LMFDB - Embedded newform 2009.4.a.i.1.9

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:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.61264 q^{2} +0.0204702 q^{3} -1.17409 q^{4} +12.1971 q^{5} -0.0534812 q^{6} +23.9686 q^{8} -26.9996 q^{9} +O(q^{10})$	\(q-2.61264 q^{2} +0.0204702 q^{3} -1.17409 q^{4} +12.1971 q^{5} -0.0534812 q^{6} +23.9686 q^{8} -26.9996 q^{9} -31.8666 q^{10} -39.3746 q^{11} -0.0240338 q^{12} -5.08979 q^{13} +0.249676 q^{15} -53.2288 q^{16} -71.6794 q^{17} +70.5403 q^{18} +52.9242 q^{19} -14.3204 q^{20} +102.872 q^{22} -16.9837 q^{23} +0.490642 q^{24} +23.7688 q^{25} +13.2978 q^{26} -1.10538 q^{27} -138.795 q^{29} -0.652315 q^{30} -208.294 q^{31} -52.6811 q^{32} -0.806004 q^{33} +187.273 q^{34} +31.6999 q^{36} -242.463 q^{37} -138.272 q^{38} -0.104189 q^{39} +292.347 q^{40} +41.0000 q^{41} +395.967 q^{43} +46.2293 q^{44} -329.316 q^{45} +44.3724 q^{46} -483.863 q^{47} -1.08960 q^{48} -62.0994 q^{50} -1.46729 q^{51} +5.97586 q^{52} +287.846 q^{53} +2.88796 q^{54} -480.255 q^{55} +1.08337 q^{57} +362.623 q^{58} -149.222 q^{59} -0.293142 q^{60} +499.157 q^{61} +544.199 q^{62} +563.467 q^{64} -62.0805 q^{65} +2.10580 q^{66} +253.265 q^{67} +84.1580 q^{68} -0.347659 q^{69} -219.863 q^{71} -647.143 q^{72} +764.369 q^{73} +633.469 q^{74} +0.486551 q^{75} -62.1377 q^{76} +0.272208 q^{78} +1314.63 q^{79} -649.236 q^{80} +728.966 q^{81} -107.118 q^{82} -266.966 q^{83} -874.280 q^{85} -1034.52 q^{86} -2.84116 q^{87} -943.756 q^{88} +1638.73 q^{89} +860.386 q^{90} +19.9404 q^{92} -4.26381 q^{93} +1264.16 q^{94} +645.521 q^{95} -1.07839 q^{96} -1303.35 q^{97} +1063.10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9}+O(q^{10}) $ 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9	\( 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9} + 80 q^{10} + 38 q^{11} - 83 q^{12} + 78 q^{13} + 24 q^{15} + 287 q^{16} + 260 q^{17} - 185 q^{18} + 336 q^{19} + 240 q^{20} - 160 q^{22} - 90 q^{23} + 1112 q^{24} + 606 q^{25} - 55 q^{26} + 432 q^{27} + 130 q^{29} - 674 q^{30} + 1320 q^{31} - 331 q^{32} + 152 q^{33} + 816 q^{34} + 983 q^{36} - 4 q^{37} + 396 q^{38} - 248 q^{39} + 934 q^{40} + 1230 q^{41} - 214 q^{43} + 926 q^{44} + 804 q^{45} - 248 q^{46} + 2262 q^{47} - 568 q^{48} - 543 q^{50} + 204 q^{51} + 650 q^{52} - 522 q^{53} + 3253 q^{54} + 1328 q^{55} - 160 q^{57} + 888 q^{58} + 656 q^{59} + 994 q^{60} + 4300 q^{61} - 728 q^{62} + 1637 q^{64} + 1848 q^{65} - 744 q^{66} + 1642 q^{67} + 4860 q^{68} - 1556 q^{69} - 980 q^{71} - 2248 q^{72} + 1112 q^{73} + 1609 q^{74} + 6916 q^{75} + 3096 q^{76} + 343 q^{78} + 2068 q^{79} - 2440 q^{80} + 3130 q^{81} + 41 q^{82} + 356 q^{83} + 788 q^{85} - 514 q^{86} + 820 q^{87} - 1130 q^{88} + 5560 q^{89} + 2160 q^{90} + 1573 q^{92} + 124 q^{93} - 2377 q^{94} + 580 q^{95} + 9857 q^{96} + 3828 q^{97} - 2870 q^{99}+O(q^{100}) \) 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9 + 80 * q^10 + 38 * q^11 - 83 * q^12 + 78 * q^13 + 24 * q^15 + 287 * q^16 + 260 * q^17 - 185 * q^18 + 336 * q^19 + 240 * q^20 - 160 * q^22 - 90 * q^23 + 1112 * q^24 + 606 * q^25 - 55 * q^26 + 432 * q^27 + 130 * q^29 - 674 * q^30 + 1320 * q^31 - 331 * q^32 + 152 * q^33 + 816 * q^34 + 983 * q^36 - 4 * q^37 + 396 * q^38 - 248 * q^39 + 934 * q^40 + 1230 * q^41 - 214 * q^43 + 926 * q^44 + 804 * q^45 - 248 * q^46 + 2262 * q^47 - 568 * q^48 - 543 * q^50 + 204 * q^51 + 650 * q^52 - 522 * q^53 + 3253 * q^54 + 1328 * q^55 - 160 * q^57 + 888 * q^58 + 656 * q^59 + 994 * q^60 + 4300 * q^61 - 728 * q^62 + 1637 * q^64 + 1848 * q^65 - 744 * q^66 + 1642 * q^67 + 4860 * q^68 - 1556 * q^69 - 980 * q^71 - 2248 * q^72 + 1112 * q^73 + 1609 * q^74 + 6916 * q^75 + 3096 * q^76 + 343 * q^78 + 2068 * q^79 - 2440 * q^80 + 3130 * q^81 + 41 * q^82 + 356 * q^83 + 788 * q^85 - 514 * q^86 + 820 * q^87 - 1130 * q^88 + 5560 * q^89 + 2160 * q^90 + 1573 * q^92 + 124 * q^93 - 2377 * q^94 + 580 * q^95 + 9857 * q^96 + 3828 * q^97 - 2870 * 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 $

$2$	−2.61264	−0.923709	−0.461855	−	0.886956i	$-0.652816\pi$
$2$	−2.61264	−0.923709	−0.461855	+	0.886956i	$0.652816\pi$
$3$	0.0204702	0.00393948	0.00196974	−	0.999998i	$-0.499373\pi$
$3$	0.0204702	0.00393948	0.00196974	+	0.999998i	$0.499373\pi$
$4$	−1.17409	−0.146761
$5$	12.1971	1.09094	0.545470	−	0.838130i	$-0.316351\pi$
$5$	12.1971	1.09094	0.545470	+	0.838130i	$0.316351\pi$
$6$	−0.0534812	−0.00363894
$7$	0	0
$7$	0	0
$8$	23.9686	1.05927
$9$	−26.9996	−0.999984
$10$	−31.8666	−1.00771
$11$	−39.3746	−1.07926	−0.539631	−	0.841901i	$-0.681436\pi$
$11$	−39.3746	−1.07926	−0.539631	+	0.841901i	$0.681436\pi$
$12$	−0.0240338	−0.000578162 0
$13$	−5.08979	−0.108589	−0.0542943	−	0.998525i	$-0.517291\pi$
$13$	−5.08979	−0.108589	−0.0542943	+	0.998525i	$0.517291\pi$
$14$	0	0
$15$	0.249676	0.00429774
$16$	−53.2288	−0.831700
$17$	−71.6794	−1.02264	−0.511318	−	0.859392i	$-0.670843\pi$
$17$	−71.6794	−1.02264	−0.511318	+	0.859392i	$0.670843\pi$
$18$	70.5403	0.923695
$19$	52.9242	0.639034	0.319517	−	0.947581i	$-0.396479\pi$
$19$	52.9242	0.639034	0.319517	+	0.947581i	$0.396479\pi$
$20$	−14.3204	−0.160107
$21$	0	0
$22$	102.872	0.996925
$23$	−16.9837	−0.153972	−0.0769858	−	0.997032i	$-0.524530\pi$
$23$	−16.9837	−0.153972	−0.0769858	+	0.997032i	$0.524530\pi$
$24$	0.490642	0.00417299
$25$	23.7688	0.190150
$26$	13.2978	0.100304
$27$	−1.10538	−0.00787890
$28$	0	0
$29$	−138.795	−0.888746	−0.444373	−	0.895842i	$-0.646574\pi$
$29$	−138.795	−0.888746	−0.444373	+	0.895842i	$0.646574\pi$
$30$	−0.652315	−0.00396986
$31$	−208.294	−1.20680	−0.603399	−	0.797439i	$-0.706187\pi$
$31$	−208.294	−1.20680	−0.603399	+	0.797439i	$0.706187\pi$
$32$	−52.6811	−0.291025
$33$	−0.806004	−0.00425174
$34$	187.273	0.944619
$35$	0	0
$36$	31.6999	0.146759
$37$	−242.463	−1.07731	−0.538657	−	0.842525i	$-0.681068\pi$
$37$	−242.463	−1.07731	−0.538657	+	0.842525i	$0.681068\pi$
$38$	−138.272	−0.590282
$39$	−0.104189	−0.000427783 0
$40$	292.347	1.15560
$41$	41.0000	0.156174
$41$	41.0000	0.156174
$42$	0	0
$43$	395.967	1.40429	0.702144	−	0.712035i	$-0.252226\pi$
$43$	395.967	1.40429	0.702144	+	0.712035i	$0.252226\pi$
$44$	46.2293	0.158394
$45$	−329.316	−1.09092
$46$	44.3724	0.142225
$47$	−483.863	−1.50167	−0.750837	−	0.660487i	$-0.770350\pi$
$47$	−483.863	−1.50167	−0.750837	+	0.660487i	$0.770350\pi$
$48$	−1.08960	−0.00327647
$49$	0	0
$50$	−62.0994	−0.175644
$51$	−1.46729	−0.00402866
$52$	5.97586	0.0159366
$53$	287.846	0.746013	0.373006	−	0.927829i	$-0.378327\pi$
$53$	287.846	0.746013	0.373006	+	0.927829i	$0.378327\pi$
$54$	2.88796	0.00727782
$55$	−480.255	−1.17741
$56$	0	0
$57$	1.08337	0.00251746
$58$	362.623	0.820943
$59$	−149.222	−0.329272	−0.164636	−	0.986354i	$-0.552645\pi$
$59$	−149.222	−0.329272	−0.164636	+	0.986354i	$0.552645\pi$
$60$	−0.293142	−0.000630741 0
$61$	499.157	1.04771	0.523857	−	0.851806i	$-0.324493\pi$
$61$	499.157	1.04771	0.523857	+	0.851806i	$0.324493\pi$
$62$	544.199	1.11473
$63$	0	0
$64$	563.467	1.10052
$65$	−62.0805	−0.118464
$66$	2.10580	0.00392737
$67$	253.265	0.461809	0.230904	−	0.972976i	$-0.425832\pi$
$67$	253.265	0.461809	0.230904	+	0.972976i	$0.425832\pi$
$68$	84.1580	0.150083
$69$	−0.347659	−0.000606569 0
$70$	0	0
$71$	−219.863	−0.367506	−0.183753	−	0.982972i	$-0.558825\pi$
$71$	−219.863	−0.367506	−0.183753	+	0.982972i	$0.558825\pi$
$72$	−647.143	−1.05926
$73$	764.369	1.22552	0.612758	−	0.790271i	$-0.290060\pi$
$73$	764.369	1.22552	0.612758	+	0.790271i	$0.290060\pi$
$74$	633.469	0.995126
$75$	0.486551	0.000749094 0
$76$	−62.1377	−0.0937853
$77$	0	0
$78$	0.272208	0.000395147 0
$79$	1314.63	1.87224	0.936120	−	0.351681i	$-0.114390\pi$
$79$	1314.63	1.87224	0.936120	+	0.351681i	$0.114390\pi$
$80$	−649.236	−0.907335
$81$	728.966	0.999953
$82$	−107.118	−0.144259
$83$	−266.966	−0.353052	−0.176526	−	0.984296i	$-0.556486\pi$
$83$	−266.966	−0.353052	−0.176526	+	0.984296i	$0.556486\pi$
$84$	0	0
$85$	−874.280	−1.11563
$86$	−1034.52	−1.29715
$87$	−2.84116	−0.00350120
$88$	−943.756	−1.14323
$89$	1638.73	1.95175	0.975874	−	0.218335i	$-0.0700625\pi$
$89$	1638.73	1.95175	0.975874	+	0.218335i	$0.0700625\pi$
$90$	860.386	1.00770
$91$	0	0
$92$	19.9404	0.0225970
$93$	−4.26381	−0.00475416
$94$	1264.16	1.38711
$95$	645.521	0.697148
$96$	−1.07839	−0.00114649
$97$	−1303.35	−1.36428	−0.682141	−	0.731220i	$-0.738951\pi$
$97$	−1303.35	−1.36428	−0.682141	+	0.731220i	$0.738951\pi$
$98$	0	0
$99$	1063.10	1.07925
$100$	−27.9066	−0.0279066
$101$	−1726.21	−1.70063	−0.850317	−	0.526270i	$-0.823590\pi$
$101$	−1726.21	−1.70063	−0.850317	+	0.526270i	$0.823590\pi$
$102$	3.83350	0.00372131
$103$	−227.562	−0.217693	−0.108846	−	0.994059i	$-0.534716\pi$
$103$	−227.562	−0.217693	−0.108846	+	0.994059i	$0.534716\pi$
$104$	−121.995	−0.115025
$105$	0	0
$106$	−752.039	−0.689099
$107$	507.021	0.458089	0.229045	−	0.973416i	$-0.426440\pi$
$107$	507.021	0.458089	0.229045	+	0.973416i	$0.426440\pi$
$108$	1.29781	0.00115632
$109$	−45.3743	−0.0398722	−0.0199361	−	0.999801i	$-0.506346\pi$
$109$	−45.3743	−0.0398722	−0.0199361	+	0.999801i	$0.506346\pi$
$110$	1254.74	1.08759
$111$	−4.96325	−0.00424406
$112$	0	0
$113$	1568.54	1.30581	0.652903	−	0.757442i	$-0.273551\pi$
$113$	1568.54	1.30581	0.652903	+	0.757442i	$0.273551\pi$
$114$	−2.83045	−0.00232540
$115$	−207.152	−0.167974
$116$	162.958	0.130433
$117$	137.422	0.108587
$118$	389.864	0.304152
$119$	0	0
$120$	5.98439	0.00455248
$121$	219.360	0.164808
$122$	−1304.12	−0.967783
$123$	0.839276	0.000615244 0
$124$	244.556	0.177111
$125$	−1234.73	−0.883498
$126$	0	0
$127$	−239.797	−0.167548	−0.0837739	−	0.996485i	$-0.526697\pi$
$127$	−239.797	−0.167548	−0.0837739	+	0.996485i	$0.526697\pi$
$128$	−1050.69	−0.725538
$129$	8.10550	0.00553217
$130$	162.194	0.109426
$131$	−2366.84	−1.57856	−0.789282	−	0.614031i	$-0.789547\pi$
$131$	−2366.84	−1.57856	−0.789282	+	0.614031i	$0.789547\pi$
$132$	0.946320	0.000623989 0
$133$	0	0
$134$	−661.690	−0.426577
$135$	−13.4824	−0.00859541
$136$	−1718.06	−1.08325
$137$	−2977.14	−1.85660	−0.928302	−	0.371828i	$-0.878731\pi$
$137$	−2977.14	−1.85660	−0.928302	+	0.371828i	$0.878731\pi$
$138$	0.908310	0.000560293 0
$139$	−283.886	−0.173229	−0.0866147	−	0.996242i	$-0.527605\pi$
$139$	−283.886	−0.173229	−0.0866147	+	0.996242i	$0.527605\pi$
$140$	0	0
$141$	−9.90475	−0.00591582
$142$	574.424	0.339469
$143$	200.408	0.117196
$144$	1437.16	0.831687
$145$	−1692.90	−0.969569
$146$	−1997.02	−1.13202
$147$	0	0
$148$	284.673	0.158108
$149$	929.802	0.511224	0.255612	−	0.966779i	$-0.417723\pi$
$149$	929.802	0.511224	0.255612	+	0.966779i	$0.417723\pi$
$150$	−1.27118	−0.000691945 0
$151$	−356.075	−0.191901	−0.0959503	−	0.995386i	$-0.530589\pi$
$151$	−356.075	−0.191901	−0.0959503	+	0.995386i	$0.530589\pi$
$152$	1268.52	0.676912
$153$	1935.31	1.02262
$154$	0	0
$155$	−2540.58	−1.31654
$156$	0.122327	6.27819e−5 0
$157$	−690.354	−0.350931	−0.175466	−	0.984486i	$-0.556143\pi$
$157$	−690.354	−0.350931	−0.175466	+	0.984486i	$0.556143\pi$
$158$	−3434.65	−1.72941
$159$	5.89225	0.00293890
$160$	−642.556	−0.317490
$161$	0	0
$162$	−1904.53	−0.923666
$163$	−1769.05	−0.850076	−0.425038	−	0.905175i	$-0.639739\pi$
$163$	−1769.05	−0.850076	−0.425038	+	0.905175i	$0.639739\pi$
$164$	−48.1376	−0.0229202
$165$	−9.83090	−0.00463839
$166$	697.487	0.326118
$167$	3189.32	1.47783	0.738914	−	0.673799i	$-0.235339\pi$
$167$	3189.32	1.47783	0.738914	+	0.673799i	$0.235339\pi$
$168$	0	0
$169$	−2171.09	−0.988209
$170$	2284.18	1.03052
$171$	−1428.93	−0.639024
$172$	−464.900	−0.206095
$173$	3016.64	1.32573	0.662864	−	0.748740i	$-0.269341\pi$
$173$	3016.64	1.32573	0.662864	+	0.748740i	$0.269341\pi$
$174$	7.42294	0.00323409
$175$	0	0
$176$	2095.86	0.897623
$177$	−3.05460	−0.00129716
$178$	−4281.43	−1.80285
$179$	−877.868	−0.366564	−0.183282	−	0.983060i	$-0.558672\pi$
$179$	−877.868	−0.366564	−0.183282	+	0.983060i	$0.558672\pi$
$180$	386.646	0.160105
$181$	2330.68	0.957116	0.478558	−	0.878056i	$-0.341160\pi$
$181$	2330.68	0.957116	0.478558	+	0.878056i	$0.341160\pi$
$182$	0	0
$183$	10.2178	0.00412745
$184$	−407.076	−0.163098
$185$	−2957.34	−1.17529
$186$	11.1398	0.00439146
$187$	2822.35	1.10369
$188$	568.098	0.220387
$189$	0	0
$190$	−1686.52	−0.643962
$191$	2613.42	0.990054	0.495027	−	0.868878i	$-0.335158\pi$
$191$	2613.42	0.990054	0.495027	+	0.868878i	$0.335158\pi$
$192$	11.5343	0.00433549
$193$	2096.67	0.781976	0.390988	−	0.920396i	$-0.372133\pi$
$193$	2096.67	0.781976	0.390988	+	0.920396i	$0.372133\pi$
$194$	3405.20	1.26020
$195$	−1.27080	−0.000466686 0
$196$	0	0
$197$	4385.46	1.58604	0.793022	−	0.609193i	$-0.208506\pi$
$197$	4385.46	1.58604	0.793022	+	0.609193i	$0.208506\pi$
$198$	−2777.50	−0.996910
$199$	−5497.07	−1.95817	−0.979087	−	0.203440i	$-0.934788\pi$
$199$	−5497.07	−1.95817	−0.979087	+	0.203440i	$0.934788\pi$
$200$	569.705	0.201421
$201$	5.18437	0.00181929
$202$	4509.97	1.57089
$203$	0	0
$204$	1.72273	0.000591250 0
$205$	500.080	0.170376
$206$	594.538	0.201085
$207$	458.553	0.153969
$208$	270.923	0.0903132
$209$	−2083.87	−0.689686
$210$	0	0
$211$	1870.24	0.610201	0.305100	−	0.952320i	$-0.401310\pi$
$211$	1870.24	0.610201	0.305100	+	0.952320i	$0.401310\pi$
$212$	−337.956	−0.109486
$213$	−4.50063	−0.00144778
$214$	−1324.66	−0.423141
$215$	4829.64	1.53199
$216$	−26.4944	−0.00834592
$217$	0	0
$218$	118.547	0.0368303
$219$	15.6467	0.00482790
$220$	563.862	0.172798
$221$	364.833	0.111047
$222$	12.9672	0.00392028
$223$	1792.16	0.538170	0.269085	−	0.963116i	$-0.413279\pi$
$223$	1792.16	0.538170	0.269085	+	0.963116i	$0.413279\pi$
$224$	0	0
$225$	−641.747	−0.190147
$226$	−4098.04	−1.20618
$227$	2306.79	0.674479	0.337240	−	0.941419i	$-0.390507\pi$
$227$	2306.79	0.674479	0.337240	+	0.941419i	$0.390507\pi$
$228$	−1.27197	−0.000369465 0
$229$	5084.67	1.46727	0.733634	−	0.679545i	$-0.237823\pi$
$229$	5084.67	1.46727	0.733634	+	0.679545i	$0.237823\pi$
$230$	541.214	0.155159
$231$	0	0
$232$	−3326.73	−0.941425
$233$	2482.36	0.697961	0.348981	−	0.937130i	$-0.386528\pi$
$233$	2482.36	0.697961	0.348981	+	0.937130i	$0.386528\pi$
$234$	−359.035	−0.100303
$235$	−5901.72	−1.63824
$236$	175.200	0.0483243
$237$	26.9106	0.00737566
$238$	0	0
$239$	−3718.03	−1.00627	−0.503137	−	0.864206i	$-0.667821\pi$
$239$	−3718.03	−1.00627	−0.503137	+	0.864206i	$0.667821\pi$
$240$	−13.2900	−0.00357443
$241$	636.955	0.170249	0.0851243	−	0.996370i	$-0.472871\pi$
$241$	636.955	0.170249	0.0851243	+	0.996370i	$0.472871\pi$
$242$	−573.110	−0.152235
$243$	44.7673	0.0118182
$244$	−586.055	−0.153764
$245$	0	0
$246$	−2.19273	−0.000568306 0
$247$	−269.373	−0.0693918
$248$	−4992.53	−1.27833
$249$	−5.46483	−0.00139084
$250$	3225.90	0.816095
$251$	−5213.21	−1.31098	−0.655488	−	0.755205i	$-0.727537\pi$
$251$	−5213.21	−1.31098	−0.655488	+	0.755205i	$0.727537\pi$
$252$	0	0
$253$	668.727	0.166176
$254$	626.505	0.154765
$255$	−17.8966	−0.00439502
$256$	−1762.66	−0.430336
$257$	3407.97	0.827172	0.413586	−	0.910465i	$-0.364276\pi$
$257$	3407.97	0.827172	0.413586	+	0.910465i	$0.364276\pi$
$258$	−21.1768	−0.00511011
$259$	0	0
$260$	72.8880	0.0173859
$261$	3747.41	0.888732
$262$	6183.71	1.45813
$263$	3112.89	0.729845	0.364923	−	0.931038i	$-0.381095\pi$
$263$	3112.89	0.729845	0.364923	+	0.931038i	$0.381095\pi$
$264$	−19.3188	−0.00450375
$265$	3510.88	0.813855
$266$	0	0
$267$	33.5452	0.00768888
$268$	−297.355	−0.0677756
$269$	−5804.74	−1.31569	−0.657847	−	0.753152i	$-0.728533\pi$
$269$	−5804.74	−1.31569	−0.657847	+	0.753152i	$0.728533\pi$
$270$	35.2247	0.00793966
$271$	2004.64	0.449348	0.224674	−	0.974434i	$-0.427868\pi$
$271$	2004.64	0.449348	0.224674	+	0.974434i	$0.427868\pi$
$272$	3815.41	0.850527
$273$	0	0
$274$	7778.22	1.71496
$275$	−935.887	−0.205222
$276$	0.408183	8.90207e−5 0
$277$	4420.44	0.958840	0.479420	−	0.877586i	$-0.340847\pi$
$277$	4420.44	0.958840	0.479420	+	0.877586i	$0.340847\pi$
$278$	741.693	0.160014
$279$	5623.86	1.20678
$280$	0	0
$281$	−1144.88	−0.243054	−0.121527	−	0.992588i	$-0.538779\pi$
$281$	−1144.88	−0.243054	−0.121527	+	0.992588i	$0.538779\pi$
$282$	25.8776	0.00546450
$283$	352.609	0.0740651	0.0370326	−	0.999314i	$-0.488209\pi$
$283$	352.609	0.0740651	0.0370326	+	0.999314i	$0.488209\pi$
$284$	258.138	0.0539355
$285$	13.2139	0.00274640
$286$	−523.596	−0.108255
$287$	0	0
$288$	1422.37	0.291020
$289$	224.940	0.0457846
$290$	4422.94	0.895600
$291$	−26.6798	−0.00537457
$292$	−897.437	−0.179858
$293$	3617.33	0.721252	0.360626	−	0.932711i	$-0.382563\pi$
$293$	3617.33	0.721252	0.360626	+	0.932711i	$0.382563\pi$
$294$	0	0
$295$	−1820.07	−0.359216
$296$	−5811.50	−1.14117
$297$	43.5239	0.00850341
$298$	−2429.24	−0.472222
$299$	86.4435	0.0167196
$300$	−0.571253	−0.000109938 0
$301$	0	0
$302$	930.298	0.177260
$303$	−35.3357	−0.00669962
$304$	−2817.09	−0.531485
$305$	6088.26	1.14299
$306$	−5056.29	−0.944604
$307$	5020.20	0.933283	0.466641	−	0.884447i	$-0.345464\pi$
$307$	5020.20	0.933283	0.466641	+	0.884447i	$0.345464\pi$
$308$	0	0
$309$	−4.65823	−0.000857596 0
$310$	6637.64	1.21610
$311$	7412.54	1.35153	0.675767	−	0.737116i	$-0.263813\pi$
$311$	7412.54	1.35153	0.675767	+	0.737116i	$0.263813\pi$
$312$	−2.49726	−0.000453140 0
$313$	1966.93	0.355200	0.177600	−	0.984103i	$-0.443167\pi$
$313$	1966.93	0.355200	0.177600	+	0.984103i	$0.443167\pi$
$314$	1803.65	0.324159
$315$	0	0
$316$	−1543.49	−0.274772
$317$	−793.718	−0.140630	−0.0703149	−	0.997525i	$-0.522400\pi$
$317$	−793.718	−0.140630	−0.0703149	+	0.997525i	$0.522400\pi$
$318$	−15.3944	−0.00271469
$319$	5465.01	0.959191
$320$	6872.66	1.20060
$321$	10.3788	0.00180463
$322$	0	0
$323$	−3793.58	−0.653499
$324$	−855.870	−0.146754
$325$	−120.978	−0.0206482
$326$	4621.89	0.785223
$327$	−0.928819	−0.000157076 0
$328$	982.714	0.165431
$329$	0	0
$330$	25.6846	0.00428452
$331$	−670.557	−0.111351	−0.0556754	−	0.998449i	$-0.517731\pi$
$331$	−670.557	−0.111351	−0.0556754	+	0.998449i	$0.517731\pi$
$332$	313.442	0.0518143
$333$	6546.40	1.07730
$334$	−8332.57	−1.36508
$335$	3089.09	0.503806
$336$	0	0
$337$	−9767.90	−1.57891	−0.789453	−	0.613811i	$-0.789636\pi$
$337$	−9767.90	−1.57891	−0.789453	+	0.613811i	$0.789636\pi$
$338$	5672.30	0.912817
$339$	32.1083	0.00514420
$340$	1026.48	0.163732
$341$	8201.50	1.30245
$342$	3733.29	0.590272
$343$	0	0
$344$	9490.78	1.48752
$345$	−4.24043	−0.000661730 0
$346$	−7881.41	−1.22459
$347$	999.004	0.154551	0.0772757	−	0.997010i	$-0.475378\pi$
$347$	999.004	0.154551	0.0772757	+	0.997010i	$0.475378\pi$
$348$	3.33577	0.000513840 0
$349$	7069.60	1.08432	0.542159	−	0.840276i	$-0.317607\pi$
$349$	7069.60	1.08432	0.542159	+	0.840276i	$0.317607\pi$
$350$	0	0
$351$	5.62615	0.000855560 0
$352$	2074.30	0.314092
$353$	5647.60	0.851534	0.425767	−	0.904833i	$-0.360004\pi$
$353$	5647.60	0.851534	0.425767	+	0.904833i	$0.360004\pi$
$354$	7.98058	0.00119820
$355$	−2681.69	−0.400927
$356$	−1924.02	−0.286441
$357$	0	0
$358$	2293.56	0.338598
$359$	4922.22	0.723635	0.361817	−	0.932249i	$-0.382156\pi$
$359$	4922.22	0.723635	0.361817	+	0.932249i	$0.382156\pi$
$360$	−7893.26	−1.15559
$361$	−4058.03	−0.591636
$362$	−6089.23	−0.884097
$363$	4.49033	0.000649260 0
$364$	0	0
$365$	9323.07	1.33696
$366$	−26.6956	−0.00381257
$367$	8052.28	1.14530	0.572651	−	0.819799i	$-0.305915\pi$
$367$	8052.28	1.14530	0.572651	+	0.819799i	$0.305915\pi$
$368$	904.023	0.128058
$369$	−1106.98	−0.156171
$370$	7726.48	1.08562
$371$	0	0
$372$	5.00609	0.000697725 0
$373$	−1040.86	−0.144487	−0.0722437	−	0.997387i	$-0.523016\pi$
$373$	−1040.86	−0.144487	−0.0722437	+	0.997387i	$0.523016\pi$
$374$	−7373.80	−1.01949
$375$	−25.2750	−0.00348052
$376$	−11597.5	−1.59068
$377$	706.438	0.0965077
$378$	0	0
$379$	6045.98	0.819422	0.409711	−	0.912215i	$-0.365630\pi$
$379$	6045.98	0.819422	0.409711	+	0.912215i	$0.365630\pi$
$380$	−757.898	−0.102314
$381$	−4.90869	−0.000660051 0
$382$	−6827.94	−0.914522
$383$	214.261	0.0285854	0.0142927	−	0.999898i	$-0.495450\pi$
$383$	214.261	0.0285854	0.0142927	+	0.999898i	$0.495450\pi$
$384$	−21.5078	−0.00285824
$385$	0	0
$386$	−5477.85	−0.722319
$387$	−10690.9	−1.40427
$388$	1530.25	0.200223
$389$	−7476.33	−0.974460	−0.487230	−	0.873274i	$-0.661993\pi$
$389$	−7476.33	−0.974460	−0.487230	+	0.873274i	$0.661993\pi$
$390$	3.32014	0.000431082 0
$391$	1217.38	0.157457
$392$	0	0
$393$	−48.4496	−0.00621872
$394$	−11457.6	−1.46504
$395$	16034.6	2.04250
$396$	−1248.17	−0.158391
$397$	2066.69	0.261270	0.130635	−	0.991431i	$-0.458298\pi$
$397$	2066.69	0.261270	0.130635	+	0.991431i	$0.458298\pi$
$398$	14361.9	1.80878
$399$	0	0
$400$	−1265.18	−0.158148
$401$	−2732.10	−0.340236	−0.170118	−	0.985424i	$-0.554415\pi$
$401$	−2732.10	−0.340236	−0.170118	+	0.985424i	$0.554415\pi$
$402$	−13.5449	−0.00168049
$403$	1060.17	0.131045
$404$	2026.72	0.249587
$405$	8891.26	1.09089
$406$	0	0
$407$	9546.88	1.16271
$408$	−35.1689	−0.00426745
$409$	2427.36	0.293460	0.146730	−	0.989177i	$-0.453125\pi$
$409$	2427.36	0.293460	0.146730	+	0.989177i	$0.453125\pi$
$410$	−1306.53	−0.157378
$411$	−60.9426	−0.00731406
$412$	267.178	0.0319488
$413$	0	0
$414$	−1198.04	−0.142223
$415$	−3256.21	−0.385159
$416$	268.135	0.0316020
$417$	−5.81119	−0.000682434 0
$418$	5444.41	0.637069
$419$	2413.12	0.281357	0.140678	−	0.990055i	$-0.455072\pi$
$419$	2413.12	0.281357	0.140678	+	0.990055i	$0.455072\pi$
$420$	0	0
$421$	525.328	0.0608146	0.0304073	−	0.999538i	$-0.490320\pi$
$421$	525.328	0.0608146	0.0304073	+	0.999538i	$0.490320\pi$
$422$	−4886.26	−0.563648
$423$	13064.1	1.50165
$424$	6899.27	0.790232
$425$	−1703.73	−0.194455
$426$	11.7585	0.00133733
$427$	0	0
$428$	−595.287	−0.0672296
$429$	4.10239	0.000461690 0
$430$	−12618.1	−1.41512
$431$	3936.91	0.439987	0.219993	−	0.975501i	$-0.429396\pi$
$431$	3936.91	0.439987	0.219993	+	0.975501i	$0.429396\pi$
$432$	58.8380	0.00655289
$433$	−2133.23	−0.236758	−0.118379	−	0.992968i	$-0.537770\pi$
$433$	−2133.23	−0.236758	−0.118379	+	0.992968i	$0.537770\pi$
$434$	0	0
$435$	−34.6539	−0.00381960
$436$	53.2734	0.00585168
$437$	−898.849	−0.0983931
$438$	−40.8794	−0.00445957
$439$	3204.38	0.348375	0.174188	−	0.984712i	$-0.444270\pi$
$439$	3204.38	0.348375	0.174188	+	0.984712i	$0.444270\pi$
$440$	−11511.1	−1.24720
$441$	0	0
$442$	−953.179	−0.102575
$443$	5799.16	0.621955	0.310978	−	0.950417i	$-0.399344\pi$
$443$	5799.16	0.621955	0.310978	+	0.950417i	$0.399344\pi$
$444$	5.82729	0.000622863 0
$445$	19987.8	2.12924
$446$	−4682.27	−0.497112
$447$	19.0332	0.00201396
$448$	0	0
$449$	8714.38	0.915940	0.457970	−	0.888968i	$-0.348577\pi$
$449$	8714.38	0.915940	0.457970	+	0.888968i	$0.348577\pi$
$450$	1676.66	0.175641
$451$	−1614.36	−0.168553
$452$	−1841.61	−0.191641
$453$	−7.28891	−0.000755989 0
$454$	−6026.81	−0.623023
$455$	0	0
$456$	25.9668	0.00266668
$457$	−15747.8	−1.61193	−0.805963	−	0.591965i	$-0.798352\pi$
$457$	−15747.8	−1.61193	−0.805963	+	0.591965i	$0.798352\pi$
$458$	−13284.4	−1.35533
$459$	79.2330	0.00805725
$460$	243.214	0.0246520
$461$	−6775.21	−0.684497	−0.342249	−	0.939609i	$-0.611188\pi$
$461$	−6775.21	−0.684497	−0.342249	+	0.939609i	$0.611188\pi$
$462$	0	0
$463$	−13339.3	−1.33894	−0.669472	−	0.742837i	$-0.733480\pi$
$463$	−13339.3	−1.33894	−0.669472	+	0.742837i	$0.733480\pi$
$464$	7387.91	0.739170
$465$	−52.0061	−0.00518650
$466$	−6485.53	−0.644713
$467$	2403.11	0.238122	0.119061	−	0.992887i	$-0.462012\pi$
$467$	2403.11	0.238122	0.119061	+	0.992887i	$0.462012\pi$
$468$	−161.346	−0.0159363
$469$	0	0
$470$	15419.1	1.51325
$471$	−14.1316	−0.00138249
$472$	−3576.65	−0.348790
$473$	−15591.0	−1.51560
$474$	−70.3078	−0.00681296
$475$	1257.94	0.121512
$476$	0	0
$477$	−7771.72	−0.746001
$478$	9713.90	0.929505
$479$	3696.14	0.352570	0.176285	−	0.984339i	$-0.443592\pi$
$479$	3696.14	0.352570	0.176285	+	0.984339i	$0.443592\pi$
$480$	−13.1532	−0.00125075
$481$	1234.08	0.116984
$482$	−1664.14	−0.157260
$483$	0	0
$484$	−257.548	−0.0241874
$485$	−15897.1	−1.48835
$486$	−116.961	−0.0109166
$487$	−17891.1	−1.66472	−0.832362	−	0.554232i	$-0.813012\pi$
$487$	−17891.1	−1.66472	−0.832362	+	0.554232i	$0.813012\pi$
$488$	11964.1	1.10982
$489$	−36.2127	−0.00334886
$490$	0	0
$491$	−2202.78	−0.202464	−0.101232	−	0.994863i	$-0.532278\pi$
$491$	−2202.78	−0.202464	−0.101232	+	0.994863i	$0.532278\pi$
$492$	−0.985384	−9.02938e−5 0
$493$	9948.76	0.908864
$494$	703.776	0.0640979
$495$	12966.7	1.17739
$496$	11087.3	1.00369
$497$	0	0
$498$	14.2777	0.00128473
$499$	20409.8	1.83100	0.915500	−	0.402318i	$-0.131795\pi$
$499$	20409.8	1.83100	0.915500	+	0.402318i	$0.131795\pi$
$500$	1449.68	0.129663
$501$	65.2860	0.00582188
$502$	13620.3	1.21096
$503$	8063.43	0.714773	0.357386	−	0.933957i	$-0.383668\pi$
$503$	8063.43	0.714773	0.357386	+	0.933957i	$0.383668\pi$
$504$	0	0
$505$	−21054.7	−1.85529
$506$	−1747.15	−0.153498
$507$	−44.4426	−0.00389303
$508$	281.543	0.0245895
$509$	−12653.9	−1.10192	−0.550959	−	0.834532i	$-0.685738\pi$
$509$	−12653.9	−1.10192	−0.550959	+	0.834532i	$0.685738\pi$
$510$	46.7576	0.00405972
$511$	0	0
$512$	13010.7	1.12304
$513$	−58.5013	−0.00503489
$514$	−8903.81	−0.764067
$515$	−2775.59	−0.237490
$516$	−9.51657	−0.000811906 0
$517$	19051.9	1.62070
$518$	0	0
$519$	61.7511	0.00522268
$520$	−1487.99	−0.125486
$521$	4709.56	0.396026	0.198013	−	0.980199i	$-0.436551\pi$
$521$	4709.56	0.396026	0.198013	+	0.980199i	$0.436551\pi$
$522$	−9790.66	−0.820930
$523$	12754.9	1.06641	0.533206	−	0.845986i	$-0.320987\pi$
$523$	12754.9	1.06641	0.533206	+	0.845986i	$0.320987\pi$
$524$	2778.88	0.231672
$525$	0	0
$526$	−8132.89	−0.674165
$527$	14930.4	1.23412
$528$	42.9026	0.00353617
$529$	−11878.6	−0.976293
$530$	−9172.68	−0.751766
$531$	4028.93	0.329267
$532$	0	0
$533$	−208.681	−0.0169587
$534$	−87.6416	−0.00710229
$535$	6184.17	0.499748
$536$	6070.41	0.489182
$537$	−17.9701	−0.00144407
$538$	15165.7	1.21532
$539$	0	0
$540$	15.8295	0.00126147
$541$	20371.0	1.61888	0.809442	−	0.587200i	$-0.199770\pi$
$541$	20371.0	1.61888	0.809442	+	0.587200i	$0.199770\pi$
$542$	−5237.41	−0.415067
$543$	47.7093	0.00377054
$544$	3776.15	0.297612
$545$	−553.434	−0.0434982
$546$	0	0
$547$	3044.86	0.238005	0.119003	−	0.992894i	$-0.462030\pi$
$547$	3044.86	0.238005	0.119003	+	0.992894i	$0.462030\pi$
$548$	3495.43	0.272477
$549$	−13477.0	−1.04770
$550$	2445.14	0.189566
$551$	−7345.63	−0.567939
$552$	−8.33291	−0.000642522 0
$553$	0	0
$554$	−11549.0	−0.885689
$555$	−60.5372	−0.00463002
$556$	333.307	0.0254233
$557$	12080.2	0.918952	0.459476	−	0.888190i	$-0.348037\pi$
$557$	12080.2	0.918952	0.459476	+	0.888190i	$0.348037\pi$
$558$	−14693.1	−1.11471
$559$	−2015.39	−0.152490
$560$	0	0
$561$	57.7739	0.00434798
$562$	2991.18	0.224511
$563$	10210.5	0.764340	0.382170	−	0.924092i	$-0.375177\pi$
$563$	10210.5	0.764340	0.382170	+	0.924092i	$0.375177\pi$
$564$	11.6291	0.000868212 0
$565$	19131.6	1.42456
$566$	−921.242	−0.0684147
$567$	0	0
$568$	−5269.81	−0.389289
$569$	1478.21	0.108910	0.0544549	−	0.998516i	$-0.482658\pi$
$569$	1478.21	0.108910	0.0544549	+	0.998516i	$0.482658\pi$
$570$	−34.5232	−0.00253688
$571$	8586.25	0.629288	0.314644	−	0.949210i	$-0.398115\pi$
$571$	8586.25	0.629288	0.314644	+	0.949210i	$0.398115\pi$
$572$	−235.297	−0.0171998
$573$	53.4971	0.00390030
$574$	0	0
$575$	−403.682	−0.0292778
$576$	−15213.4	−1.10051
$577$	4844.42	0.349525	0.174763	−	0.984611i	$-0.444084\pi$
$577$	4844.42	0.349525	0.174763	+	0.984611i	$0.444084\pi$
$578$	−587.688	−0.0422917
$579$	42.9191	0.00308058
$580$	1987.61	0.142295
$581$	0	0
$582$	69.7049	0.00496454
$583$	−11333.8	−0.805144
$584$	18320.9	1.29816
$585$	1676.15	0.118462
$586$	−9450.80	−0.666227
$587$	−4568.30	−0.321216	−0.160608	−	0.987018i	$-0.551346\pi$
$587$	−4568.30	−0.321216	−0.160608	+	0.987018i	$0.551346\pi$
$588$	0	0
$589$	−11023.8	−0.771185
$590$	4755.21	0.331811
$591$	89.7709	0.00624820
$592$	12906.0	0.896003
$593$	11058.3	0.765782	0.382891	−	0.923793i	$-0.374928\pi$
$593$	11058.3	0.765782	0.382891	+	0.923793i	$0.374928\pi$
$594$	−113.712	−0.00785468
$595$	0	0
$596$	−1091.67	−0.0750277
$597$	−112.526	−0.00771420
$598$	−225.846	−0.0154440
$599$	−24796.6	−1.69142	−0.845712	−	0.533640i	$-0.820824\pi$
$599$	−24796.6	−1.69142	−0.845712	+	0.533640i	$0.820824\pi$
$600$	11.6620	0.000793495 0
$601$	10200.6	0.692332	0.346166	−	0.938173i	$-0.387483\pi$
$601$	10200.6	0.692332	0.346166	+	0.938173i	$0.387483\pi$
$602$	0	0
$603$	−6838.04	−0.461802
$604$	418.064	0.0281635
$605$	2675.55	0.179796
$606$	92.3197	0.00618850
$607$	−20863.3	−1.39508	−0.697540	−	0.716546i	$-0.745722\pi$
$607$	−20863.3	−1.39508	−0.697540	+	0.716546i	$0.745722\pi$
$608$	−2788.10	−0.185975
$609$	0	0
$610$	−15906.5	−1.05579
$611$	2462.76	0.163065
$612$	−2272.23	−0.150081
$613$	6770.95	0.446127	0.223064	−	0.974804i	$-0.428394\pi$
$613$	6770.95	0.446127	0.223064	+	0.974804i	$0.428394\pi$
$614$	−13116.0	−0.862082
$615$	10.2367	0.000671194 0
$616$	0	0
$617$	3919.71	0.255756	0.127878	−	0.991790i	$-0.459183\pi$
$617$	3919.71	0.255756	0.127878	+	0.991790i	$0.459183\pi$
$618$	12.1703	0.000792170 0
$619$	26751.6	1.73706	0.868528	−	0.495639i	$-0.165066\pi$
$619$	26751.6	1.73706	0.868528	+	0.495639i	$0.165066\pi$
$620$	2982.87	0.193217
$621$	18.7734	0.00121313
$622$	−19366.3	−1.24842
$623$	0	0
$624$	5.54584	0.000355787 0
$625$	−18031.1	−1.15399
$626$	−5138.90	−0.328102
$627$	−42.6571	−0.00271700
$628$	810.536	0.0515030
$629$	17379.6	1.10170
$630$	0	0
$631$	23508.0	1.48310	0.741552	−	0.670895i	$-0.234090\pi$
$631$	23508.0	1.48310	0.741552	+	0.670895i	$0.234090\pi$
$632$	31509.8	1.98321
$633$	38.2840	0.00240388
$634$	2073.70	0.129901
$635$	−2924.83	−0.182785
$636$	−6.91802	−0.000431317 0
$637$	0	0
$638$	−14278.1	−0.886013
$639$	5936.21	0.367500
$640$	−12815.4	−0.791519
$641$	7882.21	0.485692	0.242846	−	0.970065i	$-0.421919\pi$
$641$	7882.21	0.485692	0.242846	+	0.970065i	$0.421919\pi$
$642$	−27.1161	−0.00166696
$643$	2476.77	0.151904	0.0759520	−	0.997111i	$-0.475800\pi$
$643$	2476.77	0.151904	0.0759520	+	0.997111i	$0.475800\pi$
$644$	0	0
$645$	98.8634	0.00603526
$646$	9911.27	0.603643
$647$	28750.8	1.74700	0.873501	−	0.486823i	$-0.161844\pi$
$647$	28750.8	1.74700	0.873501	+	0.486823i	$0.161844\pi$
$648$	17472.3	1.05922
$649$	5875.56	0.355371
$650$	316.073	0.0190729
$651$	0	0
$652$	2077.02	0.124758
$653$	−8418.64	−0.504513	−0.252256	−	0.967660i	$-0.581173\pi$
$653$	−8418.64	−0.504513	−0.252256	+	0.967660i	$0.581173\pi$
$654$	2.42667	0.000145092 0
$655$	−28868.6	−1.72212
$656$	−2182.38	−0.129890
$657$	−20637.6	−1.22550
$658$	0	0
$659$	25628.4	1.51493	0.757467	−	0.652874i	$-0.226437\pi$
$659$	25628.4	1.51493	0.757467	+	0.652874i	$0.226437\pi$
$660$	11.5423	0.000680735 0
$661$	25306.8	1.48914	0.744568	−	0.667546i	$-0.232655\pi$
$661$	25306.8	1.48914	0.744568	+	0.667546i	$0.232655\pi$
$662$	1751.93	0.102856
$663$	7.46819	0.000437466 0
$664$	−6398.81	−0.373979
$665$	0	0
$666$	−17103.4	−0.995110
$667$	2357.26	0.136842
$668$	−3744.55	−0.216888
$669$	36.6858	0.00212011
$670$	−8070.69	−0.465370
$671$	−19654.1	−1.13076
$672$	0	0
$673$	14429.3	0.826460	0.413230	−	0.910627i	$-0.364401\pi$
$673$	14429.3	0.826460	0.413230	+	0.910627i	$0.364401\pi$
$674$	25520.0	1.45845
$675$	−26.2735	−0.00149818
$676$	2549.06	0.145030
$677$	−31468.1	−1.78644	−0.893218	−	0.449624i	$-0.851558\pi$
$677$	−31468.1	−1.78644	−0.893218	+	0.449624i	$0.851558\pi$
$678$	−83.8875	−0.00475174
$679$	0	0
$680$	−20955.3	−1.18176
$681$	47.2203	0.00265710
$682$	−21427.6	−1.20309
$683$	14945.1	0.837272	0.418636	−	0.908154i	$-0.362508\pi$
$683$	14945.1	0.837272	0.418636	+	0.908154i	$0.362508\pi$
$684$	1677.69	0.0937838
$685$	−36312.5	−2.02544
$686$	0	0
$687$	104.084	0.00578028
$688$	−21076.8	−1.16795
$689$	−1465.07	−0.0810085
$690$	11.0787	0.000611246 0
$691$	−23917.2	−1.31672	−0.658361	−	0.752702i	$-0.728750\pi$
$691$	−23917.2	−1.31672	−0.658361	+	0.752702i	$0.728750\pi$
$692$	−3541.80	−0.194565
$693$	0	0
$694$	−2610.04	−0.142761
$695$	−3462.58	−0.188983
$696$	−68.0987	−0.00370873
$697$	−2938.86	−0.159709
$698$	−18470.4	−1.00160
$699$	50.8143	0.00274961
$700$	0	0
$701$	17016.8	0.916854	0.458427	−	0.888732i	$-0.348413\pi$
$701$	17016.8	0.916854	0.458427	+	0.888732i	$0.348413\pi$
$702$	−14.6991	−0.000790288 0
$703$	−12832.2	−0.688441
$704$	−22186.3	−1.18775
$705$	−120.809	−0.00645381
$706$	−14755.2	−0.786570
$707$	0	0
$708$	3.58637	0.000190373 0
$709$	−26180.0	−1.38676	−0.693379	−	0.720573i	$-0.743879\pi$
$709$	−26180.0	−1.38676	−0.693379	+	0.720573i	$0.743879\pi$
$710$	7006.29	0.370340
$711$	−35494.3	−1.87221
$712$	39278.2	2.06744
$713$	3537.61	0.185813
$714$	0	0
$715$	2444.40	0.127854
$716$	1030.69	0.0537973
$717$	−76.1087	−0.00396420
$718$	−12860.0	−0.668428
$719$	−33902.8	−1.75850	−0.879249	−	0.476362i	$-0.841955\pi$
$719$	−33902.8	−1.75850	−0.879249	+	0.476362i	$0.841955\pi$
$720$	17529.1	0.907321
$721$	0	0
$722$	10602.2	0.546499
$723$	13.0386	0.000670691 0
$724$	−2736.42	−0.140467
$725$	−3298.99	−0.168995
$726$	−11.7316	−0.000599727 0
$727$	−2655.36	−0.135463	−0.0677316	−	0.997704i	$-0.521576\pi$
$727$	−2655.36	−0.135463	−0.0677316	+	0.997704i	$0.521576\pi$
$728$	0	0
$729$	−19681.2	−0.999907
$730$	−24357.9	−1.23497
$731$	−28382.7	−1.43607
$732$	−11.9966	−0.000605749 0
$733$	26461.4	1.33339	0.666695	−	0.745330i	$-0.267708\pi$
$733$	26461.4	1.33339	0.666695	+	0.745330i	$0.267708\pi$
$734$	−21037.8	−1.05793
$735$	0	0
$736$	894.720	0.0448096
$737$	−9972.20	−0.498413
$738$	2892.15	0.144257
$739$	11739.6	0.584368	0.292184	−	0.956362i	$-0.405618\pi$
$739$	11739.6	0.584368	0.292184	+	0.956362i	$0.405618\pi$
$740$	3472.18	0.172486
$741$	−5.51410	−0.000273368 0
$742$	0	0
$743$	10639.4	0.525330	0.262665	−	0.964887i	$-0.415399\pi$
$743$	10639.4	0.525330	0.262665	+	0.964887i	$0.415399\pi$
$744$	−102.198	−0.00503596
$745$	11340.9	0.557715
$746$	2719.40	0.133464
$747$	7207.97	0.353047
$748$	−3313.69	−0.161979
$749$	0	0
$750$	66.0346	0.00321499
$751$	−248.605	−0.0120795	−0.00603976	−	0.999982i	$-0.501923\pi$
$751$	−248.605	−0.0120795	−0.00603976	+	0.999982i	$0.501923\pi$
$752$	25755.5	1.24894
$753$	−106.715	−0.00516457
$754$	−1845.67	−0.0891451
$755$	−4343.08	−0.209352
$756$	0	0
$757$	1426.14	0.0684730	0.0342365	−	0.999414i	$-0.489100\pi$
$757$	1426.14	0.0684730	0.0342365	+	0.999414i	$0.489100\pi$
$758$	−15796.0	−0.756908
$759$	13.6889	0.000654647 0
$760$	15472.2	0.738470
$761$	−12068.4	−0.574875	−0.287437	−	0.957799i	$-0.592803\pi$
$761$	−12068.4	−0.574875	−0.287437	+	0.957799i	$0.592803\pi$
$762$	12.8247	0.000609696 0
$763$	0	0
$764$	−3068.38	−0.145301
$765$	23605.2	1.11562
$766$	−559.787	−0.0264046
$767$	759.509	0.0357552
$768$	−36.0818	−0.00169530
$769$	26594.3	1.24709	0.623547	−	0.781786i	$-0.285691\pi$
$769$	26594.3	1.24709	0.623547	+	0.781786i	$0.285691\pi$
$770$	0	0
$771$	69.7616	0.00325863
$772$	−2461.67	−0.114764
$773$	−2975.54	−0.138451	−0.0692255	−	0.997601i	$-0.522053\pi$
$773$	−2975.54	−0.138451	−0.0692255	+	0.997601i	$0.522053\pi$
$774$	27931.6	1.29713
$775$	−4950.90	−0.229473
$776$	−31239.6	−1.44515
$777$	0	0
$778$	19533.0	0.900118
$779$	2169.89	0.0998003
$780$	1.49203	6.84913e−5 0
$781$	8657.01	0.396636
$782$	−3180.59	−0.145445
$783$	153.421	0.00700234
$784$	0	0
$785$	−8420.30	−0.382845
$786$	126.582	0.00574429
$787$	8534.36	0.386553	0.193276	−	0.981144i	$-0.438089\pi$
$787$	8534.36	0.386553	0.193276	+	0.981144i	$0.438089\pi$
$788$	−5148.91	−0.232770
$789$	63.7214	0.00287521
$790$	−41892.7	−1.88668
$791$	0	0
$792$	25481.0	1.14322
$793$	−2540.60	−0.113770
$794$	−5399.53	−0.241338
$795$	71.8682	0.00320617
$796$	6454.04	0.287384
$797$	−18870.3	−0.838671	−0.419335	−	0.907831i	$-0.637737\pi$
$797$	−18870.3	−0.838671	−0.419335	+	0.907831i	$0.637737\pi$
$798$	0	0
$799$	34683.0	1.53567
$800$	−1252.17	−0.0553384
$801$	−44245.2	−1.95172
$802$	7138.00	0.314279
$803$	−30096.7	−1.32265
$804$	−6.08690	−0.000267001 0
$805$	0	0
$806$	−2769.85	−0.121047
$807$	−118.824	−0.00518315
$808$	−41374.8	−1.80144
$809$	−42028.4	−1.82650	−0.913251	−	0.407396i	$-0.866437\pi$
$809$	−42028.4	−1.82650	−0.913251	+	0.407396i	$0.866437\pi$
$810$	−23229.7	−1.00766
$811$	−41961.3	−1.81685	−0.908423	−	0.418053i	$-0.862713\pi$
$811$	−41961.3	−1.81685	−0.908423	+	0.418053i	$0.862713\pi$
$812$	0	0
$813$	41.0353	0.00177020
$814$	−24942.6	−1.07400
$815$	−21577.2	−0.927382
$816$	78.1020	0.00335063
$817$	20956.2	0.897387
$818$	−6341.83	−0.271072
$819$	0	0
$820$	−587.138	−0.0250046
$821$	−27092.3	−1.15168	−0.575840	−	0.817562i	$-0.695325\pi$
$821$	−27092.3	−1.15168	−0.575840	+	0.817562i	$0.695325\pi$
$822$	159.221	0.00675606
$823$	26237.8	1.11129	0.555645	−	0.831420i	$-0.312471\pi$
$823$	26237.8	1.11129	0.555645	+	0.831420i	$0.312471\pi$
$824$	−5454.35	−0.230596
$825$	−19.1577	−0.000808469 0
$826$	0	0
$827$	30637.8	1.28825	0.644124	−	0.764921i	$-0.277222\pi$
$827$	30637.8	1.28825	0.644124	+	0.764921i	$0.277222\pi$
$828$	−538.382	−0.0225967
$829$	−3893.54	−0.163122	−0.0815611	−	0.996668i	$-0.525991\pi$
$829$	−3893.54	−0.163122	−0.0815611	+	0.996668i	$0.525991\pi$
$830$	8507.31	0.355775
$831$	90.4871	0.00377733
$832$	−2867.93	−0.119504
$833$	0	0
$834$	15.1826	0.000630371 0
$835$	38900.5	1.61222
$836$	2446.65	0.101219
$837$	230.244	0.00950825
$838$	−6304.62	−0.259892
$839$	−21457.0	−0.882931	−0.441466	−	0.897278i	$-0.645541\pi$
$839$	−21457.0	−0.882931	−0.441466	+	0.897278i	$0.645541\pi$
$840$	0	0
$841$	−5124.87	−0.210131
$842$	−1372.50	−0.0561750
$843$	−23.4360	−0.000957506 0
$844$	−2195.82	−0.0895537
$845$	−26481.0	−1.07808
$846$	−34131.9	−1.38709
$847$	0	0
$848$	−15321.7	−0.620459
$849$	7.21796	0.000291778 0
$850$	4451.25	0.179619
$851$	4117.92	0.165876
$852$	5.28413	0.000212478 0
$853$	−17177.8	−0.689516	−0.344758	−	0.938692i	$-0.612039\pi$
$853$	−17177.8	−0.689516	−0.344758	+	0.938692i	$0.612039\pi$
$854$	0	0
$855$	−17428.8	−0.697137
$856$	12152.6	0.485242
$857$	21576.5	0.860023	0.430011	−	0.902823i	$-0.358510\pi$
$857$	21576.5	0.860023	0.430011	+	0.902823i	$0.358510\pi$
$858$	−10.7181	−0.000426468 0
$859$	1823.68	0.0724368	0.0362184	−	0.999344i	$-0.488469\pi$
$859$	1823.68	0.0724368	0.0362184	+	0.999344i	$0.488469\pi$
$860$	−5670.42	−0.224837
$861$	0	0
$862$	−10285.7	−0.406420
$863$	−14704.5	−0.580009	−0.290005	−	0.957025i	$-0.593657\pi$
$863$	−14704.5	−0.580009	−0.290005	+	0.957025i	$0.593657\pi$
$864$	58.2326	0.00229296
$865$	36794.2	1.44629
$866$	5573.37	0.218696
$867$	4.60455	0.000180368 0
$868$	0	0
$869$	−51762.9	−2.02064
$870$	90.5382	0.00352820
$871$	−1289.06	−0.0501472
$872$	−1087.56	−0.0422356
$873$	35190.0	1.36426
$874$	2348.37	0.0908867
$875$	0	0
$876$	−18.3707	−0.000708547 0
$877$	26200.3	1.00881	0.504403	−	0.863469i	$-0.331713\pi$
$877$	26200.3	1.00881	0.504403	+	0.863469i	$0.331713\pi$
$878$	−8371.91	−0.321798
$879$	74.0473	0.00284136
$880$	25563.4	0.979253
$881$	−38776.3	−1.48287	−0.741434	−	0.671026i	$-0.765854\pi$
$881$	−38776.3	−1.48287	−0.741434	+	0.671026i	$0.765854\pi$
$882$	0	0
$883$	9332.90	0.355693	0.177847	−	0.984058i	$-0.443087\pi$
$883$	9332.90	0.355693	0.177847	+	0.984058i	$0.443087\pi$
$884$	−428.346	−0.0162973
$885$	−37.2572	−0.00141513
$886$	−15151.1	−0.574506
$887$	27499.2	1.04096	0.520481	−	0.853873i	$-0.325753\pi$
$887$	27499.2	1.04096	0.520481	+	0.853873i	$0.325753\pi$
$888$	−118.962	−0.00449562
$889$	0	0
$890$	−52221.0	−1.96680
$891$	−28702.8	−1.07921
$892$	−2104.15	−0.0789823
$893$	−25608.1	−0.959621
$894$	−49.7270	−0.00186031
$895$	−10707.4	−0.399899
$896$	0	0
$897$	1.76951	6.58665e−5 0
$898$	−22767.6	−0.846063
$899$	28910.2	1.07254
$900$	753.468	0.0279062
$901$	−20632.6	−0.762899
$902$	4217.75	0.155694
$903$	0	0
$904$	37595.8	1.38321
$905$	28427.5	1.04416
$906$	19.0433	0.000698314 0
$907$	27730.3	1.01518	0.507591	−	0.861598i	$-0.330536\pi$
$907$	27730.3	1.01518	0.507591	+	0.861598i	$0.330536\pi$
$908$	−2708.37	−0.0989872
$909$	46606.9	1.70061
$910$	0	0
$911$	45867.4	1.66812	0.834059	−	0.551675i	$-0.186011\pi$
$911$	45867.4	1.66812	0.834059	+	0.551675i	$0.186011\pi$
$912$	−57.6663	−0.00209377
$913$	10511.7	0.381036
$914$	41143.4	1.48895
$915$	124.628	0.00450280
$916$	−5969.85	−0.215338
$917$	0	0
$918$	−207.008	−0.00744256
$919$	7049.78	0.253048	0.126524	−	0.991964i	$-0.459618\pi$
$919$	7049.78	0.253048	0.126524	+	0.991964i	$0.459618\pi$
$920$	−4965.14	−0.177930
$921$	102.764	0.00367665
$922$	17701.2	0.632276
$923$	1119.05	0.0399070
$924$	0	0
$925$	−5763.05	−0.204852
$926$	34850.9	1.23680
$927$	6144.07	0.217689
$928$	7311.89	0.258647
$929$	−36266.5	−1.28080	−0.640401	−	0.768041i	$-0.721232\pi$
$929$	−36266.5	−1.28080	−0.640401	+	0.768041i	$0.721232\pi$
$930$	135.873	0.00479082
$931$	0	0
$932$	−2914.51	−0.102433
$933$	151.736	0.00532434
$934$	−6278.48	−0.219955
$935$	34424.4	1.20406
$936$	3293.82	0.115023
$937$	−12946.8	−0.451391	−0.225696	−	0.974198i	$-0.572465\pi$
$937$	−12946.8	−0.451391	−0.225696	+	0.974198i	$0.572465\pi$
$938$	0	0
$939$	40.2634	0.00139930
$940$	6929.14	0.240429
$941$	762.705	0.0264224	0.0132112	−	0.999913i	$-0.495795\pi$
$941$	762.705	0.0264224	0.0132112	+	0.999913i	$0.495795\pi$
$942$	36.9210	0.00127702
$943$	−696.332	−0.0240463
$944$	7942.92	0.273856
$945$	0	0
$946$	40733.8	1.39997
$947$	−35066.6	−1.20329	−0.601643	−	0.798765i	$-0.705487\pi$
$947$	−35066.6	−1.20329	−0.601643	+	0.798765i	$0.705487\pi$
$948$	−31.5954	−0.00108246
$949$	−3890.47	−0.133077
$950$	−3286.56	−0.112242
$951$	−16.2475	−0.000554009 0
$952$	0	0
$953$	10015.4	0.340431	0.170215	−	0.985407i	$-0.445554\pi$
$953$	10015.4	0.340431	0.170215	+	0.985407i	$0.445554\pi$
$954$	20304.7	0.689088
$955$	31876.1	1.08009
$956$	4365.30	0.147682
$957$	111.870	0.00377871
$958$	−9656.70	−0.325672
$959$	0	0
$960$	140.684	0.00472976
$961$	13595.5	0.456361
$962$	−3224.22	−0.108059
$963$	−13689.3	−0.458082
$964$	−747.842	−0.0249859
$965$	25573.2	0.853089
$966$	0	0
$967$	10861.5	0.361203	0.180602	−	0.983556i	$-0.442196\pi$
$967$	10861.5	0.361203	0.180602	+	0.983556i	$0.442196\pi$
$968$	5257.76	0.174577
$969$	−77.6551	−0.00257445
$970$	41533.5	1.37480
$971$	16376.3	0.541236	0.270618	−	0.962687i	$-0.412772\pi$
$971$	16376.3	0.541236	0.270618	+	0.962687i	$0.412772\pi$
$972$	−52.5608	−0.00173445
$973$	0	0
$974$	46743.0	1.53772
$975$	−2.47644	−8.13431e−5 0
$976$	−26569.6	−0.871384
$977$	−19671.0	−0.644146	−0.322073	−	0.946715i	$-0.604380\pi$
$977$	−19671.0	−0.644146	−0.322073	+	0.946715i	$0.604380\pi$
$978$	94.6108	0.00309337
$979$	−64524.6	−2.10645
$980$	0	0
$981$	1225.09	0.0398716
$982$	5755.07	0.187018
$983$	−47922.0	−1.55491	−0.777454	−	0.628940i	$-0.783489\pi$
$983$	−47922.0	−1.55491	−0.777454	+	0.628940i	$0.783489\pi$
$984$	20.1163	0.000651712 0
$985$	53489.8	1.73028
$986$	−25992.6	−0.839526
$987$	0	0
$988$	316.267	0.0101840
$989$	−6724.98	−0.216221
$990$	−33877.4	−1.08757
$991$	21728.1	0.696483	0.348242	−	0.937405i	$-0.386779\pi$
$991$	21728.1	0.696483	0.348242	+	0.937405i	$0.386779\pi$
$992$	10973.2	0.351208
$993$	−13.7264	−0.000438665 0
$994$	0	0
$995$	−67048.2	−2.13625
$996$	6.41620	0.000204122 0
$997$	37154.5	1.18024	0.590118	−	0.807317i	$-0.299081\pi$
$997$	37154.5	1.18024	0.590118	+	0.807317i	$0.299081\pi$
$998$	−53323.6	−1.69131
$999$	268.013	0.00848806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.i.1.9	yes	30
7.6	odd	2		2009.4.a.h.1.9	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.4.a.h.1.9	✓	30	7.6	odd	2
2009.4.a.i.1.9	yes	30	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)

\(f(q)\)	\(=\)	\(q-2.61264 q^{2} +0.0204702 q^{3} -1.17409 q^{4} +12.1971 q^{5} -0.0534812 q^{6} +23.9686 q^{8} -26.9996 q^{9} +O(q^{10})\)	\(q-2.61264 q^{2} +0.0204702 q^{3} -1.17409 q^{4} +12.1971 q^{5} -0.0534812 q^{6} +23.9686 q^{8} -26.9996 q^{9} -31.8666 q^{10} -39.3746 q^{11} -0.0240338 q^{12} -5.08979 q^{13} +0.249676 q^{15} -53.2288 q^{16} -71.6794 q^{17} +70.5403 q^{18} +52.9242 q^{19} -14.3204 q^{20} +102.872 q^{22} -16.9837 q^{23} +0.490642 q^{24} +23.7688 q^{25} +13.2978 q^{26} -1.10538 q^{27} -138.795 q^{29} -0.652315 q^{30} -208.294 q^{31} -52.6811 q^{32} -0.806004 q^{33} +187.273 q^{34} +31.6999 q^{36} -242.463 q^{37} -138.272 q^{38} -0.104189 q^{39} +292.347 q^{40} +41.0000 q^{41} +395.967 q^{43} +46.2293 q^{44} -329.316 q^{45} +44.3724 q^{46} -483.863 q^{47} -1.08960 q^{48} -62.0994 q^{50} -1.46729 q^{51} +5.97586 q^{52} +287.846 q^{53} +2.88796 q^{54} -480.255 q^{55} +1.08337 q^{57} +362.623 q^{58} -149.222 q^{59} -0.293142 q^{60} +499.157 q^{61} +544.199 q^{62} +563.467 q^{64} -62.0805 q^{65} +2.10580 q^{66} +253.265 q^{67} +84.1580 q^{68} -0.347659 q^{69} -219.863 q^{71} -647.143 q^{72} +764.369 q^{73} +633.469 q^{74} +0.486551 q^{75} -62.1377 q^{76} +0.272208 q^{78} +1314.63 q^{79} -649.236 q^{80} +728.966 q^{81} -107.118 q^{82} -266.966 q^{83} -874.280 q^{85} -1034.52 q^{86} -2.84116 q^{87} -943.756 q^{88} +1638.73 q^{89} +860.386 q^{90} +19.9404 q^{92} -4.26381 q^{93} +1264.16 q^{94} +645.521 q^{95} -1.07839 q^{96} -1303.35 q^{97} +1063.10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9}+O(q^{10}) \) 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9	\( 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9} + 80 q^{10} + 38 q^{11} - 83 q^{12} + 78 q^{13} + 24 q^{15} + 287 q^{16} + 260 q^{17} - 185 q^{18} + 336 q^{19} + 240 q^{20} - 160 q^{22} - 90 q^{23} + 1112 q^{24} + 606 q^{25} - 55 q^{26} + 432 q^{27} + 130 q^{29} - 674 q^{30} + 1320 q^{31} - 331 q^{32} + 152 q^{33} + 816 q^{34} + 983 q^{36} - 4 q^{37} + 396 q^{38} - 248 q^{39} + 934 q^{40} + 1230 q^{41} - 214 q^{43} + 926 q^{44} + 804 q^{45} - 248 q^{46} + 2262 q^{47} - 568 q^{48} - 543 q^{50} + 204 q^{51} + 650 q^{52} - 522 q^{53} + 3253 q^{54} + 1328 q^{55} - 160 q^{57} + 888 q^{58} + 656 q^{59} + 994 q^{60} + 4300 q^{61} - 728 q^{62} + 1637 q^{64} + 1848 q^{65} - 744 q^{66} + 1642 q^{67} + 4860 q^{68} - 1556 q^{69} - 980 q^{71} - 2248 q^{72} + 1112 q^{73} + 1609 q^{74} + 6916 q^{75} + 3096 q^{76} + 343 q^{78} + 2068 q^{79} - 2440 q^{80} + 3130 q^{81} + 41 q^{82} + 356 q^{83} + 788 q^{85} - 514 q^{86} + 820 q^{87} - 1130 q^{88} + 5560 q^{89} + 2160 q^{90} + 1573 q^{92} + 124 q^{93} - 2377 q^{94} + 580 q^{95} + 9857 q^{96} + 3828 q^{97} - 2870 q^{99}+O(q^{100}) \) 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9 + 80 * q^10 + 38 * q^11 - 83 * q^12 + 78 * q^13 + 24 * q^15 + 287 * q^16 + 260 * q^17 - 185 * q^18 + 336 * q^19 + 240 * q^20 - 160 * q^22 - 90 * q^23 + 1112 * q^24 + 606 * q^25 - 55 * q^26 + 432 * q^27 + 130 * q^29 - 674 * q^30 + 1320 * q^31 - 331 * q^32 + 152 * q^33 + 816 * q^34 + 983 * q^36 - 4 * q^37 + 396 * q^38 - 248 * q^39 + 934 * q^40 + 1230 * q^41 - 214 * q^43 + 926 * q^44 + 804 * q^45 - 248 * q^46 + 2262 * q^47 - 568 * q^48 - 543 * q^50 + 204 * q^51 + 650 * q^52 - 522 * q^53 + 3253 * q^54 + 1328 * q^55 - 160 * q^57 + 888 * q^58 + 656 * q^59 + 994 * q^60 + 4300 * q^61 - 728 * q^62 + 1637 * q^64 + 1848 * q^65 - 744 * q^66 + 1642 * q^67 + 4860 * q^68 - 1556 * q^69 - 980 * q^71 - 2248 * q^72 + 1112 * q^73 + 1609 * q^74 + 6916 * q^75 + 3096 * q^76 + 343 * q^78 + 2068 * q^79 - 2440 * q^80 + 3130 * q^81 + 41 * q^82 + 356 * q^83 + 788 * q^85 - 514 * q^86 + 820 * q^87 - 1130 * q^88 + 5560 * q^89 + 2160 * q^90 + 1573 * q^92 + 124 * q^93 - 2377 * q^94 + 580 * q^95 + 9857 * q^96 + 3828 * q^97 - 2870 * q^99

Introduction

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