LMFDB - Embedded newform 2013.4.a.f.1.2

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			1.2
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)

$f(q)$	$=$	$q-5.11974 q^{2} +3.00000 q^{3} +18.2117 q^{4} -8.33272 q^{5} -15.3592 q^{6} -0.123891 q^{7} -52.2812 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.11974 q^{2} +3.00000 q^{3} +18.2117 q^{4} -8.33272 q^{5} -15.3592 q^{6} -0.123891 q^{7} -52.2812 q^{8} +9.00000 q^{9} +42.6613 q^{10} +11.0000 q^{11} +54.6351 q^{12} -72.0958 q^{13} +0.634289 q^{14} -24.9981 q^{15} +121.972 q^{16} +35.0550 q^{17} -46.0776 q^{18} -65.3346 q^{19} -151.753 q^{20} -0.371673 q^{21} -56.3171 q^{22} -45.3789 q^{23} -156.844 q^{24} -55.5658 q^{25} +369.112 q^{26} +27.0000 q^{27} -2.25627 q^{28} -110.271 q^{29} +127.984 q^{30} +15.0750 q^{31} -206.217 q^{32} +33.0000 q^{33} -179.472 q^{34} +1.03235 q^{35} +163.905 q^{36} -250.627 q^{37} +334.496 q^{38} -216.287 q^{39} +435.644 q^{40} +232.740 q^{41} +1.90287 q^{42} +323.553 q^{43} +200.329 q^{44} -74.9944 q^{45} +232.328 q^{46} -336.498 q^{47} +365.917 q^{48} -342.985 q^{49} +284.482 q^{50} +105.165 q^{51} -1312.99 q^{52} -110.997 q^{53} -138.233 q^{54} -91.6599 q^{55} +6.47717 q^{56} -196.004 q^{57} +564.556 q^{58} +104.749 q^{59} -455.259 q^{60} -61.0000 q^{61} -77.1798 q^{62} -1.11502 q^{63} +79.9967 q^{64} +600.754 q^{65} -168.951 q^{66} -235.450 q^{67} +638.411 q^{68} -136.137 q^{69} -5.28535 q^{70} -14.8890 q^{71} -470.531 q^{72} +723.232 q^{73} +1283.14 q^{74} -166.698 q^{75} -1189.85 q^{76} -1.36280 q^{77} +1107.33 q^{78} -1262.54 q^{79} -1016.36 q^{80} +81.0000 q^{81} -1191.57 q^{82} +880.430 q^{83} -6.76880 q^{84} -292.104 q^{85} -1656.51 q^{86} -330.812 q^{87} -575.093 q^{88} -743.059 q^{89} +383.952 q^{90} +8.93202 q^{91} -826.427 q^{92} +45.2249 q^{93} +1722.78 q^{94} +544.415 q^{95} -618.651 q^{96} -580.449 q^{97} +1755.99 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.11974	−1.81010	−0.905050	−	0.425305i	$-0.860167\pi$
$2$	−5.11974	−1.81010	−0.905050	+	0.425305i	$0.860167\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	18.2117	2.27646
$5$	−8.33272	−0.745301	−0.372650	−	0.927972i	$-0.621551\pi$
$5$	−8.33272	−0.745301	−0.372650	+	0.927972i	$0.621551\pi$
$6$	−15.3592	−1.04506
$7$	−0.123891	−0.00668949	−0.00334474	−	0.999994i	$-0.501065\pi$
$7$	−0.123891	−0.00668949	−0.00334474	+	0.999994i	$0.501065\pi$
$8$	−52.2812	−2.31052
$9$	9.00000	0.333333
$10$	42.6613	1.34907
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	54.6351	1.31432
$13$	−72.0958	−1.53814	−0.769068	−	0.639166i	$-0.779279\pi$
$13$	−72.0958	−1.53814	−0.769068	+	0.639166i	$0.779279\pi$
$14$	0.634289	0.0121086
$15$	−24.9981	−0.430300
$16$	121.972	1.90582
$17$	35.0550	0.500123	0.250062	−	0.968230i	$-0.419549\pi$
$17$	35.0550	0.500123	0.250062	+	0.968230i	$0.419549\pi$
$18$	−46.0776	−0.603367
$19$	−65.3346	−0.788883	−0.394442	−	0.918921i	$-0.629062\pi$
$19$	−65.3346	−0.788883	−0.394442	+	0.918921i	$0.629062\pi$
$20$	−151.753	−1.69665
$21$	−0.371673	−0.00386218
$22$	−56.3171	−0.545766
$23$	−45.3789	−0.411398	−0.205699	−	0.978615i	$-0.565947\pi$
$23$	−45.3789	−0.411398	−0.205699	+	0.978615i	$0.565947\pi$
$24$	−156.844	−1.33398
$25$	−55.5658	−0.444527
$26$	369.112	2.78418
$27$	27.0000	0.192450
$28$	−2.25627	−0.0152284
$29$	−110.271	−0.706094	−0.353047	−	0.935606i	$-0.614854\pi$
$29$	−110.271	−0.706094	−0.353047	+	0.935606i	$0.614854\pi$
$30$	127.984	0.778885
$31$	15.0750	0.0873401	0.0436701	−	0.999046i	$-0.486095\pi$
$31$	15.0750	0.0873401	0.0436701	+	0.999046i	$0.486095\pi$
$32$	−206.217	−1.13920
$33$	33.0000	0.174078
$34$	−179.472	−0.905273
$35$	1.03235	0.00498568
$36$	163.905	0.758821
$37$	−250.627	−1.11359	−0.556795	−	0.830650i	$-0.687969\pi$
$37$	−250.627	−1.11359	−0.556795	+	0.830650i	$0.687969\pi$
$38$	334.496	1.42796
$39$	−216.287	−0.888044
$40$	435.644	1.72204
$41$	232.740	0.886535	0.443267	−	0.896389i	$-0.353819\pi$
$41$	232.740	0.886535	0.443267	+	0.896389i	$0.353819\pi$
$42$	1.90287	0.00699093
$43$	323.553	1.14747	0.573737	−	0.819039i	$-0.305493\pi$
$43$	323.553	1.14747	0.573737	+	0.819039i	$0.305493\pi$
$44$	200.329	0.686379
$45$	−74.9944	−0.248434
$46$	232.328	0.744672
$47$	−336.498	−1.04433	−0.522163	−	0.852846i	$-0.674875\pi$
$47$	−336.498	−1.04433	−0.522163	+	0.852846i	$0.674875\pi$
$48$	365.917	1.10032
$49$	−342.985	−0.999955
$50$	284.482	0.804638
$51$	105.165	0.288746
$52$	−1312.99	−3.50151
$53$	−110.997	−0.287673	−0.143836	−	0.989601i	$-0.545944\pi$
$53$	−110.997	−0.287673	−0.143836	+	0.989601i	$0.545944\pi$
$54$	−138.233	−0.348354
$55$	−91.6599	−0.224717
$56$	6.47717	0.0154562
$57$	−196.004	−0.455462
$58$	564.556	1.27810
$59$	104.749	0.231139	0.115569	−	0.993299i	$-0.463131\pi$
$59$	104.749	0.231139	0.115569	+	0.993299i	$0.463131\pi$
$60$	−455.259	−0.979561
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−77.1798	−0.158094
$63$	−1.11502	−0.00222983
$64$	79.9967	0.156244
$65$	600.754	1.14637
$66$	−168.951	−0.315098
$67$	−235.450	−0.429325	−0.214663	−	0.976688i	$-0.568865\pi$
$67$	−235.450	−0.429325	−0.214663	+	0.976688i	$0.568865\pi$
$68$	638.411	1.13851
$69$	−136.137	−0.237521
$70$	−5.28535	−0.00902458
$71$	−14.8890	−0.0248873	−0.0124436	−	0.999923i	$-0.503961\pi$
$71$	−14.8890	−0.0248873	−0.0124436	+	0.999923i	$0.503961\pi$
$72$	−470.531	−0.770175
$73$	723.232	1.15956	0.579780	−	0.814773i	$-0.303138\pi$
$73$	723.232	1.15956	0.579780	+	0.814773i	$0.303138\pi$
$74$	1283.14	2.01571
$75$	−166.698	−0.256648
$76$	−1189.85	−1.79586
$77$	−1.36280	−0.00201696
$78$	1107.33	1.60745
$79$	−1262.54	−1.79806	−0.899032	−	0.437883i	$-0.855728\pi$
$79$	−1262.54	−1.79806	−0.899032	+	0.437883i	$0.855728\pi$
$80$	−1016.36	−1.42041
$81$	81.0000	0.111111
$82$	−1191.57	−1.60472
$83$	880.430	1.16433	0.582167	−	0.813069i	$-0.302205\pi$
$83$	880.430	1.16433	0.582167	+	0.813069i	$0.302205\pi$
$84$	−6.76880	−0.00879210
$85$	−292.104	−0.372742
$86$	−1656.51	−2.07704
$87$	−330.812	−0.407664
$88$	−575.093	−0.696649
$89$	−743.059	−0.884990	−0.442495	−	0.896771i	$-0.645907\pi$
$89$	−743.059	−0.884990	−0.442495	+	0.896771i	$0.645907\pi$
$90$	383.952	0.449690
$91$	8.93202	0.0102893
$92$	−826.427	−0.936533
$93$	45.2249	0.0504258
$94$	1722.78	1.89033
$95$	544.415	0.587955
$96$	−618.651	−0.657716
$97$	−580.449	−0.607585	−0.303792	−	0.952738i	$-0.598253\pi$
$97$	−580.449	−0.607585	−0.303792	+	0.952738i	$0.598253\pi$
$98$	1755.99	1.81002
$99$	99.0000	0.100504
$100$	−1011.95	−1.01195
$101$	576.579	0.568037	0.284018	−	0.958819i	$-0.408332\pi$
$101$	576.579	0.568037	0.284018	+	0.958819i	$0.408332\pi$
$102$	−538.417	−0.522659
$103$	285.664	0.273275	0.136637	−	0.990621i	$-0.456370\pi$
$103$	285.664	0.273275	0.136637	+	0.990621i	$0.456370\pi$
$104$	3769.26	3.55390
$105$	3.09705	0.00287848
$106$	568.277	0.520717
$107$	1407.99	1.27211	0.636054	−	0.771645i	$-0.280566\pi$
$107$	1407.99	1.27211	0.636054	+	0.771645i	$0.280566\pi$
$108$	491.716	0.438105
$109$	475.562	0.417895	0.208948	−	0.977927i	$-0.432996\pi$
$109$	475.562	0.417895	0.208948	+	0.977927i	$0.432996\pi$
$110$	469.274	0.406760
$111$	−751.881	−0.642931
$112$	−15.1113	−0.0127490
$113$	1325.82	1.10374	0.551869	−	0.833931i	$-0.313915\pi$
$113$	1325.82	1.10374	0.551869	+	0.833931i	$0.313915\pi$
$114$	1003.49	0.824432
$115$	378.130	0.306615
$116$	−2008.21	−1.60740
$117$	−648.862	−0.512712
$118$	−536.288	−0.418384
$119$	−4.34300	−0.00334557
$120$	1306.93	0.994218
$121$	121.000	0.0909091
$122$	312.304	0.231760
$123$	698.221	0.511841
$124$	274.541	0.198826
$125$	1504.60	1.07661
$126$	5.70860	0.00403621
$127$	−1440.60	−1.00655	−0.503277	−	0.864125i	$-0.667872\pi$
$127$	−1440.60	−1.00655	−0.503277	+	0.864125i	$0.667872\pi$
$128$	1240.17	0.856381
$129$	970.660	0.662495
$130$	−3075.70	−2.07505
$131$	1117.75	0.745486	0.372743	−	0.927935i	$-0.378417\pi$
$131$	1117.75	0.745486	0.372743	+	0.927935i	$0.378417\pi$
$132$	600.986	0.396281
$133$	8.09437	0.00527723
$134$	1205.44	0.777122
$135$	−224.983	−0.143433
$136$	−1832.72	−1.15555
$137$	1817.52	1.13344	0.566721	−	0.823910i	$-0.308212\pi$
$137$	1817.52	1.13344	0.566721	+	0.823910i	$0.308212\pi$
$138$	696.984	0.429937
$139$	1801.13	1.09906	0.549532	−	0.835473i	$-0.314806\pi$
$139$	1801.13	1.09906	0.549532	+	0.835473i	$0.314806\pi$
$140$	18.8008	0.0113497
$141$	−1009.50	−0.602942
$142$	76.2276	0.0450484
$143$	−793.054	−0.463766
$144$	1097.75	0.635273
$145$	918.854	0.526253
$146$	−3702.76	−2.09892
$147$	−1028.95	−0.577324
$148$	−4564.34	−2.53505
$149$	−1716.39	−0.943706	−0.471853	−	0.881677i	$-0.656415\pi$
$149$	−1716.39	−0.943706	−0.471853	+	0.881677i	$0.656415\pi$
$150$	853.447	0.464558
$151$	−928.673	−0.500492	−0.250246	−	0.968182i	$-0.580512\pi$
$151$	−928.673	−0.500492	−0.250246	+	0.968182i	$0.580512\pi$
$152$	3415.77	1.82273
$153$	315.495	0.166708
$154$	6.97718	0.00365089
$155$	−125.615	−0.0650947
$156$	−3938.96	−2.02160
$157$	−2585.56	−1.31433	−0.657165	−	0.753747i	$-0.728244\pi$
$157$	−2585.56	−1.31433	−0.657165	+	0.753747i	$0.728244\pi$
$158$	6463.88	3.25468
$159$	−332.992	−0.166088
$160$	1718.35	0.849045
$161$	5.62204	0.00275204
$162$	−414.699	−0.201122
$163$	845.970	0.406512	0.203256	−	0.979126i	$-0.434848\pi$
$163$	845.970	0.406512	0.203256	+	0.979126i	$0.434848\pi$
$164$	4238.60	2.01816
$165$	−274.980	−0.129740
$166$	−4507.57	−2.10756
$167$	1758.54	0.814849	0.407424	−	0.913239i	$-0.366427\pi$
$167$	1758.54	0.814849	0.407424	+	0.913239i	$0.366427\pi$
$168$	19.4315	0.00892366
$169$	3000.81	1.36586
$170$	1495.49	0.674700
$171$	−588.011	−0.262961
$172$	5892.45	2.61218
$173$	−3136.84	−1.37855	−0.689277	−	0.724498i	$-0.742072\pi$
$173$	−3136.84	−1.37855	−0.689277	+	0.724498i	$0.742072\pi$
$174$	1693.67	0.737912
$175$	6.88411	0.00297366
$176$	1341.70	0.574626
$177$	314.247	0.133448
$178$	3804.27	1.60192
$179$	−1905.70	−0.795747	−0.397874	−	0.917440i	$-0.630252\pi$
$179$	−1905.70	−0.795747	−0.397874	+	0.917440i	$0.630252\pi$
$180$	−1365.78	−0.565550
$181$	−2176.49	−0.893795	−0.446898	−	0.894585i	$-0.647471\pi$
$181$	−2176.49	−0.893795	−0.446898	+	0.894585i	$0.647471\pi$
$182$	−45.7296	−0.0186247
$183$	−183.000	−0.0739221
$184$	2372.46	0.950546
$185$	2088.40	0.829959
$186$	−231.540	−0.0912758
$187$	385.605	0.150793
$188$	−6128.21	−2.37737
$189$	−3.34506	−0.00128739
$190$	−2787.26	−1.06426
$191$	53.7524	0.0203633	0.0101816	−	0.999948i	$-0.496759\pi$
$191$	53.7524	0.0203633	0.0101816	+	0.999948i	$0.496759\pi$
$192$	239.990	0.0902073
$193$	3061.54	1.14184	0.570919	−	0.821007i	$-0.306587\pi$
$193$	3061.54	1.14184	0.570919	+	0.821007i	$0.306587\pi$
$194$	2971.75	1.09979
$195$	1802.26	0.661860
$196$	−6246.33	−2.27636
$197$	1250.95	0.452420	0.226210	−	0.974079i	$-0.427366\pi$
$197$	1250.95	0.452420	0.226210	+	0.974079i	$0.427366\pi$
$198$	−506.854	−0.181922
$199$	−4522.20	−1.61091	−0.805453	−	0.592660i	$-0.798078\pi$
$199$	−4522.20	−1.61091	−0.805453	+	0.592660i	$0.798078\pi$
$200$	2905.05	1.02709
$201$	−706.350	−0.247871
$202$	−2951.93	−1.02820
$203$	13.6615	0.00472341
$204$	1915.23	0.657320
$205$	−1939.36	−0.660735
$206$	−1462.52	−0.494655
$207$	−408.410	−0.137133
$208$	−8793.70	−2.93141
$209$	−718.681	−0.237857
$210$	−15.8561	−0.00521034
$211$	−4128.54	−1.34702	−0.673508	−	0.739180i	$-0.735213\pi$
$211$	−4128.54	−1.34702	−0.673508	+	0.739180i	$0.735213\pi$
$212$	−2021.45	−0.654876
$213$	−44.6669	−0.0143687
$214$	−7208.54	−2.30264
$215$	−2696.08	−0.855214
$216$	−1411.59	−0.444661
$217$	−1.86765	−0.000584261 0
$218$	−2434.75	−0.756432
$219$	2169.70	0.669472
$220$	−1669.28	−0.511559
$221$	−2527.32	−0.769258
$222$	3849.43	1.16377
$223$	−598.398	−0.179694	−0.0898469	−	0.995956i	$-0.528638\pi$
$223$	−598.398	−0.179694	−0.0898469	+	0.995956i	$0.528638\pi$
$224$	25.5484	0.00762065
$225$	−500.093	−0.148176
$226$	−6787.84	−1.99788
$227$	−2932.35	−0.857387	−0.428693	−	0.903450i	$-0.641026\pi$
$227$	−2932.35	−0.857387	−0.428693	+	0.903450i	$0.641026\pi$
$228$	−3569.56	−1.03684
$229$	1232.36	0.355619	0.177810	−	0.984065i	$-0.443099\pi$
$229$	1232.36	0.355619	0.177810	+	0.984065i	$0.443099\pi$
$230$	−1935.92	−0.555005
$231$	−4.08840	−0.00116449
$232$	5765.08	1.63145
$233$	−1136.10	−0.319434	−0.159717	−	0.987163i	$-0.551058\pi$
$233$	−1136.10	−0.319434	−0.159717	+	0.987163i	$0.551058\pi$
$234$	3322.00	0.928061
$235$	2803.95	0.778337
$236$	1907.66	0.526178
$237$	−3787.63	−1.03811
$238$	22.2350	0.00605581
$239$	−5372.75	−1.45412	−0.727059	−	0.686575i	$-0.759113\pi$
$239$	−5372.75	−1.45412	−0.727059	+	0.686575i	$0.759113\pi$
$240$	−3049.08	−0.820073
$241$	1855.76	0.496018	0.248009	−	0.968758i	$-0.420224\pi$
$241$	1855.76	0.496018	0.248009	+	0.968758i	$0.420224\pi$
$242$	−619.488	−0.164555
$243$	243.000	0.0641500
$244$	−1110.91	−0.291471
$245$	2857.99	0.745267
$246$	−3574.71	−0.926484
$247$	4710.35	1.21341
$248$	−788.137	−0.201801
$249$	2641.29	0.672229
$250$	−7703.18	−1.94877
$251$	4071.74	1.02393	0.511964	−	0.859007i	$-0.328918\pi$
$251$	4071.74	1.02393	0.511964	+	0.859007i	$0.328918\pi$
$252$	−20.3064	−0.00507612
$253$	−499.168	−0.124041
$254$	7375.48	1.82196
$255$	−876.311	−0.215203
$256$	−6989.33	−1.70638
$257$	749.566	0.181933	0.0909663	−	0.995854i	$-0.471004\pi$
$257$	749.566	0.181933	0.0909663	+	0.995854i	$0.471004\pi$
$258$	−4969.52	−1.19918
$259$	31.0504	0.00744934
$260$	10940.7	2.60968
$261$	−992.435	−0.235365
$262$	−5722.61	−1.34940
$263$	2506.11	0.587579	0.293789	−	0.955870i	$-0.405084\pi$
$263$	2506.11	0.587579	0.293789	+	0.955870i	$0.405084\pi$
$264$	−1725.28	−0.402211
$265$	924.909	0.214403
$266$	−41.4410	−0.00955231
$267$	−2229.18	−0.510949
$268$	−4287.94	−0.977343
$269$	−762.364	−0.172796	−0.0863981	−	0.996261i	$-0.527536\pi$
$269$	−762.364	−0.172796	−0.0863981	+	0.996261i	$0.527536\pi$
$270$	1151.86	0.259628
$271$	5781.64	1.29598	0.647988	−	0.761650i	$-0.275611\pi$
$271$	5781.64	1.29598	0.647988	+	0.761650i	$0.275611\pi$
$272$	4275.74	0.953144
$273$	26.7961	0.00594056
$274$	−9305.24	−2.05164
$275$	−611.224	−0.134030
$276$	−2479.28	−0.540707
$277$	5854.60	1.26992	0.634962	−	0.772543i	$-0.281016\pi$
$277$	5854.60	1.26992	0.634962	+	0.772543i	$0.281016\pi$
$278$	−9221.31	−1.98941
$279$	135.675	0.0291134
$280$	−53.9724	−0.0115195
$281$	1651.96	0.350703	0.175351	−	0.984506i	$-0.443894\pi$
$281$	1651.96	0.350703	0.175351	+	0.984506i	$0.443894\pi$
$282$	5168.35	1.09139
$283$	1553.31	0.326272	0.163136	−	0.986604i	$-0.447839\pi$
$283$	1553.31	0.326272	0.163136	+	0.986604i	$0.447839\pi$
$284$	−271.153	−0.0566549
$285$	1633.24	0.339456
$286$	4060.23	0.839462
$287$	−28.8344	−0.00593046
$288$	−1855.95	−0.379733
$289$	−3684.15	−0.749877
$290$	−4704.29	−0.952570
$291$	−1741.35	−0.350789
$292$	13171.3	2.63969
$293$	−2845.46	−0.567349	−0.283675	−	0.958921i	$-0.591554\pi$
$293$	−2845.46	−0.567349	−0.283675	+	0.958921i	$0.591554\pi$
$294$	5267.97	1.04502
$295$	−872.845	−0.172268
$296$	13103.1	2.57298
$297$	297.000	0.0580259
$298$	8787.47	1.70820
$299$	3271.63	0.632787
$300$	−3035.84	−0.584249
$301$	−40.0853	−0.00767602
$302$	4754.56	0.905941
$303$	1729.74	0.327956
$304$	−7969.02	−1.50347
$305$	508.296	0.0954260
$306$	−1615.25	−0.301758
$307$	−8776.88	−1.63167	−0.815835	−	0.578284i	$-0.803722\pi$
$307$	−8776.88	−1.63167	−0.815835	+	0.578284i	$0.803722\pi$
$308$	−24.8189	−0.00459153
$309$	856.992	0.157775
$310$	643.118	0.117828
$311$	4056.37	0.739600	0.369800	−	0.929111i	$-0.379426\pi$
$311$	4056.37	0.739600	0.369800	+	0.929111i	$0.379426\pi$
$312$	11307.8	2.05185
$313$	8560.78	1.54596	0.772978	−	0.634433i	$-0.218766\pi$
$313$	8560.78	1.54596	0.772978	+	0.634433i	$0.218766\pi$
$314$	13237.4	2.37907
$315$	9.29114	0.00166189
$316$	−22993.0	−4.09322
$317$	−4233.69	−0.750119	−0.375060	−	0.927001i	$-0.622378\pi$
$317$	−4233.69	−0.750119	−0.375060	+	0.927001i	$0.622378\pi$
$318$	1704.83	0.300636
$319$	−1212.98	−0.212895
$320$	−666.590	−0.116448
$321$	4223.97	0.734452
$322$	−28.7834	−0.00498147
$323$	−2290.31	−0.394539
$324$	1475.15	0.252940
$325$	4006.06	0.683743
$326$	−4331.14	−0.735828
$327$	1426.69	0.241272
$328$	−12167.9	−2.04836
$329$	41.6891	0.00698601
$330$	1407.82	0.234843
$331$	2405.70	0.399484	0.199742	−	0.979848i	$-0.435990\pi$
$331$	2405.70	0.399484	0.199742	+	0.979848i	$0.435990\pi$
$332$	16034.1	2.65056
$333$	−2255.64	−0.371197
$334$	−9003.25	−1.47496
$335$	1961.94	0.319976
$336$	−45.3339	−0.00736061
$337$	−3711.75	−0.599976	−0.299988	−	0.953943i	$-0.596983\pi$
$337$	−3711.75	−0.599976	−0.299988	+	0.953943i	$0.596983\pi$
$338$	−15363.3	−2.47235
$339$	3977.45	0.637244
$340$	−5319.70	−0.848533
$341$	165.825	0.0263340
$342$	3010.46	0.475986
$343$	84.9873	0.0133787
$344$	−16915.8	−2.65127
$345$	1134.39	0.177025
$346$	16059.8	2.49532
$347$	5875.49	0.908970	0.454485	−	0.890754i	$-0.349823\pi$
$347$	5875.49	0.908970	0.454485	+	0.890754i	$0.349823\pi$
$348$	−6024.64	−0.928031
$349$	2684.28	0.411708	0.205854	−	0.978583i	$-0.434003\pi$
$349$	2684.28	0.411708	0.205854	+	0.978583i	$0.434003\pi$
$350$	−35.2448	−0.00538261
$351$	−1946.59	−0.296015
$352$	−2268.39	−0.343481
$353$	−2413.17	−0.363853	−0.181926	−	0.983312i	$-0.558233\pi$
$353$	−2413.17	−0.363853	−0.181926	+	0.983312i	$0.558233\pi$
$354$	−1608.86	−0.241554
$355$	124.066	0.0185485
$356$	−13532.4	−2.01465
$357$	−13.0290	−0.00193156
$358$	9756.69	1.44038
$359$	6210.66	0.913053	0.456527	−	0.889710i	$-0.349093\pi$
$359$	6210.66	0.913053	0.456527	+	0.889710i	$0.349093\pi$
$360$	3920.80	0.574012
$361$	−2590.39	−0.377663
$362$	11143.0	1.61786
$363$	363.000	0.0524864
$364$	162.667	0.0234233
$365$	−6026.49	−0.864221
$366$	936.912	0.133806
$367$	5424.51	0.771546	0.385773	−	0.922594i	$-0.373935\pi$
$367$	5424.51	0.771546	0.385773	+	0.922594i	$0.373935\pi$
$368$	−5534.98	−0.784050
$369$	2094.66	0.295512
$370$	−10692.1	−1.50231
$371$	13.7516	0.00192438
$372$	823.622	0.114793
$373$	11118.5	1.54341	0.771707	−	0.635978i	$-0.219403\pi$
$373$	11118.5	1.54341	0.771707	+	0.635978i	$0.219403\pi$
$374$	−1974.20	−0.272950
$375$	4513.81	0.621579
$376$	17592.5	2.41294
$377$	7950.05	1.08607
$378$	17.1258	0.00233031
$379$	2658.30	0.360285	0.180142	−	0.983641i	$-0.442344\pi$
$379$	2658.30	0.360285	0.180142	+	0.983641i	$0.442344\pi$
$380$	9914.72	1.33846
$381$	−4321.79	−0.581134
$382$	−275.198	−0.0368596
$383$	−1678.07	−0.223878	−0.111939	−	0.993715i	$-0.535706\pi$
$383$	−1678.07	−0.223878	−0.111939	+	0.993715i	$0.535706\pi$
$384$	3720.52	0.494432
$385$	11.3558	0.00150324
$386$	−15674.3	−2.06684
$387$	2911.98	0.382492
$388$	−10571.0	−1.38314
$389$	11101.6	1.44698	0.723488	−	0.690337i	$-0.242538\pi$
$389$	11101.6	1.44698	0.723488	+	0.690337i	$0.242538\pi$
$390$	−9227.10	−1.19803
$391$	−1590.76	−0.205750
$392$	17931.7	2.31042
$393$	3353.26	0.430406
$394$	−6404.56	−0.818926
$395$	10520.4	1.34010
$396$	1802.96	0.228793
$397$	2304.64	0.291351	0.145676	−	0.989332i	$-0.453464\pi$
$397$	2304.64	0.291351	0.145676	+	0.989332i	$0.453464\pi$
$398$	23152.5	2.91590
$399$	24.2831	0.00304681
$400$	−6777.50	−0.847187
$401$	−4102.10	−0.510846	−0.255423	−	0.966829i	$-0.582215\pi$
$401$	−4102.10	−0.510846	−0.255423	+	0.966829i	$0.582215\pi$
$402$	3616.33	0.448671
$403$	−1086.84	−0.134341
$404$	10500.5	1.29311
$405$	−674.950	−0.0828112
$406$	−69.9435	−0.00854984
$407$	−2756.90	−0.335760
$408$	−5498.16	−0.667155
$409$	3561.71	0.430599	0.215300	−	0.976548i	$-0.430927\pi$
$409$	3561.71	0.430599	0.215300	+	0.976548i	$0.430927\pi$
$410$	9929.00	1.19600
$411$	5452.57	0.654393
$412$	5202.43	0.622100
$413$	−12.9775	−0.00154620
$414$	2090.95	0.248224
$415$	−7336.38	−0.867780
$416$	14867.4	1.75224
$417$	5403.39	0.634545
$418$	3679.45	0.430546
$419$	−10107.2	−1.17845	−0.589225	−	0.807969i	$-0.700567\pi$
$419$	−10107.2	−1.17845	−0.589225	+	0.807969i	$0.700567\pi$
$420$	56.4025	0.00655276
$421$	7517.06	0.870212	0.435106	−	0.900379i	$-0.356711\pi$
$421$	7517.06	0.870212	0.435106	+	0.900379i	$0.356711\pi$
$422$	21137.0	2.43823
$423$	−3028.49	−0.348109
$424$	5803.07	0.664675
$425$	−1947.86	−0.222318
$426$	228.683	0.0260087
$427$	7.55735	0.000856501 0
$428$	25641.9	2.89591
$429$	−2379.16	−0.267755
$430$	13803.2	1.54802
$431$	14229.8	1.59031	0.795154	−	0.606407i	$-0.207390\pi$
$431$	14229.8	1.59031	0.795154	+	0.606407i	$0.207390\pi$
$432$	3293.25	0.366775
$433$	11012.1	1.22219	0.611093	−	0.791559i	$-0.290730\pi$
$433$	11012.1	1.22219	0.611093	+	0.791559i	$0.290730\pi$
$434$	9.56189	0.00105757
$435$	2756.56	0.303832
$436$	8660.79	0.951323
$437$	2964.81	0.324545
$438$	−11108.3	−1.21181
$439$	11471.4	1.24715	0.623574	−	0.781764i	$-0.285680\pi$
$439$	11471.4	1.24715	0.623574	+	0.781764i	$0.285680\pi$
$440$	4792.09	0.519213
$441$	−3086.86	−0.333318
$442$	12939.2	1.39243
$443$	5799.05	0.621944	0.310972	−	0.950419i	$-0.399346\pi$
$443$	5799.05	0.621944	0.310972	+	0.950419i	$0.399346\pi$
$444$	−13693.0	−1.46361
$445$	6191.70	0.659584
$446$	3063.64	0.325264
$447$	−5149.17	−0.544849
$448$	−9.91088	−0.00104519
$449$	−8524.47	−0.895979	−0.447990	−	0.894039i	$-0.647860\pi$
$449$	−8524.47	−0.895979	−0.447990	+	0.894039i	$0.647860\pi$
$450$	2560.34	0.268213
$451$	2560.14	0.267300
$452$	24145.4	2.51262
$453$	−2786.02	−0.288959
$454$	15012.8	1.55196
$455$	−74.4280	−0.00766866
$456$	10247.3	1.05236
$457$	14337.4	1.46756	0.733781	−	0.679386i	$-0.237754\pi$
$457$	14337.4	1.46756	0.733781	+	0.679386i	$0.237754\pi$
$458$	−6309.37	−0.643707
$459$	946.486	0.0962487
$460$	6886.38	0.697999
$461$	−9131.16	−0.922518	−0.461259	−	0.887266i	$-0.652602\pi$
$461$	−9131.16	−0.922518	−0.461259	+	0.887266i	$0.652602\pi$
$462$	20.9316	0.00210784
$463$	5259.81	0.527957	0.263978	−	0.964529i	$-0.414965\pi$
$463$	5259.81	0.527957	0.263978	+	0.964529i	$0.414965\pi$
$464$	−13450.0	−1.34569
$465$	−376.846	−0.0375824
$466$	5816.52	0.578208
$467$	11466.3	1.13618	0.568091	−	0.822965i	$-0.307682\pi$
$467$	11466.3	1.13618	0.568091	+	0.822965i	$0.307682\pi$
$468$	−11816.9	−1.16717
$469$	29.1701	0.00287197
$470$	−14355.5	−1.40887
$471$	−7756.67	−0.758829
$472$	−5476.41	−0.534051
$473$	3559.09	0.345977
$474$	19391.6	1.87909
$475$	3630.37	0.350680
$476$	−79.0935	−0.00761606
$477$	−998.976	−0.0958909
$478$	27507.0	2.63210
$479$	−14598.6	−1.39254	−0.696270	−	0.717780i	$-0.745158\pi$
$479$	−14598.6	−1.39254	−0.696270	+	0.717780i	$0.745158\pi$
$480$	5155.04	0.490196
$481$	18069.2	1.71285
$482$	−9501.02	−0.897841
$483$	16.8661	0.00158889
$484$	2203.62	0.206951
$485$	4836.72	0.452833
$486$	−1244.10	−0.116118
$487$	14095.5	1.31156	0.655780	−	0.754952i	$-0.272340\pi$
$487$	14095.5	1.31156	0.655780	+	0.754952i	$0.272340\pi$
$488$	3189.15	0.295832
$489$	2537.91	0.234700
$490$	−14632.2	−1.34901
$491$	2995.38	0.275315	0.137657	−	0.990480i	$-0.456043\pi$
$491$	2995.38	0.275315	0.137657	+	0.990480i	$0.456043\pi$
$492$	12715.8	1.16519
$493$	−3865.54	−0.353134
$494$	−24115.8	−2.19639
$495$	−824.939	−0.0749055
$496$	1838.73	0.166454
$497$	1.84461	0.000166483 0
$498$	−13522.7	−1.21680
$499$	13560.1	1.21650	0.608249	−	0.793746i	$-0.291872\pi$
$499$	13560.1	1.21650	0.608249	+	0.793746i	$0.291872\pi$
$500$	27401.4	2.45086
$501$	5275.61	0.470453
$502$	−20846.2	−1.85341
$503$	5605.18	0.496864	0.248432	−	0.968649i	$-0.420085\pi$
$503$	5605.18	0.496864	0.248432	+	0.968649i	$0.420085\pi$
$504$	58.2946	0.00515208
$505$	−4804.47	−0.423358
$506$	2555.61	0.224527
$507$	9002.42	0.788583
$508$	−26235.7	−2.29138
$509$	12521.7	1.09040	0.545200	−	0.838306i	$-0.316454\pi$
$509$	12521.7	1.09040	0.545200	+	0.838306i	$0.316454\pi$
$510$	4486.48	0.389539
$511$	−89.6019	−0.00775686
$512$	25862.2	2.23234
$513$	−1764.03	−0.151821
$514$	−3837.58	−0.329316
$515$	−2380.36	−0.203672
$516$	17677.4	1.50814
$517$	−3701.48	−0.314876
$518$	−158.970	−0.0134841
$519$	−9410.53	−0.795908
$520$	−31408.1	−2.64873
$521$	−1685.07	−0.141697	−0.0708485	−	0.997487i	$-0.522571\pi$
$521$	−1685.07	−0.141697	−0.0708485	+	0.997487i	$0.522571\pi$
$522$	5081.01	0.426034
$523$	−2521.62	−0.210827	−0.105414	−	0.994428i	$-0.533617\pi$
$523$	−2521.62	−0.210827	−0.105414	+	0.994428i	$0.533617\pi$
$524$	20356.2	1.69707
$525$	20.6523	0.00171684
$526$	−12830.6	−1.06358
$527$	528.453	0.0436808
$528$	4025.09	0.331760
$529$	−10107.8	−0.830751
$530$	−4735.29	−0.388090
$531$	942.742	0.0770462
$532$	147.412	0.0120134
$533$	−16779.6	−1.36361
$534$	11412.8	0.924870
$535$	−11732.4	−0.948103
$536$	12309.6	0.991967
$537$	−5717.10	−0.459425
$538$	3903.10	0.312778
$539$	−3772.83	−0.301498
$540$	−4097.33	−0.326520
$541$	23014.3	1.82895	0.914475	−	0.404643i	$-0.132604\pi$
$541$	23014.3	1.82895	0.914475	+	0.404643i	$0.132604\pi$
$542$	−29600.5	−2.34585
$543$	−6529.46	−0.516033
$544$	−7228.94	−0.569739
$545$	−3962.72	−0.311458
$546$	−137.189	−0.0107530
$547$	−2766.73	−0.216264	−0.108132	−	0.994137i	$-0.534487\pi$
$547$	−2766.73	−0.216264	−0.108132	+	0.994137i	$0.534487\pi$
$548$	33100.2	2.58024
$549$	−549.000	−0.0426790
$550$	3129.31	0.242607
$551$	7204.48	0.557026
$552$	7117.39	0.548798
$553$	156.418	0.0120281
$554$	−29974.0	−2.29869
$555$	6265.21	0.479177
$556$	32801.6	2.50198
$557$	21184.1	1.61149	0.805744	−	0.592264i	$-0.201766\pi$
$557$	21184.1	1.61149	0.805744	+	0.592264i	$0.201766\pi$
$558$	−694.619	−0.0526981
$559$	−23326.8	−1.76497
$560$	125.918	0.00950180
$561$	1156.82	0.0870602
$562$	−8457.58	−0.634807
$563$	−3946.14	−0.295399	−0.147700	−	0.989032i	$-0.547187\pi$
$563$	−3946.14	−0.295399	−0.147700	+	0.989032i	$0.547187\pi$
$564$	−18384.6	−1.37257
$565$	−11047.7	−0.822617
$566$	−7952.55	−0.590584
$567$	−10.0352	−0.000743276 0
$568$	778.413	0.0575026
$569$	−6982.00	−0.514412	−0.257206	−	0.966357i	$-0.582802\pi$
$569$	−6982.00	−0.514412	−0.257206	+	0.966357i	$0.582802\pi$
$570$	−8361.78	−0.614450
$571$	−21065.8	−1.54392	−0.771959	−	0.635673i	$-0.780723\pi$
$571$	−21065.8	−1.54392	−0.771959	+	0.635673i	$0.780723\pi$
$572$	−14442.9	−1.05575
$573$	161.257	0.0117568
$574$	147.625	0.0107347
$575$	2521.52	0.182878
$576$	719.970	0.0520812
$577$	16248.8	1.17235	0.586177	−	0.810183i	$-0.300632\pi$
$577$	16248.8	1.17235	0.586177	+	0.810183i	$0.300632\pi$
$578$	18861.9	1.35735
$579$	9184.62	0.659240
$580$	16733.9	1.19799
$581$	−109.077	−0.00778880
$582$	8915.24	0.634964
$583$	−1220.97	−0.0867366
$584$	−37811.4	−2.67919
$585$	5406.79	0.382125
$586$	14568.0	1.02696
$587$	−9526.66	−0.669859	−0.334930	−	0.942243i	$-0.608713\pi$
$587$	−9526.66	−0.669859	−0.334930	+	0.942243i	$0.608713\pi$
$588$	−18739.0	−1.31426
$589$	−984.917	−0.0689012
$590$	4468.74	0.311822
$591$	3752.86	0.261205
$592$	−30569.6	−2.12230
$593$	−1426.98	−0.0988179	−0.0494090	−	0.998779i	$-0.515734\pi$
$593$	−1426.98	−0.0988179	−0.0494090	+	0.998779i	$0.515734\pi$
$594$	−1520.56	−0.105033
$595$	36.1890	0.00249345
$596$	−31258.4	−2.14831
$597$	−13566.6	−0.930057
$598$	−16749.9	−1.14541
$599$	−6929.56	−0.472678	−0.236339	−	0.971671i	$-0.575948\pi$
$599$	−6929.56	−0.472678	−0.236339	+	0.971671i	$0.575948\pi$
$600$	8715.15	0.592991
$601$	−11875.9	−0.806038	−0.403019	−	0.915192i	$-0.632039\pi$
$601$	−11875.9	−0.806038	−0.403019	+	0.915192i	$0.632039\pi$
$602$	205.226	0.0138944
$603$	−2119.05	−0.143108
$604$	−16912.7	−1.13935
$605$	−1008.26	−0.0677546
$606$	−8855.79	−0.593634
$607$	6345.22	0.424291	0.212145	−	0.977238i	$-0.431955\pi$
$607$	6345.22	0.424291	0.212145	+	0.977238i	$0.431955\pi$
$608$	13473.1	0.898694
$609$	40.9846	0.00272706
$610$	−2602.34	−0.172731
$611$	24260.1	1.60632
$612$	5745.70	0.379504
$613$	−16940.2	−1.11617	−0.558083	−	0.829785i	$-0.688463\pi$
$613$	−16940.2	−1.11617	−0.558083	+	0.829785i	$0.688463\pi$
$614$	44935.3	2.95349
$615$	−5818.08	−0.381476
$616$	71.2489	0.00466023
$617$	26202.7	1.70969	0.854846	−	0.518882i	$-0.173651\pi$
$617$	26202.7	1.70969	0.854846	+	0.518882i	$0.173651\pi$
$618$	−4387.57	−0.285589
$619$	830.332	0.0539158	0.0269579	−	0.999637i	$-0.491418\pi$
$619$	830.332	0.0539158	0.0269579	+	0.999637i	$0.491418\pi$
$620$	−2287.67	−0.148186
$621$	−1225.23	−0.0791736
$622$	−20767.5	−1.33875
$623$	92.0584	0.00592013
$624$	−26381.1	−1.69245
$625$	−5591.71	−0.357869
$626$	−43829.0	−2.79833
$627$	−2156.04	−0.137327
$628$	−47087.4	−2.99202
$629$	−8785.73	−0.556932
$630$	−47.5682	−0.00300819
$631$	−18248.6	−1.15129	−0.575645	−	0.817700i	$-0.695249\pi$
$631$	−18248.6	−1.15129	−0.575645	+	0.817700i	$0.695249\pi$
$632$	66007.2	4.15447
$633$	−12385.6	−0.777700
$634$	21675.4	1.35779
$635$	12004.1	0.750185
$636$	−6064.35	−0.378093
$637$	24727.8	1.53807
$638$	6210.12	0.385362
$639$	−134.001	−0.00829575
$640$	−10334.0	−0.638262
$641$	29911.1	1.84308	0.921542	−	0.388278i	$-0.126930\pi$
$641$	29911.1	1.84308	0.921542	+	0.388278i	$0.126930\pi$
$642$	−21625.6	−1.32943
$643$	−8351.70	−0.512222	−0.256111	−	0.966647i	$-0.582441\pi$
$643$	−8351.70	−0.512222	−0.256111	+	0.966647i	$0.582441\pi$
$644$	102.387	0.00626492
$645$	−8088.23	−0.493758
$646$	11725.8	0.714155
$647$	−18605.8	−1.13056	−0.565278	−	0.824901i	$-0.691231\pi$
$647$	−18605.8	−1.13056	−0.565278	+	0.824901i	$0.691231\pi$
$648$	−4234.78	−0.256725
$649$	1152.24	0.0696909
$650$	−20510.0	−1.23764
$651$	−5.60296	−0.000337323 0
$652$	15406.6	0.925410
$653$	710.731	0.0425927	0.0212964	−	0.999773i	$-0.493221\pi$
$653$	710.731	0.0425927	0.0212964	+	0.999773i	$0.493221\pi$
$654$	−7304.26	−0.436726
$655$	−9313.93	−0.555611
$656$	28387.9	1.68957
$657$	6509.09	0.386520
$658$	−213.437	−0.0126454
$659$	11790.1	0.696932	0.348466	−	0.937321i	$-0.386703\pi$
$659$	11790.1	0.696932	0.348466	+	0.937321i	$0.386703\pi$
$660$	−5007.85	−0.295349
$661$	5796.95	0.341112	0.170556	−	0.985348i	$-0.445444\pi$
$661$	5796.95	0.341112	0.170556	+	0.985348i	$0.445444\pi$
$662$	−12316.6	−0.723107
$663$	−7581.96	−0.444131
$664$	−46030.0	−2.69022
$665$	−67.4481	−0.00393312
$666$	11548.3	0.671903
$667$	5003.96	0.290486
$668$	32026.0	1.85497
$669$	−1795.20	−0.103746
$670$	−10044.6	−0.579189
$671$	−671.000	−0.0386046
$672$	76.6453	0.00439978
$673$	−4707.07	−0.269605	−0.134802	−	0.990872i	$-0.543040\pi$
$673$	−4707.07	−0.269605	−0.134802	+	0.990872i	$0.543040\pi$
$674$	19003.2	1.08602
$675$	−1500.28	−0.0855492
$676$	54649.8	3.10934
$677$	−11513.5	−0.653621	−0.326811	−	0.945090i	$-0.605974\pi$
$677$	−11513.5	−0.653621	−0.326811	+	0.945090i	$0.605974\pi$
$678$	−20363.5	−1.15348
$679$	71.9125	0.00406443
$680$	15271.5	0.861230
$681$	−8797.04	−0.495012
$682$	−848.978	−0.0476672
$683$	8386.83	0.469858	0.234929	−	0.972012i	$-0.424514\pi$
$683$	8386.83	0.469858	0.234929	+	0.972012i	$0.424514\pi$
$684$	−10708.7	−0.598621
$685$	−15144.9	−0.844755
$686$	−435.113	−0.0242167
$687$	3697.09	0.205317
$688$	39464.6	2.18688
$689$	8002.44	0.442480
$690$	−5807.77	−0.320432
$691$	1414.86	0.0778928	0.0389464	−	0.999241i	$-0.487600\pi$
$691$	1414.86	0.0778928	0.0389464	+	0.999241i	$0.487600\pi$
$692$	−57127.3	−3.13823
$693$	−12.2652	−0.000672319 0
$694$	−30080.9	−1.64533
$695$	−15008.3	−0.819133
$696$	17295.2	0.941917
$697$	8158.71	0.443376
$698$	−13742.8	−0.745232
$699$	−3408.29	−0.184426
$700$	125.371	0.00676942
$701$	25292.1	1.36272	0.681362	−	0.731947i	$-0.261388\pi$
$701$	25292.1	1.36272	0.681362	+	0.731947i	$0.261388\pi$
$702$	9966.01	0.535816
$703$	16374.6	0.878492
$704$	879.964	0.0471092
$705$	8411.84	0.449373
$706$	12354.8	0.658610
$707$	−71.4329	−0.00379988
$708$	5722.98	0.303789
$709$	26765.0	1.41774	0.708871	−	0.705338i	$-0.249205\pi$
$709$	26765.0	1.41774	0.708871	+	0.705338i	$0.249205\pi$
$710$	−635.183	−0.0335746
$711$	−11362.9	−0.599355
$712$	38848.0	2.04479
$713$	−684.086	−0.0359316
$714$	66.7051	0.00349632
$715$	6608.29	0.345645
$716$	−34706.1	−1.81149
$717$	−16118.2	−0.839535
$718$	−31796.9	−1.65272
$719$	−17414.1	−0.903250	−0.451625	−	0.892208i	$-0.649155\pi$
$719$	−17414.1	−0.903250	−0.451625	+	0.892208i	$0.649155\pi$
$720$	−9147.25	−0.473469
$721$	−35.3912	−0.00182807
$722$	13262.1	0.683608
$723$	5567.29	0.286376
$724$	−39637.5	−2.03469
$725$	6127.28	0.313878
$726$	−1858.46	−0.0950056
$727$	−34465.4	−1.75826	−0.879128	−	0.476586i	$-0.841874\pi$
$727$	−34465.4	−1.75826	−0.879128	+	0.476586i	$0.841874\pi$
$728$	−466.977	−0.0237738
$729$	729.000	0.0370370
$730$	30854.0	1.56433
$731$	11342.2	0.573878
$732$	−3332.74	−0.168281
$733$	26617.6	1.34126	0.670629	−	0.741793i	$-0.266024\pi$
$733$	26617.6	1.34126	0.670629	+	0.741793i	$0.266024\pi$
$734$	−27772.1	−1.39658
$735$	8573.98	0.430280
$736$	9357.90	0.468664
$737$	−2589.95	−0.129446
$738$	−10724.1	−0.534906
$739$	3311.11	0.164819	0.0824095	−	0.996599i	$-0.473738\pi$
$739$	3311.11	0.164819	0.0824095	+	0.996599i	$0.473738\pi$
$740$	38033.4	1.88937
$741$	14131.1	0.700563
$742$	−70.4044	−0.00348333
$743$	14902.2	0.735814	0.367907	−	0.929863i	$-0.380074\pi$
$743$	14902.2	0.735814	0.367907	+	0.929863i	$0.380074\pi$
$744$	−2364.41	−0.116510
$745$	14302.2	0.703345
$746$	−56923.7	−2.79373
$747$	7923.87	0.388112
$748$	7022.53	0.343274
$749$	−174.437	−0.00850975
$750$	−23109.5	−1.12512
$751$	−19083.1	−0.927235	−0.463617	−	0.886035i	$-0.653449\pi$
$751$	−19083.1	−0.927235	−0.463617	+	0.886035i	$0.653449\pi$
$752$	−41043.5	−1.99030
$753$	12215.2	0.591166
$754$	−40702.1	−1.96589
$755$	7738.37	0.373017
$756$	−60.9192	−0.00293070
$757$	−32072.2	−1.53987	−0.769937	−	0.638120i	$-0.779712\pi$
$757$	−32072.2	−1.53987	−0.769937	+	0.638120i	$0.779712\pi$
$758$	−13609.8	−0.652151
$759$	−1497.50	−0.0716152
$760$	−28462.7	−1.35849
$761$	−7471.71	−0.355912	−0.177956	−	0.984038i	$-0.556949\pi$
$761$	−7471.71	−0.355912	−0.177956	+	0.984038i	$0.556949\pi$
$762$	22126.4	1.05191
$763$	−58.9179	−0.00279550
$764$	978.923	0.0463563
$765$	−2628.93	−0.124247
$766$	8591.26	0.405241
$767$	−7551.97	−0.355523
$768$	−20968.0	−0.985179
$769$	26537.2	1.24442	0.622209	−	0.782852i	$-0.286236\pi$
$769$	26537.2	1.24442	0.622209	+	0.782852i	$0.286236\pi$
$770$	−58.1389	−0.00272101
$771$	2248.70	0.105039
$772$	55755.9	2.59935
$773$	−4388.35	−0.204189	−0.102094	−	0.994775i	$-0.532554\pi$
$773$	−4388.35	−0.204189	−0.102094	+	0.994775i	$0.532554\pi$
$774$	−14908.6	−0.692348
$775$	−837.653	−0.0388250
$776$	30346.6	1.40384
$777$	93.1513	0.00430088
$778$	−56837.3	−2.61917
$779$	−15206.0	−0.699372
$780$	32822.2	1.50670
$781$	−163.779	−0.00750379
$782$	8144.27	0.372428
$783$	−2977.31	−0.135888
$784$	−41834.7	−1.90573
$785$	21544.7	0.979571
$786$	−17167.8	−0.779079
$787$	5101.11	0.231048	0.115524	−	0.993305i	$-0.463145\pi$
$787$	5101.11	0.231048	0.115524	+	0.993305i	$0.463145\pi$
$788$	22782.0	1.02992
$789$	7518.32	0.339239
$790$	−53861.7	−2.42571
$791$	−164.257	−0.00738345
$792$	−5175.84	−0.232216
$793$	4397.84	0.196938
$794$	−11799.1	−0.527375
$795$	2774.73	0.123785
$796$	−82357.0	−3.66717
$797$	43520.9	1.93424	0.967120	−	0.254320i	$-0.0818515\pi$
$797$	43520.9	1.93424	0.967120	+	0.254320i	$0.0818515\pi$
$798$	−124.323	−0.00551503
$799$	−11796.0	−0.522292
$800$	11458.6	0.506404
$801$	−6687.53	−0.294997
$802$	21001.7	0.924682
$803$	7955.55	0.349620
$804$	−12863.8	−0.564269
$805$	−46.8469	−0.00205110
$806$	5564.34	0.243171
$807$	−2287.09	−0.0997639
$808$	−30144.2	−1.31246
$809$	18471.0	0.802727	0.401363	−	0.915919i	$-0.368536\pi$
$809$	18471.0	0.802727	0.401363	+	0.915919i	$0.368536\pi$
$810$	3455.57	0.149897
$811$	26359.3	1.14131	0.570654	−	0.821191i	$-0.306690\pi$
$811$	26359.3	1.14131	0.570654	+	0.821191i	$0.306690\pi$
$812$	248.800	0.0107527
$813$	17344.9	0.748232
$814$	14114.6	0.607759
$815$	−7049.23	−0.302974
$816$	12827.2	0.550298
$817$	−21139.2	−0.905224
$818$	−18235.0	−0.779427
$819$	80.3882	0.00342978
$820$	−35319.0	−1.50414
$821$	31864.2	1.35453	0.677265	−	0.735739i	$-0.263165\pi$
$821$	31864.2	1.35453	0.677265	+	0.735739i	$0.263165\pi$
$822$	−27915.7	−1.18452
$823$	−19082.5	−0.808232	−0.404116	−	0.914708i	$-0.632421\pi$
$823$	−19082.5	−0.808232	−0.404116	+	0.914708i	$0.632421\pi$
$824$	−14934.9	−0.631408
$825$	−1833.67	−0.0773822
$826$	66.4413	0.00279877
$827$	−6702.52	−0.281825	−0.140913	−	0.990022i	$-0.545004\pi$
$827$	−6702.52	−0.281825	−0.140913	+	0.990022i	$0.545004\pi$
$828$	−7437.85	−0.312178
$829$	16800.9	0.703885	0.351942	−	0.936022i	$-0.385521\pi$
$829$	16800.9	0.703885	0.351942	+	0.936022i	$0.385521\pi$
$830$	37560.3	1.57077
$831$	17563.8	0.733191
$832$	−5767.43	−0.240324
$833$	−12023.3	−0.500101
$834$	−27663.9	−1.14859
$835$	−14653.4	−0.607308
$836$	−13088.4	−0.541473
$837$	407.024	0.0168086
$838$	51746.3	2.13311
$839$	−16562.0	−0.681508	−0.340754	−	0.940152i	$-0.610682\pi$
$839$	−16562.0	−0.681508	−0.340754	+	0.940152i	$0.610682\pi$
$840$	−161.917	−0.00665081
$841$	−12229.4	−0.501431
$842$	−38485.4	−1.57517
$843$	4955.87	0.202478
$844$	−75187.7	−3.06643
$845$	−25004.9	−1.01798
$846$	15505.0	0.630112
$847$	−14.9908	−0.000608135 0
$848$	−13538.6	−0.548252
$849$	4659.94	0.188373
$850$	9972.54	0.402418
$851$	11373.2	0.458129
$852$	−813.460	−0.0327097
$853$	1958.32	0.0786067	0.0393034	−	0.999227i	$-0.487486\pi$
$853$	1958.32	0.0786067	0.0393034	+	0.999227i	$0.487486\pi$
$854$	−38.6917	−0.00155035
$855$	4899.73	0.195985
$856$	−73611.4	−2.93924
$857$	14837.1	0.591394	0.295697	−	0.955282i	$-0.404448\pi$
$857$	14837.1	0.591394	0.295697	+	0.955282i	$0.404448\pi$
$858$	12180.7	0.484664
$859$	837.540	0.0332672	0.0166336	−	0.999862i	$-0.494705\pi$
$859$	837.540	0.0332672	0.0166336	+	0.999862i	$0.494705\pi$
$860$	−49100.2	−1.94686
$861$	−86.5033	−0.00342395
$862$	−72852.6	−2.87862
$863$	44932.8	1.77234	0.886171	−	0.463359i	$-0.153356\pi$
$863$	44932.8	1.77234	0.886171	+	0.463359i	$0.153356\pi$
$864$	−5567.86	−0.219239
$865$	26138.4	1.02744
$866$	−56378.9	−2.21228
$867$	−11052.4	−0.432942
$868$	−34.0131	−0.00133005
$869$	−13888.0	−0.542137
$870$	−14112.9	−0.549967
$871$	16975.0	0.660361
$872$	−24863.0	−0.965557
$873$	−5224.05	−0.202528
$874$	−15179.1	−0.587459
$875$	−186.407	−0.00720195
$876$	39513.8	1.52403
$877$	−8758.09	−0.337217	−0.168609	−	0.985683i	$-0.553927\pi$
$877$	−8758.09	−0.337217	−0.168609	+	0.985683i	$0.553927\pi$
$878$	−58730.3	−2.25746
$879$	−8536.37	−0.327559
$880$	−11180.0	−0.428269
$881$	−14094.4	−0.538993	−0.269497	−	0.963001i	$-0.586857\pi$
$881$	−14094.4	−0.538993	−0.269497	+	0.963001i	$0.586857\pi$
$882$	15803.9	0.603340
$883$	−5715.83	−0.217840	−0.108920	−	0.994050i	$-0.534739\pi$
$883$	−5715.83	−0.217840	−0.108920	+	0.994050i	$0.534739\pi$
$884$	−46026.8	−1.75119
$885$	−2618.53	−0.0994588
$886$	−29689.6	−1.12578
$887$	48402.1	1.83222	0.916112	−	0.400922i	$-0.131310\pi$
$887$	48402.1	1.83222	0.916112	+	0.400922i	$0.131310\pi$
$888$	39309.2	1.48551
$889$	178.477	0.00673333
$890$	−31699.9	−1.19391
$891$	891.000	0.0335013
$892$	−10897.9	−0.409066
$893$	21985.0	0.823852
$894$	26362.4	0.986231
$895$	15879.7	0.593071
$896$	−153.646	−0.00572875
$897$	9814.89	0.365340
$898$	43643.0	1.62181
$899$	−1662.33	−0.0616704
$900$	−9107.53	−0.337316
$901$	−3891.01	−0.143872
$902$	−13107.3	−0.483840
$903$	−120.256	−0.00443175
$904$	−69315.4	−2.55022
$905$	18136.0	0.666146
$906$	14263.7	0.523046
$907$	17245.4	0.631338	0.315669	−	0.948869i	$-0.397771\pi$
$907$	17245.4	0.631338	0.315669	+	0.948869i	$0.397771\pi$
$908$	−53403.0	−1.95181
$909$	5189.21	0.189346
$910$	381.052	0.0138810
$911$	−25393.6	−0.923520	−0.461760	−	0.887005i	$-0.652782\pi$
$911$	−25393.6	−0.923520	−0.461760	+	0.887005i	$0.652782\pi$
$912$	−23907.1	−0.868028
$913$	9684.73	0.351060
$914$	−73403.8	−2.65644
$915$	1524.89	0.0550942
$916$	22443.4	0.809554
$917$	−138.480	−0.00498692
$918$	−4845.76	−0.174220
$919$	29889.8	1.07288	0.536439	−	0.843939i	$-0.319769\pi$
$919$	29889.8	1.07288	0.536439	+	0.843939i	$0.319769\pi$
$920$	−19769.1	−0.708443
$921$	−26330.6	−0.942045
$922$	46749.1	1.66985
$923$	1073.43	0.0382800
$924$	−74.4568	−0.00265092
$925$	13926.3	0.495020
$926$	−26928.8	−0.955655
$927$	2570.98	0.0910916
$928$	22739.7	0.804381
$929$	−34033.9	−1.20196	−0.600978	−	0.799266i	$-0.705222\pi$
$929$	−34033.9	−1.20196	−0.600978	+	0.799266i	$0.705222\pi$
$930$	1929.35	0.0680279
$931$	22408.8	0.788848
$932$	−20690.3	−0.727181
$933$	12169.1	0.427008
$934$	−58704.5	−2.05660
$935$	−3213.14	−0.112386
$936$	33923.3	1.18463
$937$	−14210.7	−0.495457	−0.247728	−	0.968830i	$-0.579684\pi$
$937$	−14210.7	−0.495457	−0.247728	+	0.968830i	$0.579684\pi$
$938$	−149.343	−0.00519855
$939$	25682.4	0.892558
$940$	51064.6	1.77186
$941$	17184.8	0.595334	0.297667	−	0.954670i	$-0.403791\pi$
$941$	17184.8	0.595334	0.297667	+	0.954670i	$0.403791\pi$
$942$	39712.1	1.37356
$943$	−10561.5	−0.364719
$944$	12776.5	0.440508
$945$	27.8734	0.000959495 0
$946$	−18221.6	−0.626252
$947$	−12699.1	−0.435759	−0.217879	−	0.975976i	$-0.569914\pi$
$947$	−12699.1	−0.435759	−0.217879	+	0.975976i	$0.569914\pi$
$948$	−68979.1	−2.36322
$949$	−52142.0	−1.78356
$950$	−18586.5	−0.634765
$951$	−12701.1	−0.433082
$952$	227.057	0.00773001
$953$	−47099.4	−1.60094	−0.800472	−	0.599371i	$-0.795418\pi$
$953$	−47099.4	−1.60094	−0.800472	+	0.599371i	$0.795418\pi$
$954$	5114.49	0.173572
$955$	−447.904	−0.0151768
$956$	−97846.8	−3.31024
$957$	−3638.93	−0.122915
$958$	74740.9	2.52064
$959$	−225.175	−0.00758215
$960$	−1999.77	−0.0672316
$961$	−29563.7	−0.992372
$962$	−92509.3	−3.10044
$963$	12671.9	0.424036
$964$	33796.6	1.12917
$965$	−25511.0	−0.851012
$966$	−86.3501	−0.00287606
$967$	37660.6	1.25241	0.626207	−	0.779657i	$-0.284607\pi$
$967$	37660.6	1.25241	0.626207	+	0.779657i	$0.284607\pi$
$968$	−6326.03	−0.210048
$969$	−6870.92	−0.227787
$970$	−24762.7	−0.819674
$971$	−46486.9	−1.53639	−0.768196	−	0.640215i	$-0.778845\pi$
$971$	−46486.9	−1.53639	−0.768196	+	0.640215i	$0.778845\pi$
$972$	4425.44	0.146035
$973$	−223.144	−0.00735217
$974$	−72165.4	−2.37405
$975$	12018.2	0.394759
$976$	−7440.32	−0.244015
$977$	22726.5	0.744202	0.372101	−	0.928192i	$-0.378637\pi$
$977$	22726.5	0.744202	0.372101	+	0.928192i	$0.378637\pi$
$978$	−12993.4	−0.424830
$979$	−8173.65	−0.266835
$980$	52048.9	1.69657
$981$	4280.06	0.139298
$982$	−15335.6	−0.498348
$983$	−29493.4	−0.956961	−0.478481	−	0.878098i	$-0.658812\pi$
$983$	−29493.4	−0.956961	−0.478481	+	0.878098i	$0.658812\pi$
$984$	−36503.8	−1.18262
$985$	−10423.8	−0.337189
$986$	19790.5	0.639208
$987$	125.067	0.00403337
$988$	85783.5	2.76228
$989$	−14682.5	−0.472069
$990$	4223.47	0.135587
$991$	15083.1	0.483483	0.241742	−	0.970341i	$-0.422281\pi$
$991$	15083.1	0.483483	0.241742	+	0.970341i	$0.422281\pi$
$992$	−3108.71	−0.0994977
$993$	7217.10	0.230642
$994$	−9.44391	−0.000301351 0
$995$	37682.2	1.20061
$996$	48102.4	1.53030
$997$	−10188.0	−0.323629	−0.161815	−	0.986821i	$-0.551735\pi$
$997$	−10188.0	−0.323629	−0.161815	+	0.986821i	$0.551735\pi$
$998$	−69424.0	−2.20198
$999$	−6766.93	−0.214310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.f.1.2	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.f.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-5.11974 q^{2} +3.00000 q^{3} +18.2117 q^{4} -8.33272 q^{5} -15.3592 q^{6} -0.123891 q^{7} -52.2812 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.11974 q^{2} +3.00000 q^{3} +18.2117 q^{4} -8.33272 q^{5} -15.3592 q^{6} -0.123891 q^{7} -52.2812 q^{8} +9.00000 q^{9} +42.6613 q^{10} +11.0000 q^{11} +54.6351 q^{12} -72.0958 q^{13} +0.634289 q^{14} -24.9981 q^{15} +121.972 q^{16} +35.0550 q^{17} -46.0776 q^{18} -65.3346 q^{19} -151.753 q^{20} -0.371673 q^{21} -56.3171 q^{22} -45.3789 q^{23} -156.844 q^{24} -55.5658 q^{25} +369.112 q^{26} +27.0000 q^{27} -2.25627 q^{28} -110.271 q^{29} +127.984 q^{30} +15.0750 q^{31} -206.217 q^{32} +33.0000 q^{33} -179.472 q^{34} +1.03235 q^{35} +163.905 q^{36} -250.627 q^{37} +334.496 q^{38} -216.287 q^{39} +435.644 q^{40} +232.740 q^{41} +1.90287 q^{42} +323.553 q^{43} +200.329 q^{44} -74.9944 q^{45} +232.328 q^{46} -336.498 q^{47} +365.917 q^{48} -342.985 q^{49} +284.482 q^{50} +105.165 q^{51} -1312.99 q^{52} -110.997 q^{53} -138.233 q^{54} -91.6599 q^{55} +6.47717 q^{56} -196.004 q^{57} +564.556 q^{58} +104.749 q^{59} -455.259 q^{60} -61.0000 q^{61} -77.1798 q^{62} -1.11502 q^{63} +79.9967 q^{64} +600.754 q^{65} -168.951 q^{66} -235.450 q^{67} +638.411 q^{68} -136.137 q^{69} -5.28535 q^{70} -14.8890 q^{71} -470.531 q^{72} +723.232 q^{73} +1283.14 q^{74} -166.698 q^{75} -1189.85 q^{76} -1.36280 q^{77} +1107.33 q^{78} -1262.54 q^{79} -1016.36 q^{80} +81.0000 q^{81} -1191.57 q^{82} +880.430 q^{83} -6.76880 q^{84} -292.104 q^{85} -1656.51 q^{86} -330.812 q^{87} -575.093 q^{88} -743.059 q^{89} +383.952 q^{90} +8.93202 q^{91} -826.427 q^{92} +45.2249 q^{93} +1722.78 q^{94} +544.415 q^{95} -618.651 q^{96} -580.449 q^{97} +1755.99 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) \) 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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