.6849 q^{61} -560.852 q^{62} +554.734 q^{64} +61.6856 q^{65} -472.419 q^{66} -100.079 q^{67} -103.367 q^{68} -205.021 q^{69} +845.052 q^{71} +1245.70 q^{72} -1061.34 q^{73} -352.687 q^{74} +1108.31 q^{75} -29.5665 q^{76} -93.1264 q^{78} -982.964 q^{79} -889.323 q^{80} +618.105 q^{81} +109.518 q^{82} -1045.53 q^{83} +1886.97 q^{85} +922.427 q^{86} +164.723 q^{87} +469.375 q^{88} +1417.41 q^{89} -2218.39 q^{90} +19.8716 q^{92} +1873.36 q^{93} -40.0167 q^{94} +539.735 q^{95} -347.592 q^{96} -704.691 q^{97} +1042.78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 2 q^{2} + 24 q^{3} + 230 q^{4} + 40 q^{5} + 72 q^{6} - 18 q^{8} + 572 q^{9}+O(q^{10}) \) 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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