LMFDB - Embedded newform 2009.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$118.534837202$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.24204 q^{2} +1.46828 q^{3} +19.4790 q^{4} -7.63398 q^{5} -7.69676 q^{6} -60.1731 q^{8} -24.8442 q^{9} +O(q^{10})$	\(q-5.24204 q^{2} +1.46828 q^{3} +19.4790 q^{4} -7.63398 q^{5} -7.69676 q^{6} -60.1731 q^{8} -24.8442 q^{9} +40.0176 q^{10} +35.2182 q^{11} +28.6005 q^{12} -18.1744 q^{13} -11.2088 q^{15} +159.598 q^{16} +3.56195 q^{17} +130.234 q^{18} +106.918 q^{19} -148.702 q^{20} -184.615 q^{22} -98.0774 q^{23} -88.3508 q^{24} -66.7224 q^{25} +95.2709 q^{26} -76.1216 q^{27} +138.042 q^{29} +58.7569 q^{30} -223.186 q^{31} -355.234 q^{32} +51.7101 q^{33} -18.6719 q^{34} -483.938 q^{36} +39.7058 q^{37} -560.467 q^{38} -26.6850 q^{39} +459.360 q^{40} +41.0000 q^{41} +173.782 q^{43} +686.015 q^{44} +189.660 q^{45} +514.126 q^{46} +147.395 q^{47} +234.334 q^{48} +349.761 q^{50} +5.22993 q^{51} -354.018 q^{52} +531.393 q^{53} +399.032 q^{54} -268.855 q^{55} +156.985 q^{57} -723.623 q^{58} +549.012 q^{59} -218.335 q^{60} -643.282 q^{61} +1169.95 q^{62} +585.366 q^{64} +138.743 q^{65} -271.066 q^{66} +42.5326 q^{67} +69.3831 q^{68} -144.005 q^{69} -964.831 q^{71} +1494.95 q^{72} -82.2044 q^{73} -208.139 q^{74} -97.9669 q^{75} +2082.65 q^{76} +139.884 q^{78} -209.991 q^{79} -1218.37 q^{80} +559.025 q^{81} -214.924 q^{82} +950.386 q^{83} -27.1918 q^{85} -910.972 q^{86} +202.684 q^{87} -2119.19 q^{88} +496.258 q^{89} -994.204 q^{90} -1910.45 q^{92} -327.699 q^{93} -772.652 q^{94} -816.208 q^{95} -521.582 q^{96} +482.621 q^{97} -874.968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 6 q^{3} + 117 q^{4} + 4 q^{5} - 12 q^{6} - 39 q^{8} + 236 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 6 * q^3 + 117 * q^4 + 4 * q^5 - 12 * q^6 - 39 * q^8 + 236 * q^9	\( 36 q - 5 q^{2} - 6 q^{3} + 117 q^{4} + 4 q^{5} - 12 q^{6} - 39 q^{8} + 236 q^{9} - 12 q^{10} - 140 q^{11} + 186 q^{12} - 72 q^{13} - 366 q^{15} - 15 q^{16} - 2 q^{17} - 212 q^{18} + 30 q^{19} - 334 q^{20} - 346 q^{22} - 314 q^{23} + 106 q^{24} + 570 q^{25} + 303 q^{26} - 204 q^{27} - 356 q^{29} - 357 q^{30} - 4 q^{31} - 532 q^{32} - 30 q^{33} - 364 q^{34} + 113 q^{36} - 1398 q^{37} - 264 q^{38} - 1348 q^{39} + 26 q^{40} + 1476 q^{41} - 1072 q^{43} - 1507 q^{44} - 1132 q^{45} - 1356 q^{46} - 622 q^{47} + 1724 q^{48} - 1426 q^{50} - 668 q^{51} - 877 q^{52} - 412 q^{53} - 1814 q^{54} + 1114 q^{55} - 4082 q^{57} - 1309 q^{58} - 620 q^{59} - 3724 q^{60} + 774 q^{61} + 1665 q^{62} - 3285 q^{64} - 1036 q^{65} - 1056 q^{66} - 2972 q^{67} - 1525 q^{68} + 3304 q^{69} - 3540 q^{71} - 821 q^{72} - 60 q^{73} - 2043 q^{74} + 450 q^{75} + 2171 q^{76} - 1136 q^{78} - 5190 q^{79} - 1564 q^{80} + 284 q^{81} - 205 q^{82} + 1656 q^{83} - 5064 q^{85} - 782 q^{86} - 1940 q^{87} - 4232 q^{88} - 1196 q^{89} + 8030 q^{90} - 4618 q^{92} + 698 q^{93} - 35 q^{94} - 1968 q^{95} - 7926 q^{96} + 3862 q^{97} - 5964 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 6 * q^3 + 117 * q^4 + 4 * q^5 - 12 * q^6 - 39 * q^8 + 236 * q^9 - 12 * q^10 - 140 * q^11 + 186 * q^12 - 72 * q^13 - 366 * q^15 - 15 * q^16 - 2 * q^17 - 212 * q^18 + 30 * q^19 - 334 * q^20 - 346 * q^22 - 314 * q^23 + 106 * q^24 + 570 * q^25 + 303 * q^26 - 204 * q^27 - 356 * q^29 - 357 * q^30 - 4 * q^31 - 532 * q^32 - 30 * q^33 - 364 * q^34 + 113 * q^36 - 1398 * q^37 - 264 * q^38 - 1348 * q^39 + 26 * q^40 + 1476 * q^41 - 1072 * q^43 - 1507 * q^44 - 1132 * q^45 - 1356 * q^46 - 622 * q^47 + 1724 * q^48 - 1426 * q^50 - 668 * q^51 - 877 * q^52 - 412 * q^53 - 1814 * q^54 + 1114 * q^55 - 4082 * q^57 - 1309 * q^58 - 620 * q^59 - 3724 * q^60 + 774 * q^61 + 1665 * q^62 - 3285 * q^64 - 1036 * q^65 - 1056 * q^66 - 2972 * q^67 - 1525 * q^68 + 3304 * q^69 - 3540 * q^71 - 821 * q^72 - 60 * q^73 - 2043 * q^74 + 450 * q^75 + 2171 * q^76 - 1136 * q^78 - 5190 * q^79 - 1564 * q^80 + 284 * q^81 - 205 * q^82 + 1656 * q^83 - 5064 * q^85 - 782 * q^86 - 1940 * q^87 - 4232 * q^88 - 1196 * q^89 + 8030 * q^90 - 4618 * q^92 + 698 * q^93 - 35 * q^94 - 1968 * q^95 - 7926 * q^96 + 3862 * q^97 - 5964 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.24204	−1.85334	−0.926670	−	0.375876i	$-0.877342\pi$
$2$	−5.24204	−1.85334	−0.926670	+	0.375876i	$0.877342\pi$
$3$	1.46828	0.282570	0.141285	−	0.989969i	$-0.454877\pi$
$3$	1.46828	0.282570	0.141285	+	0.989969i	$0.454877\pi$
$4$	19.4790	2.43487
$5$	−7.63398	−0.682804	−0.341402	−	0.939917i	$-0.610902\pi$
$5$	−7.63398	−0.682804	−0.341402	+	0.939917i	$0.610902\pi$
$6$	−7.69676	−0.523698
$7$	0	0
$7$	0	0
$8$	−60.1731	−2.65930
$9$	−24.8442	−0.920154
$10$	40.0176	1.26547
$11$	35.2182	0.965336	0.482668	−	0.875803i	$-0.339668\pi$
$11$	35.2182	0.965336	0.482668	+	0.875803i	$0.339668\pi$
$12$	28.6005	0.688021
$13$	−18.1744	−0.387744	−0.193872	−	0.981027i	$-0.562105\pi$
$13$	−18.1744	−0.387744	−0.193872	+	0.981027i	$0.562105\pi$
$14$	0	0
$15$	−11.2088	−0.192940
$16$	159.598	2.49372
$17$	3.56195	0.0508176	0.0254088	−	0.999677i	$-0.491911\pi$
$17$	3.56195	0.0508176	0.0254088	+	0.999677i	$0.491911\pi$
$18$	130.234	1.70536
$19$	106.918	1.29098	0.645490	−	0.763768i	$-0.276653\pi$
$19$	106.918	1.29098	0.645490	+	0.763768i	$0.276653\pi$
$20$	−148.702	−1.66254
$21$	0	0
$22$	−184.615	−1.78910
$23$	−98.0774	−0.889155	−0.444577	−	0.895740i	$-0.646646\pi$
$23$	−98.0774	−0.889155	−0.444577	+	0.895740i	$0.646646\pi$
$24$	−88.3508	−0.751438
$25$	−66.7224	−0.533779
$26$	95.2709	0.718621
$27$	−76.1216	−0.542578
$28$	0	0
$29$	138.042	0.883925	0.441963	−	0.897034i	$-0.354282\pi$
$29$	138.042	0.883925	0.441963	+	0.897034i	$0.354282\pi$
$30$	58.7569	0.357583
$31$	−223.186	−1.29308	−0.646538	−	0.762881i	$-0.723784\pi$
$31$	−223.186	−1.29308	−0.646538	+	0.762881i	$0.723784\pi$
$32$	−355.234	−1.96241
$33$	51.7101	0.272775
$34$	−18.6719	−0.0941823
$35$	0	0
$36$	−483.938	−2.24046
$37$	39.7058	0.176421	0.0882107	−	0.996102i	$-0.471885\pi$
$37$	39.7058	0.176421	0.0882107	+	0.996102i	$0.471885\pi$
$38$	−560.467	−2.39263
$39$	−26.6850	−0.109565
$40$	459.360	1.81578
$41$	41.0000	0.156174
$41$	41.0000	0.156174
$42$	0	0
$43$	173.782	0.616314	0.308157	−	0.951335i	$-0.400288\pi$
$43$	173.782	0.616314	0.308157	+	0.951335i	$0.400288\pi$
$44$	686.015	2.35047
$45$	189.660	0.628285
$46$	514.126	1.64791
$47$	147.395	0.457443	0.228721	−	0.973492i	$-0.426546\pi$
$47$	147.395	0.457443	0.228721	+	0.973492i	$0.426546\pi$
$48$	234.334	0.704650
$49$	0	0
$50$	349.761	0.989274
$51$	5.22993	0.0143595
$52$	−354.018	−0.944106
$53$	531.393	1.37722	0.688608	−	0.725134i	$-0.258222\pi$
$53$	531.393	1.37722	0.688608	+	0.725134i	$0.258222\pi$
$54$	399.032	1.00558
$55$	−268.855	−0.659135
$56$	0	0
$57$	156.985	0.364792
$58$	−723.623	−1.63821
$59$	549.012	1.21145	0.605723	−	0.795676i	$-0.292884\pi$
$59$	549.012	1.21145	0.605723	+	0.795676i	$0.292884\pi$
$60$	−218.335	−0.469783
$61$	−643.282	−1.35023	−0.675114	−	0.737714i	$-0.735905\pi$
$61$	−643.282	−1.35023	−0.675114	+	0.737714i	$0.735905\pi$
$62$	1169.95	2.39651
$63$	0	0
$64$	585.366	1.14329
$65$	138.743	0.264753
$66$	−271.066	−0.505545
$67$	42.5326	0.0775549	0.0387775	−	0.999248i	$-0.487654\pi$
$67$	42.5326	0.0775549	0.0387775	+	0.999248i	$0.487654\pi$
$68$	69.3831	0.123734
$69$	−144.005	−0.251248
$70$	0	0
$71$	−964.831	−1.61274	−0.806369	−	0.591413i	$-0.798570\pi$
$71$	−964.831	−1.61274	−0.806369	+	0.591413i	$0.798570\pi$
$72$	1494.95	2.44697
$73$	−82.2044	−0.131799	−0.0658993	−	0.997826i	$-0.520992\pi$
$73$	−82.2044	−0.131799	−0.0658993	+	0.997826i	$0.520992\pi$
$74$	−208.139	−0.326969
$75$	−97.9669	−0.150830
$76$	2082.65	3.14337
$77$	0	0
$78$	139.884	0.203061
$79$	−209.991	−0.299061	−0.149530	−	0.988757i	$-0.547776\pi$
$79$	−209.991	−0.299061	−0.149530	+	0.988757i	$0.547776\pi$
$80$	−1218.37	−1.70272
$81$	559.025	0.766838
$82$	−214.924	−0.289443
$83$	950.386	1.25685	0.628424	−	0.777871i	$-0.283700\pi$
$83$	950.386	1.25685	0.628424	+	0.777871i	$0.283700\pi$
$84$	0	0
$85$	−27.1918	−0.0346985
$86$	−910.972	−1.14224
$87$	202.684	0.249771
$88$	−2119.19	−2.56712
$89$	496.258	0.591048	0.295524	−	0.955335i	$-0.404506\pi$
$89$	496.258	0.591048	0.295524	+	0.955335i	$0.404506\pi$
$90$	−994.204	−1.16443
$91$	0	0
$92$	−1910.45	−2.16498
$93$	−327.699	−0.365385
$94$	−772.652	−0.847797
$95$	−816.208	−0.881486
$96$	−521.582	−0.554518
$97$	482.621	0.505183	0.252592	−	0.967573i	$-0.418717\pi$
$97$	482.621	0.505183	0.252592	+	0.967573i	$0.418717\pi$
$98$	0	0
$99$	−874.968	−0.888258
$100$	−1299.68	−1.29968
$101$	−313.314	−0.308673	−0.154336	−	0.988018i	$-0.549324\pi$
$101$	−313.314	−0.308673	−0.154336	+	0.988018i	$0.549324\pi$
$102$	−27.4155	−0.0266131
$103$	−54.3779	−0.0520196	−0.0260098	−	0.999662i	$-0.508280\pi$
$103$	−54.3779	−0.0520196	−0.0260098	+	0.999662i	$0.508280\pi$
$104$	1093.61	1.03113
$105$	0	0
$106$	−2785.58	−2.55245
$107$	285.726	0.258151	0.129076	−	0.991635i	$-0.458799\pi$
$107$	285.726	0.258151	0.129076	+	0.991635i	$0.458799\pi$
$108$	−1482.77	−1.32111
$109$	−1696.89	−1.49113	−0.745563	−	0.666435i	$-0.767819\pi$
$109$	−1696.89	−1.49113	−0.745563	+	0.666435i	$0.767819\pi$
$110$	1409.35	1.22160
$111$	58.2991	0.0498514
$112$	0	0
$113$	989.589	0.823829	0.411915	−	0.911222i	$-0.364860\pi$
$113$	989.589	0.823829	0.411915	+	0.911222i	$0.364860\pi$
$114$	−822.921	−0.676084
$115$	748.721	0.607118
$116$	2688.92	2.15224
$117$	451.528	0.356784
$118$	−2877.94	−2.24522
$119$	0	0
$120$	674.468	0.513085
$121$	−90.6751	−0.0681256
$122$	3372.11	2.50243
$123$	60.1993	0.0441300
$124$	−4347.43	−3.14847
$125$	1463.60	1.04727
$126$	0	0
$127$	−892.111	−0.623323	−0.311662	−	0.950193i	$-0.600886\pi$
$127$	−892.111	−0.623323	−0.311662	+	0.950193i	$0.600886\pi$
$128$	−226.638	−0.156501
$129$	255.160	0.174152
$130$	−727.296	−0.490677
$131$	−2829.73	−1.88729	−0.943643	−	0.330966i	$-0.892625\pi$
$131$	−2829.73	−1.88729	−0.943643	+	0.330966i	$0.892625\pi$
$132$	1007.26	0.664172
$133$	0	0
$134$	−222.957	−0.143736
$135$	581.110	0.370474
$136$	−214.334	−0.135139
$137$	2758.17	1.72005	0.860025	−	0.510252i	$-0.170448\pi$
$137$	2758.17	1.72005	0.860025	+	0.510252i	$0.170448\pi$
$138$	754.878	0.465649
$139$	2843.19	1.73494	0.867470	−	0.497490i	$-0.165745\pi$
$139$	2843.19	1.73494	0.867470	+	0.497490i	$0.165745\pi$
$140$	0	0
$141$	216.417	0.129260
$142$	5057.68	2.98895
$143$	−640.070	−0.374303
$144$	−3965.08	−2.29461
$145$	−1053.81	−0.603547
$146$	430.919	0.244268
$147$	0	0
$148$	773.427	0.429563
$149$	−3457.19	−1.90083	−0.950415	−	0.310983i	$-0.899342\pi$
$149$	−3457.19	−1.90083	−0.950415	+	0.310983i	$0.899342\pi$
$150$	513.546	0.279539
$151$	−120.416	−0.0648963	−0.0324482	−	0.999473i	$-0.510330\pi$
$151$	−120.416	−0.0648963	−0.0324482	+	0.999473i	$0.510330\pi$
$152$	−6433.58	−3.43311
$153$	−88.4937	−0.0467601
$154$	0	0
$155$	1703.80	0.882918
$156$	−519.797	−0.266776
$157$	−887.146	−0.450968	−0.225484	−	0.974247i	$-0.572396\pi$
$157$	−887.146	−0.450968	−0.225484	+	0.974247i	$0.572396\pi$
$158$	1100.78	0.554261
$159$	780.232	0.389160
$160$	2711.85	1.33994
$161$	0	0
$162$	−2930.43	−1.42121
$163$	2055.20	0.987581	0.493791	−	0.869581i	$-0.335611\pi$
$163$	2055.20	0.987581	0.493791	+	0.869581i	$0.335611\pi$
$164$	798.637	0.380263
$165$	−394.754	−0.186252
$166$	−4981.96	−2.32937
$167$	−1792.73	−0.830691	−0.415346	−	0.909664i	$-0.636339\pi$
$167$	−1792.73	−0.830691	−0.415346	+	0.909664i	$0.636339\pi$
$168$	0	0
$169$	−1866.69	−0.849655
$170$	142.541	0.0643081
$171$	−2656.28	−1.18790
$172$	3385.09	1.50064
$173$	632.617	0.278017	0.139009	−	0.990291i	$-0.455608\pi$
$173$	632.617	0.278017	0.139009	+	0.990291i	$0.455608\pi$
$174$	−1062.48	−0.462910
$175$	0	0
$176$	5620.76	2.40728
$177$	806.102	0.342318
$178$	−2601.40	−1.09541
$179$	900.582	0.376048	0.188024	−	0.982164i	$-0.439792\pi$
$179$	900.582	0.376048	0.188024	+	0.982164i	$0.439792\pi$
$180$	3694.37	1.52979
$181$	−1006.29	−0.413243	−0.206621	−	0.978421i	$-0.566247\pi$
$181$	−1006.29	−0.413243	−0.206621	+	0.978421i	$0.566247\pi$
$182$	0	0
$183$	−944.516	−0.381534
$184$	5901.62	2.36453
$185$	−303.113	−0.120461
$186$	1717.81	0.677182
$187$	125.446	0.0490561
$188$	2871.11	1.11381
$189$	0	0
$190$	4278.59	1.63369
$191$	4668.31	1.76852	0.884259	−	0.466998i	$-0.154664\pi$
$191$	4668.31	1.76852	0.884259	+	0.466998i	$0.154664\pi$
$192$	859.479	0.323060
$193$	−2855.93	−1.06515	−0.532577	−	0.846382i	$-0.678776\pi$
$193$	−2855.93	−1.06515	−0.532577	+	0.846382i	$0.678776\pi$
$194$	−2529.92	−0.936276
$195$	203.713	0.0748112
$196$	0	0
$197$	3932.30	1.42216	0.711078	−	0.703113i	$-0.248207\pi$
$197$	3932.30	1.42216	0.711078	+	0.703113i	$0.248207\pi$
$198$	4586.61	1.64624
$199$	−1366.85	−0.486901	−0.243450	−	0.969913i	$-0.578279\pi$
$199$	−1366.85	−0.486901	−0.243450	+	0.969913i	$0.578279\pi$
$200$	4014.89	1.41948
$201$	62.4496	0.0219147
$202$	1642.41	0.572075
$203$	0	0
$204$	101.873	0.0349636
$205$	−312.993	−0.106636
$206$	285.051	0.0964099
$207$	2436.65	0.818160
$208$	−2900.60	−0.966925
$209$	3765.46	1.24623
$210$	0	0
$211$	1445.33	0.471568	0.235784	−	0.971806i	$-0.424234\pi$
$211$	1445.33	0.471568	0.235784	+	0.971806i	$0.424234\pi$
$212$	10351.0	3.35334
$213$	−1416.64	−0.455711
$214$	−1497.79	−0.478442
$215$	−1326.65	−0.420822
$216$	4580.47	1.44288
$217$	0	0
$218$	8895.17	2.76356
$219$	−120.699	−0.0372423
$220$	−5237.02	−1.60491
$221$	−64.7363	−0.0197042
$222$	−305.606	−0.0923916
$223$	4820.99	1.44770	0.723851	−	0.689957i	$-0.242371\pi$
$223$	4820.99	1.44770	0.723851	+	0.689957i	$0.242371\pi$
$224$	0	0
$225$	1657.66	0.491159
$226$	−5187.46	−1.52684
$227$	−1956.44	−0.572041	−0.286021	−	0.958223i	$-0.592333\pi$
$227$	−1956.44	−0.572041	−0.286021	+	0.958223i	$0.592333\pi$
$228$	3057.90	0.888221
$229$	207.012	0.0597368	0.0298684	−	0.999554i	$-0.490491\pi$
$229$	207.012	0.0597368	0.0298684	+	0.999554i	$0.490491\pi$
$230$	−3924.82	−1.12520
$231$	0	0
$232$	−8306.44	−2.35062
$233$	2338.55	0.657527	0.328763	−	0.944412i	$-0.393368\pi$
$233$	2338.55	0.657527	0.328763	+	0.944412i	$0.393368\pi$
$234$	−2366.92	−0.661242
$235$	−1125.21	−0.312344
$236$	10694.2	2.94971
$237$	−308.324	−0.0845055
$238$	0	0
$239$	10.0848	0.00272941	0.00136471	−	0.999999i	$-0.499566\pi$
$239$	10.0848	0.00272941	0.00136471	+	0.999999i	$0.499566\pi$
$240$	−1788.90	−0.481138
$241$	5440.34	1.45412	0.727060	−	0.686574i	$-0.240886\pi$
$241$	5440.34	1.45412	0.727060	+	0.686574i	$0.240886\pi$
$242$	475.322	0.126260
$243$	2876.08	0.759263
$244$	−12530.5	−3.28763
$245$	0	0
$246$	−315.567	−0.0817879
$247$	−1943.17	−0.500570
$248$	13429.8	3.43868
$249$	1395.43	0.355148
$250$	−7672.27	−1.94095
$251$	−2680.51	−0.674072	−0.337036	−	0.941492i	$-0.609424\pi$
$251$	−2680.51	−0.674072	−0.337036	+	0.941492i	$0.609424\pi$
$252$	0	0
$253$	−3454.12	−0.858333
$254$	4676.48	1.15523
$255$	−39.9251	−0.00980474
$256$	−3494.89	−0.853243
$257$	4254.76	1.03270	0.516351	−	0.856377i	$-0.327290\pi$
$257$	4254.76	1.03270	0.516351	+	0.856377i	$0.327290\pi$
$258$	−1337.56	−0.322763
$259$	0	0
$260$	2702.57	0.644639
$261$	−3429.55	−0.813347
$262$	14833.5	3.49778
$263$	−5092.42	−1.19396	−0.596981	−	0.802255i	$-0.703633\pi$
$263$	−5092.42	−1.19396	−0.596981	+	0.802255i	$0.703633\pi$
$264$	−3111.56	−0.725391
$265$	−4056.64	−0.940368
$266$	0	0
$267$	728.644	0.167012
$268$	828.490	0.188836
$269$	−1040.82	−0.235910	−0.117955	−	0.993019i	$-0.537634\pi$
$269$	−1040.82	−0.235910	−0.117955	+	0.993019i	$0.537634\pi$
$270$	−3046.20	−0.686614
$271$	5997.65	1.34440	0.672198	−	0.740372i	$-0.265350\pi$
$271$	5997.65	1.34440	0.672198	+	0.740372i	$0.265350\pi$
$272$	568.480	0.126725
$273$	0	0
$274$	−14458.5	−3.18784
$275$	−2349.85	−0.515276
$276$	−2805.06	−0.611757
$277$	−2513.11	−0.545120	−0.272560	−	0.962139i	$-0.587870\pi$
$277$	−2513.11	−0.545120	−0.272560	+	0.962139i	$0.587870\pi$
$278$	−14904.1	−3.21543
$279$	5544.87	1.18983
$280$	0	0
$281$	240.039	0.0509592	0.0254796	−	0.999675i	$-0.491889\pi$
$281$	240.039	0.0509592	0.0254796	+	0.999675i	$0.491889\pi$
$282$	−1134.47	−0.239562
$283$	981.379	0.206138	0.103069	−	0.994674i	$-0.467134\pi$
$283$	981.379	0.206138	0.103069	+	0.994674i	$0.467134\pi$
$284$	−18793.9	−3.92681
$285$	−1198.42	−0.249081
$286$	3355.27	0.693711
$287$	0	0
$288$	8825.50	1.80572
$289$	−4900.31	−0.997418
$290$	5524.12	1.11858
$291$	708.621	0.142750
$292$	−1601.26	−0.320912
$293$	−8089.43	−1.61293	−0.806467	−	0.591280i	$-0.798623\pi$
$293$	−8089.43	−1.61293	−0.806467	+	0.591280i	$0.798623\pi$
$294$	0	0
$295$	−4191.15	−0.827180
$296$	−2389.22	−0.469158
$297$	−2680.87	−0.523770
$298$	18122.7	3.52289
$299$	1782.50	0.344764
$300$	−1908.29	−0.367251
$301$	0	0
$302$	631.227	0.120275
$303$	−460.032	−0.0872216
$304$	17063.9	3.21934
$305$	4910.80	0.921940
$306$	463.887	0.0866623
$307$	4242.75	0.788750	0.394375	−	0.918950i	$-0.370961\pi$
$307$	4242.75	0.788750	0.394375	+	0.918950i	$0.370961\pi$
$308$	0	0
$309$	−79.8418	−0.0146992
$310$	−8931.37	−1.63635
$311$	−9982.40	−1.82010	−0.910048	−	0.414503i	$-0.863955\pi$
$311$	−9982.40	−1.82010	−0.910048	+	0.414503i	$0.863955\pi$
$312$	1605.72	0.291366
$313$	6216.29	1.12257	0.561287	−	0.827621i	$-0.310306\pi$
$313$	6216.29	1.12257	0.561287	+	0.827621i	$0.310306\pi$
$314$	4650.45	0.835797
$315$	0	0
$316$	−4090.40	−0.728174
$317$	−5302.42	−0.939475	−0.469738	−	0.882806i	$-0.655651\pi$
$317$	−5302.42	−0.939475	−0.469738	+	0.882806i	$0.655651\pi$
$318$	−4090.00	−0.721245
$319$	4861.61	0.853285
$320$	−4468.67	−0.780645
$321$	419.525	0.0729458
$322$	0	0
$323$	380.836	0.0656046
$324$	10889.2	1.86715
$325$	1212.64	0.206970
$326$	−10773.4	−1.83032
$327$	−2491.50	−0.421347
$328$	−2467.10	−0.415313
$329$	0	0
$330$	2069.31	0.345188
$331$	−2101.80	−0.349020	−0.174510	−	0.984655i	$-0.555834\pi$
$331$	−2101.80	−0.349020	−0.174510	+	0.984655i	$0.555834\pi$
$332$	18512.5	3.06026
$333$	−986.457	−0.162335
$334$	9397.55	1.53955
$335$	−324.693	−0.0529548
$336$	0	0
$337$	−6384.39	−1.03199	−0.515994	−	0.856592i	$-0.672577\pi$
$337$	−6384.39	−1.03199	−0.515994	+	0.856592i	$0.672577\pi$
$338$	9785.27	1.57470
$339$	1452.99	0.232789
$340$	−529.669	−0.0844862
$341$	−7860.22	−1.24825
$342$	13924.3	2.20159
$343$	0	0
$344$	−10457.0	−1.63896
$345$	1099.33	0.171553
$346$	−3316.20	−0.515261
$347$	−7093.32	−1.09738	−0.548688	−	0.836027i	$-0.684872\pi$
$347$	−7093.32	−1.09738	−0.548688	+	0.836027i	$0.684872\pi$
$348$	3948.08	0.608159
$349$	−6799.57	−1.04290	−0.521451	−	0.853281i	$-0.674609\pi$
$349$	−6799.57	−1.04290	−0.521451	+	0.853281i	$0.674609\pi$
$350$	0	0
$351$	1383.46	0.210381
$352$	−12510.7	−1.89439
$353$	2425.83	0.365761	0.182881	−	0.983135i	$-0.441458\pi$
$353$	2425.83	0.365761	0.182881	+	0.983135i	$0.441458\pi$
$354$	−4225.62	−0.634432
$355$	7365.50	1.10118
$356$	9666.59	1.43912
$357$	0	0
$358$	−4720.88	−0.696945
$359$	11642.1	1.71156	0.855779	−	0.517342i	$-0.173078\pi$
$359$	11642.1	1.71156	0.855779	+	0.517342i	$0.173078\pi$
$360$	−11412.4	−1.67080
$361$	4572.42	0.666631
$362$	5275.01	0.765880
$363$	−133.136	−0.0192502
$364$	0	0
$365$	627.547	0.0899926
$366$	4951.19	0.707111
$367$	−12796.0	−1.82002	−0.910008	−	0.414592i	$-0.863924\pi$
$367$	−12796.0	−1.82002	−0.910008	+	0.414592i	$0.863924\pi$
$368$	−15653.0	−2.21730
$369$	−1018.61	−0.143704
$370$	1588.93	0.223256
$371$	0	0
$372$	−6383.23	−0.889664
$373$	−1336.34	−0.185505	−0.0927523	−	0.995689i	$-0.529566\pi$
$373$	−1336.34	−0.185505	−0.0927523	+	0.995689i	$0.529566\pi$
$374$	−657.591	−0.0909176
$375$	2148.98	0.295927
$376$	−8869.24	−1.21648
$377$	−2508.84	−0.342737
$378$	0	0
$379$	−4334.88	−0.587514	−0.293757	−	0.955880i	$-0.594906\pi$
$379$	−4334.88	−0.587514	−0.293757	+	0.955880i	$0.594906\pi$
$380$	−15898.9	−2.14630
$381$	−1309.87	−0.176132
$382$	−24471.4	−3.27766
$383$	−1587.09	−0.211740	−0.105870	−	0.994380i	$-0.533763\pi$
$383$	−1587.09	−0.211740	−0.105870	+	0.994380i	$0.533763\pi$
$384$	−332.767	−0.0442225
$385$	0	0
$386$	14970.9	1.97409
$387$	−4317.47	−0.567104
$388$	9400.96	1.23005
$389$	−5879.65	−0.766350	−0.383175	−	0.923676i	$-0.625169\pi$
$389$	−5879.65	−0.766350	−0.383175	+	0.923676i	$0.625169\pi$
$390$	−1067.87	−0.138651
$391$	−349.347	−0.0451847
$392$	0	0
$393$	−4154.82	−0.533290
$394$	−20613.3	−2.63574
$395$	1603.06	0.204200
$396$	−17043.5	−2.16279
$397$	−9970.32	−1.26044	−0.630221	−	0.776415i	$-0.717036\pi$
$397$	−9970.32	−1.26044	−0.630221	+	0.776415i	$0.717036\pi$
$398$	7165.07	0.902393
$399$	0	0
$400$	−10648.8	−1.33110
$401$	−9146.44	−1.13903	−0.569516	−	0.821981i	$-0.692869\pi$
$401$	−9146.44	−1.13903	−0.569516	+	0.821981i	$0.692869\pi$
$402$	−327.363	−0.0406154
$403$	4056.27	0.501383
$404$	−6103.04	−0.751578
$405$	−4267.58	−0.523600
$406$	0	0
$407$	1398.37	0.170306
$408$	−314.701	−0.0381863
$409$	−13787.9	−1.66691	−0.833457	−	0.552584i	$-0.813642\pi$
$409$	−13787.9	−1.66691	−0.833457	+	0.552584i	$0.813642\pi$
$410$	1640.72	0.197633
$411$	4049.76	0.486034
$412$	−1059.23	−0.126661
$413$	0	0
$414$	−12773.0	−1.51633
$415$	−7255.23	−0.858181
$416$	6456.17	0.760912
$417$	4174.59	0.490242
$418$	−19738.7	−2.30969
$419$	8640.54	1.00744	0.503721	−	0.863867i	$-0.331964\pi$
$419$	8640.54	1.00744	0.503721	+	0.863867i	$0.331964\pi$
$420$	0	0
$421$	−14901.0	−1.72502	−0.862508	−	0.506044i	$-0.831107\pi$
$421$	−14901.0	−1.72502	−0.862508	+	0.506044i	$0.831107\pi$
$422$	−7576.48	−0.873975
$423$	−3661.91	−0.420918
$424$	−31975.6	−3.66243
$425$	−237.662	−0.0271254
$426$	7426.07	0.844588
$427$	0	0
$428$	5565.65	0.628565
$429$	−939.800	−0.105767
$430$	6954.34	0.779925
$431$	−6940.00	−0.775610	−0.387805	−	0.921741i	$-0.626767\pi$
$431$	−6940.00	−0.775610	−0.387805	+	0.921741i	$0.626767\pi$
$432$	−12148.9	−1.35304
$433$	−13346.5	−1.48127	−0.740637	−	0.671905i	$-0.765476\pi$
$433$	−13346.5	−1.48127	−0.740637	+	0.671905i	$0.765476\pi$
$434$	0	0
$435$	−1547.29	−0.170544
$436$	−33053.7	−3.63070
$437$	−10486.2	−1.14788
$438$	632.707	0.0690227
$439$	9900.55	1.07637	0.538186	−	0.842826i	$-0.319110\pi$
$439$	9900.55	1.07637	0.538186	+	0.842826i	$0.319110\pi$
$440$	16177.9	1.75284
$441$	0	0
$442$	339.350	0.0365186
$443$	−10075.4	−1.08058	−0.540292	−	0.841477i	$-0.681686\pi$
$443$	−10075.4	−1.08058	−0.540292	+	0.841477i	$0.681686\pi$
$444$	1135.60	0.121382
$445$	−3788.42	−0.403570
$446$	−25271.8	−2.68308
$447$	−5076.11	−0.537118
$448$	0	0
$449$	3733.61	0.392428	0.196214	−	0.980561i	$-0.437135\pi$
$449$	3733.61	0.392428	0.196214	+	0.980561i	$0.437135\pi$
$450$	−8689.53	−0.910285
$451$	1443.95	0.150760
$452$	19276.2	2.00592
$453$	−176.805	−0.0183378
$454$	10255.7	1.06019
$455$	0	0
$456$	−9446.27	−0.970092
$457$	−16646.1	−1.70388	−0.851940	−	0.523639i	$-0.824574\pi$
$457$	−16646.1	−1.70388	−0.851940	+	0.523639i	$0.824574\pi$
$458$	−1085.16	−0.110713
$459$	−271.141	−0.0275725
$460$	14584.3	1.47825
$461$	−2065.33	−0.208660	−0.104330	−	0.994543i	$-0.533270\pi$
$461$	−2065.33	−0.208660	−0.104330	+	0.994543i	$0.533270\pi$
$462$	0	0
$463$	8816.23	0.884935	0.442468	−	0.896784i	$-0.354103\pi$
$463$	8816.23	0.884935	0.442468	+	0.896784i	$0.354103\pi$
$464$	22031.3	2.20426
$465$	2501.64	0.249486
$466$	−12258.8	−1.21862
$467$	18256.3	1.80899	0.904496	−	0.426483i	$-0.140248\pi$
$467$	18256.3	1.80899	0.904496	+	0.426483i	$0.140248\pi$
$468$	8795.29	0.868723
$469$	0	0
$470$	5898.41	0.578879
$471$	−1302.58	−0.127430
$472$	−33035.8	−3.22160
$473$	6120.30	0.594950
$474$	1616.25	0.156617
$475$	−7133.81	−0.689099
$476$	0	0
$477$	−13202.0	−1.26725
$478$	−52.8647	−0.00505853
$479$	16013.9	1.52755	0.763773	−	0.645485i	$-0.223345\pi$
$479$	16013.9	1.52755	0.763773	+	0.645485i	$0.223345\pi$
$480$	3981.74	0.378627
$481$	−721.629	−0.0684063
$482$	−28518.5	−2.69498
$483$	0	0
$484$	−1766.26	−0.165877
$485$	−3684.32	−0.344941
$486$	−15076.5	−1.40717
$487$	10955.0	1.01934	0.509672	−	0.860369i	$-0.329767\pi$
$487$	10955.0	1.01934	0.509672	+	0.860369i	$0.329767\pi$
$488$	38708.3	3.59066
$489$	3017.60	0.279061
$490$	0	0
$491$	−17514.3	−1.60980	−0.804898	−	0.593413i	$-0.797780\pi$
$491$	−17514.3	−1.60980	−0.804898	+	0.593413i	$0.797780\pi$
$492$	1172.62	0.107451
$493$	491.700	0.0449190
$494$	10186.2	0.927726
$495$	6679.49	0.606506
$496$	−35620.0	−3.22457
$497$	0	0
$498$	−7314.89	−0.658209
$499$	−8994.13	−0.806878	−0.403439	−	0.915006i	$-0.632185\pi$
$499$	−8994.13	−0.806878	−0.403439	+	0.915006i	$0.632185\pi$
$500$	28509.5	2.54997
$501$	−2632.22	−0.234728
$502$	14051.3	1.24928
$503$	−41.3189	−0.00366267	−0.00183133	−	0.999998i	$-0.500583\pi$
$503$	−41.3189	−0.00366267	−0.00183133	+	0.999998i	$0.500583\pi$
$504$	0	0
$505$	2391.83	0.210763
$506$	18106.6	1.59078
$507$	−2740.82	−0.240087
$508$	−17377.4	−1.51771
$509$	7078.95	0.616442	0.308221	−	0.951315i	$-0.400266\pi$
$509$	7078.95	0.616442	0.308221	+	0.951315i	$0.400266\pi$
$510$	209.289	0.0181715
$511$	0	0
$512$	20133.4	1.73785
$513$	−8138.75	−0.700457
$514$	−22303.6	−1.91395
$515$	415.120	0.0355192
$516$	4970.25	0.424037
$517$	5191.00	0.441586
$518$	0	0
$519$	928.857	0.0785593
$520$	−8348.59	−0.704058
$521$	−14018.1	−1.17878	−0.589388	−	0.807850i	$-0.700631\pi$
$521$	−14018.1	−1.17878	−0.589388	+	0.807850i	$0.700631\pi$
$522$	17977.8	1.50741
$523$	−4641.92	−0.388101	−0.194051	−	0.980991i	$-0.562163\pi$
$523$	−4641.92	−0.388101	−0.194051	+	0.980991i	$0.562163\pi$
$524$	−55120.1	−4.59529
$525$	0	0
$526$	26694.7	2.21282
$527$	−794.977	−0.0657111
$528$	8252.83	0.680224
$529$	−2547.82	−0.209404
$530$	21265.1	1.74282
$531$	−13639.8	−1.11472
$532$	0	0
$533$	−745.150	−0.0605554
$534$	−3819.58	−0.309531
$535$	−2181.23	−0.176267
$536$	−2559.32	−0.206242
$537$	1322.30	0.106260
$538$	5456.01	0.437222
$539$	0	0
$540$	11319.4	0.902056
$541$	−9219.75	−0.732695	−0.366347	−	0.930478i	$-0.619392\pi$
$541$	−9219.75	−0.732695	−0.366347	+	0.930478i	$0.619392\pi$
$542$	−31439.9	−2.49162
$543$	−1477.51	−0.116770
$544$	−1265.33	−0.0997250
$545$	12954.0	1.01815
$546$	0	0
$547$	−23869.8	−1.86581	−0.932904	−	0.360125i	$-0.882734\pi$
$547$	−23869.8	−1.86581	−0.932904	+	0.360125i	$0.882734\pi$
$548$	53726.4	4.18810
$549$	15981.8	1.24242
$550$	12318.0	0.954982
$551$	14759.2	1.14113
$552$	8665.22	0.668145
$553$	0	0
$554$	13173.8	1.01029
$555$	−445.054	−0.0340387
$556$	55382.5	4.22435
$557$	18186.3	1.38345	0.691723	−	0.722163i	$-0.256852\pi$
$557$	18186.3	1.38345	0.691723	+	0.722163i	$0.256852\pi$
$558$	−29066.4	−2.20516
$559$	−3158.38	−0.238972
$560$	0	0
$561$	184.189	0.0138618
$562$	−1258.29	−0.0944447
$563$	243.367	0.0182179	0.00910895	−	0.999959i	$-0.497100\pi$
$563$	243.367	0.0182179	0.00910895	+	0.999959i	$0.497100\pi$
$564$	4215.58	0.314730
$565$	−7554.50	−0.562514
$566$	−5144.42	−0.382043
$567$	0	0
$568$	58056.9	4.28876
$569$	−5339.50	−0.393398	−0.196699	−	0.980464i	$-0.563022\pi$
$569$	−5339.50	−0.393398	−0.196699	+	0.980464i	$0.563022\pi$
$570$	6282.16	0.461633
$571$	−6956.36	−0.509833	−0.254917	−	0.966963i	$-0.582048\pi$
$571$	−6956.36	−0.509833	−0.254917	+	0.966963i	$0.582048\pi$
$572$	−12467.9	−0.911380
$573$	6854.36	0.499730
$574$	0	0
$575$	6543.96	0.474612
$576$	−14542.9	−1.05201
$577$	21360.4	1.54115	0.770575	−	0.637349i	$-0.219969\pi$
$577$	21360.4	1.54115	0.770575	+	0.637349i	$0.219969\pi$
$578$	25687.6	1.84855
$579$	−4193.30	−0.300980
$580$	−20527.2	−1.46956
$581$	0	0
$582$	−3714.62	−0.264563
$583$	18714.7	1.32948
$584$	4946.49	0.350492
$585$	−3446.95	−0.243614
$586$	42405.1	2.98931
$587$	9725.11	0.683813	0.341907	−	0.939734i	$-0.388927\pi$
$587$	9725.11	0.683813	0.341907	+	0.939734i	$0.388927\pi$
$588$	0	0
$589$	−23862.6	−1.66934
$590$	21970.2	1.53305
$591$	5773.70	0.401859
$592$	6336.97	0.439946
$593$	−24944.5	−1.72740	−0.863698	−	0.504010i	$-0.831858\pi$
$593$	−24944.5	−1.72740	−0.863698	+	0.504010i	$0.831858\pi$
$594$	14053.2	0.970724
$595$	0	0
$596$	−67342.4	−4.62827
$597$	−2006.91	−0.137583
$598$	−9343.92	−0.638966
$599$	−6655.34	−0.453973	−0.226987	−	0.973898i	$-0.572887\pi$
$599$	−6655.34	−0.453973	−0.226987	+	0.973898i	$0.572887\pi$
$600$	5894.97	0.401102
$601$	4860.95	0.329921	0.164960	−	0.986300i	$-0.447250\pi$
$601$	4860.95	0.329921	0.164960	+	0.986300i	$0.447250\pi$
$602$	0	0
$603$	−1056.69	−0.0713625
$604$	−2345.59	−0.158014
$605$	692.212	0.0465164
$606$	2411.50	0.161651
$607$	−2040.29	−0.136430	−0.0682148	−	0.997671i	$-0.521730\pi$
$607$	−2040.29	−0.136430	−0.0682148	+	0.997671i	$0.521730\pi$
$608$	−37980.9	−2.53343
$609$	0	0
$610$	−25742.6	−1.70867
$611$	−2678.82	−0.177371
$612$	−1723.76	−0.113855
$613$	−21978.5	−1.44813	−0.724063	−	0.689733i	$-0.757728\pi$
$613$	−21978.5	−1.44813	−0.724063	+	0.689733i	$0.757728\pi$
$614$	−22240.6	−1.46182
$615$	−459.560	−0.0301321
$616$	0	0
$617$	−3997.68	−0.260843	−0.130422	−	0.991459i	$-0.541633\pi$
$617$	−3997.68	−0.260843	−0.130422	+	0.991459i	$0.541633\pi$
$618$	418.534	0.0272425
$619$	−2013.01	−0.130710	−0.0653552	−	0.997862i	$-0.520818\pi$
$619$	−2013.01	−0.130710	−0.0653552	+	0.997862i	$0.520818\pi$
$620$	33188.2	2.14979
$621$	7465.81	0.482436
$622$	52328.1	3.37326
$623$	0	0
$624$	−4258.88	−0.273224
$625$	−2832.82	−0.181301
$626$	−32586.0	−2.08051
$627$	5528.73	0.352147
$628$	−17280.7	−1.09805
$629$	141.430	0.00896532
$630$	0	0
$631$	−10583.9	−0.667731	−0.333866	−	0.942621i	$-0.608353\pi$
$631$	−10583.9	−0.667731	−0.333866	+	0.942621i	$0.608353\pi$
$632$	12635.8	0.795292
$633$	2122.15	0.133251
$634$	27795.5	1.74117
$635$	6810.36	0.425608
$636$	15198.1	0.947553
$637$	0	0
$638$	−25484.7	−1.58143
$639$	23970.4	1.48397
$640$	1730.15	0.106859
$641$	−20065.2	−1.23639	−0.618196	−	0.786024i	$-0.712136\pi$
$641$	−20065.2	−1.23639	−0.618196	+	0.786024i	$0.712136\pi$
$642$	−2199.16	−0.135193
$643$	24092.2	1.47761	0.738805	−	0.673919i	$-0.235390\pi$
$643$	24092.2	1.47761	0.738805	+	0.673919i	$0.235390\pi$
$644$	0	0
$645$	−1947.89	−0.118911
$646$	−1996.36	−0.121588
$647$	−1351.08	−0.0820966	−0.0410483	−	0.999157i	$-0.513070\pi$
$647$	−1351.08	−0.0820966	−0.0410483	+	0.999157i	$0.513070\pi$
$648$	−33638.3	−2.03925
$649$	19335.3	1.16945
$650$	−6356.70	−0.383585
$651$	0	0
$652$	40033.2	2.40463
$653$	2954.46	0.177055	0.0885275	−	0.996074i	$-0.471784\pi$
$653$	2954.46	0.177055	0.0885275	+	0.996074i	$0.471784\pi$
$654$	13060.6	0.780900
$655$	21602.1	1.28865
$656$	6543.52	0.389454
$657$	2042.30	0.121275
$658$	0	0
$659$	25668.7	1.51732	0.758659	−	0.651488i	$-0.225855\pi$
$659$	25668.7	1.51732	0.758659	+	0.651488i	$0.225855\pi$
$660$	−7689.39	−0.453499
$661$	20142.2	1.18523	0.592617	−	0.805484i	$-0.298095\pi$
$661$	20142.2	1.18523	0.592617	+	0.805484i	$0.298095\pi$
$662$	11017.7	0.646852
$663$	−95.0507	−0.00556782
$664$	−57187.7	−3.34234
$665$	0	0
$666$	5171.05	0.300862
$667$	−13538.8	−0.785946
$668$	−34920.5	−2.02263
$669$	7078.54	0.409077
$670$	1702.05	0.0981433
$671$	−22655.3	−1.30342
$672$	0	0
$673$	3934.29	0.225343	0.112671	−	0.993632i	$-0.464059\pi$
$673$	3934.29	0.225343	0.112671	+	0.993632i	$0.464059\pi$
$674$	33467.2	1.91262
$675$	5079.01	0.289617
$676$	−36361.2	−2.06880
$677$	−13728.0	−0.779336	−0.389668	−	0.920955i	$-0.627410\pi$
$677$	−13728.0	−0.779336	−0.389668	+	0.920955i	$0.627410\pi$
$678$	−7616.63	−0.431438
$679$	0	0
$680$	1636.22	0.0922737
$681$	−2872.59	−0.161642
$682$	41203.6	2.31344
$683$	−19718.3	−1.10468	−0.552341	−	0.833618i	$-0.686265\pi$
$683$	−19718.3	−1.10468	−0.552341	+	0.833618i	$0.686265\pi$
$684$	−51741.6	−2.89238
$685$	−21055.8	−1.17446
$686$	0	0
$687$	303.950	0.0168798
$688$	27735.3	1.53691
$689$	−9657.75	−0.534007
$690$	−5762.72	−0.317947
$691$	−7613.79	−0.419164	−0.209582	−	0.977791i	$-0.567210\pi$
$691$	−7613.79	−0.419164	−0.209582	+	0.977791i	$0.567210\pi$
$692$	12322.7	0.676936
$693$	0	0
$694$	37183.4	2.03381
$695$	−21704.9	−1.18462
$696$	−12196.1	−0.664215
$697$	146.040	0.00793638
$698$	35643.6	1.93285
$699$	3433.64	0.185797
$700$	0	0
$701$	425.724	0.0229378	0.0114689	−	0.999934i	$-0.496349\pi$
$701$	425.724	0.0229378	0.0114689	+	0.999934i	$0.496349\pi$
$702$	−7252.17	−0.389908
$703$	4245.26	0.227757
$704$	20615.6	1.10366
$705$	−1652.12	−0.0882589
$706$	−12716.3	−0.677880
$707$	0	0
$708$	15702.0	0.833500
$709$	−19738.8	−1.04557	−0.522784	−	0.852465i	$-0.675107\pi$
$709$	−19738.8	−1.04557	−0.522784	+	0.852465i	$0.675107\pi$
$710$	−38610.2	−2.04087
$711$	5217.04	0.275182
$712$	−29861.4	−1.57177
$713$	21889.5	1.14975
$714$	0	0
$715$	4886.28	0.255576
$716$	17542.4	0.915628
$717$	14.8072	0.000771250 0
$718$	−61028.6	−3.17210
$719$	12782.1	0.662992	0.331496	−	0.943457i	$-0.392447\pi$
$719$	12782.1	0.662992	0.331496	+	0.943457i	$0.392447\pi$
$720$	30269.3	1.56677
$721$	0	0
$722$	−23968.8	−1.23549
$723$	7987.92	0.410891
$724$	−19601.5	−1.00619
$725$	−9210.52	−0.471821
$726$	697.905	0.0356772
$727$	1612.28	0.0822508	0.0411254	−	0.999154i	$-0.486906\pi$
$727$	1612.28	0.0822508	0.0411254	+	0.999154i	$0.486906\pi$
$728$	0	0
$729$	−10870.8	−0.552293
$730$	−3289.62	−0.166787
$731$	619.003	0.0313196
$732$	−18398.2	−0.928984
$733$	−31722.4	−1.59849	−0.799245	−	0.601005i	$-0.794767\pi$
$733$	−31722.4	−1.59849	−0.799245	+	0.601005i	$0.794767\pi$
$734$	67077.1	3.37311
$735$	0	0
$736$	34840.5	1.74489
$737$	1497.92	0.0748666
$738$	5339.60	0.266332
$739$	−34923.8	−1.73842	−0.869209	−	0.494444i	$-0.835372\pi$
$739$	−34923.8	−1.73842	−0.869209	+	0.494444i	$0.835372\pi$
$740$	−5904.33	−0.293307
$741$	−2853.11	−0.141446
$742$	0	0
$743$	6981.82	0.344735	0.172367	−	0.985033i	$-0.444858\pi$
$743$	6981.82	0.344735	0.172367	+	0.985033i	$0.444858\pi$
$744$	19718.6	0.971668
$745$	26392.1	1.29789
$746$	7005.16	0.343803
$747$	−23611.6	−1.15649
$748$	2443.55	0.119445
$749$	0	0
$750$	−11265.0	−0.548453
$751$	2752.50	0.133742	0.0668710	−	0.997762i	$-0.478698\pi$
$751$	2752.50	0.133742	0.0668710	+	0.997762i	$0.478698\pi$
$752$	23524.0	1.14073
$753$	−3935.72	−0.190472
$754$	13151.4	0.635207
$755$	919.256	0.0443115
$756$	0	0
$757$	−13352.0	−0.641066	−0.320533	−	0.947237i	$-0.603862\pi$
$757$	−13352.0	−0.641066	−0.320533	+	0.947237i	$0.603862\pi$
$758$	22723.6	1.08886
$759$	−5071.60	−0.242539
$760$	49113.8	2.34414
$761$	34985.6	1.66653	0.833264	−	0.552875i	$-0.186469\pi$
$761$	34985.6	1.66653	0.833264	+	0.552875i	$0.186469\pi$
$762$	6866.37	0.326433
$763$	0	0
$764$	90933.7	4.30611
$765$	675.559	0.0319279
$766$	8319.58	0.392427
$767$	−9977.97	−0.469731
$768$	−5131.46	−0.241101
$769$	−7824.38	−0.366911	−0.183455	−	0.983028i	$-0.558728\pi$
$769$	−7824.38	−0.366911	−0.183455	+	0.983028i	$0.558728\pi$
$770$	0	0
$771$	6247.16	0.291811
$772$	−55630.6	−2.59351
$773$	−8380.72	−0.389953	−0.194976	−	0.980808i	$-0.562463\pi$
$773$	−8380.72	−0.389953	−0.194976	+	0.980808i	$0.562463\pi$
$774$	22632.3	1.05104
$775$	14891.5	0.690217
$776$	−29040.8	−1.34343
$777$	0	0
$778$	30821.3	1.42031
$779$	4383.63	0.201617
$780$	3968.12	0.182156
$781$	−33979.7	−1.55683
$782$	1831.29	0.0837427
$783$	−10508.0	−0.479598
$784$	0	0
$785$	6772.46	0.307923
$786$	21779.7	0.988368
$787$	−32119.6	−1.45482	−0.727408	−	0.686206i	$-0.759275\pi$
$787$	−32119.6	−1.45482	−0.727408	+	0.686206i	$0.759275\pi$
$788$	76597.1	3.46276
$789$	−7477.08	−0.337378
$790$	−8403.32	−0.378451
$791$	0	0
$792$	52649.5	2.36215
$793$	11691.3	0.523542
$794$	52264.8	2.33603
$795$	−5956.27	−0.265720
$796$	−26624.8	−1.18554
$797$	−23594.9	−1.04865	−0.524324	−	0.851519i	$-0.675682\pi$
$797$	−23594.9	−1.04865	−0.524324	+	0.851519i	$0.675682\pi$
$798$	0	0
$799$	525.015	0.0232462
$800$	23702.1	1.04749
$801$	−12329.1	−0.543855
$802$	47946.0	2.11101
$803$	−2895.09	−0.127230
$804$	1216.45	0.0533594
$805$	0	0
$806$	−21263.1	−0.929233
$807$	−1528.21	−0.0666611
$808$	18853.1	0.820854
$809$	−25291.0	−1.09911	−0.549557	−	0.835456i	$-0.685204\pi$
$809$	−25291.0	−1.09911	−0.549557	+	0.835456i	$0.685204\pi$
$810$	22370.8	0.970409
$811$	−41992.3	−1.81819	−0.909093	−	0.416594i	$-0.863224\pi$
$811$	−41992.3	−1.81819	−0.909093	+	0.416594i	$0.863224\pi$
$812$	0	0
$813$	8806.20	0.379886
$814$	−7330.30	−0.315635
$815$	−15689.4	−0.674324
$816$	834.686	0.0358086
$817$	18580.4	0.795650
$818$	72276.7	3.08936
$819$	0	0
$820$	−6096.78	−0.259645
$821$	−17625.6	−0.749255	−0.374628	−	0.927175i	$-0.622229\pi$
$821$	−17625.6	−0.749255	−0.374628	+	0.927175i	$0.622229\pi$
$822$	−21229.0	−0.900787
$823$	2125.73	0.0900344	0.0450172	−	0.998986i	$-0.485666\pi$
$823$	2125.73	0.0900344	0.0450172	+	0.998986i	$0.485666\pi$
$824$	3272.09	0.138336
$825$	−3450.22	−0.145602
$826$	0	0
$827$	−24450.9	−1.02810	−0.514051	−	0.857760i	$-0.671856\pi$
$827$	−24450.9	−1.02810	−0.514051	+	0.857760i	$0.671856\pi$
$828$	47463.4	1.99211
$829$	1136.26	0.0476041	0.0238021	−	0.999717i	$-0.492423\pi$
$829$	1136.26	0.0476041	0.0238021	+	0.999717i	$0.492423\pi$
$830$	38032.2	1.59050
$831$	−3689.94	−0.154034
$832$	−10638.7	−0.443305
$833$	0	0
$834$	−21883.4	−0.908585
$835$	13685.6	0.567199
$836$	73347.2	3.03441
$837$	16989.3	0.701595
$838$	−45294.0	−1.86713
$839$	18014.1	0.741259	0.370629	−	0.928781i	$-0.379142\pi$
$839$	18014.1	0.741259	0.370629	+	0.928781i	$0.379142\pi$
$840$	0	0
$841$	−5333.30	−0.218677
$842$	78111.7	3.19704
$843$	352.444	0.0143995
$844$	28153.6	1.14821
$845$	14250.3	0.580147
$846$	19195.9	0.780104
$847$	0	0
$848$	84809.3	3.43439
$849$	1440.94	0.0582483
$850$	1245.83	0.0502726
$851$	−3894.24	−0.156866
$852$	−27594.6	−1.10960
$853$	6002.06	0.240922	0.120461	−	0.992718i	$-0.461563\pi$
$853$	6002.06	0.240922	0.120461	+	0.992718i	$0.461563\pi$
$854$	0	0
$855$	20278.0	0.811103
$856$	−17193.0	−0.686502
$857$	−22139.6	−0.882468	−0.441234	−	0.897392i	$-0.645459\pi$
$857$	−22139.6	−0.882468	−0.441234	+	0.897392i	$0.645459\pi$
$858$	4926.47	0.196022
$859$	34185.0	1.35783	0.678915	−	0.734217i	$-0.262451\pi$
$859$	34185.0	1.35783	0.678915	+	0.734217i	$0.262451\pi$
$860$	−25841.7	−1.02465
$861$	0	0
$862$	36379.7	1.43747
$863$	−44926.0	−1.77207	−0.886036	−	0.463617i	$-0.846551\pi$
$863$	−44926.0	−1.77207	−0.886036	+	0.463617i	$0.846551\pi$
$864$	27041.0	1.06476
$865$	−4829.39	−0.189831
$866$	69962.8	2.74530
$867$	−7195.01	−0.281840
$868$	0	0
$869$	−7395.50	−0.288694
$870$	8110.94	0.316077
$871$	−773.004	−0.0300715
$872$	102107.	3.96535
$873$	−11990.3	−0.464846
$874$	54969.2	2.12741
$875$	0	0
$876$	−2351.09	−0.0906802
$877$	25197.8	0.970205	0.485103	−	0.874457i	$-0.338782\pi$
$877$	25197.8	0.970205	0.485103	+	0.874457i	$0.338782\pi$
$878$	−51899.1	−1.99488
$879$	−11877.5	−0.455766
$880$	−42908.8	−1.64370
$881$	10356.6	0.396052	0.198026	−	0.980197i	$-0.436547\pi$
$881$	10356.6	0.396052	0.198026	+	0.980197i	$0.436547\pi$
$882$	0	0
$883$	−23262.0	−0.886555	−0.443278	−	0.896384i	$-0.646184\pi$
$883$	−23262.0	−0.886555	−0.443278	+	0.896384i	$0.646184\pi$
$884$	−1261.00	−0.0479772
$885$	−6153.76	−0.233736
$886$	52815.9	2.00269
$887$	12862.2	0.486889	0.243444	−	0.969915i	$-0.421723\pi$
$887$	12862.2	0.486889	0.243444	+	0.969915i	$0.421723\pi$
$888$	−3508.04	−0.132570
$889$	0	0
$890$	19859.1	0.747952
$891$	19687.9	0.740257
$892$	93907.8	3.52496
$893$	15759.2	0.590550
$894$	26609.1	0.995461
$895$	−6875.02	−0.256767
$896$	0	0
$897$	2617.20	0.0974200
$898$	−19571.7	−0.727302
$899$	−30809.1	−1.14298
$900$	32289.5	1.19591
$901$	1892.80	0.0699869
$902$	−7569.23	−0.279410
$903$	0	0
$904$	−59546.7	−2.19081
$905$	7682.00	0.282164
$906$	926.816	0.0339861
$907$	−11715.7	−0.428899	−0.214450	−	0.976735i	$-0.568796\pi$
$907$	−11715.7	−0.428899	−0.214450	+	0.976735i	$0.568796\pi$
$908$	−38109.4	−1.39285
$909$	7784.03	0.284026
$910$	0	0
$911$	−51454.2	−1.87130	−0.935650	−	0.352930i	$-0.885185\pi$
$911$	−51454.2	−1.87130	−0.935650	+	0.352930i	$0.885185\pi$
$912$	25054.5	0.909690
$913$	33470.9	1.21328
$914$	87259.7	3.15787
$915$	7210.41	0.260512
$916$	4032.37	0.145451
$917$	0	0
$918$	1421.33	0.0511012
$919$	25584.1	0.918326	0.459163	−	0.888352i	$-0.348149\pi$
$919$	25584.1	0.918326	0.459163	+	0.888352i	$0.348149\pi$
$920$	−45052.9	−1.61451
$921$	6229.52	0.222877
$922$	10826.5	0.386717
$923$	17535.2	0.625329
$924$	0	0
$925$	−2649.27	−0.0941701
$926$	−46215.0	−1.64009
$927$	1350.97	0.0478660
$928$	−49037.4	−1.73462
$929$	−49946.6	−1.76393	−0.881967	−	0.471311i	$-0.843781\pi$
$929$	−49946.6	−1.76393	−0.881967	+	0.471311i	$0.843781\pi$
$930$	−13113.7	−0.462382
$931$	0	0
$932$	45552.6	1.60099
$933$	−14656.9	−0.514304
$934$	−95700.0	−3.35268
$935$	−957.649	−0.0334957
$936$	−27169.8	−0.948797
$937$	−10887.8	−0.379603	−0.189802	−	0.981822i	$-0.560785\pi$
$937$	−10887.8	−0.379603	−0.189802	+	0.981822i	$0.560785\pi$
$938$	0	0
$939$	9127.24	0.317206
$940$	−21918.0	−0.760516
$941$	18992.1	0.657945	0.328973	−	0.944339i	$-0.393298\pi$
$941$	18992.1	0.657945	0.328973	+	0.944339i	$0.393298\pi$
$942$	6828.15	0.236171
$943$	−4021.17	−0.138863
$944$	87621.3	3.02101
$945$	0	0
$946$	−32082.8	−1.10265
$947$	13506.0	0.463450	0.231725	−	0.972781i	$-0.425563\pi$
$947$	13506.0	0.463450	0.231725	+	0.972781i	$0.425563\pi$
$948$	−6005.83	−0.205760
$949$	1494.02	0.0511041
$950$	37395.7	1.27713
$951$	−7785.42	−0.265467
$952$	0	0
$953$	41338.8	1.40514	0.702568	−	0.711616i	$-0.252037\pi$
$953$	41338.8	1.40514	0.702568	+	0.711616i	$0.252037\pi$
$954$	69205.5	2.34865
$955$	−35637.7	−1.20755
$956$	196.441	0.00664576
$957$	7138.19	0.241113
$958$	−83945.6	−2.83106
$959$	0	0
$960$	−6561.24	−0.220587
$961$	20021.0	0.672048
$962$	3782.81	0.126780
$963$	−7098.63	−0.237539
$964$	105972.	3.54059
$965$	21802.1	0.727291
$966$	0	0
$967$	−2718.28	−0.0903972	−0.0451986	−	0.998978i	$-0.514392\pi$
$967$	−2718.28	−0.0903972	−0.0451986	+	0.998978i	$0.514392\pi$
$968$	5456.21	0.181166
$969$	559.172	0.0185379
$970$	19313.3	0.639293
$971$	43962.0	1.45294	0.726471	−	0.687197i	$-0.241159\pi$
$971$	43962.0	1.45294	0.726471	+	0.687197i	$0.241159\pi$
$972$	56023.1	1.84871
$973$	0	0
$974$	−57426.7	−1.88919
$975$	1780.49	0.0584834
$976$	−102667.	−3.36709
$977$	26479.1	0.867084	0.433542	−	0.901133i	$-0.357264\pi$
$977$	26479.1	0.867084	0.433542	+	0.901133i	$0.357264\pi$
$978$	−15818.4	−0.517194
$979$	17477.3	0.570560
$980$	0	0
$981$	42157.8	1.37207
$982$	91810.7	2.98350
$983$	−42394.3	−1.37555	−0.687776	−	0.725923i	$-0.741413\pi$
$983$	−42394.3	−1.37555	−0.687776	+	0.725923i	$0.741413\pi$
$984$	−3622.38	−0.117355
$985$	−30019.1	−0.971053
$986$	−2577.51	−0.0832501
$987$	0	0
$988$	−37850.9	−1.21882
$989$	−17044.1	−0.547999
$990$	−35014.1	−1.12406
$991$	−19997.7	−0.641018	−0.320509	−	0.947245i	$-0.603854\pi$
$991$	−19997.7	−0.641018	−0.320509	+	0.947245i	$0.603854\pi$
$992$	79283.3	2.53755
$993$	−3086.03	−0.0986225
$994$	0	0
$995$	10434.5	0.332458
$996$	27181.5	0.864738
$997$	30310.5	0.962832	0.481416	−	0.876492i	$-0.340123\pi$
$997$	30310.5	0.962832	0.481416	+	0.876492i	$0.340123\pi$
$998$	47147.5	1.49542
$999$	−3022.47	−0.0957223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.j.1.1		36
7.2	even	3		287.4.e.a.165.36	✓	72
7.4	even	3		287.4.e.a.247.36	yes	72
7.6	odd	2		2009.4.a.k.1.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.4.e.a.165.36	✓	72	7.2	even	3
287.4.e.a.247.36	yes	72	7.4	even	3
2009.4.a.j.1.1		36	1.1	even	1	trivial
2009.4.a.k.1.1		36	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.24204 q^{2} +1.46828 q^{3} +19.4790 q^{4} -7.63398 q^{5} -7.69676 q^{6} -60.1731 q^{8} -24.8442 q^{9} +O(q^{10})\)	\(q-5.24204 q^{2} +1.46828 q^{3} +19.4790 q^{4} -7.63398 q^{5} -7.69676 q^{6} -60.1731 q^{8} -24.8442 q^{9} +40.0176 q^{10} +35.2182 q^{11} +28.6005 q^{12} -18.1744 q^{13} -11.2088 q^{15} +159.598 q^{16} +3.56195 q^{17} +130.234 q^{18} +106.918 q^{19} -148.702 q^{20} -184.615 q^{22} -98.0774 q^{23} -88.3508 q^{24} -66.7224 q^{25} +95.2709 q^{26} -76.1216 q^{27} +138.042 q^{29} +58.7569 q^{30} -223.186 q^{31} -355.234 q^{32} +51.7101 q^{33} -18.6719 q^{34} -483.938 q^{36} +39.7058 q^{37} -560.467 q^{38} -26.6850 q^{39} +459.360 q^{40} +41.0000 q^{41} +173.782 q^{43} +686.015 q^{44} +189.660 q^{45} +514.126 q^{46} +147.395 q^{47} +234.334 q^{48} +349.761 q^{50} +5.22993 q^{51} -354.018 q^{52} +531.393 q^{53} +399.032 q^{54} -268.855 q^{55} +156.985 q^{57} -723.623 q^{58} +549.012 q^{59} -218.335 q^{60} -643.282 q^{61} +1169.95 q^{62} +585.366 q^{64} +138.743 q^{65} -271.066 q^{66} +42.5326 q^{67} +69.3831 q^{68} -144.005 q^{69} -964.831 q^{71} +1494.95 q^{72} -82.2044 q^{73} -208.139 q^{74} -97.9669 q^{75} +2082.65 q^{76} +139.884 q^{78} -209.991 q^{79} -1218.37 q^{80} +559.025 q^{81} -214.924 q^{82} +950.386 q^{83} -27.1918 q^{85} -910.972 q^{86} +202.684 q^{87} -2119.19 q^{88} +496.258 q^{89} -994.204 q^{90} -1910.45 q^{92} -327.699 q^{93} -772.652 q^{94} -816.208 q^{95} -521.582 q^{96} +482.621 q^{97} -874.968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 6 q^{3} + 117 q^{4} + 4 q^{5} - 12 q^{6} - 39 q^{8} + 236 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 6 * q^3 + 117 * q^4 + 4 * q^5 - 12 * q^6 - 39 * q^8 + 236 * q^9	\( 36 q - 5 q^{2} - 6 q^{3} + 117 q^{4} + 4 q^{5} - 12 q^{6} - 39 q^{8} + 236 q^{9} - 12 q^{10} - 140 q^{11} + 186 q^{12} - 72 q^{13} - 366 q^{15} - 15 q^{16} - 2 q^{17} - 212 q^{18} + 30 q^{19} - 334 q^{20} - 346 q^{22} - 314 q^{23} + 106 q^{24} + 570 q^{25} + 303 q^{26} - 204 q^{27} - 356 q^{29} - 357 q^{30} - 4 q^{31} - 532 q^{32} - 30 q^{33} - 364 q^{34} + 113 q^{36} - 1398 q^{37} - 264 q^{38} - 1348 q^{39} + 26 q^{40} + 1476 q^{41} - 1072 q^{43} - 1507 q^{44} - 1132 q^{45} - 1356 q^{46} - 622 q^{47} + 1724 q^{48} - 1426 q^{50} - 668 q^{51} - 877 q^{52} - 412 q^{53} - 1814 q^{54} + 1114 q^{55} - 4082 q^{57} - 1309 q^{58} - 620 q^{59} - 3724 q^{60} + 774 q^{61} + 1665 q^{62} - 3285 q^{64} - 1036 q^{65} - 1056 q^{66} - 2972 q^{67} - 1525 q^{68} + 3304 q^{69} - 3540 q^{71} - 821 q^{72} - 60 q^{73} - 2043 q^{74} + 450 q^{75} + 2171 q^{76} - 1136 q^{78} - 5190 q^{79} - 1564 q^{80} + 284 q^{81} - 205 q^{82} + 1656 q^{83} - 5064 q^{85} - 782 q^{86} - 1940 q^{87} - 4232 q^{88} - 1196 q^{89} + 8030 q^{90} - 4618 q^{92} + 698 q^{93} - 35 q^{94} - 1968 q^{95} - 7926 q^{96} + 3862 q^{97} - 5964 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 6 * q^3 + 117 * q^4 + 4 * q^5 - 12 * q^6 - 39 * q^8 + 236 * q^9 - 12 * q^10 - 140 * q^11 + 186 * q^12 - 72 * q^13 - 366 * q^15 - 15 * q^16 - 2 * q^17 - 212 * q^18 + 30 * q^19 - 334 * q^20 - 346 * q^22 - 314 * q^23 + 106 * q^24 + 570 * q^25 + 303 * q^26 - 204 * q^27 - 356 * q^29 - 357 * q^30 - 4 * q^31 - 532 * q^32 - 30 * q^33 - 364 * q^34 + 113 * q^36 - 1398 * q^37 - 264 * q^38 - 1348 * q^39 + 26 * q^40 + 1476 * q^41 - 1072 * q^43 - 1507 * q^44 - 1132 * q^45 - 1356 * q^46 - 622 * q^47 + 1724 * q^48 - 1426 * q^50 - 668 * q^51 - 877 * q^52 - 412 * q^53 - 1814 * q^54 + 1114 * q^55 - 4082 * q^57 - 1309 * q^58 - 620 * q^59 - 3724 * q^60 + 774 * q^61 + 1665 * q^62 - 3285 * q^64 - 1036 * q^65 - 1056 * q^66 - 2972 * q^67 - 1525 * q^68 + 3304 * q^69 - 3540 * q^71 - 821 * q^72 - 60 * q^73 - 2043 * q^74 + 450 * q^75 + 2171 * q^76 - 1136 * q^78 - 5190 * q^79 - 1564 * q^80 + 284 * q^81 - 205 * q^82 + 1656 * q^83 - 5064 * q^85 - 782 * q^86 - 1940 * q^87 - 4232 * q^88 - 1196 * q^89 + 8030 * q^90 - 4618 * q^92 + 698 * q^93 - 35 * q^94 - 1968 * q^95 - 7926 * q^96 + 3862 * q^97 - 5964 * q^99

Introduction

L-functions

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