LMFDB - Embedded newform 2013.4.a.h.1.15

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:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.69454 q^{2} +3.00000 q^{3} -5.12852 q^{4} -5.42092 q^{5} -5.08363 q^{6} -29.9078 q^{7} +22.2469 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.69454 q^{2} +3.00000 q^{3} -5.12852 q^{4} -5.42092 q^{5} -5.08363 q^{6} -29.9078 q^{7} +22.2469 q^{8} +9.00000 q^{9} +9.18599 q^{10} -11.0000 q^{11} -15.3856 q^{12} +55.7400 q^{13} +50.6800 q^{14} -16.2628 q^{15} +3.32985 q^{16} +101.295 q^{17} -15.2509 q^{18} -42.8109 q^{19} +27.8013 q^{20} -89.7233 q^{21} +18.6400 q^{22} -12.1081 q^{23} +66.7406 q^{24} -95.6136 q^{25} -94.4540 q^{26} +27.0000 q^{27} +153.382 q^{28} -53.5811 q^{29} +27.5580 q^{30} +238.804 q^{31} -183.617 q^{32} -33.0000 q^{33} -171.649 q^{34} +162.128 q^{35} -46.1567 q^{36} -355.068 q^{37} +72.5450 q^{38} +167.220 q^{39} -120.598 q^{40} -228.522 q^{41} +152.040 q^{42} +29.3331 q^{43} +56.4137 q^{44} -48.7883 q^{45} +20.5176 q^{46} -323.450 q^{47} +9.98955 q^{48} +551.474 q^{49} +162.022 q^{50} +303.885 q^{51} -285.864 q^{52} -707.821 q^{53} -45.7527 q^{54} +59.6301 q^{55} -665.354 q^{56} -128.433 q^{57} +90.7955 q^{58} -199.910 q^{59} +83.4039 q^{60} +61.0000 q^{61} -404.664 q^{62} -269.170 q^{63} +284.509 q^{64} -302.162 q^{65} +55.9200 q^{66} -297.322 q^{67} -519.493 q^{68} -36.3242 q^{69} -274.732 q^{70} +131.800 q^{71} +200.222 q^{72} +196.508 q^{73} +601.678 q^{74} -286.841 q^{75} +219.556 q^{76} +328.985 q^{77} -283.362 q^{78} -871.693 q^{79} -18.0508 q^{80} +81.0000 q^{81} +387.241 q^{82} +290.202 q^{83} +460.147 q^{84} -549.112 q^{85} -49.7062 q^{86} -160.743 q^{87} -244.715 q^{88} -1161.15 q^{89} +82.6739 q^{90} -1667.06 q^{91} +62.0964 q^{92} +716.412 q^{93} +548.100 q^{94} +232.074 q^{95} -550.852 q^{96} +1253.87 q^{97} -934.497 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * 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 $

$2$	−1.69454	−0.599112	−0.299556	−	0.954079i	$-0.596839\pi$
$2$	−1.69454	−0.599112	−0.299556	+	0.954079i	$0.596839\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−5.12852	−0.641065
$5$	−5.42092	−0.484862	−0.242431	−	0.970169i	$-0.577945\pi$
$5$	−5.42092	−0.484862	−0.242431	+	0.970169i	$0.577945\pi$
$6$	−5.08363	−0.345897
$7$	−29.9078	−1.61487	−0.807433	−	0.589959i	$-0.799144\pi$
$7$	−29.9078	−1.61487	−0.807433	+	0.589959i	$0.799144\pi$
$8$	22.2469	0.983182
$9$	9.00000	0.333333
$10$	9.18599	0.290487
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−15.3856	−0.370119
$13$	55.7400	1.18919	0.594596	−	0.804024i	$-0.297312\pi$
$13$	55.7400	1.18919	0.594596	+	0.804024i	$0.297312\pi$
$14$	50.6800	0.967486
$15$	−16.2628	−0.279935
$16$	3.32985	0.0520289
$17$	101.295	1.44516	0.722578	−	0.691289i	$-0.242957\pi$
$17$	101.295	1.44516	0.722578	+	0.691289i	$0.242957\pi$
$18$	−15.2509	−0.199704
$19$	−42.8109	−0.516921	−0.258460	−	0.966022i	$-0.583215\pi$
$19$	−42.8109	−0.516921	−0.258460	+	0.966022i	$0.583215\pi$
$20$	27.8013	0.310828
$21$	−89.7233	−0.932344
$22$	18.6400	0.180639
$23$	−12.1081	−0.109770	−0.0548849	−	0.998493i	$-0.517479\pi$
$23$	−12.1081	−0.109770	−0.0548849	+	0.998493i	$0.517479\pi$
$24$	66.7406	0.567640
$25$	−95.6136	−0.764909
$26$	−94.4540	−0.712460
$27$	27.0000	0.192450
$28$	153.382	1.03523
$29$	−53.5811	−0.343095	−0.171548	−	0.985176i	$-0.554877\pi$
$29$	−53.5811	−0.343095	−0.171548	+	0.985176i	$0.554877\pi$
$30$	27.5580	0.167712
$31$	238.804	1.38356	0.691781	−	0.722107i	$-0.256826\pi$
$31$	238.804	1.38356	0.691781	+	0.722107i	$0.256826\pi$
$32$	−183.617	−1.01435
$33$	−33.0000	−0.174078
$34$	−171.649	−0.865810
$35$	162.128	0.782987
$36$	−46.1567	−0.213688
$37$	−355.068	−1.57764	−0.788821	−	0.614623i	$-0.789308\pi$
$37$	−355.068	−1.57764	−0.788821	+	0.614623i	$0.789308\pi$
$38$	72.5450	0.309693
$39$	167.220	0.686581
$40$	−120.598	−0.476707
$41$	−228.522	−0.870468	−0.435234	−	0.900317i	$-0.643334\pi$
$41$	−228.522	−0.870468	−0.435234	+	0.900317i	$0.643334\pi$
$42$	152.040	0.558578
$43$	29.3331	0.104029	0.0520146	−	0.998646i	$-0.483436\pi$
$43$	29.3331	0.104029	0.0520146	+	0.998646i	$0.483436\pi$
$44$	56.4137	0.193288
$45$	−48.7883	−0.161621
$46$	20.5176	0.0657644
$47$	−323.450	−1.00383	−0.501915	−	0.864917i	$-0.667371\pi$
$47$	−323.450	−1.00383	−0.501915	+	0.864917i	$0.667371\pi$
$48$	9.98955	0.0300389
$49$	551.474	1.60779
$50$	162.022	0.458266
$51$	303.885	0.834361
$52$	−285.864	−0.762350
$53$	−707.821	−1.83447	−0.917233	−	0.398352i	$-0.869582\pi$
$53$	−707.821	−1.83447	−0.917233	+	0.398352i	$0.869582\pi$
$54$	−45.7527	−0.115299
$55$	59.6301	0.146191
$56$	−665.354	−1.58771
$57$	−128.433	−0.298444
$58$	90.7955	0.205552
$59$	−199.910	−0.441119	−0.220560	−	0.975373i	$-0.570788\pi$
$59$	−199.910	−0.441119	−0.220560	+	0.975373i	$0.570788\pi$
$60$	83.4039	0.179457
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−404.664	−0.828909
$63$	−269.170	−0.538289
$64$	284.509	0.555682
$65$	−302.162	−0.576594
$66$	55.9200	0.104292
$67$	−297.322	−0.542145	−0.271072	−	0.962559i	$-0.587378\pi$
$67$	−297.322	−0.542145	−0.271072	+	0.962559i	$0.587378\pi$
$68$	−519.493	−0.926439
$69$	−36.3242	−0.0633756
$70$	−274.732	−0.469097
$71$	131.800	0.220307	0.110154	−	0.993915i	$-0.464866\pi$
$71$	131.800	0.220307	0.110154	+	0.993915i	$0.464866\pi$
$72$	200.222	0.327727
$73$	196.508	0.315063	0.157531	−	0.987514i	$-0.449646\pi$
$73$	196.508	0.315063	0.157531	+	0.987514i	$0.449646\pi$
$74$	601.678	0.945184
$75$	−286.841	−0.441620
$76$	219.556	0.331380
$77$	328.985	0.486901
$78$	−283.362	−0.411339
$79$	−871.693	−1.24143	−0.620716	−	0.784035i	$-0.713158\pi$
$79$	−871.693	−1.24143	−0.620716	+	0.784035i	$0.713158\pi$
$80$	−18.0508	−0.0252268
$81$	81.0000	0.111111
$82$	387.241	0.521508
$83$	290.202	0.383781	0.191890	−	0.981416i	$-0.438538\pi$
$83$	290.202	0.383781	0.191890	+	0.981416i	$0.438538\pi$
$84$	460.147	0.597693
$85$	−549.112	−0.700701
$86$	−49.7062	−0.0623251
$87$	−160.743	−0.198086
$88$	−244.715	−0.296440
$89$	−1161.15	−1.38294	−0.691472	−	0.722403i	$-0.743037\pi$
$89$	−1161.15	−1.38294	−0.691472	+	0.722403i	$0.743037\pi$
$90$	82.6739	0.0968288
$91$	−1667.06	−1.92039
$92$	62.0964	0.0703695
$93$	716.412	0.798800
$94$	548.100	0.601406
$95$	232.074	0.250635
$96$	−550.852	−0.585637
$97$	1253.87	1.31249	0.656245	−	0.754548i	$-0.272144\pi$
$97$	1253.87	1.31249	0.656245	+	0.754548i	$0.272144\pi$
$98$	−934.497	−0.963249
$99$	−99.0000	−0.100504
$100$	490.356	0.490356
$101$	750.786	0.739663	0.369831	−	0.929099i	$-0.379415\pi$
$101$	750.786	0.739663	0.369831	+	0.929099i	$0.379415\pi$
$102$	−514.947	−0.499876
$103$	1090.36	1.04307	0.521536	−	0.853229i	$-0.325359\pi$
$103$	1090.36	1.04307	0.521536	+	0.853229i	$0.325359\pi$
$104$	1240.04	1.16919
$105$	486.383	0.452058
$106$	1199.43	1.09905
$107$	285.117	0.257601	0.128800	−	0.991671i	$-0.458887\pi$
$107$	285.117	0.257601	0.128800	+	0.991671i	$0.458887\pi$
$108$	−138.470	−0.123373
$109$	−295.360	−0.259544	−0.129772	−	0.991544i	$-0.541425\pi$
$109$	−295.360	−0.259544	−0.129772	+	0.991544i	$0.541425\pi$
$110$	−101.046	−0.0875850
$111$	−1065.20	−0.910852
$112$	−99.5883	−0.0840198
$113$	1820.34	1.51543	0.757715	−	0.652585i	$-0.226316\pi$
$113$	1820.34	1.51543	0.757715	+	0.652585i	$0.226316\pi$
$114$	217.635	0.178802
$115$	65.6368	0.0532232
$116$	274.792	0.219946
$117$	501.660	0.396398
$118$	338.756	0.264280
$119$	−3029.51	−2.33373
$120$	−361.795	−0.275227
$121$	121.000	0.0909091
$122$	−103.367	−0.0767084
$123$	−685.567	−0.502565
$124$	−1224.71	−0.886953
$125$	1195.93	0.855737
$126$	456.120	0.322495
$127$	626.477	0.437723	0.218861	−	0.975756i	$-0.429766\pi$
$127$	626.477	0.437723	0.218861	+	0.975756i	$0.429766\pi$
$128$	986.826	0.681437
$129$	87.9992	0.0600612
$130$	512.027	0.345444
$131$	1419.38	0.946652	0.473326	−	0.880887i	$-0.343053\pi$
$131$	1419.38	0.946652	0.473326	+	0.880887i	$0.343053\pi$
$132$	169.241	0.111595
$133$	1280.38	0.834758
$134$	503.826	0.324805
$135$	−146.365	−0.0933117
$136$	2253.50	1.42085
$137$	−509.974	−0.318029	−0.159015	−	0.987276i	$-0.550832\pi$
$137$	−509.974	−0.318029	−0.159015	+	0.987276i	$0.550832\pi$
$138$	61.5529	0.0379691
$139$	−1983.00	−1.21004	−0.605022	−	0.796209i	$-0.706836\pi$
$139$	−1983.00	−1.21004	−0.605022	+	0.796209i	$0.706836\pi$
$140$	−831.474	−0.501946
$141$	−970.349	−0.579561
$142$	−223.341	−0.131989
$143$	−613.140	−0.358555
$144$	29.9686	0.0173430
$145$	290.459	0.166354
$146$	−332.992	−0.188758
$147$	1654.42	0.928261
$148$	1820.97	1.01137
$149$	1615.49	0.888227	0.444113	−	0.895971i	$-0.353519\pi$
$149$	1615.49	0.888227	0.444113	+	0.895971i	$0.353519\pi$
$150$	486.065	0.264580
$151$	3131.81	1.68784	0.843918	−	0.536472i	$-0.180243\pi$
$151$	3131.81	1.68784	0.843918	+	0.536472i	$0.180243\pi$
$152$	−952.408	−0.508227
$153$	911.655	0.481719
$154$	−557.480	−0.291708
$155$	−1294.54	−0.670837
$156$	−857.591	−0.440143
$157$	−655.262	−0.333093	−0.166546	−	0.986034i	$-0.553262\pi$
$157$	−655.262	−0.333093	−0.166546	+	0.986034i	$0.553262\pi$
$158$	1477.12	0.743757
$159$	−2123.46	−1.05913
$160$	995.376	0.491821
$161$	362.125	0.177263
$162$	−137.258	−0.0665680
$163$	3064.24	1.47245	0.736226	−	0.676736i	$-0.236606\pi$
$163$	3064.24	1.47245	0.736226	+	0.676736i	$0.236606\pi$
$164$	1171.98	0.558027
$165$	178.890	0.0844036
$166$	−491.760	−0.229928
$167$	1627.75	0.754244	0.377122	−	0.926164i	$-0.376914\pi$
$167$	1627.75	0.754244	0.377122	+	0.926164i	$0.376914\pi$
$168$	−1996.06	−0.916663
$169$	909.952	0.414179
$170$	930.495	0.419798
$171$	−385.298	−0.172307
$172$	−150.435	−0.0666894
$173$	1806.89	0.794076	0.397038	−	0.917802i	$-0.370038\pi$
$173$	1806.89	0.794076	0.397038	+	0.917802i	$0.370038\pi$
$174$	272.387	0.118676
$175$	2859.59	1.23523
$176$	−36.6283	−0.0156873
$177$	−599.730	−0.254680
$178$	1967.63	0.828538
$179$	−2208.74	−0.922284	−0.461142	−	0.887326i	$-0.652560\pi$
$179$	−2208.74	−0.922284	−0.461142	+	0.887326i	$0.652560\pi$
$180$	250.212	0.103609
$181$	2976.30	1.22225	0.611124	−	0.791535i	$-0.290718\pi$
$181$	2976.30	1.22225	0.611124	+	0.791535i	$0.290718\pi$
$182$	2824.91	1.15053
$183$	183.000	0.0739221
$184$	−269.366	−0.107924
$185$	1924.79	0.764938
$186$	−1213.99	−0.478571
$187$	−1114.25	−0.435731
$188$	1658.82	0.643520
$189$	−807.509	−0.310781
$190$	−393.260	−0.150158
$191$	−1704.47	−0.645711	−0.322856	−	0.946448i	$-0.604643\pi$
$191$	−1704.47	−0.645711	−0.322856	+	0.946448i	$0.604643\pi$
$192$	853.528	0.320823
$193$	−3364.59	−1.25486	−0.627431	−	0.778672i	$-0.715894\pi$
$193$	−3364.59	−1.25486	−0.627431	+	0.778672i	$0.715894\pi$
$194$	−2124.74	−0.786328
$195$	−906.487	−0.332897
$196$	−2828.24	−1.03070
$197$	−2645.53	−0.956784	−0.478392	−	0.878146i	$-0.658780\pi$
$197$	−2645.53	−0.956784	−0.478392	+	0.878146i	$0.658780\pi$
$198$	167.760	0.0602130
$199$	−2706.49	−0.964111	−0.482055	−	0.876141i	$-0.660110\pi$
$199$	−2706.49	−0.964111	−0.482055	+	0.876141i	$0.660110\pi$
$200$	−2127.10	−0.752044
$201$	−891.967	−0.313007
$202$	−1272.24	−0.443141
$203$	1602.49	0.554053
$204$	−1558.48	−0.534880
$205$	1238.80	0.422057
$206$	−1847.67	−0.624917
$207$	−108.972	−0.0365899
$208$	185.606	0.0618724
$209$	470.920	0.155857
$210$	−824.197	−0.270833
$211$	−85.0116	−0.0277367	−0.0138683	−	0.999904i	$-0.504415\pi$
$211$	−85.0116	−0.0277367	−0.0138683	+	0.999904i	$0.504415\pi$
$212$	3630.07	1.17601
$213$	395.400	0.127194
$214$	−483.143	−0.154332
$215$	−159.012	−0.0504397
$216$	600.665	0.189213
$217$	−7142.09	−2.23427
$218$	500.500	0.155496
$219$	589.525	0.181902
$220$	−305.814	−0.0937181
$221$	5646.19	1.71857
$222$	1805.03	0.545702
$223$	2798.88	0.840478	0.420239	−	0.907413i	$-0.361946\pi$
$223$	2798.88	0.840478	0.420239	+	0.907413i	$0.361946\pi$
$224$	5491.59	1.63804
$225$	−860.523	−0.254970
$226$	−3084.66	−0.907912
$227$	217.796	0.0636813	0.0318406	−	0.999493i	$-0.489863\pi$
$227$	217.796	0.0636813	0.0318406	+	0.999493i	$0.489863\pi$
$228$	658.669	0.191322
$229$	338.360	0.0976395	0.0488197	−	0.998808i	$-0.484454\pi$
$229$	338.360	0.0976395	0.0488197	+	0.998808i	$0.484454\pi$
$230$	−111.224	−0.0318866
$231$	986.956	0.281112
$232$	−1192.01	−0.337325
$233$	−2169.31	−0.609942	−0.304971	−	0.952362i	$-0.598647\pi$
$233$	−2169.31	−0.609942	−0.304971	+	0.952362i	$0.598647\pi$
$234$	−850.086	−0.237487
$235$	1753.39	0.486718
$236$	1025.24	0.282786
$237$	−2615.08	−0.716741
$238$	5133.63	1.39817
$239$	5417.25	1.46616	0.733081	−	0.680141i	$-0.238082\pi$
$239$	5417.25	1.46616	0.733081	+	0.680141i	$0.238082\pi$
$240$	−54.1525	−0.0145647
$241$	4234.93	1.13193	0.565967	−	0.824428i	$-0.308503\pi$
$241$	4234.93	1.13193	0.565967	+	0.824428i	$0.308503\pi$
$242$	−205.040	−0.0544647
$243$	243.000	0.0641500
$244$	−312.840	−0.0820799
$245$	−2989.49	−0.779558
$246$	1161.72	0.301093
$247$	−2386.28	−0.614718
$248$	5312.64	1.36029
$249$	870.606	0.221576
$250$	−2026.55	−0.512682
$251$	1935.53	0.486731	0.243365	−	0.969935i	$-0.421749\pi$
$251$	1935.53	0.486731	0.243365	+	0.969935i	$0.421749\pi$
$252$	1380.44	0.345078
$253$	133.189	0.0330968
$254$	−1061.59	−0.262245
$255$	−1647.34	−0.404550
$256$	−3948.29	−0.963939
$257$	−1021.47	−0.247928	−0.123964	−	0.992287i	$-0.539561\pi$
$257$	−1021.47	−0.247928	−0.123964	+	0.992287i	$0.539561\pi$
$258$	−149.119	−0.0359834
$259$	10619.3	2.54768
$260$	1549.64	0.369634
$261$	−482.230	−0.114365
$262$	−2405.20	−0.567151
$263$	−269.068	−0.0630854	−0.0315427	−	0.999502i	$-0.510042\pi$
$263$	−269.068	−0.0630854	−0.0315427	+	0.999502i	$0.510042\pi$
$264$	−734.146	−0.171150
$265$	3837.04	0.889462
$266$	−2169.66	−0.500113
$267$	−3483.46	−0.798443
$268$	1524.82	0.347550
$269$	−4369.51	−0.990386	−0.495193	−	0.868783i	$-0.664903\pi$
$269$	−4369.51	−0.990386	−0.495193	+	0.868783i	$0.664903\pi$
$270$	248.022	0.0559042
$271$	−3986.20	−0.893522	−0.446761	−	0.894653i	$-0.647423\pi$
$271$	−3986.20	−0.893522	−0.446761	+	0.894653i	$0.647423\pi$
$272$	337.297	0.0751899
$273$	−5001.18	−1.10874
$274$	864.174	0.190535
$275$	1051.75	0.230629
$276$	186.289	0.0406279
$277$	−5288.57	−1.14715	−0.573573	−	0.819155i	$-0.694443\pi$
$277$	−5288.57	−1.14715	−0.573573	+	0.819155i	$0.694443\pi$
$278$	3360.28	0.724951
$279$	2149.23	0.461187
$280$	3606.83	0.769819
$281$	2818.88	0.598435	0.299218	−	0.954185i	$-0.403274\pi$
$281$	2818.88	0.598435	0.299218	+	0.954185i	$0.403274\pi$
$282$	1644.30	0.347222
$283$	4466.75	0.938236	0.469118	−	0.883136i	$-0.344572\pi$
$283$	4466.75	0.938236	0.469118	+	0.883136i	$0.344572\pi$
$284$	−675.939	−0.141231
$285$	696.223	0.144704
$286$	1038.99	0.214815
$287$	6834.59	1.40569
$288$	−1652.56	−0.338118
$289$	5347.68	1.08848
$290$	−492.195	−0.0996645
$291$	3761.62	0.757766
$292$	−1007.80	−0.201976
$293$	−3682.08	−0.734161	−0.367080	−	0.930189i	$-0.619643\pi$
$293$	−3682.08	−0.734161	−0.367080	+	0.930189i	$0.619643\pi$
$294$	−2803.49	−0.556132
$295$	1083.70	0.213882
$296$	−7899.14	−1.55111
$297$	−297.000	−0.0580259
$298$	−2737.51	−0.532147
$299$	−674.903	−0.130537
$300$	1471.07	0.283107
$301$	−877.286	−0.167993
$302$	−5307.00	−1.01120
$303$	2252.36	0.427045
$304$	−142.554	−0.0268948
$305$	−330.676	−0.0620802
$306$	−1544.84	−0.288603
$307$	6586.90	1.22454	0.612271	−	0.790648i	$-0.290256\pi$
$307$	6586.90	1.22454	0.612271	+	0.790648i	$0.290256\pi$
$308$	−1687.21	−0.312135
$309$	3271.08	0.602218
$310$	2193.65	0.401906
$311$	−5548.14	−1.01159	−0.505797	−	0.862652i	$-0.668802\pi$
$311$	−5548.14	−1.01159	−0.505797	+	0.862652i	$0.668802\pi$
$312$	3720.12	0.675034
$313$	−5004.52	−0.903745	−0.451873	−	0.892083i	$-0.649244\pi$
$313$	−5004.52	−0.903745	−0.451873	+	0.892083i	$0.649244\pi$
$314$	1110.37	0.199560
$315$	1459.15	0.260996
$316$	4470.49	0.795838
$317$	1252.86	0.221980	0.110990	−	0.993822i	$-0.464598\pi$
$317$	1252.86	0.221980	0.110990	+	0.993822i	$0.464598\pi$
$318$	3598.30	0.634537
$319$	589.392	0.103447
$320$	−1542.30	−0.269429
$321$	855.350	0.148726
$322$	−613.636	−0.106201
$323$	−4336.53	−0.747031
$324$	−415.410	−0.0712294
$325$	−5329.51	−0.909624
$326$	−5192.49	−0.882164
$327$	−886.079	−0.149848
$328$	−5083.90	−0.855828
$329$	9673.65	1.62105
$330$	−303.138	−0.0505672
$331$	9251.89	1.53634	0.768172	−	0.640244i	$-0.221167\pi$
$331$	9251.89	1.53634	0.768172	+	0.640244i	$0.221167\pi$
$332$	−1488.31	−0.246028
$333$	−3195.61	−0.525881
$334$	−2758.29	−0.451877
$335$	1611.76	0.262865
$336$	−298.765	−0.0485088
$337$	−6266.23	−1.01289	−0.506444	−	0.862273i	$-0.669040\pi$
$337$	−6266.23	−1.01289	−0.506444	+	0.862273i	$0.669040\pi$
$338$	−1541.95	−0.248140
$339$	5461.03	0.874934
$340$	2816.13	0.449195
$341$	−2626.84	−0.417160
$342$	652.905	0.103231
$343$	−6234.98	−0.981508
$344$	652.569	0.102280
$345$	196.910	0.0307284
$346$	−3061.85	−0.475740
$347$	−2257.74	−0.349285	−0.174642	−	0.984632i	$-0.555877\pi$
$347$	−2257.74	−0.349285	−0.174642	+	0.984632i	$0.555877\pi$
$348$	824.375	0.126986
$349$	−4727.10	−0.725031	−0.362516	−	0.931978i	$-0.618082\pi$
$349$	−4727.10	−0.725031	−0.362516	+	0.931978i	$0.618082\pi$
$350$	−4845.70	−0.740039
$351$	1504.98	0.228860
$352$	2019.79	0.305839
$353$	2709.34	0.408508	0.204254	−	0.978918i	$-0.434523\pi$
$353$	2709.34	0.408508	0.204254	+	0.978918i	$0.434523\pi$
$354$	1016.27	0.152582
$355$	−714.478	−0.106818
$356$	5955.00	0.886557
$357$	−9088.52	−1.34738
$358$	3742.81	0.552552
$359$	−3416.92	−0.502335	−0.251167	−	0.967944i	$-0.580814\pi$
$359$	−3416.92	−0.502335	−0.251167	+	0.967944i	$0.580814\pi$
$360$	−1085.39	−0.158902
$361$	−5026.23	−0.732793
$362$	−5043.48	−0.732264
$363$	363.000	0.0524864
$364$	8549.54	1.23109
$365$	−1065.26	−0.152762
$366$	−310.102	−0.0442876
$367$	−3768.30	−0.535977	−0.267989	−	0.963422i	$-0.586359\pi$
$367$	−3768.30	−0.535977	−0.267989	+	0.963422i	$0.586359\pi$
$368$	−40.3180	−0.00571120
$369$	−2056.70	−0.290156
$370$	−3261.65	−0.458284
$371$	21169.3	2.96242
$372$	−3674.13	−0.512083
$373$	−7739.83	−1.07440	−0.537202	−	0.843453i	$-0.680519\pi$
$373$	−7739.83	−1.07440	−0.537202	+	0.843453i	$0.680519\pi$
$374$	1888.14	0.261052
$375$	3587.79	0.494060
$376$	−7195.74	−0.986947
$377$	−2986.61	−0.408006
$378$	1368.36	0.186193
$379$	−2719.31	−0.368554	−0.184277	−	0.982874i	$-0.558994\pi$
$379$	−2719.31	−0.368554	−0.184277	+	0.982874i	$0.558994\pi$
$380$	−1190.20	−0.160673
$381$	1879.43	0.252719
$382$	2888.29	0.386853
$383$	10207.4	1.36181	0.680903	−	0.732374i	$-0.261587\pi$
$383$	10207.4	1.36181	0.680903	+	0.732374i	$0.261587\pi$
$384$	2960.48	0.393428
$385$	−1783.40	−0.236080
$386$	5701.45	0.751803
$387$	263.998	0.0346764
$388$	−6430.51	−0.841391
$389$	1964.64	0.256070	0.128035	−	0.991770i	$-0.459133\pi$
$389$	1964.64	0.256070	0.128035	+	0.991770i	$0.459133\pi$
$390$	1536.08	0.199442
$391$	−1226.49	−0.158634
$392$	12268.6	1.58075
$393$	4258.13	0.546550
$394$	4482.98	0.573221
$395$	4725.38	0.601923
$396$	507.723	0.0644294
$397$	−1159.14	−0.146537	−0.0732687	−	0.997312i	$-0.523343\pi$
$397$	−1159.14	−0.146537	−0.0732687	+	0.997312i	$0.523343\pi$
$398$	4586.27	0.577610
$399$	3841.13	0.481948
$400$	−318.379	−0.0397974
$401$	13121.5	1.63406	0.817030	−	0.576595i	$-0.195619\pi$
$401$	13121.5	1.63406	0.817030	+	0.576595i	$0.195619\pi$
$402$	1511.48	0.187526
$403$	13310.9	1.64532
$404$	−3850.42	−0.474172
$405$	−439.095	−0.0538735
$406$	−2715.49	−0.331940
$407$	3905.74	0.475677
$408$	6760.49	0.820329
$409$	−10169.6	−1.22947	−0.614735	−	0.788734i	$-0.710737\pi$
$409$	−10169.6	−1.22947	−0.614735	+	0.788734i	$0.710737\pi$
$410$	−2099.20	−0.252859
$411$	−1529.92	−0.183614
$412$	−5591.94	−0.668677
$413$	5978.86	0.712349
$414$	184.659	0.0219215
$415$	−1573.16	−0.186081
$416$	−10234.8	−1.20626
$417$	−5949.00	−0.698619
$418$	−797.994	−0.0933760
$419$	7844.38	0.914614	0.457307	−	0.889309i	$-0.348814\pi$
$419$	7844.38	0.914614	0.457307	+	0.889309i	$0.348814\pi$
$420$	−2494.42	−0.289798
$421$	7646.81	0.885232	0.442616	−	0.896711i	$-0.354051\pi$
$421$	7646.81	0.885232	0.442616	+	0.896711i	$0.354051\pi$
$422$	144.056	0.0166174
$423$	−2911.05	−0.334610
$424$	−15746.8	−1.80361
$425$	−9685.19	−1.10541
$426$	−670.024	−0.0762036
$427$	−1824.37	−0.206763
$428$	−1462.23	−0.165139
$429$	−1839.42	−0.207012
$430$	269.453	0.0302191
$431$	5743.74	0.641917	0.320959	−	0.947093i	$-0.395995\pi$
$431$	5743.74	0.641917	0.320959	+	0.947093i	$0.395995\pi$
$432$	89.9059	0.0100130
$433$	−5316.69	−0.590079	−0.295039	−	0.955485i	$-0.595333\pi$
$433$	−5316.69	−0.590079	−0.295039	+	0.955485i	$0.595333\pi$
$434$	12102.6	1.33858
$435$	871.376	0.0960444
$436$	1514.76	0.166385
$437$	518.356	0.0567422
$438$	−998.977	−0.108979
$439$	−10742.3	−1.16788	−0.583942	−	0.811795i	$-0.698490\pi$
$439$	−10742.3	−1.16788	−0.583942	+	0.811795i	$0.698490\pi$
$440$	1326.58	0.143733
$441$	4963.26	0.535932
$442$	−9567.72	−1.02962
$443$	6071.99	0.651217	0.325608	−	0.945505i	$-0.394431\pi$
$443$	6071.99	0.651217	0.325608	+	0.945505i	$0.394431\pi$
$444$	5462.91	0.583915
$445$	6294.52	0.670537
$446$	−4742.82	−0.503541
$447$	4846.46	0.512818
$448$	−8509.03	−0.897352
$449$	10442.8	1.09761	0.548803	−	0.835952i	$-0.315084\pi$
$449$	10442.8	1.09761	0.548803	+	0.835952i	$0.315084\pi$
$450$	1458.19	0.152755
$451$	2513.75	0.262456
$452$	−9335.67	−0.971489
$453$	9395.44	0.974473
$454$	−369.065	−0.0381522
$455$	9036.99	0.931123
$456$	−2857.22	−0.293425
$457$	12919.0	1.32238	0.661189	−	0.750220i	$-0.270052\pi$
$457$	12919.0	1.32238	0.661189	+	0.750220i	$0.270052\pi$
$458$	−573.366	−0.0584970
$459$	2734.97	0.278120
$460$	−336.619	−0.0341195
$461$	6129.61	0.619272	0.309636	−	0.950855i	$-0.399793\pi$
$461$	6129.61	0.619272	0.309636	+	0.950855i	$0.399793\pi$
$462$	−1672.44	−0.168418
$463$	5419.10	0.543946	0.271973	−	0.962305i	$-0.412324\pi$
$463$	5419.10	0.543946	0.271973	+	0.962305i	$0.412324\pi$
$464$	−178.417	−0.0178509
$465$	−3883.61	−0.387308
$466$	3676.00	0.365424
$467$	16993.4	1.68385	0.841927	−	0.539592i	$-0.181421\pi$
$467$	16993.4	1.68385	0.841927	+	0.539592i	$0.181421\pi$
$468$	−2572.77	−0.254117
$469$	8892.24	0.875491
$470$	−2971.21	−0.291599
$471$	−1965.79	−0.192311
$472$	−4447.37	−0.433701
$473$	−322.664	−0.0313660
$474$	4431.37	0.429408
$475$	4093.30	0.395397
$476$	15536.9	1.49608
$477$	−6370.39	−0.611488
$478$	−9179.77	−0.878395
$479$	18095.7	1.72612	0.863060	−	0.505101i	$-0.168545\pi$
$479$	18095.7	1.72612	0.863060	+	0.505101i	$0.168545\pi$
$480$	2986.13	0.283953
$481$	−19791.5	−1.87612
$482$	−7176.28	−0.678155
$483$	1086.37	0.102343
$484$	−620.551	−0.0582786
$485$	−6797.15	−0.636376
$486$	−411.774	−0.0384331
$487$	−16599.0	−1.54451	−0.772253	−	0.635315i	$-0.780870\pi$
$487$	−16599.0	−1.54451	−0.772253	+	0.635315i	$0.780870\pi$
$488$	1357.06	0.125884
$489$	9192.72	0.850121
$490$	5065.83	0.467043
$491$	19066.1	1.75243	0.876215	−	0.481920i	$-0.160060\pi$
$491$	19066.1	1.75243	0.876215	+	0.481920i	$0.160060\pi$
$492$	3515.94	0.322177
$493$	−5427.50	−0.495826
$494$	4043.66	0.368285
$495$	536.671	0.0487304
$496$	795.181	0.0719852
$497$	−3941.85	−0.355767
$498$	−1475.28	−0.132749
$499$	10784.2	0.967471	0.483736	−	0.875214i	$-0.339280\pi$
$499$	10784.2	0.967471	0.483736	+	0.875214i	$0.339280\pi$
$500$	−6133.34	−0.548583
$501$	4883.24	0.435463
$502$	−3279.84	−0.291606
$503$	8072.36	0.715564	0.357782	−	0.933805i	$-0.383533\pi$
$503$	8072.36	0.715564	0.357782	+	0.933805i	$0.383533\pi$
$504$	−5988.18	−0.529236
$505$	−4069.95	−0.358634
$506$	−225.694	−0.0198287
$507$	2729.85	0.239126
$508$	−3212.90	−0.280609
$509$	22557.0	1.96429	0.982143	−	0.188135i	$-0.0602442\pi$
$509$	22557.0	1.96429	0.982143	+	0.188135i	$0.0602442\pi$
$510$	2791.49	0.242371
$511$	−5877.13	−0.508784
$512$	−1204.05	−0.103930
$513$	−1155.89	−0.0994814
$514$	1730.92	0.148536
$515$	−5910.76	−0.505746
$516$	−451.306	−0.0385031
$517$	3557.95	0.302666
$518$	−17994.8	−1.52635
$519$	5420.66	0.458460
$520$	−6722.16	−0.566897
$521$	16554.2	1.39204	0.696021	−	0.718021i	$-0.254952\pi$
$521$	16554.2	1.39204	0.696021	+	0.718021i	$0.254952\pi$
$522$	817.160	0.0685175
$523$	15417.4	1.28901	0.644507	−	0.764598i	$-0.277063\pi$
$523$	15417.4	1.28901	0.644507	+	0.764598i	$0.277063\pi$
$524$	−7279.30	−0.606866
$525$	8578.77	0.713158
$526$	455.948	0.0377952
$527$	24189.6	1.99946
$528$	−109.885	−0.00905707
$529$	−12020.4	−0.987951
$530$	−6502.04	−0.532888
$531$	−1799.19	−0.147040
$532$	−6566.44	−0.535134
$533$	−12737.8	−1.03515
$534$	5902.88	0.478357
$535$	−1545.60	−0.124901
$536$	−6614.49	−0.533027
$537$	−6626.22	−0.532481
$538$	7404.33	0.593352
$539$	−6066.21	−0.484768
$540$	750.635	0.0598188
$541$	23365.8	1.85688	0.928441	−	0.371479i	$-0.121149\pi$
$541$	23365.8	1.85688	0.928441	+	0.371479i	$0.121149\pi$
$542$	6754.80	0.535320
$543$	8928.91	0.705666
$544$	−18599.5	−1.46590
$545$	1601.12	0.125843
$546$	8474.72	0.664257
$547$	−20042.6	−1.56666	−0.783328	−	0.621608i	$-0.786480\pi$
$547$	−20042.6	−1.56666	−0.783328	+	0.621608i	$0.786480\pi$
$548$	2615.41	0.203878
$549$	549.000	0.0426790
$550$	−1782.24	−0.138172
$551$	2293.85	0.177353
$552$	−808.099	−0.0623097
$553$	26070.4	2.00475
$554$	8961.72	0.687269
$555$	5774.38	0.441637
$556$	10169.9	0.775716
$557$	−367.533	−0.0279585	−0.0139792	−	0.999902i	$-0.504450\pi$
$557$	−367.533	−0.0279585	−0.0139792	+	0.999902i	$0.504450\pi$
$558$	−3641.97	−0.276303
$559$	1635.03	0.123711
$560$	539.860	0.0407380
$561$	−3342.74	−0.251569
$562$	−4776.72	−0.358530
$563$	−8743.91	−0.654550	−0.327275	−	0.944929i	$-0.606130\pi$
$563$	−8743.91	−0.654550	−0.327275	+	0.944929i	$0.606130\pi$
$564$	4976.45	0.371536
$565$	−9867.94	−0.734774
$566$	−7569.11	−0.562108
$567$	−2422.53	−0.179430
$568$	2932.14	0.216602
$569$	7284.45	0.536696	0.268348	−	0.963322i	$-0.413522\pi$
$569$	7284.45	0.536696	0.268348	+	0.963322i	$0.413522\pi$
$570$	−1179.78	−0.0866940
$571$	18488.3	1.35501	0.677504	−	0.735519i	$-0.263061\pi$
$571$	18488.3	1.35501	0.677504	+	0.735519i	$0.263061\pi$
$572$	3144.50	0.229857
$573$	−5113.40	−0.372802
$574$	−11581.5	−0.842166
$575$	1157.69	0.0839639
$576$	2560.58	0.185227
$577$	6998.94	0.504973	0.252487	−	0.967600i	$-0.418752\pi$
$577$	6998.94	0.504973	0.252487	+	0.967600i	$0.418752\pi$
$578$	−9061.89	−0.652119
$579$	−10093.8	−0.724495
$580$	−1489.62	−0.106644
$581$	−8679.29	−0.619755
$582$	−6374.23	−0.453987
$583$	7786.03	0.553112
$584$	4371.70	0.309764
$585$	−2719.46	−0.192198
$586$	6239.44	0.439845
$587$	24185.3	1.70057	0.850285	−	0.526323i	$-0.176430\pi$
$587$	24185.3	1.70057	0.850285	+	0.526323i	$0.176430\pi$
$588$	−8484.73	−0.595075
$589$	−10223.4	−0.715192
$590$	−1836.37	−0.128139
$591$	−7936.60	−0.552400
$592$	−1182.32	−0.0820830
$593$	−22054.1	−1.52724	−0.763620	−	0.645666i	$-0.776580\pi$
$593$	−22054.1	−1.52724	−0.763620	+	0.645666i	$0.776580\pi$
$594$	503.280	0.0347640
$595$	16422.7	1.13154
$596$	−8285.05	−0.569411
$597$	−8119.47	−0.556630
$598$	1143.65	0.0782065
$599$	7568.46	0.516258	0.258129	−	0.966110i	$-0.416894\pi$
$599$	7568.46	0.516258	0.258129	+	0.966110i	$0.416894\pi$
$600$	−6381.31	−0.434193
$601$	−1638.33	−0.111196	−0.0555982	−	0.998453i	$-0.517707\pi$
$601$	−1638.33	−0.111196	−0.0555982	+	0.998453i	$0.517707\pi$
$602$	1486.60	0.100647
$603$	−2675.90	−0.180715
$604$	−16061.6	−1.08201
$605$	−655.931	−0.0440783
$606$	−3816.72	−0.255848
$607$	−3376.52	−0.225780	−0.112890	−	0.993607i	$-0.536011\pi$
$607$	−3376.52	−0.225780	−0.112890	+	0.993607i	$0.536011\pi$
$608$	7860.83	0.524340
$609$	4807.47	0.319883
$610$	560.345	0.0371930
$611$	−18029.1	−1.19375
$612$	−4675.44	−0.308813
$613$	−8201.66	−0.540394	−0.270197	−	0.962805i	$-0.587089\pi$
$613$	−8201.66	−0.540394	−0.270197	+	0.962805i	$0.587089\pi$
$614$	−11161.8	−0.733638
$615$	3716.40	0.243675
$616$	7318.89	0.478712
$617$	21552.1	1.40624	0.703122	−	0.711069i	$-0.251789\pi$
$617$	21552.1	1.40624	0.703122	+	0.711069i	$0.251789\pi$
$618$	−5543.00	−0.360796
$619$	−13659.7	−0.886965	−0.443482	−	0.896283i	$-0.646257\pi$
$619$	−13659.7	−0.886965	−0.443482	+	0.896283i	$0.646257\pi$
$620$	6639.05	0.430050
$621$	−326.917	−0.0211252
$622$	9401.56	0.606059
$623$	34727.5	2.23327
$624$	556.818	0.0357220
$625$	5468.67	0.349995
$626$	8480.38	0.541444
$627$	1412.76	0.0899843
$628$	3360.52	0.213534
$629$	−35966.6	−2.27994
$630$	−2472.59	−0.156366
$631$	13789.4	0.869961	0.434981	−	0.900440i	$-0.356755\pi$
$631$	13789.4	0.869961	0.434981	+	0.900440i	$0.356755\pi$
$632$	−19392.4	−1.22055
$633$	−255.035	−0.0160138
$634$	−2123.03	−0.132991
$635$	−3396.08	−0.212235
$636$	10890.2	0.678970
$637$	30739.2	1.91198
$638$	−998.751	−0.0619764
$639$	1186.20	0.0734357
$640$	−5349.51	−0.330403
$641$	−466.921	−0.0287711	−0.0143855	−	0.999897i	$-0.504579\pi$
$641$	−466.921	−0.0287711	−0.0143855	+	0.999897i	$0.504579\pi$
$642$	−1449.43	−0.0891034
$643$	19298.8	1.18362	0.591812	−	0.806076i	$-0.298413\pi$
$643$	19298.8	1.18362	0.591812	+	0.806076i	$0.298413\pi$
$644$	−1857.16	−0.113637
$645$	−477.037	−0.0291214
$646$	7348.44	0.447555
$647$	−9470.50	−0.575462	−0.287731	−	0.957711i	$-0.592901\pi$
$647$	−9470.50	−0.575462	−0.287731	+	0.957711i	$0.592901\pi$
$648$	1802.00	0.109242
$649$	2199.01	0.133003
$650$	9031.09	0.544967
$651$	−21426.3	−1.28996
$652$	−15715.0	−0.943937
$653$	−23802.2	−1.42642	−0.713209	−	0.700951i	$-0.752759\pi$
$653$	−23802.2	−1.42642	−0.713209	+	0.700951i	$0.752759\pi$
$654$	1501.50	0.0897757
$655$	−7694.32	−0.458996
$656$	−760.945	−0.0452895
$657$	1768.58	0.105021
$658$	−16392.4	−0.971191
$659$	16382.6	0.968401	0.484201	−	0.874957i	$-0.339111\pi$
$659$	16382.6	0.968401	0.484201	+	0.874957i	$0.339111\pi$
$660$	−917.442	−0.0541082
$661$	2525.66	0.148619	0.0743093	−	0.997235i	$-0.476325\pi$
$661$	2525.66	0.148619	0.0743093	+	0.997235i	$0.476325\pi$
$662$	−15677.7	−0.920442
$663$	16938.6	0.992216
$664$	6456.08	0.377326
$665$	−6940.82	−0.404742
$666$	5415.10	0.315061
$667$	648.763	0.0376615
$668$	−8347.93	−0.483519
$669$	8396.63	0.485250
$670$	−2731.20	−0.157486
$671$	−671.000	−0.0386046
$672$	16474.8	0.945726
$673$	26626.8	1.52509	0.762547	−	0.646933i	$-0.223949\pi$
$673$	26626.8	1.52509	0.762547	+	0.646933i	$0.223949\pi$
$674$	10618.4	0.606833
$675$	−2581.57	−0.147207
$676$	−4666.70	−0.265516
$677$	−8342.67	−0.473612	−0.236806	−	0.971557i	$-0.576101\pi$
$677$	−8342.67	−0.473612	−0.236806	+	0.971557i	$0.576101\pi$
$678$	−9253.97	−0.524184
$679$	−37500.5	−2.11950
$680$	−12216.0	−0.688916
$681$	653.389	0.0367664
$682$	4451.30	0.249925
$683$	−27018.6	−1.51367	−0.756836	−	0.653604i	$-0.773256\pi$
$683$	−27018.6	−1.51367	−0.756836	+	0.653604i	$0.773256\pi$
$684$	1976.01	0.110460
$685$	2764.53	0.154200
$686$	10565.4	0.588033
$687$	1015.08	0.0563722
$688$	97.6747	0.00541252
$689$	−39454.0	−2.18153
$690$	−333.673	−0.0184098
$691$	−18630.6	−1.02568	−0.512838	−	0.858485i	$-0.671406\pi$
$691$	−18630.6	−1.02568	−0.512838	+	0.858485i	$0.671406\pi$
$692$	−9266.65	−0.509054
$693$	2960.87	0.162300
$694$	3825.84	0.209261
$695$	10749.7	0.586704
$696$	−3576.03	−0.194755
$697$	−23148.2	−1.25796
$698$	8010.28	0.434375
$699$	−6507.94	−0.352150
$700$	−14665.5	−0.791860
$701$	645.826	0.0347967	0.0173984	−	0.999849i	$-0.494462\pi$
$701$	645.826	0.0347967	0.0173984	+	0.999849i	$0.494462\pi$
$702$	−2550.26	−0.137113
$703$	15200.8	0.815515
$704$	−3129.60	−0.167544
$705$	5260.18	0.281007
$706$	−4591.09	−0.244742
$707$	−22454.3	−1.19446
$708$	3075.72	0.163267
$709$	36935.4	1.95647	0.978235	−	0.207502i	$-0.0665334\pi$
$709$	36935.4	1.95647	0.978235	+	0.207502i	$0.0665334\pi$
$710$	1210.71	0.0639962
$711$	−7845.24	−0.413811
$712$	−25832.0	−1.35969
$713$	−2891.45	−0.151873
$714$	15400.9	0.807233
$715$	3323.78	0.173850
$716$	11327.6	0.591244
$717$	16251.7	0.846489
$718$	5790.12	0.300955
$719$	−10217.1	−0.529950	−0.264975	−	0.964255i	$-0.585364\pi$
$719$	−10217.1	−0.529950	−0.264975	+	0.964255i	$0.585364\pi$
$720$	−162.458	−0.00840894
$721$	−32610.3	−1.68442
$722$	8517.17	0.439025
$723$	12704.8	0.653522
$724$	−15264.0	−0.783541
$725$	5123.08	0.262437
$726$	−615.120	−0.0314452
$727$	−33164.3	−1.69188	−0.845939	−	0.533279i	$-0.820960\pi$
$727$	−33164.3	−1.69188	−0.845939	+	0.533279i	$0.820960\pi$
$728$	−37086.8	−1.88809
$729$	729.000	0.0370370
$730$	1805.12	0.0915215
$731$	2971.29	0.150338
$732$	−938.519	−0.0473889
$733$	−10538.7	−0.531043	−0.265522	−	0.964105i	$-0.585544\pi$
$733$	−10538.7	−0.531043	−0.265522	+	0.964105i	$0.585544\pi$
$734$	6385.55	0.321110
$735$	−8968.48	−0.450078
$736$	2223.25	0.111345
$737$	3270.54	0.163463
$738$	3485.17	0.173836
$739$	12510.0	0.622718	0.311359	−	0.950292i	$-0.399216\pi$
$739$	12510.0	0.622718	0.311359	+	0.950292i	$0.399216\pi$
$740$	−9871.33	−0.490375
$741$	−7158.84	−0.354908
$742$	−35872.4	−1.77482
$743$	7194.01	0.355212	0.177606	−	0.984102i	$-0.443165\pi$
$743$	7194.01	0.355212	0.177606	+	0.984102i	$0.443165\pi$
$744$	15937.9	0.785366
$745$	−8757.42	−0.430667
$746$	13115.5	0.643689
$747$	2611.82	0.127927
$748$	5714.43	0.279332
$749$	−8527.20	−0.415991
$750$	−6079.66	−0.295997
$751$	5542.76	0.269318	0.134659	−	0.990892i	$-0.457006\pi$
$751$	5542.76	0.269318	0.134659	+	0.990892i	$0.457006\pi$
$752$	−1077.04	−0.0522281
$753$	5806.58	0.281014
$754$	5060.95	0.244441
$755$	−16977.3	−0.818367
$756$	4141.33	0.199231
$757$	−4946.11	−0.237476	−0.118738	−	0.992926i	$-0.537885\pi$
$757$	−4946.11	−0.237476	−0.118738	+	0.992926i	$0.537885\pi$
$758$	4608.00	0.220805
$759$	399.566	0.0191085
$760$	5162.93	0.246420
$761$	−22228.7	−1.05886	−0.529428	−	0.848355i	$-0.677593\pi$
$761$	−22228.7	−1.05886	−0.529428	+	0.848355i	$0.677593\pi$
$762$	−3184.78	−0.151407
$763$	8833.55	0.419130
$764$	8741.39	0.413943
$765$	−4942.01	−0.233567
$766$	−17296.8	−0.815874
$767$	−11143.0	−0.524576
$768$	−11844.9	−0.556530
$769$	25471.2	1.19443	0.597214	−	0.802082i	$-0.296274\pi$
$769$	25471.2	1.19443	0.597214	+	0.802082i	$0.296274\pi$
$770$	3022.06	0.141438
$771$	−3064.40	−0.143141
$772$	17255.4	0.804448
$773$	23994.4	1.11645	0.558226	−	0.829689i	$-0.311482\pi$
$773$	23994.4	1.11645	0.558226	+	0.829689i	$0.311482\pi$
$774$	−447.356	−0.0207750
$775$	−22832.9	−1.05830
$776$	27894.7	1.29042
$777$	31857.8	1.47090
$778$	−3329.17	−0.153415
$779$	9783.24	0.449963
$780$	4648.93	0.213408
$781$	−1449.80	−0.0664251
$782$	2078.33	0.0950398
$783$	−1446.69	−0.0660287
$784$	1836.32	0.0836518
$785$	3552.12	0.161504
$786$	−7215.59	−0.327445
$787$	19406.9	0.879012	0.439506	−	0.898240i	$-0.355154\pi$
$787$	19406.9	0.879012	0.439506	+	0.898240i	$0.355154\pi$
$788$	13567.7	0.613361
$789$	−807.205	−0.0364224
$790$	−8007.37	−0.360619
$791$	−54442.4	−2.44722
$792$	−2202.44	−0.0988135
$793$	3400.14	0.152261
$794$	1964.21	0.0877923
$795$	11511.1	0.513531
$796$	13880.3	0.618057
$797$	24518.1	1.08968	0.544840	−	0.838540i	$-0.316590\pi$
$797$	24518.1	1.08968	0.544840	+	0.838540i	$0.316590\pi$
$798$	−6508.97	−0.288741
$799$	−32763.8	−1.45069
$800$	17556.3	0.775888
$801$	−10450.4	−0.460981
$802$	−22235.0	−0.978985
$803$	−2161.59	−0.0949950
$804$	4574.47	0.200658
$805$	−1963.05	−0.0859483
$806$	−22556.0	−0.985732
$807$	−13108.5	−0.571799
$808$	16702.6	0.727223
$809$	−12323.8	−0.535578	−0.267789	−	0.963478i	$-0.586293\pi$
$809$	−12323.8	−0.535578	−0.267789	+	0.963478i	$0.586293\pi$
$810$	744.065	0.0322763
$811$	−32314.8	−1.39917	−0.699584	−	0.714550i	$-0.746631\pi$
$811$	−32314.8	−1.39917	−0.699584	+	0.714550i	$0.746631\pi$
$812$	−8218.40	−0.355184
$813$	−11958.6	−0.515875
$814$	−6618.46	−0.284984
$815$	−16611.0	−0.713936
$816$	1011.89	0.0434109
$817$	−1255.77	−0.0537748
$818$	17232.8	0.736590
$819$	−15003.5	−0.640129
$820$	−6353.22	−0.270566
$821$	20455.3	0.869545	0.434773	−	0.900540i	$-0.356829\pi$
$821$	20455.3	0.869545	0.434773	+	0.900540i	$0.356829\pi$
$822$	2592.52	0.110006
$823$	37184.4	1.57493	0.787464	−	0.616360i	$-0.211393\pi$
$823$	37184.4	1.57493	0.787464	+	0.616360i	$0.211393\pi$
$824$	24257.1	1.02553
$825$	3155.25	0.133154
$826$	−10131.4	−0.426777
$827$	19974.4	0.839876	0.419938	−	0.907553i	$-0.362052\pi$
$827$	19974.4	0.839876	0.419938	+	0.907553i	$0.362052\pi$
$828$	558.867	0.0234565
$829$	−25009.5	−1.04779	−0.523893	−	0.851784i	$-0.675521\pi$
$829$	−25009.5	−1.04779	−0.523893	+	0.851784i	$0.675521\pi$
$830$	2665.79	0.111483
$831$	−15865.7	−0.662305
$832$	15858.6	0.660813
$833$	55861.5	2.32351
$834$	10080.9	0.418551
$835$	−8823.88	−0.365704
$836$	−2415.12	−0.0999147
$837$	6447.70	0.266267
$838$	−13292.7	−0.547956
$839$	−23493.8	−0.966740	−0.483370	−	0.875416i	$-0.660587\pi$
$839$	−23493.8	−0.966740	−0.483370	+	0.875416i	$0.660587\pi$
$840$	10820.5	0.444455
$841$	−21518.1	−0.882286
$842$	−12957.9	−0.530353
$843$	8456.64	0.345507
$844$	435.983	0.0177810
$845$	−4932.77	−0.200820
$846$	4932.90	0.200469
$847$	−3618.84	−0.146806
$848$	−2356.94	−0.0954452
$849$	13400.2	0.541691
$850$	16412.0	0.662266
$851$	4299.18	0.173177
$852$	−2027.82	−0.0815398
$853$	19575.2	0.785745	0.392873	−	0.919593i	$-0.371481\pi$
$853$	19575.2	0.785745	0.392873	+	0.919593i	$0.371481\pi$
$854$	3091.48	0.123874
$855$	2088.67	0.0835450
$856$	6342.95	0.253268
$857$	38384.0	1.52996	0.764978	−	0.644057i	$-0.222750\pi$
$857$	38384.0	1.52996	0.764978	+	0.644057i	$0.222750\pi$
$858$	3116.98	0.124023
$859$	5715.77	0.227031	0.113515	−	0.993536i	$-0.463789\pi$
$859$	5715.77	0.227031	0.113515	+	0.993536i	$0.463789\pi$
$860$	815.497	0.0323351
$861$	20503.8	0.811576
$862$	−9733.03	−0.384580
$863$	9666.14	0.381274	0.190637	−	0.981661i	$-0.438945\pi$
$863$	9666.14	0.381274	0.190637	+	0.981661i	$0.438945\pi$
$864$	−4957.67	−0.195212
$865$	−9794.99	−0.385017
$866$	9009.38	0.353523
$867$	16043.0	0.628432
$868$	36628.3	1.43231
$869$	9588.62	0.374306
$870$	−1476.59	−0.0575413
$871$	−16572.8	−0.644714
$872$	−6570.83	−0.255179
$873$	11284.9	0.437497
$874$	−878.378	−0.0339949
$875$	−35767.5	−1.38190
$876$	−3023.39	−0.116611
$877$	−25194.1	−0.970060	−0.485030	−	0.874497i	$-0.661191\pi$
$877$	−25194.1	−0.970060	−0.485030	+	0.874497i	$0.661191\pi$
$878$	18203.3	0.699693
$879$	−11046.2	−0.423868
$880$	198.559	0.00760617
$881$	−5596.40	−0.214015	−0.107008	−	0.994258i	$-0.534127\pi$
$881$	−5596.40	−0.214015	−0.107008	+	0.994258i	$0.534127\pi$
$882$	−8410.47	−0.321083
$883$	33839.2	1.28967	0.644836	−	0.764321i	$-0.276926\pi$
$883$	33839.2	1.28967	0.644836	+	0.764321i	$0.276926\pi$
$884$	−28956.6	−1.10171
$885$	3251.09	0.123485
$886$	−10289.3	−0.390152
$887$	−49335.3	−1.86755	−0.933776	−	0.357859i	$-0.883507\pi$
$887$	−49335.3	−1.86755	−0.933776	+	0.357859i	$0.883507\pi$
$888$	−23697.4	−0.895533
$889$	−18736.5	−0.706864
$890$	−10666.3	−0.401727
$891$	−891.000	−0.0335013
$892$	−14354.1	−0.538801
$893$	13847.2	0.518900
$894$	−8212.54	−0.307235
$895$	11973.4	0.447180
$896$	−29513.8	−1.10043
$897$	−2024.71	−0.0753658
$898$	−17695.8	−0.657589
$899$	−12795.4	−0.474693
$900$	4413.21	0.163452
$901$	−71698.7	−2.65109
$902$	−4259.65	−0.157241
$903$	−2631.86	−0.0969909
$904$	40497.0	1.48994
$905$	−16134.3	−0.592622
$906$	−15921.0	−0.583818
$907$	13542.7	0.495786	0.247893	−	0.968787i	$-0.420262\pi$
$907$	13542.7	0.495786	0.247893	+	0.968787i	$0.420262\pi$
$908$	−1116.97	−0.0408238
$909$	6757.07	0.246554
$910$	−15313.6	−0.557847
$911$	11857.0	0.431220	0.215610	−	0.976480i	$-0.430826\pi$
$911$	11857.0	0.431220	0.215610	+	0.976480i	$0.430826\pi$
$912$	−427.661	−0.0155277
$913$	−3192.22	−0.115714
$914$	−21891.9	−0.792252
$915$	−992.028	−0.0358420
$916$	−1735.28	−0.0625932
$917$	−42450.4	−1.52872
$918$	−4634.52	−0.166625
$919$	−41379.2	−1.48528	−0.742641	−	0.669690i	$-0.766427\pi$
$919$	−41379.2	−1.48528	−0.742641	+	0.669690i	$0.766427\pi$
$920$	1460.21	0.0523280
$921$	19760.7	0.706989
$922$	−10386.9	−0.371013
$923$	7346.54	0.261987
$924$	−5061.62	−0.180211
$925$	33949.3	1.20675
$926$	−9182.90	−0.325884
$927$	9813.25	0.347691
$928$	9838.42	0.348019
$929$	46358.1	1.63720	0.818601	−	0.574363i	$-0.194750\pi$
$929$	46358.1	1.63720	0.818601	+	0.574363i	$0.194750\pi$
$930$	6580.95	0.232041
$931$	−23609.1	−0.831102
$932$	11125.4	0.391013
$933$	−16644.4	−0.584044
$934$	−28796.0	−1.00882
$935$	6040.23	0.211269
$936$	11160.4	0.389731
$937$	−49092.3	−1.71161	−0.855804	−	0.517300i	$-0.826937\pi$
$937$	−49092.3	−1.71161	−0.855804	+	0.517300i	$0.826937\pi$
$938$	−15068.3	−0.524517
$939$	−15013.6	−0.521777
$940$	−8992.32	−0.312018
$941$	−3143.69	−0.108907	−0.0544534	−	0.998516i	$-0.517342\pi$
$941$	−3143.69	−0.108907	−0.0544534	+	0.998516i	$0.517342\pi$
$942$	3331.11	0.115216
$943$	2766.96	0.0955511
$944$	−665.670	−0.0229510
$945$	4377.44	0.150686
$946$	546.768	0.0187917
$947$	−6654.39	−0.228341	−0.114170	−	0.993461i	$-0.536421\pi$
$947$	−6654.39	−0.228341	−0.114170	+	0.993461i	$0.536421\pi$
$948$	13411.5	0.459478
$949$	10953.4	0.374670
$950$	−6936.29	−0.236887
$951$	3758.58	0.128160
$952$	−67397.0	−2.29449
$953$	−38770.2	−1.31783	−0.658913	−	0.752219i	$-0.728984\pi$
$953$	−38770.2	−1.31783	−0.658913	+	0.752219i	$0.728984\pi$
$954$	10794.9	0.366350
$955$	9239.78	0.313081
$956$	−27782.5	−0.939905
$957$	1768.18	0.0597252
$958$	−30663.9	−1.03414
$959$	15252.2	0.513575
$960$	−4626.90	−0.155555
$961$	27236.3	0.914245
$962$	33537.5	1.12401
$963$	2566.05	0.0858669
$964$	−21718.9	−0.725643
$965$	18239.2	0.608435
$966$	−1840.91	−0.0613150
$967$	34125.0	1.13484	0.567418	−	0.823430i	$-0.307942\pi$
$967$	34125.0	1.13484	0.567418	+	0.823430i	$0.307942\pi$
$968$	2691.87	0.0893801
$969$	−13009.6	−0.431298
$970$	11518.1	0.381261
$971$	40432.4	1.33629	0.668145	−	0.744031i	$-0.267089\pi$
$971$	40432.4	1.33629	0.668145	+	0.744031i	$0.267089\pi$
$972$	−1246.23	−0.0411243
$973$	59307.1	1.95406
$974$	28127.8	0.925332
$975$	−15988.5	−0.525172
$976$	203.121	0.00666162
$977$	24699.0	0.808793	0.404396	−	0.914584i	$-0.367482\pi$
$977$	24699.0	0.808793	0.404396	+	0.914584i	$0.367482\pi$
$978$	−15577.5	−0.509318
$979$	12772.7	0.416973
$980$	15331.7	0.499747
$981$	−2658.24	−0.0865148
$982$	−32308.4	−1.04990
$983$	−36817.6	−1.19461	−0.597304	−	0.802015i	$-0.703761\pi$
$983$	−36817.6	−1.19461	−0.597304	+	0.802015i	$0.703761\pi$
$984$	−15251.7	−0.494113
$985$	14341.2	0.463908
$986$	9197.14	0.297055
$987$	29021.0	0.935914
$988$	12238.1	0.394074
$989$	−355.166	−0.0114192
$990$	−909.413	−0.0291950
$991$	33544.6	1.07526	0.537628	−	0.843182i	$-0.319320\pi$
$991$	33544.6	1.07526	0.537628	+	0.843182i	$0.319320\pi$
$992$	−43848.6	−1.40342
$993$	27755.7	0.887008
$994$	6679.63	0.213144
$995$	14671.7	0.467460
$996$	−4464.92	−0.142045
$997$	7922.75	0.251671	0.125835	−	0.992051i	$-0.459839\pi$
$997$	7922.75	0.251671	0.125835	+	0.992051i	$0.459839\pi$
$998$	−18274.3	−0.579624
$999$	−9586.82	−0.303617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.h.1.15	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.h.1.15	✓	39	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)

\(f(q)\)	\(=\)	\(q-1.69454 q^{2} +3.00000 q^{3} -5.12852 q^{4} -5.42092 q^{5} -5.08363 q^{6} -29.9078 q^{7} +22.2469 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.69454 q^{2} +3.00000 q^{3} -5.12852 q^{4} -5.42092 q^{5} -5.08363 q^{6} -29.9078 q^{7} +22.2469 q^{8} +9.00000 q^{9} +9.18599 q^{10} -11.0000 q^{11} -15.3856 q^{12} +55.7400 q^{13} +50.6800 q^{14} -16.2628 q^{15} +3.32985 q^{16} +101.295 q^{17} -15.2509 q^{18} -42.8109 q^{19} +27.8013 q^{20} -89.7233 q^{21} +18.6400 q^{22} -12.1081 q^{23} +66.7406 q^{24} -95.6136 q^{25} -94.4540 q^{26} +27.0000 q^{27} +153.382 q^{28} -53.5811 q^{29} +27.5580 q^{30} +238.804 q^{31} -183.617 q^{32} -33.0000 q^{33} -171.649 q^{34} +162.128 q^{35} -46.1567 q^{36} -355.068 q^{37} +72.5450 q^{38} +167.220 q^{39} -120.598 q^{40} -228.522 q^{41} +152.040 q^{42} +29.3331 q^{43} +56.4137 q^{44} -48.7883 q^{45} +20.5176 q^{46} -323.450 q^{47} +9.98955 q^{48} +551.474 q^{49} +162.022 q^{50} +303.885 q^{51} -285.864 q^{52} -707.821 q^{53} -45.7527 q^{54} +59.6301 q^{55} -665.354 q^{56} -128.433 q^{57} +90.7955 q^{58} -199.910 q^{59} +83.4039 q^{60} +61.0000 q^{61} -404.664 q^{62} -269.170 q^{63} +284.509 q^{64} -302.162 q^{65} +55.9200 q^{66} -297.322 q^{67} -519.493 q^{68} -36.3242 q^{69} -274.732 q^{70} +131.800 q^{71} +200.222 q^{72} +196.508 q^{73} +601.678 q^{74} -286.841 q^{75} +219.556 q^{76} +328.985 q^{77} -283.362 q^{78} -871.693 q^{79} -18.0508 q^{80} +81.0000 q^{81} +387.241 q^{82} +290.202 q^{83} +460.147 q^{84} -549.112 q^{85} -49.7062 q^{86} -160.743 q^{87} -244.715 q^{88} -1161.15 q^{89} +82.6739 q^{90} -1667.06 q^{91} +62.0964 q^{92} +716.412 q^{93} +548.100 q^{94} +232.074 q^{95} -550.852 q^{96} +1253.87 q^{97} -934.497 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

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