LMFDB - Embedded newform 2009.4.a.n.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-4.08931 q^{2} +7.07895 q^{3} +8.72244 q^{4} +1.42150 q^{5} -28.9480 q^{6} -2.95427 q^{8} +23.1115 q^{9} +O(q^{10})$	\(q-4.08931 q^{2} +7.07895 q^{3} +8.72244 q^{4} +1.42150 q^{5} -28.9480 q^{6} -2.95427 q^{8} +23.1115 q^{9} -5.81297 q^{10} -0.443165 q^{11} +61.7457 q^{12} +64.4823 q^{13} +10.0628 q^{15} -57.6986 q^{16} -92.0664 q^{17} -94.5101 q^{18} +110.432 q^{19} +12.3990 q^{20} +1.81224 q^{22} +46.8679 q^{23} -20.9131 q^{24} -122.979 q^{25} -263.688 q^{26} -27.5264 q^{27} -84.6016 q^{29} -41.1497 q^{30} -22.6404 q^{31} +259.581 q^{32} -3.13714 q^{33} +376.488 q^{34} +201.589 q^{36} -416.907 q^{37} -451.590 q^{38} +456.467 q^{39} -4.19951 q^{40} +41.0000 q^{41} -423.747 q^{43} -3.86548 q^{44} +32.8531 q^{45} -191.657 q^{46} -598.465 q^{47} -408.445 q^{48} +502.900 q^{50} -651.733 q^{51} +562.443 q^{52} +386.740 q^{53} +112.564 q^{54} -0.629961 q^{55} +781.742 q^{57} +345.962 q^{58} +335.463 q^{59} +87.7718 q^{60} -607.222 q^{61} +92.5836 q^{62} -599.920 q^{64} +91.6619 q^{65} +12.8287 q^{66} +898.110 q^{67} -803.044 q^{68} +331.776 q^{69} -33.8041 q^{71} -68.2777 q^{72} -376.733 q^{73} +1704.86 q^{74} -870.564 q^{75} +963.235 q^{76} -1866.63 q^{78} -1369.36 q^{79} -82.0188 q^{80} -818.869 q^{81} -167.662 q^{82} +986.916 q^{83} -130.873 q^{85} +1732.83 q^{86} -598.890 q^{87} +1.30923 q^{88} +36.7885 q^{89} -134.347 q^{90} +408.803 q^{92} -160.270 q^{93} +2447.31 q^{94} +156.979 q^{95} +1837.56 q^{96} +464.373 q^{97} -10.2422 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.08931	−1.44579	−0.722894	−	0.690959i	$-0.757189\pi$
$2$	−4.08931	−1.44579	−0.722894	+	0.690959i	$0.757189\pi$
$3$	7.07895	1.36234	0.681172	−	0.732123i	$-0.261471\pi$
$3$	7.07895	1.36234	0.681172	+	0.732123i	$0.261471\pi$
$4$	8.72244	1.09030
$5$	1.42150	0.127143	0.0635716	−	0.997977i	$-0.479751\pi$
$5$	1.42150	0.127143	0.0635716	+	0.997977i	$0.479751\pi$
$6$	−28.9480	−1.96966
$7$	0	0
$7$	0	0
$8$	−2.95427	−0.130562
$9$	23.1115	0.855982
$10$	−5.81297	−0.183822
$11$	−0.443165	−0.0121472	−0.00607360	−	0.999982i	$-0.501933\pi$
$11$	−0.443165	−0.0121472	−0.00607360	+	0.999982i	$0.501933\pi$
$12$	61.7457	1.48537
$13$	64.4823	1.37571	0.687853	−	0.725850i	$-0.258553\pi$
$13$	64.4823	1.37571	0.687853	+	0.725850i	$0.258553\pi$
$14$	0	0
$15$	10.0628	0.173213
$16$	−57.6986	−0.901540
$17$	−92.0664	−1.31349	−0.656747	−	0.754111i	$-0.728068\pi$
$17$	−92.0664	−1.31349	−0.656747	+	0.754111i	$0.728068\pi$
$18$	−94.5101	−1.23757
$19$	110.432	1.33341	0.666705	−	0.745321i	$-0.267704\pi$
$19$	110.432	1.33341	0.666705	+	0.745321i	$0.267704\pi$
$20$	12.3990	0.138625
$21$	0	0
$22$	1.81224	0.0175623
$23$	46.8679	0.424897	0.212449	−	0.977172i	$-0.431856\pi$
$23$	46.8679	0.424897	0.212449	+	0.977172i	$0.431856\pi$
$24$	−20.9131	−0.177870
$25$	−122.979	−0.983835
$26$	−263.688	−1.98898
$27$	−27.5264	−0.196202
$28$	0	0
$29$	−84.6016	−0.541728	−0.270864	−	0.962618i	$-0.587309\pi$
$29$	−84.6016	−0.541728	−0.270864	+	0.962618i	$0.587309\pi$
$30$	−41.1497	−0.250429
$31$	−22.6404	−0.131172	−0.0655861	−	0.997847i	$-0.520892\pi$
$31$	−22.6404	−0.131172	−0.0655861	+	0.997847i	$0.520892\pi$
$32$	259.581	1.43400
$33$	−3.13714	−0.0165487
$34$	376.488	1.89903
$35$	0	0
$36$	201.589	0.933281
$37$	−416.907	−1.85241	−0.926205	−	0.377021i	$-0.876948\pi$
$37$	−416.907	−1.85241	−0.926205	+	0.377021i	$0.876948\pi$
$38$	−451.590	−1.92783
$39$	456.467	1.87418
$40$	−4.19951	−0.0166000
$41$	41.0000	0.156174
$41$	41.0000	0.156174
$42$	0	0
$43$	−423.747	−1.50281	−0.751405	−	0.659842i	$-0.770623\pi$
$43$	−423.747	−1.50281	−0.751405	+	0.659842i	$0.770623\pi$
$44$	−3.86548	−0.0132442
$45$	32.8531	0.108832
$46$	−191.657	−0.614312
$47$	−598.465	−1.85734	−0.928672	−	0.370903i	$-0.879048\pi$
$47$	−598.465	−1.85734	−0.928672	+	0.370903i	$0.879048\pi$
$48$	−408.445	−1.22821
$49$	0	0
$50$	502.900	1.42242
$51$	−651.733	−1.78943
$52$	562.443	1.49994
$53$	386.740	1.00232	0.501159	−	0.865355i	$-0.332907\pi$
$53$	386.740	1.00232	0.501159	+	0.865355i	$0.332907\pi$
$54$	112.564	0.283667
$55$	−0.629961	−0.00154443
$56$	0	0
$57$	781.742	1.81656
$58$	345.962	0.783225
$59$	335.463	0.740230	0.370115	−	0.928986i	$-0.379318\pi$
$59$	335.463	0.740230	0.370115	+	0.928986i	$0.379318\pi$
$60$	87.7718	0.188855
$61$	−607.222	−1.27454	−0.637268	−	0.770642i	$-0.719936\pi$
$61$	−607.222	−1.27454	−0.637268	+	0.770642i	$0.719936\pi$
$62$	92.5836	0.189647
$63$	0	0
$64$	−599.920	−1.17172
$65$	91.6619	0.174912
$66$	12.8287	0.0239259
$67$	898.110	1.63764	0.818818	−	0.574054i	$-0.194630\pi$
$67$	898.110	1.63764	0.818818	+	0.574054i	$0.194630\pi$
$68$	−803.044	−1.43211
$69$	331.776	0.578856
$70$	0	0
$71$	−33.8041	−0.0565044	−0.0282522	−	0.999601i	$-0.508994\pi$
$71$	−33.8041	−0.0565044	−0.0282522	+	0.999601i	$0.508994\pi$
$72$	−68.2777	−0.111758
$73$	−376.733	−0.604017	−0.302008	−	0.953305i	$-0.597657\pi$
$73$	−376.733	−0.604017	−0.302008	+	0.953305i	$0.597657\pi$
$74$	1704.86	2.67819
$75$	−870.564	−1.34032
$76$	963.235	1.45382
$77$	0	0
$78$	−1866.63	−2.70968
$79$	−1369.36	−1.95019	−0.975093	−	0.221797i	$-0.928808\pi$
$79$	−1369.36	−1.95019	−0.975093	+	0.221797i	$0.928808\pi$
$80$	−82.0188	−0.114625
$81$	−818.869	−1.12328
$82$	−167.662	−0.225794
$83$	986.916	1.30516	0.652579	−	0.757721i	$-0.273687\pi$
$83$	986.916	1.30516	0.652579	+	0.757721i	$0.273687\pi$
$84$	0	0
$85$	−130.873	−0.167002
$86$	1732.83	2.17274
$87$	−598.890	−0.738021
$88$	1.30923	0.00158596
$89$	36.7885	0.0438154	0.0219077	−	0.999760i	$-0.493026\pi$
$89$	36.7885	0.0438154	0.0219077	+	0.999760i	$0.493026\pi$
$90$	−134.347	−0.157349
$91$	0	0
$92$	408.803	0.463268
$93$	−160.270	−0.178702
$94$	2447.31	2.68533
$95$	156.979	0.169534
$96$	1837.56	1.95360
$97$	464.373	0.486081	0.243041	−	0.970016i	$-0.421855\pi$
$97$	464.373	0.486081	0.243041	+	0.970016i	$0.421855\pi$
$98$	0	0
$99$	−10.2422	−0.0103978
$100$	−1072.68	−1.07268
$101$	−597.970	−0.589111	−0.294556	−	0.955634i	$-0.595172\pi$
$101$	−597.970	−0.589111	−0.294556	+	0.955634i	$0.595172\pi$
$102$	2665.14	2.58714
$103$	1623.12	1.55273	0.776363	−	0.630287i	$-0.217063\pi$
$103$	1623.12	1.55273	0.776363	+	0.630287i	$0.217063\pi$
$104$	−190.498	−0.179614
$105$	0	0
$106$	−1581.50	−1.44914
$107$	−1456.63	−1.31605	−0.658026	−	0.752995i	$-0.728608\pi$
$107$	−1456.63	−1.31605	−0.658026	+	0.752995i	$0.728608\pi$
$108$	−240.097	−0.213920
$109$	194.605	0.171007	0.0855035	−	0.996338i	$-0.472750\pi$
$109$	194.605	0.171007	0.0855035	+	0.996338i	$0.472750\pi$
$110$	2.57610	0.00223293
$111$	−2951.27	−2.52362
$112$	0	0
$113$	−873.093	−0.726846	−0.363423	−	0.931624i	$-0.618392\pi$
$113$	−873.093	−0.726846	−0.363423	+	0.931624i	$0.618392\pi$
$114$	−3196.78	−2.62637
$115$	66.6230	0.0540228
$116$	−737.932	−0.590649
$117$	1490.28	1.17758
$118$	−1371.81	−1.07022
$119$	0	0
$120$	−29.7281	−0.0226150
$121$	−1330.80	−0.999852
$122$	2483.12	1.84271
$123$	290.237	0.212762
$124$	−197.480	−0.143018
$125$	−352.504	−0.252231
$126$	0	0
$127$	−428.426	−0.299344	−0.149672	−	0.988736i	$-0.547822\pi$
$127$	−428.426	−0.299344	−0.149672	+	0.988736i	$0.547822\pi$
$128$	376.605	0.260059
$129$	−2999.68	−2.04734
$130$	−374.834	−0.252885
$131$	1121.62	0.748064	0.374032	−	0.927416i	$-0.377975\pi$
$131$	1121.62	0.748064	0.374032	+	0.927416i	$0.377975\pi$
$132$	−27.3635	−0.0180431
$133$	0	0
$134$	−3672.65	−2.36767
$135$	−39.1289	−0.0249458
$136$	271.989	0.171492
$137$	−360.664	−0.224917	−0.112458	−	0.993656i	$-0.535872\pi$
$137$	−360.664	−0.224917	−0.112458	+	0.993656i	$0.535872\pi$
$138$	−1356.73	−0.836904
$139$	−1791.36	−1.09310	−0.546552	−	0.837425i	$-0.684060\pi$
$139$	−1791.36	−1.09310	−0.546552	+	0.837425i	$0.684060\pi$
$140$	0	0
$141$	−4236.50	−2.53034
$142$	138.236	0.0816934
$143$	−28.5763	−0.0167110
$144$	−1333.50	−0.771702
$145$	−120.262	−0.0688771
$146$	1540.58	0.873280
$147$	0	0
$148$	−3636.45	−2.01969
$149$	−1358.92	−0.747160	−0.373580	−	0.927598i	$-0.621870\pi$
$149$	−1358.92	−0.747160	−0.373580	+	0.927598i	$0.621870\pi$
$150$	3560.01	1.93782
$151$	11.3793	0.00613269	0.00306634	−	0.999995i	$-0.499024\pi$
$151$	11.3793	0.00613269	0.00306634	+	0.999995i	$0.499024\pi$
$152$	−326.246	−0.174092
$153$	−2127.79	−1.12433
$154$	0	0
$155$	−32.1835	−0.0166777
$156$	3981.50	2.04343
$157$	1448.58	0.736367	0.368184	−	0.929753i	$-0.379980\pi$
$157$	1448.58	0.736367	0.368184	+	0.929753i	$0.379980\pi$
$158$	5599.72	2.81956
$159$	2737.71	1.36550
$160$	368.996	0.182323
$161$	0	0
$162$	3348.61	1.62402
$163$	−3623.55	−1.74122	−0.870609	−	0.491975i	$-0.836275\pi$
$163$	−3623.55	−1.74122	−0.870609	+	0.491975i	$0.836275\pi$
$164$	357.620	0.170277
$165$	−4.45946	−0.00210405
$166$	−4035.80	−1.88698
$167$	2324.38	1.07704	0.538520	−	0.842613i	$-0.318984\pi$
$167$	2324.38	1.07704	0.538520	+	0.842613i	$0.318984\pi$
$168$	0	0
$169$	1960.97	0.892566
$170$	535.179	0.241449
$171$	2552.25	1.14138
$172$	−3696.11	−1.63852
$173$	1631.00	0.716777	0.358388	−	0.933573i	$-0.383326\pi$
$173$	1631.00	0.716777	0.358388	+	0.933573i	$0.383326\pi$
$174$	2449.05	1.06702
$175$	0	0
$176$	25.5700	0.0109512
$177$	2374.73	1.00845
$178$	−150.439	−0.0633478
$179$	−726.863	−0.303510	−0.151755	−	0.988418i	$-0.548492\pi$
$179$	−726.863	−0.303510	−0.151755	+	0.988418i	$0.548492\pi$
$180$	286.559	0.118660
$181$	−2095.37	−0.860485	−0.430243	−	0.902713i	$-0.641572\pi$
$181$	−2095.37	−0.860485	−0.430243	+	0.902713i	$0.641572\pi$
$182$	0	0
$183$	−4298.49	−1.73636
$184$	−138.461	−0.0554753
$185$	−592.636	−0.235521
$186$	655.395	0.258365
$187$	40.8006	0.0159553
$188$	−5220.08	−2.02507
$189$	0	0
$190$	−641.937	−0.245111
$191$	4021.22	1.52338	0.761688	−	0.647943i	$-0.224371\pi$
$191$	4021.22	1.52338	0.761688	+	0.647943i	$0.224371\pi$
$192$	−4246.80	−1.59628
$193$	−1840.45	−0.686418	−0.343209	−	0.939259i	$-0.611514\pi$
$193$	−1840.45	−0.686418	−0.343209	+	0.939259i	$0.611514\pi$
$194$	−1898.96	−0.702771
$195$	648.870	0.238290
$196$	0	0
$197$	773.389	0.279704	0.139852	−	0.990172i	$-0.455337\pi$
$197$	773.389	0.279704	0.139852	+	0.990172i	$0.455337\pi$
$198$	41.8836	0.0150330
$199$	−318.267	−0.113374	−0.0566868	−	0.998392i	$-0.518054\pi$
$199$	−318.267	−0.113374	−0.0566868	+	0.998392i	$0.518054\pi$
$200$	363.314	0.128451
$201$	6357.67	2.23102
$202$	2445.28	0.851730
$203$	0	0
$204$	−5684.70	−1.95102
$205$	58.2817	0.0198564
$206$	−6637.43	−2.24491
$207$	1083.19	0.363705
$208$	−3720.54	−1.24025
$209$	−48.9395	−0.0161972
$210$	0	0
$211$	3115.90	1.01662	0.508312	−	0.861173i	$-0.330270\pi$
$211$	3115.90	1.01662	0.508312	+	0.861173i	$0.330270\pi$
$212$	3373.32	1.09283
$213$	−239.298	−0.0769785
$214$	5956.60	1.90273
$215$	−602.358	−0.191072
$216$	81.3204	0.0256165
$217$	0	0
$218$	−795.799	−0.247240
$219$	−2666.87	−0.822878
$220$	−5.49480	−0.00168390
$221$	−5936.65	−1.80698
$222$	12068.6	3.64862
$223$	5895.18	1.77027	0.885135	−	0.465334i	$-0.154066\pi$
$223$	5895.18	1.77027	0.885135	+	0.465334i	$0.154066\pi$
$224$	0	0
$225$	−2842.24	−0.842145
$226$	3570.34	1.05087
$227$	5516.68	1.61302	0.806509	−	0.591222i	$-0.201354\pi$
$227$	5516.68	1.61302	0.806509	+	0.591222i	$0.201354\pi$
$228$	6818.69	1.98061
$229$	1940.65	0.560009	0.280004	−	0.959999i	$-0.409664\pi$
$229$	1940.65	0.560009	0.280004	+	0.959999i	$0.409664\pi$
$230$	−272.442	−0.0781056
$231$	0	0
$232$	249.936	0.0707290
$233$	−5371.80	−1.51038	−0.755189	−	0.655507i	$-0.772455\pi$
$233$	−5371.80	−1.51038	−0.755189	+	0.655507i	$0.772455\pi$
$234$	−6094.23	−1.70253
$235$	−850.721	−0.236149
$236$	2926.06	0.807077
$237$	−9693.61	−2.65682
$238$	0	0
$239$	−686.208	−0.185720	−0.0928601	−	0.995679i	$-0.529601\pi$
$239$	−686.208	−0.185720	−0.0928601	+	0.995679i	$0.529601\pi$
$240$	−580.607	−0.156158
$241$	−3181.94	−0.850485	−0.425242	−	0.905079i	$-0.639811\pi$
$241$	−3181.94	−0.850485	−0.425242	+	0.905079i	$0.639811\pi$
$242$	5442.07	1.44558
$243$	−5053.52	−1.33409
$244$	−5296.45	−1.38963
$245$	0	0
$246$	−1186.87	−0.307610
$247$	7120.90	1.83438
$248$	66.8860	0.0171261
$249$	6986.33	1.77807
$250$	1441.50	0.364673
$251$	2350.99	0.591209	0.295605	−	0.955310i	$-0.404479\pi$
$251$	2350.99	0.591209	0.295605	+	0.955310i	$0.404479\pi$
$252$	0	0
$253$	−20.7702	−0.00516131
$254$	1751.97	0.432788
$255$	−926.442	−0.227514
$256$	3259.30	0.795728
$257$	−4564.13	−1.10779	−0.553897	−	0.832585i	$-0.686860\pi$
$257$	−4564.13	−1.10779	−0.553897	+	0.832585i	$0.686860\pi$
$258$	12266.6	2.96003
$259$	0	0
$260$	799.515	0.190707
$261$	−1955.27	−0.463710
$262$	−4586.65	−1.08154
$263$	−2052.97	−0.481337	−0.240668	−	0.970607i	$-0.577367\pi$
$263$	−2052.97	−0.481337	−0.240668	+	0.970607i	$0.577367\pi$
$264$	9.26797	0.00216062
$265$	549.753	0.127438
$266$	0	0
$267$	260.424	0.0596917
$268$	7833.71	1.78552
$269$	2667.62	0.604638	0.302319	−	0.953207i	$-0.402239\pi$
$269$	2667.62	0.604638	0.302319	+	0.953207i	$0.402239\pi$
$270$	160.010	0.0360663
$271$	−4750.66	−1.06488	−0.532439	−	0.846468i	$-0.678724\pi$
$271$	−4750.66	−1.06488	−0.532439	+	0.846468i	$0.678724\pi$
$272$	5312.10	1.18417
$273$	0	0
$274$	1474.87	0.325182
$275$	54.5001	0.0119508
$276$	2893.89	0.631130
$277$	742.520	0.161060	0.0805301	−	0.996752i	$-0.474339\pi$
$277$	742.520	0.161060	0.0805301	+	0.996752i	$0.474339\pi$
$278$	7325.44	1.58040
$279$	−523.254	−0.112281
$280$	0	0
$281$	3614.96	0.767438	0.383719	−	0.923450i	$-0.374643\pi$
$281$	3614.96	0.767438	0.383719	+	0.923450i	$0.374643\pi$
$282$	17324.4	3.65834
$283$	3228.25	0.678090	0.339045	−	0.940770i	$-0.389896\pi$
$283$	3228.25	0.678090	0.339045	+	0.940770i	$0.389896\pi$
$284$	−294.855	−0.0616070
$285$	1111.25	0.230964
$286$	116.857	0.0241605
$287$	0	0
$288$	5999.32	1.22748
$289$	3563.22	0.725264
$290$	491.787	0.0995817
$291$	3287.27	0.662210
$292$	−3286.03	−0.658562
$293$	3630.04	0.723785	0.361893	−	0.932220i	$-0.382131\pi$
$293$	3630.04	0.723785	0.361893	+	0.932220i	$0.382131\pi$
$294$	0	0
$295$	476.862	0.0941153
$296$	1231.66	0.241854
$297$	12.1987	0.00238331
$298$	5557.03	1.08023
$299$	3022.15	0.584534
$300$	−7593.44	−1.46136
$301$	0	0
$302$	−46.5335	−0.00886657
$303$	−4233.00	−0.802572
$304$	−6371.76	−1.20212
$305$	−863.168	−0.162049
$306$	8701.21	1.62554
$307$	−639.170	−0.118825	−0.0594127	−	0.998234i	$-0.518923\pi$
$307$	−639.170	−0.118825	−0.0594127	+	0.998234i	$0.518923\pi$
$308$	0	0
$309$	11490.0	2.11535
$310$	131.608	0.0241124
$311$	−2883.44	−0.525740	−0.262870	−	0.964831i	$-0.584669\pi$
$311$	−2883.44	−0.525740	−0.262870	+	0.964831i	$0.584669\pi$
$312$	−1348.53	−0.244697
$313$	−2679.89	−0.483951	−0.241975	−	0.970282i	$-0.577795\pi$
$313$	−2679.89	−0.483951	−0.241975	+	0.970282i	$0.577795\pi$
$314$	−5923.71	−1.06463
$315$	0	0
$316$	−11944.1	−2.12630
$317$	−6345.80	−1.12434	−0.562170	−	0.827022i	$-0.690033\pi$
$317$	−6345.80	−1.12434	−0.562170	+	0.827022i	$0.690033\pi$
$318$	−11195.4	−1.97423
$319$	37.4925	0.00658049
$320$	−852.789	−0.148976
$321$	−10311.4	−1.79292
$322$	0	0
$323$	−10167.1	−1.75143
$324$	−7142.53	−1.22471
$325$	−7929.99	−1.35347
$326$	14817.8	2.51743
$327$	1377.60	0.232970
$328$	−121.125	−0.0203903
$329$	0	0
$330$	18.2361	0.00304201
$331$	5273.78	0.875749	0.437875	−	0.899036i	$-0.355731\pi$
$331$	5273.78	0.875749	0.437875	+	0.899036i	$0.355731\pi$
$332$	8608.31	1.42302
$333$	−9635.36	−1.58563
$334$	−9505.09	−1.55717
$335$	1276.67	0.208214
$336$	0	0
$337$	−9269.40	−1.49833	−0.749164	−	0.662385i	$-0.769544\pi$
$337$	−9269.40	−1.49833	−0.749164	+	0.662385i	$0.769544\pi$
$338$	−8019.00	−1.29046
$339$	−6180.58	−0.990215
$340$	−1141.53	−0.182083
$341$	10.0334	0.00159338
$342$	−10436.9	−1.65019
$343$	0	0
$344$	1251.86	0.196209
$345$	471.621	0.0735977
$346$	−6669.65	−1.03631
$347$	9018.35	1.39519	0.697594	−	0.716493i	$-0.254254\pi$
$347$	9018.35	1.39519	0.697594	+	0.716493i	$0.254254\pi$
$348$	−5223.79	−0.804668
$349$	9339.16	1.43242	0.716209	−	0.697886i	$-0.245876\pi$
$349$	9339.16	1.43242	0.716209	+	0.697886i	$0.245876\pi$
$350$	0	0
$351$	−1774.96	−0.269916
$352$	−115.037	−0.0174191
$353$	−7162.24	−1.07991	−0.539954	−	0.841694i	$-0.681559\pi$
$353$	−7162.24	−1.07991	−0.539954	+	0.841694i	$0.681559\pi$
$354$	−9710.99	−1.45800
$355$	−48.0527	−0.00718415
$356$	320.885	0.0477722
$357$	0	0
$358$	2972.37	0.438811
$359$	4997.02	0.734632	0.367316	−	0.930096i	$-0.380277\pi$
$359$	4997.02	0.734632	0.367316	+	0.930096i	$0.380277\pi$
$360$	−97.0571	−0.0142093
$361$	5336.20	0.777985
$362$	8568.63	1.24408
$363$	−9420.69	−1.36214
$364$	0	0
$365$	−535.527	−0.0767966
$366$	17577.8	2.51041
$367$	−9994.87	−1.42160	−0.710801	−	0.703393i	$-0.751667\pi$
$367$	−9994.87	−1.42160	−0.710801	+	0.703393i	$0.751667\pi$
$368$	−2704.21	−0.383062
$369$	947.572	0.133682
$370$	2423.47	0.340514
$371$	0	0
$372$	−1397.95	−0.194839
$373$	−13406.3	−1.86100	−0.930500	−	0.366293i	$-0.880627\pi$
$373$	−13406.3	−1.86100	−0.930500	+	0.366293i	$0.880627\pi$
$374$	−166.846	−0.0230679
$375$	−2495.36	−0.343626
$376$	1768.03	0.242498
$377$	−5455.31	−0.745259
$378$	0	0
$379$	2796.87	0.379065	0.189533	−	0.981874i	$-0.439303\pi$
$379$	2796.87	0.379065	0.189533	+	0.981874i	$0.439303\pi$
$380$	1369.24	0.184844
$381$	−3032.81	−0.407809
$382$	−16444.0	−2.20248
$383$	−14364.8	−1.91646	−0.958231	−	0.285995i	$-0.907676\pi$
$383$	−14364.8	−1.91646	−0.958231	+	0.285995i	$0.907676\pi$
$384$	2665.97	0.354289
$385$	0	0
$386$	7526.18	0.992415
$387$	−9793.43	−1.28638
$388$	4050.46	0.529977
$389$	−14534.0	−1.89435	−0.947176	−	0.320715i	$-0.896077\pi$
$389$	−14534.0	−1.89435	−0.947176	+	0.320715i	$0.896077\pi$
$390$	−2653.43	−0.344517
$391$	−4314.96	−0.558100
$392$	0	0
$393$	7939.89	1.01912
$394$	−3162.63	−0.404393
$395$	−1946.55	−0.247953
$396$	−89.3371	−0.0113368
$397$	806.635	0.101974	0.0509872	−	0.998699i	$-0.483763\pi$
$397$	806.635	0.101974	0.0509872	+	0.998699i	$0.483763\pi$
$398$	1301.49	0.163914
$399$	0	0
$400$	7095.73	0.886966
$401$	8355.35	1.04051	0.520257	−	0.854010i	$-0.325836\pi$
$401$	8355.35	1.04051	0.520257	+	0.854010i	$0.325836\pi$
$402$	−25998.5	−3.22559
$403$	−1459.91	−0.180454
$404$	−5215.76	−0.642311
$405$	−1164.03	−0.142817
$406$	0	0
$407$	184.759	0.0225016
$408$	1925.40	0.233631
$409$	12493.6	1.51043	0.755217	−	0.655475i	$-0.227531\pi$
$409$	12493.6	1.51043	0.755217	+	0.655475i	$0.227531\pi$
$410$	−238.332	−0.0287082
$411$	−2553.12	−0.306414
$412$	14157.6	1.69294
$413$	0	0
$414$	−4429.49	−0.525840
$415$	1402.91	0.165942
$416$	16738.4	1.97276
$417$	−12681.0	−1.48918
$418$	200.129	0.0234177
$419$	−15197.6	−1.77196	−0.885978	−	0.463727i	$-0.846512\pi$
$419$	−15197.6	−1.77196	−0.885978	+	0.463727i	$0.846512\pi$
$420$	0	0
$421$	−9793.07	−1.13369	−0.566847	−	0.823823i	$-0.691837\pi$
$421$	−9793.07	−1.13369	−0.566847	+	0.823823i	$0.691837\pi$
$422$	−12741.9	−1.46982
$423$	−13831.4	−1.58985
$424$	−1142.54	−0.130864
$425$	11322.3	1.29226
$426$	978.562	0.111295
$427$	0	0
$428$	−12705.4	−1.43490
$429$	−202.290	−0.0227661
$430$	2463.23	0.276250
$431$	3305.27	0.369395	0.184697	−	0.982795i	$-0.440870\pi$
$431$	3305.27	0.369395	0.184697	+	0.982795i	$0.440870\pi$
$432$	1588.23	0.176884
$433$	1573.63	0.174651	0.0873257	−	0.996180i	$-0.472168\pi$
$433$	1573.63	0.174651	0.0873257	+	0.996180i	$0.472168\pi$
$434$	0	0
$435$	−851.326	−0.0938343
$436$	1697.43	0.186450
$437$	5175.71	0.566563
$438$	10905.7	1.18971
$439$	−9839.76	−1.06976	−0.534882	−	0.844927i	$-0.679644\pi$
$439$	−9839.76	−1.06976	−0.534882	+	0.844927i	$0.679644\pi$
$440$	1.86108	0.000201644 0
$441$	0	0
$442$	24276.8	2.61251
$443$	7477.25	0.801930	0.400965	−	0.916093i	$-0.368675\pi$
$443$	7477.25	0.801930	0.400965	+	0.916093i	$0.368675\pi$
$444$	−25742.2	−2.75151
$445$	52.2950	0.00557084
$446$	−24107.2	−2.55944
$447$	−9619.70	−1.01789
$448$	0	0
$449$	12696.6	1.33450	0.667250	−	0.744834i	$-0.267471\pi$
$449$	12696.6	1.33450	0.667250	+	0.744834i	$0.267471\pi$
$450$	11622.8	1.21756
$451$	−18.1698	−0.00189707
$452$	−7615.50	−0.792484
$453$	80.5536	0.00835483
$454$	−22559.4	−2.33208
$455$	0	0
$456$	−2309.48	−0.237174
$457$	−1679.52	−0.171914	−0.0859569	−	0.996299i	$-0.527395\pi$
$457$	−1679.52	−0.171914	−0.0859569	+	0.996299i	$0.527395\pi$
$458$	−7935.93	−0.809655
$459$	2534.25	0.257710
$460$	581.115	0.0589013
$461$	−7090.48	−0.716348	−0.358174	−	0.933655i	$-0.616601\pi$
$461$	−7090.48	−0.716348	−0.358174	+	0.933655i	$0.616601\pi$
$462$	0	0
$463$	−5139.68	−0.515899	−0.257949	−	0.966158i	$-0.583047\pi$
$463$	−5139.68	−0.515899	−0.257949	+	0.966158i	$0.583047\pi$
$464$	4881.39	0.488390
$465$	−227.825	−0.0227207
$466$	21966.9	2.18369
$467$	−14308.1	−1.41778	−0.708888	−	0.705321i	$-0.750803\pi$
$467$	−14308.1	−1.41778	−0.708888	+	0.705321i	$0.750803\pi$
$468$	12998.9	1.28392
$469$	0	0
$470$	3478.86	0.341421
$471$	10254.5	1.00319
$472$	−991.050	−0.0966457
$473$	187.790	0.0182549
$474$	39640.1	3.84121
$475$	−13580.8	−1.31186
$476$	0	0
$477$	8938.15	0.857966
$478$	2806.12	0.268512
$479$	12233.0	1.16689	0.583447	−	0.812151i	$-0.301704\pi$
$479$	12233.0	1.16689	0.583447	+	0.812151i	$0.301704\pi$
$480$	2612.11	0.248387
$481$	−26883.1	−2.54837
$482$	13011.9	1.22962
$483$	0	0
$484$	−11607.9	−1.09014
$485$	660.108	0.0618020
$486$	20665.4	1.92881
$487$	−14271.9	−1.32797	−0.663983	−	0.747748i	$-0.731135\pi$
$487$	−14271.9	−1.32797	−0.663983	+	0.747748i	$0.731135\pi$
$488$	1793.90	0.166406
$489$	−25650.9	−2.37214
$490$	0	0
$491$	−5568.25	−0.511795	−0.255898	−	0.966704i	$-0.582371\pi$
$491$	−5568.25	−0.511795	−0.255898	+	0.966704i	$0.582371\pi$
$492$	2531.57	0.231976
$493$	7788.97	0.711557
$494$	−29119.6	−2.65213
$495$	−14.5594	−0.00132201
$496$	1306.32	0.118257
$497$	0	0
$498$	−28569.2	−2.57072
$499$	9605.95	0.861766	0.430883	−	0.902408i	$-0.358202\pi$
$499$	9605.95	0.861766	0.430883	+	0.902408i	$0.358202\pi$
$500$	−3074.69	−0.275009
$501$	16454.1	1.46730
$502$	−9613.94	−0.854763
$503$	−10790.6	−0.956521	−0.478261	−	0.878218i	$-0.658733\pi$
$503$	−10790.6	−0.956521	−0.478261	+	0.878218i	$0.658733\pi$
$504$	0	0
$505$	−850.017	−0.0749015
$506$	84.9358	0.00746217
$507$	13881.6	1.21598
$508$	−3736.92	−0.326376
$509$	21164.7	1.84305	0.921523	−	0.388325i	$-0.126946\pi$
$509$	21164.7	1.84305	0.921523	+	0.388325i	$0.126946\pi$
$510$	3788.51	0.328937
$511$	0	0
$512$	−16341.1	−1.41051
$513$	−3039.79	−0.261618
$514$	18664.1	1.60163
$515$	2307.27	0.197419
$516$	−26164.5	−2.23223
$517$	265.219	0.0225615
$518$	0	0
$519$	11545.7	0.976497
$520$	−270.794	−0.0228368
$521$	−10417.2	−0.875982	−0.437991	−	0.898979i	$-0.644310\pi$
$521$	−10417.2	−0.875982	−0.437991	+	0.898979i	$0.644310\pi$
$522$	7995.71	0.670426
$523$	−21337.9	−1.78402	−0.892009	−	0.452017i	$-0.850705\pi$
$523$	−21337.9	−1.78402	−0.892009	+	0.452017i	$0.850705\pi$
$524$	9783.26	0.815618
$525$	0	0
$526$	8395.22	0.695911
$527$	2084.42	0.172294
$528$	181.009	0.0149193
$529$	−9970.40	−0.819462
$530$	−2248.11	−0.184248
$531$	7753.06	0.633624
$532$	0	0
$533$	2643.77	0.214849
$534$	−1064.95	−0.0863016
$535$	−2070.60	−0.167327
$536$	−2653.26	−0.213812
$537$	−5145.43	−0.413485
$538$	−10908.7	−0.874178
$539$	0	0
$540$	−341.299	−0.0271985
$541$	1166.74	0.0927211	0.0463606	−	0.998925i	$-0.485238\pi$
$541$	1166.74	0.0927211	0.0463606	+	0.998925i	$0.485238\pi$
$542$	19426.9	1.53959
$543$	−14833.0	−1.17228
$544$	−23898.7	−1.88355
$545$	276.632	0.0217424
$546$	0	0
$547$	1415.20	0.110621	0.0553104	−	0.998469i	$-0.482385\pi$
$547$	1415.20	0.110621	0.0553104	+	0.998469i	$0.482385\pi$
$548$	−3145.87	−0.245228
$549$	−14033.8	−1.09098
$550$	−222.868	−0.0172784
$551$	−9342.71	−0.722347
$552$	−980.156	−0.0755765
$553$	0	0
$554$	−3036.39	−0.232859
$555$	−4195.24	−0.320861
$556$	−15625.1	−1.19182
$557$	−12608.8	−0.959157	−0.479579	−	0.877499i	$-0.659210\pi$
$557$	−12608.8	−0.959157	−0.479579	+	0.877499i	$0.659210\pi$
$558$	2139.75	0.162335
$559$	−27324.2	−2.06742
$560$	0	0
$561$	288.825	0.0217366
$562$	−14782.7	−1.10955
$563$	2553.01	0.191113	0.0955565	−	0.995424i	$-0.469537\pi$
$563$	2553.01	0.191113	0.0955565	+	0.995424i	$0.469537\pi$
$564$	−36952.7	−2.75884
$565$	−1241.11	−0.0924136
$566$	−13201.3	−0.980375
$567$	0	0
$568$	99.8666	0.00737731
$569$	−15993.3	−1.17834	−0.589169	−	0.808010i	$-0.700545\pi$
$569$	−15993.3	−1.17834	−0.589169	+	0.808010i	$0.700545\pi$
$570$	−4544.24	−0.333925
$571$	−20133.8	−1.47561	−0.737804	−	0.675015i	$-0.764137\pi$
$571$	−20133.8	−1.47561	−0.737804	+	0.675015i	$0.764137\pi$
$572$	−249.255	−0.0182201
$573$	28466.0	2.07536
$574$	0	0
$575$	−5763.79	−0.418029
$576$	−13865.1	−1.00297
$577$	84.9551	0.00612951	0.00306475	−	0.999995i	$-0.499024\pi$
$577$	84.9551	0.00612951	0.00306475	+	0.999995i	$0.499024\pi$
$578$	−14571.1	−1.04858
$579$	−13028.5	−0.935137
$580$	−1048.97	−0.0750970
$581$	0	0
$582$	−13442.7	−0.957416
$583$	−171.390	−0.0121754
$584$	1112.97	0.0788614
$585$	2118.45	0.149721
$586$	−14844.3	−1.04644
$587$	7667.08	0.539104	0.269552	−	0.962986i	$-0.413124\pi$
$587$	7667.08	0.539104	0.269552	+	0.962986i	$0.413124\pi$
$588$	0	0
$589$	−2500.22	−0.174906
$590$	−1950.04	−0.136071
$591$	5474.78	0.381053
$592$	24055.0	1.67002
$593$	3719.32	0.257562	0.128781	−	0.991673i	$-0.458894\pi$
$593$	3719.32	0.257562	0.128781	+	0.991673i	$0.458894\pi$
$594$	−49.8843	−0.00344576
$595$	0	0
$596$	−11853.1	−0.814632
$597$	−2253.00	−0.154454
$598$	−12358.5	−0.845112
$599$	9714.86	0.662669	0.331334	−	0.943513i	$-0.392501\pi$
$599$	9714.86	0.662669	0.331334	+	0.943513i	$0.392501\pi$
$600$	2571.88	0.174995
$601$	−11489.3	−0.779798	−0.389899	−	0.920858i	$-0.627490\pi$
$601$	−11489.3	−0.779798	−0.389899	+	0.920858i	$0.627490\pi$
$602$	0	0
$603$	20756.7	1.40179
$604$	99.2554	0.00668650
$605$	−1891.74	−0.127124
$606$	17310.0	1.16035
$607$	17561.7	1.17431	0.587156	−	0.809474i	$-0.300248\pi$
$607$	17561.7	1.17431	0.587156	+	0.809474i	$0.300248\pi$
$608$	28666.1	1.91211
$609$	0	0
$610$	3529.76	0.234288
$611$	−38590.4	−2.55516
$612$	−18559.6	−1.22586
$613$	−12593.5	−0.829765	−0.414882	−	0.909875i	$-0.636177\pi$
$613$	−12593.5	−0.829765	−0.414882	+	0.909875i	$0.636177\pi$
$614$	2613.76	0.171796
$615$	412.573	0.0270513
$616$	0	0
$617$	28778.8	1.87778	0.938889	−	0.344219i	$-0.111856\pi$
$617$	28778.8	1.87778	0.938889	+	0.344219i	$0.111856\pi$
$618$	−46986.1	−3.05834
$619$	19154.3	1.24374	0.621872	−	0.783119i	$-0.286372\pi$
$619$	19154.3	1.24374	0.621872	+	0.783119i	$0.286372\pi$
$620$	−280.718	−0.0181837
$621$	−1290.10	−0.0833657
$622$	11791.3	0.760109
$623$	0	0
$624$	−26337.5	−1.68965
$625$	14871.3	0.951765
$626$	10958.9	0.699690
$627$	−346.440	−0.0220662
$628$	12635.2	0.802865
$629$	38383.2	2.43313
$630$	0	0
$631$	−15611.9	−0.984943	−0.492472	−	0.870328i	$-0.663906\pi$
$631$	−15611.9	−0.984943	−0.492472	+	0.870328i	$0.663906\pi$
$632$	4045.45	0.254619
$633$	22057.3	1.38499
$634$	25949.9	1.62556
$635$	−609.010	−0.0380595
$636$	23879.5	1.48881
$637$	0	0
$638$	−153.318	−0.00951399
$639$	−781.265	−0.0483668
$640$	535.346	0.0330647
$641$	−15727.8	−0.969125	−0.484563	−	0.874757i	$-0.661021\pi$
$641$	−15727.8	−0.969125	−0.484563	+	0.874757i	$0.661021\pi$
$642$	42166.5	2.59218
$643$	−3262.00	−0.200063	−0.100032	−	0.994984i	$-0.531894\pi$
$643$	−3262.00	−0.200063	−0.100032	+	0.994984i	$0.531894\pi$
$644$	0	0
$645$	−4264.06	−0.260306
$646$	41576.3	2.53219
$647$	−10999.7	−0.668383	−0.334191	−	0.942505i	$-0.608463\pi$
$647$	−10999.7	−0.668383	−0.334191	+	0.942505i	$0.608463\pi$
$648$	2419.16	0.146657
$649$	−148.665	−0.00899173
$650$	32428.2	1.95683
$651$	0	0
$652$	−31606.2	−1.89846
$653$	−4179.66	−0.250479	−0.125240	−	0.992127i	$-0.539970\pi$
$653$	−4179.66	−0.250479	−0.125240	+	0.992127i	$0.539970\pi$
$654$	−5633.42	−0.336826
$655$	1594.39	0.0951113
$656$	−2365.64	−0.140797
$657$	−8706.86	−0.517027
$658$	0	0
$659$	−11285.5	−0.667105	−0.333552	−	0.942732i	$-0.608247\pi$
$659$	−11285.5	−0.667105	−0.333552	+	0.942732i	$0.608247\pi$
$660$	−38.8974	−0.00229406
$661$	−9571.75	−0.563235	−0.281617	−	0.959527i	$-0.590871\pi$
$661$	−9571.75	−0.563235	−0.281617	+	0.959527i	$0.590871\pi$
$662$	−21566.1	−1.26615
$663$	−42025.3	−2.46173
$664$	−2915.62	−0.170404
$665$	0	0
$666$	39402.0	2.29248
$667$	−3965.10	−0.230179
$668$	20274.2	1.17430
$669$	41731.7	2.41172
$670$	−5220.68	−0.301034
$671$	269.099	0.0154821
$672$	0	0
$673$	3807.87	0.218102	0.109051	−	0.994036i	$-0.465219\pi$
$673$	3807.87	0.218102	0.109051	+	0.994036i	$0.465219\pi$
$674$	37905.4	2.16626
$675$	3385.18	0.193030
$676$	17104.4	0.973169
$677$	26320.9	1.49423	0.747117	−	0.664693i	$-0.231438\pi$
$677$	26320.9	1.49423	0.747117	+	0.664693i	$0.231438\pi$
$678$	25274.3	1.43164
$679$	0	0
$680$	386.634	0.0218040
$681$	39052.3	2.19748
$682$	−41.0298	−0.00230368
$683$	27730.3	1.55354	0.776771	−	0.629783i	$-0.216856\pi$
$683$	27730.3	1.55354	0.776771	+	0.629783i	$0.216856\pi$
$684$	22261.8	1.24445
$685$	−512.685	−0.0285966
$686$	0	0
$687$	13737.8	0.762925
$688$	24449.6	1.35484
$689$	24937.9	1.37889
$690$	−1928.60	−0.106407
$691$	22356.5	1.23080	0.615400	−	0.788215i	$-0.288995\pi$
$691$	22356.5	1.23080	0.615400	+	0.788215i	$0.288995\pi$
$692$	14226.3	0.781505
$693$	0	0
$694$	−36878.8	−2.01715
$695$	−2546.43	−0.138981
$696$	1769.29	0.0963572
$697$	−3774.72	−0.205133
$698$	−38190.7	−2.07097
$699$	−38026.7	−2.05766
$700$	0	0
$701$	24877.9	1.34040	0.670202	−	0.742178i	$-0.266207\pi$
$701$	24877.9	1.34040	0.670202	+	0.742178i	$0.266207\pi$
$702$	7258.38	0.390242
$703$	−46039.9	−2.47002
$704$	265.863	0.0142331
$705$	−6022.21	−0.321716
$706$	29288.6	1.56132
$707$	0	0
$708$	20713.4	1.09952
$709$	−16422.4	−0.869895	−0.434948	−	0.900456i	$-0.643233\pi$
$709$	−16422.4	−0.869895	−0.434948	+	0.900456i	$0.643233\pi$
$710$	196.502	0.0103868
$711$	−31647.9	−1.66932
$712$	−108.683	−0.00572061
$713$	−1061.11	−0.0557347
$714$	0	0
$715$	−40.6213	−0.00212469
$716$	−6340.02	−0.330918
$717$	−4857.63	−0.253015
$718$	−20434.4	−1.06212
$719$	503.826	0.0261329	0.0130664	−	0.999915i	$-0.495841\pi$
$719$	503.826	0.0261329	0.0130664	+	0.999915i	$0.495841\pi$
$720$	−1895.58	−0.0981167
$721$	0	0
$722$	−21821.3	−1.12480
$723$	−22524.8	−1.15865
$724$	−18276.8	−0.938191
$725$	10404.2	0.532971
$726$	38524.1	1.96937
$727$	13609.7	0.694301	0.347150	−	0.937809i	$-0.387149\pi$
$727$	13609.7	0.694301	0.347150	+	0.937809i	$0.387149\pi$
$728$	0	0
$729$	−13664.1	−0.694210
$730$	2189.93	0.111032
$731$	39012.9	1.97393
$732$	−37493.3	−1.89316
$733$	−7638.07	−0.384882	−0.192441	−	0.981309i	$-0.561640\pi$
$733$	−7638.07	−0.384882	−0.192441	+	0.981309i	$0.561640\pi$
$734$	40872.1	2.05534
$735$	0	0
$736$	12166.0	0.609302
$737$	−398.011	−0.0198927
$738$	−3874.91	−0.193276
$739$	−7373.88	−0.367053	−0.183527	−	0.983015i	$-0.558751\pi$
$739$	−7373.88	−0.367053	−0.183527	+	0.983015i	$0.558751\pi$
$740$	−5169.23	−0.256790
$741$	50408.5	2.49906
$742$	0	0
$743$	5274.83	0.260450	0.130225	−	0.991484i	$-0.458430\pi$
$743$	5274.83	0.260450	0.130225	+	0.991484i	$0.458430\pi$
$744$	473.482	0.0233316
$745$	−1931.71	−0.0949963
$746$	54822.6	2.69061
$747$	22809.1	1.11719
$748$	355.881	0.0173961
$749$	0	0
$750$	10204.3	0.496810
$751$	23106.8	1.12274	0.561371	−	0.827564i	$-0.310274\pi$
$751$	23106.8	1.12274	0.561371	+	0.827564i	$0.310274\pi$
$752$	34530.6	1.67447
$753$	16642.6	0.805430
$754$	22308.4	1.07749
$755$	16.1758	0.000779730 0
$756$	0	0
$757$	−1680.06	−0.0806642	−0.0403321	−	0.999186i	$-0.512842\pi$
$757$	−1680.06	−0.0806642	−0.0403321	+	0.999186i	$0.512842\pi$
$758$	−11437.3	−0.548048
$759$	−147.031	−0.00703149
$760$	−463.760	−0.0221347
$761$	−34574.9	−1.64697	−0.823483	−	0.567341i	$-0.807972\pi$
$761$	−34574.9	−1.64697	−0.823483	+	0.567341i	$0.807972\pi$
$762$	12402.1	0.589606
$763$	0	0
$764$	35074.8	1.66095
$765$	−3024.67	−0.142951
$766$	58741.9	2.77080
$767$	21631.4	1.01834
$768$	23072.4	1.08406
$769$	−27231.8	−1.27699	−0.638495	−	0.769626i	$-0.720443\pi$
$769$	−27231.8	−1.27699	−0.638495	+	0.769626i	$0.720443\pi$
$770$	0	0
$771$	−32309.3	−1.50920
$772$	−16053.2	−0.748405
$773$	3917.59	0.182284	0.0911422	−	0.995838i	$-0.470948\pi$
$773$	3917.59	0.182284	0.0911422	+	0.995838i	$0.470948\pi$
$774$	40048.4	1.85983
$775$	2784.30	0.129052
$776$	−1371.88	−0.0634636
$777$	0	0
$778$	59434.0	2.73883
$779$	4527.71	0.208244
$780$	5659.73	0.259809
$781$	14.9808	0.000686371 0
$782$	17645.2	0.806894
$783$	2328.78	0.106288
$784$	0	0
$785$	2059.17	0.0936241
$786$	−32468.7	−1.47343
$787$	−19805.2	−0.897052	−0.448526	−	0.893770i	$-0.648051\pi$
$787$	−19805.2	−0.897052	−0.448526	+	0.893770i	$0.648051\pi$
$788$	6745.84	0.304963
$789$	−14532.9	−0.655746
$790$	7960.03	0.358488
$791$	0	0
$792$	30.2583	0.00135755
$793$	−39155.0	−1.75339
$794$	−3298.58	−0.147434
$795$	3891.67	0.173614
$796$	−2776.06	−0.123612
$797$	−16785.4	−0.746007	−0.373004	−	0.927830i	$-0.621672\pi$
$797$	−16785.4	−0.746007	−0.373004	+	0.927830i	$0.621672\pi$
$798$	0	0
$799$	55098.5	2.43961
$800$	−31923.1	−1.41082
$801$	850.238	0.0375052
$802$	−34167.6	−1.50436
$803$	166.955	0.00733711
$804$	55454.4	2.43250
$805$	0	0
$806$	5970.01	0.260899
$807$	18883.9	0.823725
$808$	1766.57	0.0769153
$809$	18468.0	0.802594	0.401297	−	0.915948i	$-0.368559\pi$
$809$	18468.0	0.802594	0.401297	+	0.915948i	$0.368559\pi$
$810$	4760.06	0.206483
$811$	−19533.4	−0.845757	−0.422878	−	0.906186i	$-0.638980\pi$
$811$	−19533.4	−0.845757	−0.422878	+	0.906186i	$0.638980\pi$
$812$	0	0
$813$	−33629.7	−1.45073
$814$	−755.535	−0.0325325
$815$	−5150.90	−0.221384
$816$	37604.1	1.61324
$817$	−46795.2	−2.00386
$818$	−51090.1	−2.18377
$819$	0	0
$820$	508.358	0.0216496
$821$	7331.04	0.311638	0.155819	−	0.987786i	$-0.450198\pi$
$821$	7331.04	0.311638	0.155819	+	0.987786i	$0.450198\pi$
$822$	10440.5	0.443010
$823$	23520.8	0.996213	0.498106	−	0.867116i	$-0.334029\pi$
$823$	23520.8	0.996213	0.498106	+	0.867116i	$0.334029\pi$
$824$	−4795.14	−0.202726
$825$	385.804	0.0162812
$826$	0	0
$827$	23518.7	0.988908	0.494454	−	0.869204i	$-0.335368\pi$
$827$	23518.7	0.988908	0.494454	+	0.869204i	$0.335368\pi$
$828$	9448.05	0.396549
$829$	−21805.3	−0.913544	−0.456772	−	0.889584i	$-0.650994\pi$
$829$	−21805.3	−0.913544	−0.456772	+	0.889584i	$0.650994\pi$
$830$	−5736.91	−0.239917
$831$	5256.26	0.219420
$832$	−38684.2	−1.61194
$833$	0	0
$834$	51856.4	2.15305
$835$	3304.11	0.136938
$836$	−426.872	−0.0176599
$837$	623.209	0.0257363
$838$	62147.5	2.56187
$839$	−8162.43	−0.335874	−0.167937	−	0.985798i	$-0.553711\pi$
$839$	−8162.43	−0.335874	−0.167937	+	0.985798i	$0.553711\pi$
$840$	0	0
$841$	−17231.6	−0.706530
$842$	40046.9	1.63908
$843$	25590.1	1.04552
$844$	27178.3	1.10843
$845$	2787.52	0.113484
$846$	56561.0	2.29859
$847$	0	0
$848$	−22314.3	−0.903630
$849$	22852.6	0.923792
$850$	−46300.2	−1.86833
$851$	−19539.6	−0.787084
$852$	−2087.26	−0.0839300
$853$	−40044.5	−1.60738	−0.803692	−	0.595046i	$-0.797134\pi$
$853$	−40044.5	−1.60738	−0.803692	+	0.595046i	$0.797134\pi$
$854$	0	0
$855$	3628.03	0.145118
$856$	4303.28	0.171826
$857$	−2627.05	−0.104712	−0.0523560	−	0.998628i	$-0.516673\pi$
$857$	−2627.05	−0.104712	−0.0523560	+	0.998628i	$0.516673\pi$
$858$	827.227	0.0329150
$859$	29663.0	1.17822	0.589109	−	0.808054i	$-0.299479\pi$
$859$	29663.0	1.17822	0.589109	+	0.808054i	$0.299479\pi$
$860$	−5254.03	−0.208327
$861$	0	0
$862$	−13516.3	−0.534067
$863$	14241.7	0.561753	0.280876	−	0.959744i	$-0.409375\pi$
$863$	14241.7	0.561753	0.280876	+	0.959744i	$0.409375\pi$
$864$	−7145.34	−0.281353
$865$	2318.47	0.0911333
$866$	−6435.08	−0.252509
$867$	25223.9	0.988060
$868$	0	0
$869$	606.851	0.0236893
$870$	3481.33	0.135665
$871$	57912.2	2.25290
$872$	−574.916	−0.0223270
$873$	10732.4	0.416077
$874$	−21165.1	−0.819130
$875$	0	0
$876$	−23261.6	−0.897188
$877$	28414.7	1.09407	0.547034	−	0.837110i	$-0.315757\pi$
$877$	28414.7	1.09407	0.547034	+	0.837110i	$0.315757\pi$
$878$	40237.8	1.54665
$879$	25696.8	0.986045
$880$	36.3478	0.00139237
$881$	5469.81	0.209174	0.104587	−	0.994516i	$-0.466648\pi$
$881$	5469.81	0.209174	0.104587	+	0.994516i	$0.466648\pi$
$882$	0	0
$883$	−36038.6	−1.37350	−0.686748	−	0.726896i	$-0.740962\pi$
$883$	−36038.6	−1.37350	−0.686748	+	0.726896i	$0.740962\pi$
$884$	−51782.1	−1.97016
$885$	3375.68	0.128217
$886$	−30576.8	−1.15942
$887$	30844.0	1.16758	0.583789	−	0.811905i	$-0.301570\pi$
$887$	30844.0	1.16758	0.583789	+	0.811905i	$0.301570\pi$
$888$	8718.84	0.329488
$889$	0	0
$890$	−213.850	−0.00805425
$891$	362.894	0.0136447
$892$	51420.3	1.93013
$893$	−66089.6	−2.47660
$894$	39337.9	1.47165
$895$	−1033.24	−0.0385893
$896$	0	0
$897$	21393.7	0.796336
$898$	−51920.4	−1.92940
$899$	1915.42	0.0710597
$900$	−24791.3	−0.918194
$901$	−35605.8	−1.31654
$902$	74.3017	0.00274277
$903$	0	0
$904$	2579.35	0.0948983
$905$	−2978.58	−0.109405
$906$	−329.409	−0.0120793
$907$	−19283.6	−0.705956	−0.352978	−	0.935632i	$-0.614831\pi$
$907$	−19283.6	−0.705956	−0.352978	+	0.935632i	$0.614831\pi$
$908$	48118.9	1.75868
$909$	−13820.0	−0.504269
$910$	0	0
$911$	12302.1	0.447406	0.223703	−	0.974657i	$-0.428185\pi$
$911$	12302.1	0.447406	0.223703	+	0.974657i	$0.428185\pi$
$912$	−45105.4	−1.63771
$913$	−437.366	−0.0158540
$914$	6868.07	0.248551
$915$	−6110.32	−0.220766
$916$	16927.2	0.610580
$917$	0	0
$918$	−10363.3	−0.372594
$919$	32839.7	1.17876	0.589381	−	0.807855i	$-0.299372\pi$
$919$	32839.7	1.17876	0.589381	+	0.807855i	$0.299372\pi$
$920$	−196.822	−0.00705331
$921$	−4524.65	−0.161881
$922$	28995.1	1.03569
$923$	−2179.77	−0.0777334
$924$	0	0
$925$	51271.0	1.82246
$926$	21017.7	0.745880
$927$	37512.7	1.32910
$928$	−21961.0	−0.776838
$929$	−39502.9	−1.39510	−0.697550	−	0.716536i	$-0.745726\pi$
$929$	−39502.9	−1.39510	−0.697550	+	0.716536i	$0.745726\pi$
$930$	931.647	0.0328494
$931$	0	0
$932$	−46855.2	−1.64677
$933$	−20411.7	−0.716239
$934$	58510.3	2.04980
$935$	57.9982	0.00202860
$936$	−4402.70	−0.153747
$937$	22914.6	0.798918	0.399459	−	0.916751i	$-0.369198\pi$
$937$	22914.6	0.798918	0.399459	+	0.916751i	$0.369198\pi$
$938$	0	0
$939$	−18970.8	−0.659307
$940$	−7420.36	−0.257474
$941$	15688.6	0.543502	0.271751	−	0.962368i	$-0.412397\pi$
$941$	15688.6	0.543502	0.271751	+	0.962368i	$0.412397\pi$
$942$	−41933.6	−1.45039
$943$	1921.59	0.0663578
$944$	−19355.7	−0.667347
$945$	0	0
$946$	−767.930	−0.0263928
$947$	−16605.2	−0.569797	−0.284898	−	0.958558i	$-0.591960\pi$
$947$	−16605.2	−0.569797	−0.284898	+	0.958558i	$0.591960\pi$
$948$	−84551.9	−2.89675
$949$	−24292.6	−0.830949
$950$	55536.2	1.89667
$951$	−44921.6	−1.53174
$952$	0	0
$953$	28512.6	0.969163	0.484582	−	0.874746i	$-0.338972\pi$
$953$	28512.6	0.969163	0.484582	+	0.874746i	$0.338972\pi$
$954$	−36550.8	−1.24044
$955$	5716.18	0.193687
$956$	−5985.41	−0.202492
$957$	265.407	0.00896489
$958$	−50024.7	−1.68708
$959$	0	0
$960$	−6036.85	−0.202957
$961$	−29278.4	−0.982794
$962$	109933.	3.68440
$963$	−33664.9	−1.12652
$964$	−27754.3	−0.927288
$965$	−2616.21	−0.0872734
$966$	0	0
$967$	24286.3	0.807646	0.403823	−	0.914837i	$-0.367681\pi$
$967$	24286.3	0.807646	0.403823	+	0.914837i	$0.367681\pi$
$968$	3931.56	0.130542
$969$	−71972.1	−2.38605
$970$	−2699.38	−0.0893526
$971$	24151.0	0.798191	0.399095	−	0.916909i	$-0.369324\pi$
$971$	24151.0	0.798191	0.399095	+	0.916909i	$0.369324\pi$
$972$	−44079.0	−1.45456
$973$	0	0
$974$	58362.0	1.91996
$975$	−56136.0	−1.84389
$976$	35035.8	1.14905
$977$	46579.9	1.52531	0.762653	−	0.646808i	$-0.223896\pi$
$977$	46579.9	1.52531	0.762653	+	0.646808i	$0.223896\pi$
$978$	104895.	3.42961
$979$	−16.3034	−0.000532235 0
$980$	0	0
$981$	4497.61	0.146379
$982$	22770.3	0.739948
$983$	−12068.2	−0.391573	−0.195786	−	0.980647i	$-0.562726\pi$
$983$	−12068.2	−0.391573	−0.195786	+	0.980647i	$0.562726\pi$
$984$	−857.439	−0.0277786
$985$	1099.38	0.0355625
$986$	−31851.5	−1.02876
$987$	0	0
$988$	62111.6	2.00003
$989$	−19860.1	−0.638540
$990$	59.5377	0.00191134
$991$	−1736.75	−0.0556708	−0.0278354	−	0.999613i	$-0.508861\pi$
$991$	−1736.75	−0.0556708	−0.0278354	+	0.999613i	$0.508861\pi$
$992$	−5877.03	−0.188101
$993$	37332.8	1.19307
$994$	0	0
$995$	−452.418	−0.0144147
$996$	60937.8	1.93864
$997$	−8120.26	−0.257945	−0.128973	−	0.991648i	$-0.541168\pi$
$997$	−8120.26	−0.257945	−0.128973	+	0.991648i	$0.541168\pi$
$998$	−39281.7	−1.24593
$999$	11476.0	0.363446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.n.1.10	✓	60
7.6	odd	2		2009.4.a.o.1.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.4.a.n.1.10	✓	60	1.1	even	1	trivial
2009.4.a.o.1.10	yes	60	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.08931 q^{2} +7.07895 q^{3} +8.72244 q^{4} +1.42150 q^{5} -28.9480 q^{6} -2.95427 q^{8} +23.1115 q^{9} +O(q^{10})\)	\(q-4.08931 q^{2} +7.07895 q^{3} +8.72244 q^{4} +1.42150 q^{5} -28.9480 q^{6} -2.95427 q^{8} +23.1115 q^{9} -5.81297 q^{10} -0.443165 q^{11} +61.7457 q^{12} +64.4823 q^{13} +10.0628 q^{15} -57.6986 q^{16} -92.0664 q^{17} -94.5101 q^{18} +110.432 q^{19} +12.3990 q^{20} +1.81224 q^{22} +46.8679 q^{23} -20.9131 q^{24} -122.979 q^{25} -263.688 q^{26} -27.5264 q^{27} -84.6016 q^{29} -41.1497 q^{30} -22.6404 q^{31} +259.581 q^{32} -3.13714 q^{33} +376.488 q^{34} +201.589 q^{36} -416.907 q^{37} -451.590 q^{38} +456.467 q^{39} -4.19951 q^{40} +41.0000 q^{41} -423.747 q^{43} -3.86548 q^{44} +32.8531 q^{45} -191.657 q^{46} -598.465 q^{47} -408.445 q^{48} +502.900 q^{50} -651.733 q^{51} +562.443 q^{52} +386.740 q^{53} +112.564 q^{54} -0.629961 q^{55} +781.742 q^{57} +345.962 q^{58} +335.463 q^{59} +87.7718 q^{60} -607.222 q^{61} +92.5836 q^{62} -599.920 q^{64} +91.6619 q^{65} +12.8287 q^{66} +898.110 q^{67} -803.044 q^{68} +331.776 q^{69} -33.8041 q^{71} -68.2777 q^{72} -376.733 q^{73} +1704.86 q^{74} -870.564 q^{75} +963.235 q^{76} -1866.63 q^{78} -1369.36 q^{79} -82.0188 q^{80} -818.869 q^{81} -167.662 q^{82} +986.916 q^{83} -130.873 q^{85} +1732.83 q^{86} -598.890 q^{87} +1.30923 q^{88} +36.7885 q^{89} -134.347 q^{90} +408.803 q^{92} -160.270 q^{93} +2447.31 q^{94} +156.979 q^{95} +1837.56 q^{96} +464.373 q^{97} -10.2422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 2 q^{2} - 24 q^{3} + 230 q^{4} - 40 q^{5} - 72 q^{6} - 18 q^{8} + 572 q^{9}+O(q^{10}) \) 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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