LMFDB - Embedded newform 2013.4.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.86674 q^{2} +3.00000 q^{3} +0.218214 q^{4} +1.45116 q^{5} -8.60023 q^{6} +27.7506 q^{7} +22.3084 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.86674 q^{2} +3.00000 q^{3} +0.218214 q^{4} +1.45116 q^{5} -8.60023 q^{6} +27.7506 q^{7} +22.3084 q^{8} +9.00000 q^{9} -4.16011 q^{10} +11.0000 q^{11} +0.654642 q^{12} -1.31157 q^{13} -79.5537 q^{14} +4.35349 q^{15} -65.6981 q^{16} -8.78840 q^{17} -25.8007 q^{18} +115.645 q^{19} +0.316664 q^{20} +83.2517 q^{21} -31.5342 q^{22} +6.76727 q^{23} +66.9251 q^{24} -122.894 q^{25} +3.75993 q^{26} +27.0000 q^{27} +6.05556 q^{28} +183.898 q^{29} -12.4803 q^{30} +258.929 q^{31} +9.87250 q^{32} +33.0000 q^{33} +25.1941 q^{34} +40.2706 q^{35} +1.96393 q^{36} -133.736 q^{37} -331.526 q^{38} -3.93471 q^{39} +32.3731 q^{40} -39.4173 q^{41} -238.661 q^{42} -201.153 q^{43} +2.40035 q^{44} +13.0605 q^{45} -19.4000 q^{46} +379.137 q^{47} -197.094 q^{48} +427.093 q^{49} +352.306 q^{50} -26.3652 q^{51} -0.286203 q^{52} +717.187 q^{53} -77.4021 q^{54} +15.9628 q^{55} +619.070 q^{56} +346.936 q^{57} -527.188 q^{58} -175.605 q^{59} +0.949992 q^{60} -61.0000 q^{61} -742.284 q^{62} +249.755 q^{63} +497.283 q^{64} -1.90330 q^{65} -94.6025 q^{66} +701.944 q^{67} -1.91775 q^{68} +20.3018 q^{69} -115.445 q^{70} -69.3213 q^{71} +200.775 q^{72} +62.7793 q^{73} +383.387 q^{74} -368.682 q^{75} +25.2354 q^{76} +305.256 q^{77} +11.2798 q^{78} -295.626 q^{79} -95.3386 q^{80} +81.0000 q^{81} +112.999 q^{82} +90.5508 q^{83} +18.1667 q^{84} -12.7534 q^{85} +576.655 q^{86} +551.693 q^{87} +245.392 q^{88} -9.22991 q^{89} -37.4410 q^{90} -36.3968 q^{91} +1.47671 q^{92} +776.788 q^{93} -1086.89 q^{94} +167.820 q^{95} +29.6175 q^{96} -984.511 q^{97} -1224.37 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9} + 99 q^{10} + 418 q^{11} + 510 q^{12} + 209 q^{13} + 128 q^{14} + 105 q^{15} + 798 q^{16} + 512 q^{17} + 126 q^{18} + 487 q^{19} + 328 q^{20} + 315 q^{21} + 154 q^{22} + 417 q^{23} + 441 q^{24} + 925 q^{25} + 177 q^{26} + 1026 q^{27} + 902 q^{28} + 626 q^{29} + 297 q^{30} + 300 q^{31} + 1625 q^{32} + 1254 q^{33} - 180 q^{34} + 1086 q^{35} + 1530 q^{36} + 554 q^{37} + 845 q^{38} + 627 q^{39} + 329 q^{40} + 1378 q^{41} + 384 q^{42} + 1979 q^{43} + 1870 q^{44} + 315 q^{45} + 937 q^{46} + 1345 q^{47} + 2394 q^{48} + 2635 q^{49} + 800 q^{50} + 1536 q^{51} + 2006 q^{52} + 1497 q^{53} + 378 q^{54} + 385 q^{55} + 415 q^{56} + 1461 q^{57} + 1241 q^{58} + 2827 q^{59} + 984 q^{60} - 2318 q^{61} + 509 q^{62} + 945 q^{63} + 1003 q^{64} + 2810 q^{65} + 462 q^{66} + 369 q^{67} + 3936 q^{68} + 1251 q^{69} + 922 q^{70} + 965 q^{71} + 1323 q^{72} + 3081 q^{73} + 722 q^{74} + 2775 q^{75} + 2210 q^{76} + 1155 q^{77} + 531 q^{78} + 3795 q^{79} + 3793 q^{80} + 3078 q^{81} - 1678 q^{82} + 3869 q^{83} + 2706 q^{84} + 3553 q^{85} + 3305 q^{86} + 1878 q^{87} + 1617 q^{88} + 2849 q^{89} + 891 q^{90} + 1252 q^{91} + 4519 q^{92} + 900 q^{93} + 340 q^{94} + 1504 q^{95} + 4875 q^{96} + 2562 q^{97} + 6164 q^{98} + 3762 q^{99}+O(q^{100}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9 + 99 * q^10 + 418 * q^11 + 510 * q^12 + 209 * q^13 + 128 * q^14 + 105 * q^15 + 798 * q^16 + 512 * q^17 + 126 * q^18 + 487 * q^19 + 328 * q^20 + 315 * q^21 + 154 * q^22 + 417 * q^23 + 441 * q^24 + 925 * q^25 + 177 * q^26 + 1026 * q^27 + 902 * q^28 + 626 * q^29 + 297 * q^30 + 300 * q^31 + 1625 * q^32 + 1254 * q^33 - 180 * q^34 + 1086 * q^35 + 1530 * q^36 + 554 * q^37 + 845 * q^38 + 627 * q^39 + 329 * q^40 + 1378 * q^41 + 384 * q^42 + 1979 * q^43 + 1870 * q^44 + 315 * q^45 + 937 * q^46 + 1345 * q^47 + 2394 * q^48 + 2635 * q^49 + 800 * q^50 + 1536 * q^51 + 2006 * q^52 + 1497 * q^53 + 378 * q^54 + 385 * q^55 + 415 * q^56 + 1461 * q^57 + 1241 * q^58 + 2827 * q^59 + 984 * q^60 - 2318 * q^61 + 509 * q^62 + 945 * q^63 + 1003 * q^64 + 2810 * q^65 + 462 * q^66 + 369 * q^67 + 3936 * q^68 + 1251 * q^69 + 922 * q^70 + 965 * q^71 + 1323 * q^72 + 3081 * q^73 + 722 * q^74 + 2775 * q^75 + 2210 * q^76 + 1155 * q^77 + 531 * q^78 + 3795 * q^79 + 3793 * q^80 + 3078 * q^81 - 1678 * q^82 + 3869 * q^83 + 2706 * q^84 + 3553 * q^85 + 3305 * q^86 + 1878 * q^87 + 1617 * q^88 + 2849 * q^89 + 891 * q^90 + 1252 * q^91 + 4519 * q^92 + 900 * q^93 + 340 * q^94 + 1504 * q^95 + 4875 * q^96 + 2562 * q^97 + 6164 * q^98 + 3762 * 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 $

$2$	−2.86674	−1.01355	−0.506773	−	0.862079i	$-0.669162\pi$
$2$	−2.86674	−1.01355	−0.506773	+	0.862079i	$0.669162\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	0.218214	0.0272767
$5$	1.45116	0.129796	0.0648980	−	0.997892i	$-0.479328\pi$
$5$	1.45116	0.129796	0.0648980	+	0.997892i	$0.479328\pi$
$6$	−8.60023	−0.585171
$7$	27.7506	1.49839	0.749195	−	0.662350i	$-0.230441\pi$
$7$	27.7506	1.49839	0.749195	+	0.662350i	$0.230441\pi$
$8$	22.3084	0.985900
$9$	9.00000	0.333333
$10$	−4.16011	−0.131554
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0.654642	0.0157482
$13$	−1.31157	−0.0279818	−0.0139909	−	0.999902i	$-0.504454\pi$
$13$	−1.31157	−0.0279818	−0.0139909	+	0.999902i	$0.504454\pi$
$14$	−79.5537	−1.51869
$15$	4.35349	0.0749377
$16$	−65.6981	−1.02653
$17$	−8.78840	−0.125382	−0.0626912	−	0.998033i	$-0.519968\pi$
$17$	−8.78840	−0.125382	−0.0626912	+	0.998033i	$0.519968\pi$
$18$	−25.8007	−0.337849
$19$	115.645	1.39636	0.698181	−	0.715921i	$-0.253993\pi$
$19$	115.645	1.39636	0.698181	+	0.715921i	$0.253993\pi$
$20$	0.316664	0.00354041
$21$	83.2517	0.865095
$22$	−31.5342	−0.305596
$23$	6.76727	0.0613510	0.0306755	−	0.999529i	$-0.490234\pi$
$23$	6.76727	0.0613510	0.0306755	+	0.999529i	$0.490234\pi$
$24$	66.9251	0.569210
$25$	−122.894	−0.983153
$26$	3.75993	0.0283609
$27$	27.0000	0.192450
$28$	6.05556	0.0408712
$29$	183.898	1.17755	0.588775	−	0.808297i	$-0.299610\pi$
$29$	183.898	1.17755	0.588775	+	0.808297i	$0.299610\pi$
$30$	−12.4803	−0.0759529
$31$	258.929	1.50016	0.750082	−	0.661345i	$-0.230014\pi$
$31$	258.929	1.50016	0.750082	+	0.661345i	$0.230014\pi$
$32$	9.87250	0.0545384
$33$	33.0000	0.174078
$34$	25.1941	0.127081
$35$	40.2706	0.194485
$36$	1.96393	0.00909225
$37$	−133.736	−0.594218	−0.297109	−	0.954844i	$-0.596022\pi$
$37$	−133.736	−0.594218	−0.297109	+	0.954844i	$0.596022\pi$
$38$	−331.526	−1.41528
$39$	−3.93471	−0.0161553
$40$	32.3731	0.127966
$41$	−39.4173	−0.150145	−0.0750726	−	0.997178i	$-0.523919\pi$
$41$	−39.4173	−0.150145	−0.0750726	+	0.997178i	$0.523919\pi$
$42$	−238.661	−0.876814
$43$	−201.153	−0.713386	−0.356693	−	0.934222i	$-0.616096\pi$
$43$	−201.153	−0.713386	−0.356693	+	0.934222i	$0.616096\pi$
$44$	2.40035	0.00822425
$45$	13.0605	0.0432653
$46$	−19.4000	−0.0621821
$47$	379.137	1.17666	0.588328	−	0.808622i	$-0.299786\pi$
$47$	379.137	1.17666	0.588328	+	0.808622i	$0.299786\pi$
$48$	−197.094	−0.592669
$49$	427.093	1.24517
$50$	352.306	0.996471
$51$	−26.3652	−0.0723896
$52$	−0.286203	−0.000763253 0
$53$	717.187	1.85874	0.929370	−	0.369150i	$-0.120351\pi$
$53$	717.187	1.85874	0.929370	+	0.369150i	$0.120351\pi$
$54$	−77.4021	−0.195057
$55$	15.9628	0.0391349
$56$	619.070	1.47726
$57$	346.936	0.806190
$58$	−527.188	−1.19350
$59$	−175.605	−0.387488	−0.193744	−	0.981052i	$-0.562063\pi$
$59$	−175.605	−0.387488	−0.193744	+	0.981052i	$0.562063\pi$
$60$	0.949992	0.00204406
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−742.284	−1.52049
$63$	249.755	0.499463
$64$	497.283	0.971256
$65$	−1.90330	−0.00363193
$66$	−94.6025	−0.176436
$67$	701.944	1.27994	0.639971	−	0.768399i	$-0.278946\pi$
$67$	701.944	1.27994	0.639971	+	0.768399i	$0.278946\pi$
$68$	−1.91775	−0.00342002
$69$	20.3018	0.0354210
$70$	−115.445	−0.197119
$71$	−69.3213	−0.115872	−0.0579361	−	0.998320i	$-0.518452\pi$
$71$	−69.3213	−0.115872	−0.0579361	+	0.998320i	$0.518452\pi$
$72$	200.775	0.328633
$73$	62.7793	0.100654	0.0503271	−	0.998733i	$-0.483974\pi$
$73$	62.7793	0.100654	0.0503271	+	0.998733i	$0.483974\pi$
$74$	383.387	0.602267
$75$	−368.682	−0.567624
$76$	25.2354	0.0380882
$77$	305.256	0.451781
$78$	11.2798	0.0163742
$79$	−295.626	−0.421019	−0.210510	−	0.977592i	$-0.567512\pi$
$79$	−295.626	−0.421019	−0.210510	+	0.977592i	$0.567512\pi$
$80$	−95.3386	−0.133240
$81$	81.0000	0.111111
$82$	112.999	0.152179
$83$	90.5508	0.119750	0.0598749	−	0.998206i	$-0.480930\pi$
$83$	90.5508	0.119750	0.0598749	+	0.998206i	$0.480930\pi$
$84$	18.1667	0.0235970
$85$	−12.7534	−0.0162741
$86$	576.655	0.723050
$87$	551.693	0.679859
$88$	245.392	0.297260
$89$	−9.22991	−0.0109929	−0.00549645	−	0.999985i	$-0.501750\pi$
$89$	−9.22991	−0.0109929	−0.00549645	+	0.999985i	$0.501750\pi$
$90$	−37.4410	−0.0438514
$91$	−36.3968	−0.0419277
$92$	1.47671	0.00167345
$93$	776.788	0.866120
$94$	−1086.89	−1.19260
$95$	167.820	0.181242
$96$	29.6175	0.0314878
$97$	−984.511	−1.03054	−0.515268	−	0.857029i	$-0.672308\pi$
$97$	−984.511	−1.03054	−0.515268	+	0.857029i	$0.672308\pi$
$98$	−1224.37	−1.26204
$99$	99.0000	0.100504
$100$	−26.8172	−0.0268172
$101$	−1412.41	−1.39149	−0.695744	−	0.718290i	$-0.744925\pi$
$101$	−1412.41	−1.39149	−0.695744	+	0.718290i	$0.744925\pi$
$102$	75.5823	0.0733702
$103$	311.680	0.298163	0.149081	−	0.988825i	$-0.452368\pi$
$103$	311.680	0.298163	0.149081	+	0.988825i	$0.452368\pi$
$104$	−29.2590	−0.0275873
$105$	120.812	0.112286
$106$	−2055.99	−1.88392
$107$	−796.649	−0.719766	−0.359883	−	0.932997i	$-0.617183\pi$
$107$	−796.649	−0.719766	−0.359883	+	0.932997i	$0.617183\pi$
$108$	5.89178	0.00524941
$109$	−664.106	−0.583577	−0.291788	−	0.956483i	$-0.594250\pi$
$109$	−664.106	−0.583577	−0.291788	+	0.956483i	$0.594250\pi$
$110$	−45.7612	−0.0396651
$111$	−401.208	−0.343072
$112$	−1823.16	−1.53815
$113$	93.1230	0.0775246	0.0387623	−	0.999248i	$-0.487658\pi$
$113$	93.1230	0.0775246	0.0387623	+	0.999248i	$0.487658\pi$
$114$	−994.577	−0.817111
$115$	9.82040	0.00796311
$116$	40.1290	0.0321197
$117$	−11.8041	−0.00932728
$118$	503.414	0.392737
$119$	−243.883	−0.187872
$120$	97.1193	0.0738811
$121$	121.000	0.0909091
$122$	174.871	0.129771
$123$	−118.252	−0.0866864
$124$	56.5020	0.0409196
$125$	−359.735	−0.257405
$126$	−715.983	−0.506229
$127$	−163.395	−0.114165	−0.0570824	−	0.998369i	$-0.518180\pi$
$127$	−163.395	−0.114165	−0.0570824	+	0.998369i	$0.518180\pi$
$128$	−1504.56	−1.03895
$129$	−603.460	−0.411873
$130$	5.45627	0.00368113
$131$	71.9114	0.0479613	0.0239807	−	0.999712i	$-0.492366\pi$
$131$	71.9114	0.0479613	0.0239807	+	0.999712i	$0.492366\pi$
$132$	7.20106	0.00474827
$133$	3209.23	2.09229
$134$	−2012.29	−1.29728
$135$	39.1814	0.0249792
$136$	−196.055	−0.123615
$137$	1366.00	0.851863	0.425931	−	0.904755i	$-0.359947\pi$
$137$	1366.00	0.851863	0.425931	+	0.904755i	$0.359947\pi$
$138$	−58.2000	−0.0359008
$139$	−383.224	−0.233846	−0.116923	−	0.993141i	$-0.537303\pi$
$139$	−383.224	−0.233846	−0.116923	+	0.993141i	$0.537303\pi$
$140$	8.78760	0.00530491
$141$	1137.41	0.679343
$142$	198.726	0.117442
$143$	−14.4273	−0.00843684
$144$	−591.283	−0.342178
$145$	266.866	0.152841
$146$	−179.972	−0.102018
$147$	1281.28	0.718899
$148$	−29.1830	−0.0162083
$149$	604.953	0.332615	0.166308	−	0.986074i	$-0.446816\pi$
$149$	604.953	0.332615	0.166308	+	0.986074i	$0.446816\pi$
$150$	1056.92	0.575313
$151$	672.431	0.362395	0.181197	−	0.983447i	$-0.442003\pi$
$151$	672.431	0.362395	0.181197	+	0.983447i	$0.442003\pi$
$152$	2579.86	1.37667
$153$	−79.0956	−0.0417941
$154$	−875.091	−0.457901
$155$	375.749	0.194715
$156$	−0.858608	−0.000440664 0
$157$	−2311.18	−1.17485	−0.587426	−	0.809278i	$-0.699859\pi$
$157$	−2311.18	−1.17485	−0.587426	+	0.809278i	$0.699859\pi$
$158$	847.483	0.426722
$159$	2151.56	1.07314
$160$	14.3266	0.00707886
$161$	187.795	0.0919276
$162$	−232.206	−0.112616
$163$	−1304.87	−0.627026	−0.313513	−	0.949584i	$-0.601506\pi$
$163$	−1304.87	−0.627026	−0.313513	+	0.949584i	$0.601506\pi$
$164$	−8.60141	−0.00409547
$165$	47.8884	0.0225946
$166$	−259.586	−0.121372
$167$	2937.07	1.36094	0.680470	−	0.732776i	$-0.261776\pi$
$167$	2937.07	1.36094	0.680470	+	0.732776i	$0.261776\pi$
$168$	1857.21	0.852898
$169$	−2195.28	−0.999217
$170$	36.5607	0.0164946
$171$	1040.81	0.465454
$172$	−43.8944	−0.0194588
$173$	94.6705	0.0416050	0.0208025	−	0.999784i	$-0.493378\pi$
$173$	94.6705	0.0416050	0.0208025	+	0.999784i	$0.493378\pi$
$174$	−1581.56	−0.689069
$175$	−3410.38	−1.47315
$176$	−722.679	−0.309511
$177$	−526.815	−0.223716
$178$	26.4598	0.0111418
$179$	−3742.69	−1.56280	−0.781401	−	0.624030i	$-0.785494\pi$
$179$	−3742.69	−1.56280	−0.781401	+	0.624030i	$0.785494\pi$
$180$	2.84997	0.00118014
$181$	4228.96	1.73666	0.868332	−	0.495983i	$-0.165192\pi$
$181$	4228.96	1.73666	0.868332	+	0.495983i	$0.165192\pi$
$182$	104.340	0.0424957
$183$	−183.000	−0.0739221
$184$	150.967	0.0604859
$185$	−194.073	−0.0771270
$186$	−2226.85	−0.877853
$187$	−96.6724	−0.0378042
$188$	82.7330	0.0320953
$189$	749.265	0.288365
$190$	−481.098	−0.183697
$191$	1735.33	0.657405	0.328703	−	0.944433i	$-0.393389\pi$
$191$	1735.33	0.657405	0.328703	+	0.944433i	$0.393389\pi$
$192$	1491.85	0.560755
$193$	−704.917	−0.262907	−0.131453	−	0.991322i	$-0.541964\pi$
$193$	−704.917	−0.262907	−0.131453	+	0.991322i	$0.541964\pi$
$194$	2822.34	1.04450
$195$	−5.70990	−0.00209689
$196$	93.1977	0.0339642
$197$	1398.44	0.505758	0.252879	−	0.967498i	$-0.418622\pi$
$197$	1398.44	0.505758	0.252879	+	0.967498i	$0.418622\pi$
$198$	−283.808	−0.101865
$199$	−4915.30	−1.75094	−0.875468	−	0.483277i	$-0.839446\pi$
$199$	−4915.30	−1.75094	−0.875468	+	0.483277i	$0.839446\pi$
$200$	−2741.57	−0.969291
$201$	2105.83	0.738975
$202$	4049.02	1.41034
$203$	5103.26	1.76443
$204$	−5.75325	−0.00197455
$205$	−57.2010	−0.0194882
$206$	−893.507	−0.302202
$207$	60.9054	0.0204503
$208$	86.1676	0.0287243
$209$	1272.10	0.421019
$210$	−346.336	−0.113807
$211$	−3614.30	−1.17923	−0.589617	−	0.807683i	$-0.700721\pi$
$211$	−3614.30	−1.17923	−0.589617	+	0.807683i	$0.700721\pi$
$212$	156.500	0.0507004
$213$	−207.964	−0.0668988
$214$	2283.79	0.729516
$215$	−291.906	−0.0925945
$216$	602.326	0.189737
$217$	7185.44	2.24783
$218$	1903.82	0.591482
$219$	188.338	0.0581128
$220$	3.48330	0.00106747
$221$	11.5266	0.00350843
$222$	1150.16	0.347719
$223$	−316.776	−0.0951251	−0.0475626	−	0.998868i	$-0.515145\pi$
$223$	−316.776	−0.0951251	−0.0475626	+	0.998868i	$0.515145\pi$
$224$	273.967	0.0817197
$225$	−1106.05	−0.327718
$226$	−266.960	−0.0785748
$227$	−1172.89	−0.342941	−0.171471	−	0.985189i	$-0.554852\pi$
$227$	−1172.89	−0.342941	−0.171471	+	0.985189i	$0.554852\pi$
$228$	75.7063	0.0219902
$229$	4569.17	1.31851	0.659256	−	0.751919i	$-0.270871\pi$
$229$	4569.17	1.31851	0.659256	+	0.751919i	$0.270871\pi$
$230$	−28.1526	−0.00807098
$231$	915.768	0.260836
$232$	4102.46	1.16095
$233$	−4143.02	−1.16489	−0.582443	−	0.812871i	$-0.697903\pi$
$233$	−4143.02	−1.16489	−0.582443	+	0.812871i	$0.697903\pi$
$234$	33.8394	0.00945363
$235$	550.190	0.152725
$236$	−38.3194	−0.0105694
$237$	−886.877	−0.243075
$238$	699.150	0.190417
$239$	2405.27	0.650979	0.325490	−	0.945546i	$-0.394471\pi$
$239$	2405.27	0.650979	0.325490	+	0.945546i	$0.394471\pi$
$240$	−286.016	−0.0769260
$241$	4194.87	1.12123	0.560613	−	0.828078i	$-0.310566\pi$
$241$	4194.87	1.12123	0.560613	+	0.828078i	$0.310566\pi$
$242$	−346.876	−0.0921406
$243$	243.000	0.0641500
$244$	−13.3110	−0.00349243
$245$	619.782	0.161618
$246$	338.998	0.0878607
$247$	−151.677	−0.0390728
$248$	5776.30	1.47901
$249$	271.652	0.0691376
$250$	1031.27	0.260892
$251$	4897.55	1.23160	0.615798	−	0.787904i	$-0.288834\pi$
$251$	4897.55	1.23160	0.615798	+	0.787904i	$0.288834\pi$
$252$	54.5000	0.0136237
$253$	74.4399	0.0184980
$254$	468.410	0.115711
$255$	−38.2602	−0.00939587
$256$	334.929	0.0817699
$257$	838.254	0.203459	0.101729	−	0.994812i	$-0.467562\pi$
$257$	838.254	0.203459	0.101729	+	0.994812i	$0.467562\pi$
$258$	1729.96	0.417453
$259$	−3711.25	−0.890369
$260$	−0.415327	−9.90672e−5 0
$261$	1655.08	0.392517
$262$	−206.152	−0.0486110
$263$	3487.44	0.817661	0.408831	−	0.912610i	$-0.365937\pi$
$263$	3487.44	0.817661	0.408831	+	0.912610i	$0.365937\pi$
$264$	736.176	0.171623
$265$	1040.75	0.241257
$266$	−9200.02	−2.12064
$267$	−27.6897	−0.00634676
$268$	153.174	0.0349127
$269$	4524.80	1.02558	0.512792	−	0.858513i	$-0.328611\pi$
$269$	4524.80	1.02558	0.512792	+	0.858513i	$0.328611\pi$
$270$	−112.323	−0.0253176
$271$	−87.5083	−0.0196153	−0.00980766	−	0.999952i	$-0.503122\pi$
$271$	−87.5083	−0.0196153	−0.00980766	+	0.999952i	$0.503122\pi$
$272$	577.381	0.128709
$273$	−109.190	−0.0242070
$274$	−3915.97	−0.863403
$275$	−1351.84	−0.296432
$276$	4.43013	0.000966169 0
$277$	2932.59	0.636109	0.318054	−	0.948072i	$-0.396971\pi$
$277$	2932.59	0.636109	0.318054	+	0.948072i	$0.396971\pi$
$278$	1098.60	0.237014
$279$	2330.36	0.500055
$280$	898.371	0.191743
$281$	−1767.27	−0.375183	−0.187592	−	0.982247i	$-0.560068\pi$
$281$	−1767.27	−0.375183	−0.187592	+	0.982247i	$0.560068\pi$
$282$	−3260.67	−0.688546
$283$	−6761.29	−1.42020	−0.710100	−	0.704101i	$-0.751350\pi$
$283$	−6761.29	−1.42020	−0.710100	+	0.704101i	$0.751350\pi$
$284$	−15.1269	−0.00316061
$285$	503.461	0.104640
$286$	41.3593	0.00855113
$287$	−1093.85	−0.224976
$288$	88.8525	0.0181795
$289$	−4835.76	−0.984279
$290$	−765.035	−0.154912
$291$	−2953.53	−0.594980
$292$	13.6993	0.00274552
$293$	3650.46	0.727857	0.363928	−	0.931427i	$-0.381435\pi$
$293$	3650.46	0.727857	0.363928	+	0.931427i	$0.381435\pi$
$294$	−3673.10	−0.728638
$295$	−254.831	−0.0502944
$296$	−2983.43	−0.585839
$297$	297.000	0.0580259
$298$	−1734.24	−0.337121
$299$	−8.87574	−0.00171671
$300$	−80.4516	−0.0154829
$301$	−5582.11	−1.06893
$302$	−1927.69	−0.367304
$303$	−4237.24	−0.803376
$304$	−7597.69	−1.43341
$305$	−88.5209	−0.0166187
$306$	226.747	0.0423603
$307$	−248.920	−0.0462755	−0.0231378	−	0.999732i	$-0.507366\pi$
$307$	−248.920	−0.0462755	−0.0231378	+	0.999732i	$0.507366\pi$
$308$	66.6111	0.0123231
$309$	935.041	0.172144
$310$	−1077.17	−0.197353
$311$	−4439.30	−0.809420	−0.404710	−	0.914445i	$-0.632628\pi$
$311$	−4439.30	−0.809420	−0.404710	+	0.914445i	$0.632628\pi$
$312$	−87.7770	−0.0159275
$313$	−2539.65	−0.458625	−0.229313	−	0.973353i	$-0.573648\pi$
$313$	−2539.65	−0.458625	−0.229313	+	0.973353i	$0.573648\pi$
$314$	6625.55	1.19077
$315$	362.435	0.0648283
$316$	−64.5097	−0.0114840
$317$	2180.19	0.386283	0.193142	−	0.981171i	$-0.438132\pi$
$317$	2180.19	0.386283	0.193142	+	0.981171i	$0.438132\pi$
$318$	−6167.97	−1.08768
$319$	2022.88	0.355045
$320$	721.638	0.126065
$321$	−2389.95	−0.415557
$322$	−538.361	−0.0931729
$323$	−1016.34	−0.175079
$324$	17.6753	0.00303075
$325$	161.184	0.0275104
$326$	3740.73	0.635520
$327$	−1992.32	−0.336928
$328$	−879.337	−0.148028
$329$	10521.3	1.76309
$330$	−137.284	−0.0229007
$331$	837.131	0.139012	0.0695059	−	0.997582i	$-0.477858\pi$
$331$	837.131	0.139012	0.0695059	+	0.997582i	$0.477858\pi$
$332$	19.7594	0.00326639
$333$	−1203.62	−0.198073
$334$	−8419.82	−1.37938
$335$	1018.64	0.166131
$336$	−5469.48	−0.888049
$337$	665.362	0.107551	0.0537754	−	0.998553i	$-0.482875\pi$
$337$	665.362	0.107551	0.0537754	+	0.998553i	$0.482875\pi$
$338$	6293.30	1.01275
$339$	279.369	0.0447588
$340$	−2.78297	−0.000443905 0
$341$	2848.22	0.452317
$342$	−2983.73	−0.471760
$343$	2333.63	0.367360
$344$	−4487.40	−0.703327
$345$	29.4612	0.00459750
$346$	−271.396	−0.0421686
$347$	8438.88	1.30554	0.652771	−	0.757555i	$-0.273606\pi$
$347$	8438.88	1.30554	0.652771	+	0.757555i	$0.273606\pi$
$348$	120.387	0.0185443
$349$	4342.83	0.666093	0.333046	−	0.942910i	$-0.391923\pi$
$349$	4342.83	0.666093	0.333046	+	0.942910i	$0.391923\pi$
$350$	9776.68	1.49310
$351$	−35.4124	−0.00538511
$352$	108.598	0.0164439
$353$	8917.54	1.34457	0.672285	−	0.740293i	$-0.265313\pi$
$353$	8917.54	1.34457	0.672285	+	0.740293i	$0.265313\pi$
$354$	1510.24	0.226747
$355$	−100.596	−0.0150397
$356$	−2.01410	−0.000299851 0
$357$	−731.649	−0.108468
$358$	10729.3	1.58397
$359$	1884.08	0.276986	0.138493	−	0.990363i	$-0.455774\pi$
$359$	1884.08	0.276986	0.138493	+	0.990363i	$0.455774\pi$
$360$	291.358	0.0426553
$361$	6514.87	0.949829
$362$	−12123.3	−1.76019
$363$	363.000	0.0524864
$364$	−7.94228	−0.00114365
$365$	91.1030	0.0130645
$366$	524.614	0.0749235
$367$	−3148.28	−0.447789	−0.223895	−	0.974613i	$-0.571877\pi$
$367$	−3148.28	−0.447789	−0.223895	+	0.974613i	$0.571877\pi$
$368$	−444.596	−0.0629788
$369$	−354.756	−0.0500484
$370$	556.356	0.0781718
$371$	19902.3	2.78512
$372$	169.506	0.0236249
$373$	3101.21	0.430495	0.215247	−	0.976560i	$-0.430944\pi$
$373$	3101.21	0.430495	0.215247	+	0.976560i	$0.430944\pi$
$374$	277.135	0.0383163
$375$	−1079.20	−0.148613
$376$	8457.94	1.16007
$377$	−241.195	−0.0329500
$378$	−2147.95	−0.292271
$379$	−3752.21	−0.508543	−0.254272	−	0.967133i	$-0.581836\pi$
$379$	−3752.21	−0.508543	−0.254272	+	0.967133i	$0.581836\pi$
$380$	36.6207	0.00494370
$381$	−490.184	−0.0659131
$382$	−4974.76	−0.666311
$383$	−5819.70	−0.776430	−0.388215	−	0.921569i	$-0.626908\pi$
$383$	−5819.70	−0.776430	−0.388215	+	0.921569i	$0.626908\pi$
$384$	−4513.69	−0.599839
$385$	442.976	0.0586394
$386$	2020.81	0.266468
$387$	−1810.38	−0.237795
$388$	−214.834	−0.0281097
$389$	10812.9	1.40935	0.704673	−	0.709532i	$-0.251094\pi$
$389$	10812.9	1.40935	0.704673	+	0.709532i	$0.251094\pi$
$390$	16.3688	0.00212530
$391$	−59.4734	−0.00769233
$392$	9527.76	1.22761
$393$	215.734	0.0276905
$394$	−4008.96	−0.512610
$395$	−429.001	−0.0546466
$396$	21.6032	0.00274142
$397$	−7377.14	−0.932615	−0.466308	−	0.884623i	$-0.654416\pi$
$397$	−7377.14	−0.932615	−0.466308	+	0.884623i	$0.654416\pi$
$398$	14090.9	1.77465
$399$	9627.68	1.20799
$400$	8073.91	1.00924
$401$	6369.78	0.793245	0.396623	−	0.917982i	$-0.370182\pi$
$401$	6369.78	0.793245	0.396623	+	0.917982i	$0.370182\pi$
$402$	−6036.88	−0.748986
$403$	−339.604	−0.0419774
$404$	−308.208	−0.0379552
$405$	117.544	0.0144218
$406$	−14629.7	−1.78833
$407$	−1471.10	−0.179163
$408$	−588.165	−0.0713689
$409$	−1412.16	−0.170726	−0.0853629	−	0.996350i	$-0.527205\pi$
$409$	−1412.16	−0.170726	−0.0853629	+	0.996350i	$0.527205\pi$
$410$	163.980	0.0197522
$411$	4098.00	0.491823
$412$	68.0129	0.00813291
$413$	−4873.13	−0.580608
$414$	−174.600	−0.0207274
$415$	131.404	0.0155430
$416$	−12.9485	−0.00152608
$417$	−1149.67	−0.135011
$418$	−3646.78	−0.426723
$419$	−3439.55	−0.401034	−0.200517	−	0.979690i	$-0.564262\pi$
$419$	−3439.55	−0.401034	−0.200517	+	0.979690i	$0.564262\pi$
$420$	26.3628	0.00306279
$421$	−4524.18	−0.523741	−0.261871	−	0.965103i	$-0.584339\pi$
$421$	−4524.18	−0.523741	−0.261871	+	0.965103i	$0.584339\pi$
$422$	10361.3	1.19521
$423$	3412.23	0.392219
$424$	15999.3	1.83253
$425$	1080.04	0.123270
$426$	596.179	0.0678051
$427$	−1692.78	−0.191849
$428$	−173.840	−0.0196329
$429$	−43.2818	−0.00487101
$430$	836.820	0.0938489
$431$	2834.35	0.316765	0.158382	−	0.987378i	$-0.449372\pi$
$431$	2834.35	0.316765	0.158382	+	0.987378i	$0.449372\pi$
$432$	−1773.85	−0.197556
$433$	−559.886	−0.0621395	−0.0310697	−	0.999517i	$-0.509891\pi$
$433$	−559.886	−0.0621395	−0.0310697	+	0.999517i	$0.509891\pi$
$434$	−20598.8	−2.27828
$435$	800.597	0.0882429
$436$	−144.917	−0.0159181
$437$	782.604	0.0856682
$438$	−539.916	−0.0589000
$439$	13145.3	1.42914	0.714570	−	0.699564i	$-0.246622\pi$
$439$	13145.3	1.42914	0.714570	+	0.699564i	$0.246622\pi$
$440$	356.104	0.0385832
$441$	3843.84	0.415057
$442$	−33.0438	−0.00355596
$443$	7231.35	0.775558	0.387779	−	0.921752i	$-0.373242\pi$
$443$	7231.35	0.775558	0.387779	+	0.921752i	$0.373242\pi$
$444$	−87.5491	−0.00935788
$445$	−13.3941	−0.00142683
$446$	908.116	0.0964137
$447$	1814.86	0.192035
$448$	13799.9	1.45532
$449$	−12063.0	−1.26790	−0.633952	−	0.773372i	$-0.718568\pi$
$449$	−12063.0	−1.26790	−0.633952	+	0.773372i	$0.718568\pi$
$450$	3170.75	0.332157
$451$	−433.591	−0.0452705
$452$	20.3207	0.00211462
$453$	2017.29	0.209229
$454$	3362.38	0.347587
$455$	−52.8176	−0.00544204
$456$	7739.59	0.794823
$457$	12556.0	1.28522	0.642611	−	0.766193i	$-0.277851\pi$
$457$	12556.0	1.28522	0.642611	+	0.766193i	$0.277851\pi$
$458$	−13098.6	−1.33637
$459$	−237.287	−0.0241299
$460$	2.14295	0.000217208 0
$461$	10363.2	1.04699	0.523496	−	0.852028i	$-0.324628\pi$
$461$	10363.2	1.04699	0.523496	+	0.852028i	$0.324628\pi$
$462$	−2625.27	−0.264370
$463$	−6194.16	−0.621743	−0.310872	−	0.950452i	$-0.600621\pi$
$463$	−6194.16	−0.621743	−0.310872	+	0.950452i	$0.600621\pi$
$464$	−12081.7	−1.20879
$465$	1127.25	0.112419
$466$	11877.0	1.18067
$467$	−5628.88	−0.557759	−0.278880	−	0.960326i	$-0.589963\pi$
$467$	−5628.88	−0.557759	−0.278880	+	0.960326i	$0.589963\pi$
$468$	−2.57582	−0.000254418 0
$469$	19479.3	1.91785
$470$	−1577.25	−0.154794
$471$	−6933.53	−0.678302
$472$	−3917.46	−0.382025
$473$	−2212.69	−0.215094
$474$	2542.45	0.246368
$475$	−14212.1	−1.37284
$476$	−53.2187	−0.00512452
$477$	6454.68	0.619580
$478$	−6895.29	−0.659798
$479$	8959.65	0.854649	0.427324	−	0.904098i	$-0.359456\pi$
$479$	8959.65	0.854649	0.427324	+	0.904098i	$0.359456\pi$
$480$	42.9798	0.00408698
$481$	175.404	0.0166273
$482$	−12025.6	−1.13641
$483$	563.386	0.0530744
$484$	26.4039	0.00247970
$485$	−1428.69	−0.133759
$486$	−696.618	−0.0650190
$487$	17307.0	1.61038	0.805190	−	0.593017i	$-0.202063\pi$
$487$	17307.0	1.61038	0.805190	+	0.593017i	$0.202063\pi$
$488$	−1360.81	−0.126232
$489$	−3914.61	−0.362014
$490$	−1776.75	−0.163807
$491$	−5236.21	−0.481276	−0.240638	−	0.970615i	$-0.577357\pi$
$491$	−5236.21	−0.481276	−0.240638	+	0.970615i	$0.577357\pi$
$492$	−25.8042	−0.00236452
$493$	−1616.17	−0.147644
$494$	434.819	0.0396021
$495$	143.665	0.0130450
$496$	−17011.2	−1.53997
$497$	−1923.70	−0.173622
$498$	−778.757	−0.0700742
$499$	15606.0	1.40004	0.700019	−	0.714124i	$-0.253175\pi$
$499$	15606.0	1.40004	0.700019	+	0.714124i	$0.253175\pi$
$500$	−78.4991	−0.00702117
$501$	8811.20	0.785739
$502$	−14040.0	−1.24828
$503$	11027.0	0.977476	0.488738	−	0.872431i	$-0.337457\pi$
$503$	11027.0	0.977476	0.488738	+	0.872431i	$0.337457\pi$
$504$	5571.63	0.492421
$505$	−2049.64	−0.180609
$506$	−213.400	−0.0187486
$507$	−6585.84	−0.576898
$508$	−35.6550	−0.00311404
$509$	12486.1	1.08730	0.543651	−	0.839311i	$-0.317041\pi$
$509$	12486.1	1.08730	0.543651	+	0.839311i	$0.317041\pi$
$510$	109.682	0.00952315
$511$	1742.16	0.150819
$512$	11076.3	0.956074
$513$	3122.43	0.268730
$514$	−2403.06	−0.206215
$515$	452.299	0.0387003
$516$	−131.683	−0.0112346
$517$	4170.51	0.354775
$518$	10639.2	0.902431
$519$	284.012	0.0240207
$520$	−42.4595	−0.00358072
$521$	8054.07	0.677265	0.338633	−	0.940919i	$-0.390036\pi$
$521$	8054.07	0.677265	0.338633	+	0.940919i	$0.390036\pi$
$522$	−4744.69	−0.397834
$523$	−595.598	−0.0497967	−0.0248984	−	0.999690i	$-0.507926\pi$
$523$	−595.598	−0.0497967	−0.0248984	+	0.999690i	$0.507926\pi$
$524$	15.6921	0.00130823
$525$	−10231.1	−0.850521
$526$	−9997.60	−0.828738
$527$	−2275.58	−0.188094
$528$	−2168.04	−0.178696
$529$	−12121.2	−0.996236
$530$	−2983.58	−0.244525
$531$	−1580.44	−0.129163
$532$	700.298	0.0570710
$533$	51.6986	0.00420134
$534$	79.3794	0.00643274
$535$	−1156.07	−0.0934227
$536$	15659.2	1.26190
$537$	−11228.1	−0.902284
$538$	−12971.4	−1.03948
$539$	4698.03	0.375433
$540$	8.54992	0.000681352 0
$541$	3865.96	0.307228	0.153614	−	0.988131i	$-0.450909\pi$
$541$	3865.96	0.307228	0.153614	+	0.988131i	$0.450909\pi$
$542$	250.864	0.0198810
$543$	12686.9	1.00266
$544$	−86.7635	−0.00683815
$545$	−963.726	−0.0757459
$546$	313.021	0.0245349
$547$	−2556.04	−0.199796	−0.0998980	−	0.994998i	$-0.531852\pi$
$547$	−2556.04	−0.199796	−0.0998980	+	0.994998i	$0.531852\pi$
$548$	298.080	0.0232360
$549$	−549.000	−0.0426790
$550$	3875.36	0.300447
$551$	21266.9	1.64429
$552$	452.900	0.0349216
$553$	−8203.78	−0.630850
$554$	−8406.98	−0.644726
$555$	−582.218	−0.0445293
$556$	−83.6248	−0.00637857
$557$	−8348.92	−0.635108	−0.317554	−	0.948240i	$-0.602861\pi$
$557$	−8348.92	−0.635108	−0.317554	+	0.948240i	$0.602861\pi$
$558$	−6680.56	−0.506829
$559$	263.826	0.0199618
$560$	−2645.70	−0.199645
$561$	−290.017	−0.0218263
$562$	5066.31	0.380266
$563$	22504.1	1.68461	0.842304	−	0.539003i	$-0.181199\pi$
$563$	22504.1	1.68461	0.842304	+	0.539003i	$0.181199\pi$
$564$	248.199	0.0185303
$565$	135.137	0.0100624
$566$	19382.9	1.43944
$567$	2247.79	0.166488
$568$	−1546.45	−0.114238
$569$	15203.8	1.12017	0.560084	−	0.828436i	$-0.310769\pi$
$569$	15203.8	1.12017	0.560084	+	0.828436i	$0.310769\pi$
$570$	−1443.29	−0.106058
$571$	−12291.6	−0.900852	−0.450426	−	0.892814i	$-0.648728\pi$
$571$	−12291.6	−0.900852	−0.450426	+	0.892814i	$0.648728\pi$
$572$	−3.14823	−0.000230130 0
$573$	5206.00	0.379553
$574$	3135.79	0.228024
$575$	−831.657	−0.0603174
$576$	4475.55	0.323752
$577$	16615.8	1.19883	0.599414	−	0.800439i	$-0.295400\pi$
$577$	16615.8	1.19883	0.599414	+	0.800439i	$0.295400\pi$
$578$	13862.9	0.997613
$579$	−2114.75	−0.151789
$580$	58.2338	0.00416901
$581$	2512.83	0.179432
$582$	8467.02	0.603040
$583$	7889.06	0.560431
$584$	1400.50	0.0992351
$585$	−17.1297	−0.00121064
$586$	−10464.9	−0.737717
$587$	6780.11	0.476738	0.238369	−	0.971175i	$-0.423387\pi$
$587$	6780.11	0.476738	0.238369	+	0.971175i	$0.423387\pi$
$588$	279.593	0.0196092
$589$	29944.0	2.09477
$590$	730.535	0.0509757
$591$	4195.31	0.292000
$592$	8786.20	0.609984
$593$	−24709.4	−1.71112	−0.855559	−	0.517706i	$-0.826786\pi$
$593$	−24709.4	−1.71112	−0.855559	+	0.517706i	$0.826786\pi$
$594$	−851.423	−0.0588119
$595$	−353.914	−0.0243850
$596$	132.009	0.00907266
$597$	−14745.9	−1.01090
$598$	25.4445	0.00173997
$599$	16842.4	1.14885	0.574424	−	0.818558i	$-0.305226\pi$
$599$	16842.4	1.14885	0.574424	+	0.818558i	$0.305226\pi$
$600$	−8224.71	−0.559620
$601$	−105.145	−0.00713636	−0.00356818	−	0.999994i	$-0.501136\pi$
$601$	−105.145	−0.00713636	−0.00356818	+	0.999994i	$0.501136\pi$
$602$	16002.5	1.08341
$603$	6317.50	0.426648
$604$	146.734	0.00988495
$605$	175.591	0.0117996
$606$	12147.1	0.814259
$607$	−7966.40	−0.532695	−0.266348	−	0.963877i	$-0.585817\pi$
$607$	−7966.40	−0.532695	−0.266348	+	0.963877i	$0.585817\pi$
$608$	1141.71	0.0761554
$609$	15309.8	1.01869
$610$	253.767	0.0168438
$611$	−497.265	−0.0329250
$612$	−17.2598	−0.00114001
$613$	−9929.09	−0.654213	−0.327106	−	0.944988i	$-0.606074\pi$
$613$	−9929.09	−0.654213	−0.327106	+	0.944988i	$0.606074\pi$
$614$	713.588	0.0469024
$615$	−171.603	−0.0112515
$616$	6809.77	0.445411
$617$	−13894.7	−0.906611	−0.453305	−	0.891355i	$-0.649755\pi$
$617$	−13894.7	−0.906611	−0.453305	+	0.891355i	$0.649755\pi$
$618$	−2680.52	−0.174476
$619$	−7902.12	−0.513107	−0.256553	−	0.966530i	$-0.582587\pi$
$619$	−7902.12	−0.513107	−0.256553	+	0.966530i	$0.582587\pi$
$620$	81.9936	0.00531120
$621$	182.716	0.0118070
$622$	12726.3	0.820385
$623$	−256.135	−0.0164717
$624$	258.503	0.0165840
$625$	14839.7	0.949743
$626$	7280.54	0.464838
$627$	3816.30	0.243076
$628$	−504.331	−0.0320461
$629$	1175.33	0.0745044
$630$	−1039.01	−0.0657065
$631$	−538.908	−0.0339994	−0.0169997	−	0.999855i	$-0.505411\pi$
$631$	−538.908	−0.0339994	−0.0169997	+	0.999855i	$0.505411\pi$
$632$	−6594.93	−0.415083
$633$	−10842.9	−0.680831
$634$	−6250.05	−0.391516
$635$	−237.112	−0.0148181
$636$	469.501	0.0292719
$637$	−560.162	−0.0348421
$638$	−5799.06	−0.359854
$639$	−623.892	−0.0386241
$640$	−2183.36	−0.134852
$641$	6914.98	0.426092	0.213046	−	0.977042i	$-0.431662\pi$
$641$	6914.98	0.426092	0.213046	+	0.977042i	$0.431662\pi$
$642$	6851.36	0.421186
$643$	−25275.2	−1.55016	−0.775082	−	0.631861i	$-0.782292\pi$
$643$	−25275.2	−1.55016	−0.775082	+	0.631861i	$0.782292\pi$
$644$	40.9796	0.00250749
$645$	−875.718	−0.0534595
$646$	2913.58	0.177451
$647$	−27702.0	−1.68328	−0.841638	−	0.540043i	$-0.818408\pi$
$647$	−27702.0	−1.68328	−0.841638	+	0.540043i	$0.818408\pi$
$648$	1806.98	0.109544
$649$	−1931.65	−0.116832
$650$	−462.074	−0.0278831
$651$	21556.3	1.29779
$652$	−284.741	−0.0171032
$653$	−13618.4	−0.816123	−0.408062	−	0.912954i	$-0.633795\pi$
$653$	−13618.4	−0.816123	−0.408062	+	0.912954i	$0.633795\pi$
$654$	5711.47	0.341492
$655$	104.355	0.00622518
$656$	2589.64	0.154129
$657$	565.014	0.0335514
$658$	−30161.8	−1.78697
$659$	21493.3	1.27050	0.635252	−	0.772305i	$-0.280896\pi$
$659$	21493.3	1.27050	0.635252	+	0.772305i	$0.280896\pi$
$660$	10.4499	0.000616306 0
$661$	−17182.0	−1.01105	−0.505525	−	0.862812i	$-0.668701\pi$
$661$	−17182.0	−1.01105	−0.505525	+	0.862812i	$0.668701\pi$
$662$	−2399.84	−0.140895
$663$	34.5798	0.00202559
$664$	2020.04	0.118061
$665$	4657.11	0.271571
$666$	3450.48	0.200756
$667$	1244.48	0.0722438
$668$	640.909	0.0371220
$669$	−950.328	−0.0549205
$670$	−2920.17	−0.168382
$671$	−671.000	−0.0386046
$672$	821.902	0.0471809
$673$	4652.84	0.266499	0.133249	−	0.991083i	$-0.457459\pi$
$673$	4652.84	0.266499	0.133249	+	0.991083i	$0.457459\pi$
$674$	−1907.42	−0.109008
$675$	−3318.14	−0.189208
$676$	−479.041	−0.0272554
$677$	14988.6	0.850899	0.425450	−	0.904982i	$-0.360116\pi$
$677$	14988.6	0.850899	0.425450	+	0.904982i	$0.360116\pi$
$678$	−800.879	−0.0453652
$679$	−27320.7	−1.54414
$680$	−284.508	−0.0160447
$681$	−3518.68	−0.197997
$682$	−8165.13	−0.458444
$683$	−3098.90	−0.173611	−0.0868054	−	0.996225i	$-0.527666\pi$
$683$	−3098.90	−0.173611	−0.0868054	+	0.996225i	$0.527666\pi$
$684$	227.119	0.0126961
$685$	1982.29	0.110568
$686$	−6689.93	−0.372336
$687$	13707.5	0.761243
$688$	13215.4	0.732314
$689$	−940.641	−0.0520110
$690$	−84.4577	−0.00465978
$691$	−8339.49	−0.459116	−0.229558	−	0.973295i	$-0.573728\pi$
$691$	−8339.49	−0.459116	−0.229558	+	0.973295i	$0.573728\pi$
$692$	20.6584	0.00113485
$693$	2747.30	0.150594
$694$	−24192.1	−1.32323
$695$	−556.120	−0.0303523
$696$	12307.4	0.670273
$697$	346.415	0.0188256
$698$	−12449.8	−0.675116
$699$	−12429.1	−0.672547
$700$	−744.192	−0.0401826
$701$	11770.8	0.634202	0.317101	−	0.948392i	$-0.397291\pi$
$701$	11770.8	0.634202	0.317101	+	0.948392i	$0.397291\pi$
$702$	101.518	0.00545806
$703$	−15466.0	−0.829743
$704$	5470.11	0.292845
$705$	1650.57	0.0881759
$706$	−25564.3	−1.36278
$707$	−39195.2	−2.08499
$708$	−114.958	−0.00610225
$709$	2244.47	0.118890	0.0594450	−	0.998232i	$-0.481067\pi$
$709$	2244.47	0.118890	0.0594450	+	0.998232i	$0.481067\pi$
$710$	288.384	0.0152435
$711$	−2660.63	−0.140340
$712$	−205.904	−0.0108379
$713$	1752.24	0.0920366
$714$	2097.45	0.109937
$715$	−20.9363	−0.00109507
$716$	−816.706	−0.0426281
$717$	7215.81	0.375843
$718$	−5401.18	−0.280738
$719$	19329.5	1.00260	0.501298	−	0.865274i	$-0.332856\pi$
$719$	19329.5	1.00260	0.501298	+	0.865274i	$0.332856\pi$
$720$	−858.048	−0.0444133
$721$	8649.30	0.446764
$722$	−18676.5	−0.962696
$723$	12584.6	0.647340
$724$	922.818	0.0473705
$725$	−22600.0	−1.15771
$726$	−1040.63	−0.0531974
$727$	8993.32	0.458795	0.229397	−	0.973333i	$-0.426324\pi$
$727$	8993.32	0.458795	0.229397	+	0.973333i	$0.426324\pi$
$728$	−811.953	−0.0413365
$729$	729.000	0.0370370
$730$	−261.169	−0.0132415
$731$	1767.82	0.0894460
$732$	−39.9331	−0.00201635
$733$	−10547.1	−0.531470	−0.265735	−	0.964046i	$-0.585615\pi$
$733$	−10547.1	−0.531470	−0.265735	+	0.964046i	$0.585615\pi$
$734$	9025.30	0.453855
$735$	1859.35	0.0933102
$736$	66.8098	0.00334598
$737$	7721.39	0.385917
$738$	1016.99	0.0507264
$739$	−14247.5	−0.709206	−0.354603	−	0.935017i	$-0.615384\pi$
$739$	−14247.5	−0.709206	−0.354603	+	0.935017i	$0.615384\pi$
$740$	−42.3493	−0.00210377
$741$	−455.031	−0.0225587
$742$	−57054.9	−2.82284
$743$	−24616.7	−1.21547	−0.607737	−	0.794138i	$-0.707923\pi$
$743$	−24616.7	−1.21547	−0.607737	+	0.794138i	$0.707923\pi$
$744$	17328.9	0.853908
$745$	877.885	0.0431721
$746$	−8890.37	−0.436326
$747$	814.957	0.0399166
$748$	−21.0953	−0.00103118
$749$	−22107.4	−1.07849
$750$	3093.80	0.150626
$751$	−28163.1	−1.36843	−0.684213	−	0.729282i	$-0.739854\pi$
$751$	−28163.1	−1.36843	−0.684213	+	0.729282i	$0.739854\pi$
$752$	−24908.6	−1.20788
$753$	14692.6	0.711062
$754$	691.443	0.0333964
$755$	975.806	0.0470374
$756$	163.500	0.00786566
$757$	29288.8	1.40624	0.703118	−	0.711073i	$-0.251791\pi$
$757$	29288.8	1.40624	0.703118	+	0.711073i	$0.251791\pi$
$758$	10756.6	0.515432
$759$	223.320	0.0106798
$760$	3743.80	0.178687
$761$	6587.04	0.313771	0.156886	−	0.987617i	$-0.449855\pi$
$761$	6587.04	0.313771	0.156886	+	0.987617i	$0.449855\pi$
$762$	1405.23	0.0668060
$763$	−18429.3	−0.874425
$764$	378.674	0.0179319
$765$	−114.781	−0.00542471
$766$	16683.6	0.786948
$767$	230.318	0.0108426
$768$	1004.79	0.0472099
$769$	−12719.2	−0.596445	−0.298222	−	0.954496i	$-0.596394\pi$
$769$	−12719.2	−0.596445	−0.298222	+	0.954496i	$0.596394\pi$
$770$	−1269.90	−0.0594337
$771$	2514.76	0.117467
$772$	−153.823	−0.00717124
$773$	1022.81	0.0475910	0.0237955	−	0.999717i	$-0.492425\pi$
$773$	1022.81	0.0475910	0.0237955	+	0.999717i	$0.492425\pi$
$774$	5189.89	0.241017
$775$	−31820.9	−1.47489
$776$	−21962.8	−1.01601
$777$	−11133.7	−0.514055
$778$	−30997.8	−1.42844
$779$	−4558.44	−0.209657
$780$	−1.24598	−5.71965e−5 0
$781$	−762.534	−0.0349368
$782$	170.495	0.00779654
$783$	4965.24	0.226620
$784$	−28059.2	−1.27821
$785$	−3353.89	−0.152491
$786$	−618.455	−0.0280656
$787$	−34327.8	−1.55483	−0.777416	−	0.628986i	$-0.783470\pi$
$787$	−34327.8	−1.55483	−0.777416	+	0.628986i	$0.783470\pi$
$788$	305.158	0.0137954
$789$	10462.3	0.472077
$790$	1229.84	0.0553868
$791$	2584.22	0.116162
$792$	2208.53	0.0990867
$793$	80.0057	0.00358271
$794$	21148.4	0.945249
$795$	3122.26	0.139290
$796$	−1072.59	−0.0477598
$797$	5516.11	0.245158	0.122579	−	0.992459i	$-0.460884\pi$
$797$	5516.11	0.245158	0.122579	+	0.992459i	$0.460884\pi$
$798$	−27600.1	−1.22435
$799$	−3332.01	−0.147532
$800$	−1213.27	−0.0536196
$801$	−83.0692	−0.00366430
$802$	−18260.5	−0.803991
$803$	690.572	0.0303484
$804$	459.522	0.0201568
$805$	272.522	0.0119318
$806$	973.557	0.0425460
$807$	13574.4	0.592121
$808$	−31508.6	−1.37187
$809$	42015.2	1.82593	0.912965	−	0.408039i	$-0.133787\pi$
$809$	42015.2	1.82593	0.912965	+	0.408039i	$0.133787\pi$
$810$	−336.969	−0.0146171
$811$	−15029.0	−0.650728	−0.325364	−	0.945589i	$-0.605487\pi$
$811$	−15029.0	−0.650728	−0.325364	+	0.945589i	$0.605487\pi$
$812$	1113.60	0.0481278
$813$	−262.525	−0.0113249
$814$	4217.25	0.181590
$815$	−1893.58	−0.0813855
$816$	1732.14	0.0743102
$817$	−23262.5	−0.996145
$818$	4048.30	0.173039
$819$	−327.571	−0.0139759
$820$	−12.4820	−0.000531575 0
$821$	−32852.8	−1.39655	−0.698277	−	0.715828i	$-0.746050\pi$
$821$	−32852.8	−1.39655	−0.698277	+	0.715828i	$0.746050\pi$
$822$	−11747.9	−0.498486
$823$	15948.9	0.675509	0.337755	−	0.941234i	$-0.390333\pi$
$823$	15948.9	0.675509	0.337755	+	0.941234i	$0.390333\pi$
$824$	6953.08	0.293959
$825$	−4055.51	−0.171145
$826$	13970.0	0.588473
$827$	−24188.7	−1.01708	−0.508539	−	0.861039i	$-0.669814\pi$
$827$	−24188.7	−1.01708	−0.508539	+	0.861039i	$0.669814\pi$
$828$	13.2904	0.000557818 0
$829$	−38874.3	−1.62866	−0.814331	−	0.580400i	$-0.802896\pi$
$829$	−38874.3	−1.62866	−0.814331	+	0.580400i	$0.802896\pi$
$830$	−376.701	−0.0157536
$831$	8797.77	0.367258
$832$	−652.221	−0.0271775
$833$	−3753.47	−0.156122
$834$	3295.81	0.136840
$835$	4262.16	0.176645
$836$	277.590	0.0114840
$837$	6991.09	0.288707
$838$	9860.31	0.406466
$839$	2166.40	0.0891448	0.0445724	−	0.999006i	$-0.485807\pi$
$839$	2166.40	0.0891448	0.0445724	+	0.999006i	$0.485807\pi$
$840$	2695.11	0.110703
$841$	9429.38	0.386624
$842$	12969.7	0.530836
$843$	−5301.81	−0.216612
$844$	−788.690	−0.0321657
$845$	−3185.71	−0.129694
$846$	−9782.00	−0.397532
$847$	3357.82	0.136217
$848$	−47117.8	−1.90806
$849$	−20283.9	−0.819953
$850$	−3096.21	−0.124940
$851$	−905.027	−0.0364558
$852$	−45.3806	−0.00182478
$853$	5634.86	0.226183	0.113091	−	0.993585i	$-0.463925\pi$
$853$	5634.86	0.226183	0.113091	+	0.993585i	$0.463925\pi$
$854$	4852.78	0.194448
$855$	1510.38	0.0604141
$856$	−17771.9	−0.709617
$857$	12780.9	0.509438	0.254719	−	0.967015i	$-0.418017\pi$
$857$	12780.9	0.509438	0.254719	+	0.967015i	$0.418017\pi$
$858$	124.078	0.00493700
$859$	−30741.3	−1.22105	−0.610523	−	0.791998i	$-0.709041\pi$
$859$	−30741.3	−1.22105	−0.610523	+	0.791998i	$0.709041\pi$
$860$	−63.6980	−0.00252568
$861$	−3281.56	−0.129890
$862$	−8125.34	−0.321056
$863$	24210.4	0.954963	0.477481	−	0.878642i	$-0.341550\pi$
$863$	24210.4	0.954963	0.477481	+	0.878642i	$0.341550\pi$
$864$	266.558	0.0104959
$865$	137.382	0.00540016
$866$	1605.05	0.0629813
$867$	−14507.3	−0.568274
$868$	1567.96	0.0613135
$869$	−3251.88	−0.126942
$870$	−2295.10	−0.0894383
$871$	−920.649	−0.0358151
$872$	−14815.1	−0.575348
$873$	−8860.60	−0.343512
$874$	−2243.52	−0.0868287
$875$	−9982.84	−0.385693
$876$	41.0979	0.00158513
$877$	10200.3	0.392747	0.196374	−	0.980529i	$-0.437083\pi$
$877$	10200.3	0.392747	0.196374	+	0.980529i	$0.437083\pi$
$878$	−37684.3	−1.44850
$879$	10951.4	0.420228
$880$	−1048.72	−0.0401733
$881$	1643.65	0.0628558	0.0314279	−	0.999506i	$-0.489995\pi$
$881$	1643.65	0.0628558	0.0314279	+	0.999506i	$0.489995\pi$
$882$	−11019.3	−0.420679
$883$	19162.8	0.730329	0.365165	−	0.930943i	$-0.381013\pi$
$883$	19162.8	0.730329	0.365165	+	0.930943i	$0.381013\pi$
$884$	2.51526	9.56985e−5 0
$885$	−764.494	−0.0290375
$886$	−20730.4	−0.786064
$887$	−34426.6	−1.30319	−0.651596	−	0.758566i	$-0.725900\pi$
$887$	−34426.6	−1.30319	−0.651596	+	0.758566i	$0.725900\pi$
$888$	−8950.30	−0.338235
$889$	−4534.29	−0.171063
$890$	38.3975	0.00144616
$891$	891.000	0.0335013
$892$	−69.1250	−0.00259470
$893$	43845.5	1.64304
$894$	−5202.73	−0.194637
$895$	−5431.25	−0.202845
$896$	−41752.4	−1.55675
$897$	−26.6272	−0.000991145 0
$898$	34581.6	1.28508
$899$	47616.5	1.76652
$900$	−241.355	−0.00893907
$901$	−6302.93	−0.233053
$902$	1242.99	0.0458837
$903$	−16746.3	−0.617147
$904$	2077.42	0.0764315
$905$	6136.91	0.225412
$906$	−5783.06	−0.212063
$907$	−14617.3	−0.535126	−0.267563	−	0.963540i	$-0.586218\pi$
$907$	−14617.3	−0.535126	−0.267563	+	0.963540i	$0.586218\pi$
$908$	−255.942	−0.00935432
$909$	−12711.7	−0.463829
$910$	151.415	0.00551576
$911$	20548.1	0.747297	0.373648	−	0.927570i	$-0.378107\pi$
$911$	20548.1	0.747297	0.373648	+	0.927570i	$0.378107\pi$
$912$	−22793.1	−0.827581
$913$	996.059	0.0361059
$914$	−35994.9	−1.30263
$915$	−265.563	−0.00959479
$916$	997.056	0.0359647
$917$	1995.58	0.0718647
$918$	680.240	0.0244567
$919$	−25615.9	−0.919466	−0.459733	−	0.888057i	$-0.652055\pi$
$919$	−25615.9	−0.919466	−0.459733	+	0.888057i	$0.652055\pi$
$920$	219.077	0.00785083
$921$	−746.759	−0.0267172
$922$	−29708.7	−1.06117
$923$	90.9197	0.00324232
$924$	199.833	0.00711476
$925$	16435.4	0.584207
$926$	17757.1	0.630166
$927$	2805.12	0.0993876
$928$	1815.53	0.0642217
$929$	19978.8	0.705579	0.352789	−	0.935703i	$-0.385233\pi$
$929$	19978.8	0.705579	0.352789	+	0.935703i	$0.385233\pi$
$930$	−3231.52	−0.113942
$931$	49391.4	1.73871
$932$	−904.065	−0.0317743
$933$	−13317.9	−0.467319
$934$	16136.6	0.565315
$935$	−140.287	−0.00490683
$936$	−263.331	−0.00919577
$937$	−34603.3	−1.20645	−0.603224	−	0.797572i	$-0.706117\pi$
$937$	−34603.3	−1.20645	−0.603224	+	0.797572i	$0.706117\pi$
$938$	−55842.3	−1.94383
$939$	−7618.96	−0.264787
$940$	120.059	0.00416584
$941$	37330.3	1.29323	0.646617	−	0.762815i	$-0.276183\pi$
$941$	37330.3	1.29323	0.646617	+	0.762815i	$0.276183\pi$
$942$	19876.6	0.687490
$943$	−266.748	−0.00921155
$944$	11536.9	0.397769
$945$	1087.31	0.0374286
$946$	6343.20	0.218008
$947$	−14951.2	−0.513040	−0.256520	−	0.966539i	$-0.582576\pi$
$947$	−14951.2	−0.513040	−0.256520	+	0.966539i	$0.582576\pi$
$948$	−193.529	−0.00663031
$949$	−82.3394	−0.00281649
$950$	40742.6	1.39144
$951$	6540.57	0.223021
$952$	−5440.63	−0.185223
$953$	12502.8	0.424979	0.212489	−	0.977163i	$-0.431843\pi$
$953$	12502.8	0.424979	0.212489	+	0.977163i	$0.431843\pi$
$954$	−18503.9	−0.627973
$955$	2518.25	0.0853285
$956$	524.864	0.0177566
$957$	6068.63	0.204985
$958$	−25685.0	−0.866227
$959$	37907.2	1.27642
$960$	2164.91	0.0727837
$961$	37253.5	1.25049
$962$	−502.838	−0.0168525
$963$	−7169.84	−0.239922
$964$	915.379	0.0305834
$965$	−1022.95	−0.0341242
$966$	−1615.08	−0.0537934
$967$	−22008.5	−0.731898	−0.365949	−	0.930635i	$-0.619255\pi$
$967$	−22008.5	−0.731898	−0.365949	+	0.930635i	$0.619255\pi$
$968$	2699.31	0.0896273
$969$	−3049.02	−0.101082
$970$	4095.67	0.135571
$971$	−31506.7	−1.04130	−0.520648	−	0.853772i	$-0.674309\pi$
$971$	−31506.7	−1.04130	−0.520648	+	0.853772i	$0.674309\pi$
$972$	53.0260	0.00174980
$973$	−10634.7	−0.350393
$974$	−49614.7	−1.63220
$975$	483.553	0.0158832
$976$	4007.58	0.131434
$977$	−9644.19	−0.315809	−0.157904	−	0.987454i	$-0.550474\pi$
$977$	−9644.19	−0.315809	−0.157904	+	0.987454i	$0.550474\pi$
$978$	11222.2	0.366918
$979$	−101.529	−0.00331449
$980$	135.245	0.00440841
$981$	−5976.96	−0.194526
$982$	15010.9	0.487796
$983$	1009.56	0.0327568	0.0163784	−	0.999866i	$-0.494786\pi$
$983$	1009.56	0.0327568	0.0163784	+	0.999866i	$0.494786\pi$
$984$	−2638.01	−0.0854641
$985$	2029.36	0.0656454
$986$	4633.14	0.149644
$987$	31563.8	1.01792
$988$	−33.0980	−0.00106578
$989$	−1361.26	−0.0437669
$990$	−411.851	−0.0132217
$991$	29245.7	0.937456	0.468728	−	0.883342i	$-0.344712\pi$
$991$	29245.7	0.937456	0.468728	+	0.883342i	$0.344712\pi$
$992$	2556.28	0.0818166
$993$	2511.39	0.0802585
$994$	5514.76	0.175974
$995$	−7132.89	−0.227264
$996$	59.2783	0.00188585
$997$	20178.3	0.640976	0.320488	−	0.947253i	$-0.396153\pi$
$997$	20178.3	0.640976	0.320488	+	0.947253i	$0.396153\pi$
$998$	−44738.3	−1.41900
$999$	−3610.87	−0.114357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.f.1.10	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.f.1.10	✓	38	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.86674 q^{2} +3.00000 q^{3} +0.218214 q^{4} +1.45116 q^{5} -8.60023 q^{6} +27.7506 q^{7} +22.3084 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.86674 q^{2} +3.00000 q^{3} +0.218214 q^{4} +1.45116 q^{5} -8.60023 q^{6} +27.7506 q^{7} +22.3084 q^{8} +9.00000 q^{9} -4.16011 q^{10} +11.0000 q^{11} +0.654642 q^{12} -1.31157 q^{13} -79.5537 q^{14} +4.35349 q^{15} -65.6981 q^{16} -8.78840 q^{17} -25.8007 q^{18} +115.645 q^{19} +0.316664 q^{20} +83.2517 q^{21} -31.5342 q^{22} +6.76727 q^{23} +66.9251 q^{24} -122.894 q^{25} +3.75993 q^{26} +27.0000 q^{27} +6.05556 q^{28} +183.898 q^{29} -12.4803 q^{30} +258.929 q^{31} +9.87250 q^{32} +33.0000 q^{33} +25.1941 q^{34} +40.2706 q^{35} +1.96393 q^{36} -133.736 q^{37} -331.526 q^{38} -3.93471 q^{39} +32.3731 q^{40} -39.4173 q^{41} -238.661 q^{42} -201.153 q^{43} +2.40035 q^{44} +13.0605 q^{45} -19.4000 q^{46} +379.137 q^{47} -197.094 q^{48} +427.093 q^{49} +352.306 q^{50} -26.3652 q^{51} -0.286203 q^{52} +717.187 q^{53} -77.4021 q^{54} +15.9628 q^{55} +619.070 q^{56} +346.936 q^{57} -527.188 q^{58} -175.605 q^{59} +0.949992 q^{60} -61.0000 q^{61} -742.284 q^{62} +249.755 q^{63} +497.283 q^{64} -1.90330 q^{65} -94.6025 q^{66} +701.944 q^{67} -1.91775 q^{68} +20.3018 q^{69} -115.445 q^{70} -69.3213 q^{71} +200.775 q^{72} +62.7793 q^{73} +383.387 q^{74} -368.682 q^{75} +25.2354 q^{76} +305.256 q^{77} +11.2798 q^{78} -295.626 q^{79} -95.3386 q^{80} +81.0000 q^{81} +112.999 q^{82} +90.5508 q^{83} +18.1667 q^{84} -12.7534 q^{85} +576.655 q^{86} +551.693 q^{87} +245.392 q^{88} -9.22991 q^{89} -37.4410 q^{90} -36.3968 q^{91} +1.47671 q^{92} +776.788 q^{93} -1086.89 q^{94} +167.820 q^{95} +29.6175 q^{96} -984.511 q^{97} -1224.37 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9} + 99 q^{10} + 418 q^{11} + 510 q^{12} + 209 q^{13} + 128 q^{14} + 105 q^{15} + 798 q^{16} + 512 q^{17} + 126 q^{18} + 487 q^{19} + 328 q^{20} + 315 q^{21} + 154 q^{22} + 417 q^{23} + 441 q^{24} + 925 q^{25} + 177 q^{26} + 1026 q^{27} + 902 q^{28} + 626 q^{29} + 297 q^{30} + 300 q^{31} + 1625 q^{32} + 1254 q^{33} - 180 q^{34} + 1086 q^{35} + 1530 q^{36} + 554 q^{37} + 845 q^{38} + 627 q^{39} + 329 q^{40} + 1378 q^{41} + 384 q^{42} + 1979 q^{43} + 1870 q^{44} + 315 q^{45} + 937 q^{46} + 1345 q^{47} + 2394 q^{48} + 2635 q^{49} + 800 q^{50} + 1536 q^{51} + 2006 q^{52} + 1497 q^{53} + 378 q^{54} + 385 q^{55} + 415 q^{56} + 1461 q^{57} + 1241 q^{58} + 2827 q^{59} + 984 q^{60} - 2318 q^{61} + 509 q^{62} + 945 q^{63} + 1003 q^{64} + 2810 q^{65} + 462 q^{66} + 369 q^{67} + 3936 q^{68} + 1251 q^{69} + 922 q^{70} + 965 q^{71} + 1323 q^{72} + 3081 q^{73} + 722 q^{74} + 2775 q^{75} + 2210 q^{76} + 1155 q^{77} + 531 q^{78} + 3795 q^{79} + 3793 q^{80} + 3078 q^{81} - 1678 q^{82} + 3869 q^{83} + 2706 q^{84} + 3553 q^{85} + 3305 q^{86} + 1878 q^{87} + 1617 q^{88} + 2849 q^{89} + 891 q^{90} + 1252 q^{91} + 4519 q^{92} + 900 q^{93} + 340 q^{94} + 1504 q^{95} + 4875 q^{96} + 2562 q^{97} + 6164 q^{98} + 3762 q^{99}+O(q^{100}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9 + 99 * q^10 + 418 * q^11 + 510 * q^12 + 209 * q^13 + 128 * q^14 + 105 * q^15 + 798 * q^16 + 512 * q^17 + 126 * q^18 + 487 * q^19 + 328 * q^20 + 315 * q^21 + 154 * q^22 + 417 * q^23 + 441 * q^24 + 925 * q^25 + 177 * q^26 + 1026 * q^27 + 902 * q^28 + 626 * q^29 + 297 * q^30 + 300 * q^31 + 1625 * q^32 + 1254 * q^33 - 180 * q^34 + 1086 * q^35 + 1530 * q^36 + 554 * q^37 + 845 * q^38 + 627 * q^39 + 329 * q^40 + 1378 * q^41 + 384 * q^42 + 1979 * q^43 + 1870 * q^44 + 315 * q^45 + 937 * q^46 + 1345 * q^47 + 2394 * q^48 + 2635 * q^49 + 800 * q^50 + 1536 * q^51 + 2006 * q^52 + 1497 * q^53 + 378 * q^54 + 385 * q^55 + 415 * q^56 + 1461 * q^57 + 1241 * q^58 + 2827 * q^59 + 984 * q^60 - 2318 * q^61 + 509 * q^62 + 945 * q^63 + 1003 * q^64 + 2810 * q^65 + 462 * q^66 + 369 * q^67 + 3936 * q^68 + 1251 * q^69 + 922 * q^70 + 965 * q^71 + 1323 * q^72 + 3081 * q^73 + 722 * q^74 + 2775 * q^75 + 2210 * q^76 + 1155 * q^77 + 531 * q^78 + 3795 * q^79 + 3793 * q^80 + 3078 * q^81 - 1678 * q^82 + 3869 * q^83 + 2706 * q^84 + 3553 * q^85 + 3305 * q^86 + 1878 * q^87 + 1617 * q^88 + 2849 * q^89 + 891 * q^90 + 1252 * q^91 + 4519 * q^92 + 900 * q^93 + 340 * q^94 + 1504 * q^95 + 4875 * q^96 + 2562 * q^97 + 6164 * q^98 + 3762 * q^99

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