LMFDB - Embedded newform 39.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(1,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("39.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.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:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.3144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 16x - 8 $ x^3 - x^2 - 16*x - 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.73549$ of defining polynomial
Character	$\chi$	$=$	39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.73549 q^{2} +3.00000 q^{3} +5.95388 q^{4} -3.90776 q^{5} -11.2065 q^{6} +36.4129 q^{7} +7.64325 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.73549 q^{2} +3.00000 q^{3} +5.95388 q^{4} -3.90776 q^{5} -11.2065 q^{6} +36.4129 q^{7} +7.64325 q^{8} +9.00000 q^{9} +14.5974 q^{10} +19.1943 q^{11} +17.8616 q^{12} +13.0000 q^{13} -136.020 q^{14} -11.7233 q^{15} -76.1823 q^{16} -83.8839 q^{17} -33.6194 q^{18} +46.8492 q^{19} -23.2664 q^{20} +109.239 q^{21} -71.7000 q^{22} +103.905 q^{23} +22.9298 q^{24} -109.729 q^{25} -48.5614 q^{26} +27.0000 q^{27} +216.798 q^{28} +108.341 q^{29} +43.7922 q^{30} -147.532 q^{31} +223.432 q^{32} +57.5828 q^{33} +313.347 q^{34} -142.293 q^{35} +53.5849 q^{36} -160.012 q^{37} -175.005 q^{38} +39.0000 q^{39} -29.8680 q^{40} +231.490 q^{41} -408.060 q^{42} -340.314 q^{43} +114.280 q^{44} -35.1699 q^{45} -388.135 q^{46} +119.653 q^{47} -228.547 q^{48} +982.902 q^{49} +409.893 q^{50} -251.652 q^{51} +77.4005 q^{52} -732.879 q^{53} -100.858 q^{54} -75.0067 q^{55} +278.313 q^{56} +140.548 q^{57} -404.706 q^{58} -229.782 q^{59} -69.7991 q^{60} +108.943 q^{61} +551.104 q^{62} +327.716 q^{63} -225.170 q^{64} -50.8009 q^{65} -215.100 q^{66} +10.3955 q^{67} -499.435 q^{68} +311.714 q^{69} +531.535 q^{70} -869.201 q^{71} +68.7893 q^{72} -1099.07 q^{73} +597.724 q^{74} -329.188 q^{75} +278.934 q^{76} +698.920 q^{77} -145.684 q^{78} +140.410 q^{79} +297.703 q^{80} +81.0000 q^{81} -864.729 q^{82} -159.474 q^{83} +650.395 q^{84} +327.799 q^{85} +1271.24 q^{86} +325.023 q^{87} +146.707 q^{88} +1067.93 q^{89} +131.377 q^{90} +473.368 q^{91} +618.636 q^{92} -442.596 q^{93} -446.964 q^{94} -183.075 q^{95} +670.297 q^{96} +858.881 q^{97} -3671.62 q^{98} +172.748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 9 q^{3} + 10 q^{4} + 4 q^{5} + 6 q^{6} + 30 q^{7} - 6 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 9 * q^3 + 10 * q^4 + 4 * q^5 + 6 * q^6 + 30 * q^7 - 6 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 10 q^{4} + 4 q^{5} + 6 q^{6} + 30 q^{7} - 6 q^{8} + 27 q^{9} - 4 q^{10} - 16 q^{11} + 30 q^{12} + 39 q^{13} - 176 q^{14} + 12 q^{15} - 110 q^{16} - 146 q^{17} + 18 q^{18} + 94 q^{19} - 244 q^{20} + 90 q^{21} - 56 q^{22} - 48 q^{23} - 18 q^{24} + 145 q^{25} + 26 q^{26} + 81 q^{27} + 80 q^{28} - 2 q^{29} - 12 q^{30} + 302 q^{31} + 154 q^{32} - 48 q^{33} + 164 q^{34} + 80 q^{35} + 90 q^{36} + 374 q^{37} + 312 q^{38} + 117 q^{39} - 516 q^{40} + 480 q^{41} - 528 q^{42} - 260 q^{43} + 712 q^{44} + 36 q^{45} - 1104 q^{46} - 24 q^{47} - 330 q^{48} + 447 q^{49} + 814 q^{50} - 438 q^{51} + 130 q^{52} - 678 q^{53} + 54 q^{54} - 1552 q^{55} + 96 q^{56} + 282 q^{57} - 628 q^{58} - 1788 q^{59} - 732 q^{60} + 230 q^{61} + 1952 q^{62} + 270 q^{63} - 750 q^{64} + 52 q^{65} - 168 q^{66} + 74 q^{67} - 460 q^{68} - 144 q^{69} + 1216 q^{70} - 948 q^{71} - 54 q^{72} - 222 q^{73} + 1724 q^{74} + 435 q^{75} + 2392 q^{76} + 112 q^{77} + 78 q^{78} - 24 q^{79} + 1100 q^{80} + 243 q^{81} + 564 q^{82} - 796 q^{83} + 240 q^{84} - 248 q^{85} + 1800 q^{86} - 6 q^{87} + 1608 q^{88} + 1436 q^{89} - 36 q^{90} + 390 q^{91} - 1296 q^{92} + 906 q^{93} - 1920 q^{94} - 4032 q^{95} + 462 q^{96} + 3242 q^{97} - 5070 q^{98} - 144 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 10 * q^4 + 4 * q^5 + 6 * q^6 + 30 * q^7 - 6 * q^8 + 27 * q^9 - 4 * q^10 - 16 * q^11 + 30 * q^12 + 39 * q^13 - 176 * q^14 + 12 * q^15 - 110 * q^16 - 146 * q^17 + 18 * q^18 + 94 * q^19 - 244 * q^20 + 90 * q^21 - 56 * q^22 - 48 * q^23 - 18 * q^24 + 145 * q^25 + 26 * q^26 + 81 * q^27 + 80 * q^28 - 2 * q^29 - 12 * q^30 + 302 * q^31 + 154 * q^32 - 48 * q^33 + 164 * q^34 + 80 * q^35 + 90 * q^36 + 374 * q^37 + 312 * q^38 + 117 * q^39 - 516 * q^40 + 480 * q^41 - 528 * q^42 - 260 * q^43 + 712 * q^44 + 36 * q^45 - 1104 * q^46 - 24 * q^47 - 330 * q^48 + 447 * q^49 + 814 * q^50 - 438 * q^51 + 130 * q^52 - 678 * q^53 + 54 * q^54 - 1552 * q^55 + 96 * q^56 + 282 * q^57 - 628 * q^58 - 1788 * q^59 - 732 * q^60 + 230 * q^61 + 1952 * q^62 + 270 * q^63 - 750 * q^64 + 52 * q^65 - 168 * q^66 + 74 * q^67 - 460 * q^68 - 144 * q^69 + 1216 * q^70 - 948 * q^71 - 54 * q^72 - 222 * q^73 + 1724 * q^74 + 435 * q^75 + 2392 * q^76 + 112 * q^77 + 78 * q^78 - 24 * q^79 + 1100 * q^80 + 243 * q^81 + 564 * q^82 - 796 * q^83 + 240 * q^84 - 248 * q^85 + 1800 * q^86 - 6 * q^87 + 1608 * q^88 + 1436 * q^89 - 36 * q^90 + 390 * q^91 - 1296 * q^92 + 906 * q^93 - 1920 * q^94 - 4032 * q^95 + 462 * q^96 + 3242 * q^97 - 5070 * q^98 - 144 * 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 $

$2$	−3.73549	−1.32069	−0.660347	−	0.750960i	$-0.729591\pi$
$2$	−3.73549	−1.32069	−0.660347	+	0.750960i	$0.729591\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.95388	0.744235
$5$	−3.90776	−0.349521	−0.174761	−	0.984611i	$-0.555915\pi$
$5$	−3.90776	−0.349521	−0.174761	+	0.984611i	$0.555915\pi$
$6$	−11.2065	−0.762504
$7$	36.4129	1.96611	0.983057	−	0.183301i	$-0.0586782\pi$
$7$	36.4129	1.96611	0.983057	+	0.183301i	$0.0586782\pi$
$8$	7.64325	0.337787
$9$	9.00000	0.333333
$10$	14.5974	0.461611
$11$	19.1943	0.526117	0.263059	−	0.964780i	$-0.415269\pi$
$11$	19.1943	0.526117	0.263059	+	0.964780i	$0.415269\pi$
$12$	17.8616	0.429684
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−136.020	−2.59664
$15$	−11.7233	−0.201796
$16$	−76.1823	−1.19035
$17$	−83.8839	−1.19676	−0.598378	−	0.801214i	$-0.704188\pi$
$17$	−83.8839	−1.19676	−0.598378	+	0.801214i	$0.704188\pi$
$18$	−33.6194	−0.440232
$19$	46.8492	0.565681	0.282840	−	0.959167i	$-0.408723\pi$
$19$	46.8492	0.565681	0.282840	+	0.959167i	$0.408723\pi$
$20$	−23.2664	−0.260126
$21$	109.239	1.13514
$22$	−71.7000	−0.694840
$23$	103.905	0.941983	0.470991	−	0.882138i	$-0.343896\pi$
$23$	103.905	0.941983	0.470991	+	0.882138i	$0.343896\pi$
$24$	22.9298	0.195022
$25$	−109.729	−0.877835
$26$	−48.5614	−0.366295
$27$	27.0000	0.192450
$28$	216.798	1.46325
$29$	108.341	0.693738	0.346869	−	0.937914i	$-0.387245\pi$
$29$	108.341	0.693738	0.346869	+	0.937914i	$0.387245\pi$
$30$	43.7922	0.266511
$31$	−147.532	−0.854759	−0.427379	−	0.904072i	$-0.640563\pi$
$31$	−147.532	−0.854759	−0.427379	+	0.904072i	$0.640563\pi$
$32$	223.432	1.23430
$33$	57.5828	0.303754
$34$	313.347	1.58055
$35$	−142.293	−0.687198
$36$	53.5849	0.248078
$37$	−160.012	−0.710969	−0.355484	−	0.934682i	$-0.615684\pi$
$37$	−160.012	−0.710969	−0.355484	+	0.934682i	$0.615684\pi$
$38$	−175.005	−0.747092
$39$	39.0000	0.160128
$40$	−29.8680	−0.118064
$41$	231.490	0.881772	0.440886	−	0.897563i	$-0.354664\pi$
$41$	231.490	0.881772	0.440886	+	0.897563i	$0.354664\pi$
$42$	−408.060	−1.49917
$43$	−340.314	−1.20692	−0.603458	−	0.797395i	$-0.706211\pi$
$43$	−340.314	−1.20692	−0.603458	+	0.797395i	$0.706211\pi$
$44$	114.280	0.391555
$45$	−35.1699	−0.116507
$46$	−388.135	−1.24407
$47$	119.653	0.371346	0.185673	−	0.982612i	$-0.440554\pi$
$47$	119.653	0.371346	0.185673	+	0.982612i	$0.440554\pi$
$48$	−228.547	−0.687248
$49$	982.902	2.86560
$50$	409.893	1.15935
$51$	−251.652	−0.690947
$52$	77.4005	0.206414
$53$	−732.879	−1.89941	−0.949705	−	0.313146i	$-0.898617\pi$
$53$	−732.879	−1.89941	−0.949705	+	0.313146i	$0.898617\pi$
$54$	−100.858	−0.254168
$55$	−75.0067	−0.183889
$56$	278.313	0.664128
$57$	140.548	0.326596
$58$	−404.706	−0.916216
$59$	−229.782	−0.507035	−0.253518	−	0.967331i	$-0.581588\pi$
$59$	−229.782	−0.507035	−0.253518	+	0.967331i	$0.581588\pi$
$60$	−69.7991	−0.150184
$61$	108.943	0.228668	0.114334	−	0.993442i	$-0.463527\pi$
$61$	108.943	0.228668	0.114334	+	0.993442i	$0.463527\pi$
$62$	551.104	1.12888
$63$	327.716	0.655371
$64$	−225.170	−0.439786
$65$	−50.8009	−0.0969397
$66$	−215.100	−0.401166
$67$	10.3955	0.0189555	0.00947774	−	0.999955i	$-0.496983\pi$
$67$	10.3955	0.0189555	0.00947774	+	0.999955i	$0.496983\pi$
$68$	−499.435	−0.890667
$69$	311.714	0.543854
$70$	531.535	0.907579
$71$	−869.201	−1.45289	−0.726445	−	0.687224i	$-0.758829\pi$
$71$	−869.201	−1.45289	−0.726445	+	0.687224i	$0.758829\pi$
$72$	68.7893	0.112596
$73$	−1099.07	−1.76214	−0.881072	−	0.472982i	$-0.843178\pi$
$73$	−1099.07	−1.76214	−0.881072	+	0.472982i	$0.843178\pi$
$74$	597.724	0.938973
$75$	−329.188	−0.506818
$76$	278.934	0.421000
$77$	698.920	1.03441
$78$	−145.684	−0.211480
$79$	140.410	0.199967	0.0999835	−	0.994989i	$-0.468121\pi$
$79$	140.410	0.199967	0.0999835	+	0.994989i	$0.468121\pi$
$80$	297.703	0.416052
$81$	81.0000	0.111111
$82$	−864.729	−1.16455
$83$	−159.474	−0.210898	−0.105449	−	0.994425i	$-0.533628\pi$
$83$	−159.474	−0.210898	−0.105449	+	0.994425i	$0.533628\pi$
$84$	650.395	0.844808
$85$	327.799	0.418291
$86$	1271.24	1.59397
$87$	325.023	0.400530
$88$	146.707	0.177716
$89$	1067.93	1.27192	0.635959	−	0.771723i	$-0.280605\pi$
$89$	1067.93	1.27192	0.635959	+	0.771723i	$0.280605\pi$
$90$	131.377	0.153870
$91$	473.368	0.545302
$92$	618.636	0.701057
$93$	−442.596	−0.493495
$94$	−446.964	−0.490434
$95$	−183.075	−0.197717
$96$	670.297	0.712624
$97$	858.881	0.899032	0.449516	−	0.893272i	$-0.351596\pi$
$97$	858.881	0.899032	0.449516	+	0.893272i	$0.351596\pi$
$98$	−3671.62	−3.78459
$99$	172.748	0.175372
$100$	−653.316	−0.653316
$101$	−1574.16	−1.55084	−0.775421	−	0.631444i	$-0.782462\pi$
$101$	−1574.16	−1.55084	−0.775421	+	0.631444i	$0.782462\pi$
$102$	940.042	0.912530
$103$	−129.724	−0.124098	−0.0620489	−	0.998073i	$-0.519763\pi$
$103$	−129.724	−0.124098	−0.0620489	+	0.998073i	$0.519763\pi$
$104$	99.3623	0.0936853
$105$	−426.879	−0.396754
$106$	2737.66	2.50854
$107$	−1957.43	−1.76853	−0.884263	−	0.466990i	$-0.845339\pi$
$107$	−1957.43	−1.76853	−0.884263	+	0.466990i	$0.845339\pi$
$108$	160.755	0.143228
$109$	1228.77	1.07977	0.539886	−	0.841738i	$-0.318467\pi$
$109$	1228.77	1.07977	0.539886	+	0.841738i	$0.318467\pi$
$110$	280.187	0.242861
$111$	−480.037	−0.410478
$112$	−2774.02	−2.34036
$113$	1629.50	1.35655	0.678275	−	0.734808i	$-0.262728\pi$
$113$	1629.50	1.35655	0.678275	+	0.734808i	$0.262728\pi$
$114$	−525.014	−0.431334
$115$	−406.035	−0.329243
$116$	645.049	0.516304
$117$	117.000	0.0924500
$118$	858.349	0.669639
$119$	−3054.46	−2.35296
$120$	−89.6041	−0.0681641
$121$	−962.580	−0.723201
$122$	−406.956	−0.302000
$123$	694.470	0.509092
$124$	−878.388	−0.636142
$125$	917.267	0.656343
$126$	−1224.18	−0.865546
$127$	276.112	0.192921	0.0964607	−	0.995337i	$-0.469248\pi$
$127$	276.112	0.192921	0.0964607	+	0.995337i	$0.469248\pi$
$128$	−946.337	−0.653478
$129$	−1020.94	−0.696813
$130$	189.766	0.128028
$131$	−96.2240	−0.0641765	−0.0320883	−	0.999485i	$-0.510216\pi$
$131$	−96.2240	−0.0641765	−0.0320883	+	0.999485i	$0.510216\pi$
$132$	342.841	0.226064
$133$	1705.92	1.11219
$134$	−38.8324	−0.0250344
$135$	−105.510	−0.0672653
$136$	−641.146	−0.404249
$137$	2618.38	1.63287	0.816435	−	0.577438i	$-0.195947\pi$
$137$	2618.38	1.63287	0.816435	+	0.577438i	$0.195947\pi$
$138$	−1164.40	−0.718265
$139$	1963.34	1.19805	0.599023	−	0.800732i	$-0.295556\pi$
$139$	1963.34	1.19805	0.599023	+	0.800732i	$0.295556\pi$
$140$	−847.197	−0.511437
$141$	358.960	0.214396
$142$	3246.89	1.91882
$143$	249.526	0.145919
$144$	−685.641	−0.396783
$145$	−423.370	−0.242476
$146$	4105.57	2.32725
$147$	2948.71	1.65446
$148$	−952.694	−0.529128
$149$	−301.111	−0.165557	−0.0827784	−	0.996568i	$-0.526379\pi$
$149$	−301.111	−0.165557	−0.0827784	+	0.996568i	$0.526379\pi$
$150$	1229.68	0.669352
$151$	342.973	0.184839	0.0924197	−	0.995720i	$-0.470540\pi$
$151$	342.973	0.184839	0.0924197	+	0.995720i	$0.470540\pi$
$152$	358.080	0.191080
$153$	−754.955	−0.398918
$154$	−2610.81	−1.36614
$155$	576.520	0.298756
$156$	232.201	0.119173
$157$	−1286.97	−0.654211	−0.327106	−	0.944988i	$-0.606073\pi$
$157$	−1286.97	−0.654211	−0.327106	+	0.944988i	$0.606073\pi$
$158$	−524.501	−0.264095
$159$	−2198.64	−1.09662
$160$	−873.121	−0.431414
$161$	3783.47	1.85205
$162$	−302.575	−0.146744
$163$	532.561	0.255910	0.127955	−	0.991780i	$-0.459159\pi$
$163$	532.561	0.255910	0.127955	+	0.991780i	$0.459159\pi$
$164$	1378.26	0.656246
$165$	−225.020	−0.106168
$166$	595.714	0.278532
$167$	41.9542	0.0194402	0.00972011	−	0.999953i	$-0.496906\pi$
$167$	41.9542	0.0194402	0.00972011	+	0.999953i	$0.496906\pi$
$168$	834.940	0.383435
$169$	169.000	0.0769231
$170$	−1224.49	−0.552435
$171$	421.643	0.188560
$172$	−2026.19	−0.898229
$173$	−1066.50	−0.468694	−0.234347	−	0.972153i	$-0.575295\pi$
$173$	−1066.50	−0.468694	−0.234347	+	0.972153i	$0.575295\pi$
$174$	−1214.12	−0.528977
$175$	−3995.57	−1.72592
$176$	−1462.26	−0.626263
$177$	−689.346	−0.292737
$178$	−3989.25	−1.67982
$179$	3174.61	1.32559	0.662797	−	0.748799i	$-0.269369\pi$
$179$	3174.61	1.32559	0.662797	+	0.748799i	$0.269369\pi$
$180$	−209.397	−0.0867086
$181$	−2725.43	−1.11923	−0.559613	−	0.828754i	$-0.689050\pi$
$181$	−2725.43	−1.11923	−0.559613	+	0.828754i	$0.689050\pi$
$182$	−1768.26	−0.720177
$183$	326.829	0.132021
$184$	794.169	0.318190
$185$	625.290	0.248498
$186$	1653.31	0.651757
$187$	−1610.09	−0.629634
$188$	712.402	0.276368
$189$	983.149	0.378379
$190$	683.877	0.261124
$191$	784.888	0.297343	0.148672	−	0.988887i	$-0.452500\pi$
$191$	784.888	0.297343	0.148672	+	0.988887i	$0.452500\pi$
$192$	−675.511	−0.253910
$193$	−1255.87	−0.468391	−0.234195	−	0.972190i	$-0.575246\pi$
$193$	−1255.87	−0.468391	−0.234195	+	0.972190i	$0.575246\pi$
$194$	−3208.34	−1.18735
$195$	−152.403	−0.0559682
$196$	5852.08	2.13268
$197$	−2777.35	−1.00446	−0.502229	−	0.864734i	$-0.667487\pi$
$197$	−2777.35	−1.00446	−0.502229	+	0.864734i	$0.667487\pi$
$198$	−645.300	−0.231613
$199$	1490.43	0.530924	0.265462	−	0.964121i	$-0.414476\pi$
$199$	1490.43	0.530924	0.265462	+	0.964121i	$0.414476\pi$
$200$	−838.689	−0.296521
$201$	31.1866	0.0109440
$202$	5880.27	2.04819
$203$	3945.01	1.36397
$204$	−1498.30	−0.514227
$205$	−904.608	−0.308198
$206$	484.582	0.163895
$207$	935.141	0.313994
$208$	−990.370	−0.330143
$209$	899.236	0.297614
$210$	1594.60	0.523991
$211$	2305.63	0.752255	0.376127	−	0.926568i	$-0.377255\pi$
$211$	2305.63	0.752255	0.376127	+	0.926568i	$0.377255\pi$
$212$	−4363.48	−1.41361
$213$	−2607.60	−0.838827
$214$	7311.97	2.33568
$215$	1329.87	0.421842
$216$	206.368	0.0650072
$217$	−5372.07	−1.68055
$218$	−4590.07	−1.42605
$219$	−3297.21	−1.01737
$220$	−446.581	−0.136857
$221$	−1090.49	−0.331920
$222$	1793.17	0.542116
$223$	1241.98	0.372956	0.186478	−	0.982459i	$-0.440293\pi$
$223$	1241.98	0.372956	0.186478	+	0.982459i	$0.440293\pi$
$224$	8135.83	2.42678
$225$	−987.564	−0.292612
$226$	−6086.97	−1.79159
$227$	−1724.76	−0.504300	−0.252150	−	0.967688i	$-0.581138\pi$
$227$	−1724.76	−0.504300	−0.252150	+	0.967688i	$0.581138\pi$
$228$	836.803	0.243064
$229$	−3273.72	−0.944688	−0.472344	−	0.881414i	$-0.656592\pi$
$229$	−3273.72	−0.944688	−0.472344	+	0.881414i	$0.656592\pi$
$230$	1516.74	0.434829
$231$	2096.76	0.597215
$232$	828.076	0.234336
$233$	−2129.52	−0.598752	−0.299376	−	0.954135i	$-0.596778\pi$
$233$	−2129.52	−0.598752	−0.299376	+	0.954135i	$0.596778\pi$
$234$	−437.052	−0.122098
$235$	−467.577	−0.129793
$236$	−1368.10	−0.377354
$237$	421.231	0.115451
$238$	11409.9	3.10754
$239$	−5082.38	−1.37553	−0.687765	−	0.725933i	$-0.741408\pi$
$239$	−5082.38	−1.37553	−0.687765	+	0.725933i	$0.741408\pi$
$240$	893.108	0.240208
$241$	4765.65	1.27379	0.636893	−	0.770953i	$-0.280219\pi$
$241$	4765.65	1.27379	0.636893	+	0.770953i	$0.280219\pi$
$242$	3595.71	0.955127
$243$	243.000	0.0641500
$244$	648.634	0.170183
$245$	−3840.95	−1.00159
$246$	−2594.19	−0.672355
$247$	609.039	0.156892
$248$	−1127.62	−0.288727
$249$	−478.422	−0.121762
$250$	−3426.44	−0.866829
$251$	−4339.96	−1.09138	−0.545689	−	0.837988i	$-0.683732\pi$
$251$	−4339.96	−1.09138	−0.545689	+	0.837988i	$0.683732\pi$
$252$	1951.18	0.487750
$253$	1994.37	0.495594
$254$	−1031.41	−0.254790
$255$	983.396	0.241500
$256$	5336.40	1.30283
$257$	4359.49	1.05812	0.529062	−	0.848583i	$-0.322544\pi$
$257$	4359.49	1.05812	0.529062	+	0.848583i	$0.322544\pi$
$258$	3813.72	0.920278
$259$	−5826.51	−1.39785
$260$	−302.463	−0.0721459
$261$	975.068	0.231246
$262$	359.444	0.0847576
$263$	608.077	0.142569	0.0712844	−	0.997456i	$-0.477290\pi$
$263$	608.077	0.142569	0.0712844	+	0.997456i	$0.477290\pi$
$264$	440.120	0.102604
$265$	2863.92	0.663884
$266$	−6372.43	−1.46887
$267$	3203.80	0.734342
$268$	61.8938	0.0141073
$269$	3454.29	0.782942	0.391471	−	0.920190i	$-0.371966\pi$
$269$	3454.29	0.782942	0.391471	+	0.920190i	$0.371966\pi$
$270$	394.130	0.0888370
$271$	3703.72	0.830204	0.415102	−	0.909775i	$-0.363746\pi$
$271$	3703.72	0.830204	0.415102	+	0.909775i	$0.363746\pi$
$272$	6390.47	1.42456
$273$	1420.10	0.314830
$274$	−9780.92	−2.15652
$275$	−2106.18	−0.461844
$276$	1855.91	0.404755
$277$	−3566.89	−0.773696	−0.386848	−	0.922144i	$-0.626436\pi$
$277$	−3566.89	−0.773696	−0.386848	+	0.922144i	$0.626436\pi$
$278$	−7334.04	−1.58225
$279$	−1327.79	−0.284920
$280$	−1087.58	−0.232127
$281$	−117.474	−0.0249392	−0.0124696	−	0.999922i	$-0.503969\pi$
$281$	−117.474	−0.0249392	−0.0124696	+	0.999922i	$0.503969\pi$
$282$	−1340.89	−0.283152
$283$	−1737.62	−0.364984	−0.182492	−	0.983207i	$-0.558416\pi$
$283$	−1737.62	−0.364984	−0.182492	+	0.983207i	$0.558416\pi$
$284$	−5175.12	−1.08129
$285$	−549.226	−0.114152
$286$	−932.100	−0.192714
$287$	8429.23	1.73366
$288$	2010.89	0.411434
$289$	2123.51	0.432223
$290$	1581.50	0.320237
$291$	2576.64	0.519057
$292$	−6543.74	−1.31145
$293$	1904.05	0.379643	0.189822	−	0.981819i	$-0.439209\pi$
$293$	1904.05	0.379643	0.189822	+	0.981819i	$0.439209\pi$
$294$	−11014.9	−2.18503
$295$	897.934	0.177219
$296$	−1223.01	−0.240156
$297$	518.245	0.101251
$298$	1124.80	0.218650
$299$	1350.76	0.261259
$300$	−1959.95	−0.377192
$301$	−12391.8	−2.37293
$302$	−1281.17	−0.244117
$303$	−4722.49	−0.895379
$304$	−3569.08	−0.673358
$305$	−425.724	−0.0799242
$306$	2820.13	0.526850
$307$	2862.39	0.532134	0.266067	−	0.963955i	$-0.414276\pi$
$307$	2862.39	0.532134	0.266067	+	0.963955i	$0.414276\pi$
$308$	4161.29	0.769842
$309$	−389.172	−0.0716479
$310$	−2153.58	−0.394566
$311$	4201.55	0.766071	0.383036	−	0.923734i	$-0.374879\pi$
$311$	4201.55	0.766071	0.383036	+	0.923734i	$0.374879\pi$
$312$	298.087	0.0540892
$313$	3427.74	0.619002	0.309501	−	0.950899i	$-0.399838\pi$
$313$	3427.74	0.619002	0.309501	+	0.950899i	$0.399838\pi$
$314$	4807.45	0.864014
$315$	−1280.64	−0.229066
$316$	835.987	0.148823
$317$	1676.09	0.296966	0.148483	−	0.988915i	$-0.452561\pi$
$317$	1676.09	0.296966	0.148483	+	0.988915i	$0.452561\pi$
$318$	8212.99	1.44831
$319$	2079.52	0.364987
$320$	879.912	0.153714
$321$	−5872.30	−1.02106
$322$	−14133.1	−2.44599
$323$	−3929.89	−0.676982
$324$	482.264	0.0826928
$325$	−1426.48	−0.243468
$326$	−1989.37	−0.337979
$327$	3686.32	0.623406
$328$	1769.34	0.297851
$329$	4356.93	0.730108
$330$	840.560	0.140216
$331$	11156.6	1.85264	0.926319	−	0.376740i	$-0.122955\pi$
$331$	11156.6	1.85264	0.926319	+	0.376740i	$0.122955\pi$
$332$	−949.490	−0.156958
$333$	−1440.11	−0.236990
$334$	−156.720	−0.0256746
$335$	−40.6233	−0.00662534
$336$	−8322.07	−1.35121
$337$	1636.44	0.264517	0.132259	−	0.991215i	$-0.457777\pi$
$337$	1636.44	0.264517	0.132259	+	0.991215i	$0.457777\pi$
$338$	−631.298	−0.101592
$339$	4888.49	0.783205
$340$	1951.67	0.311307
$341$	−2831.77	−0.449703
$342$	−1575.04	−0.249031
$343$	23300.7	3.66799
$344$	−2601.10	−0.407681
$345$	−1218.10	−0.190088
$346$	3983.88	0.619002
$347$	−2977.87	−0.460693	−0.230347	−	0.973109i	$-0.573986\pi$
$347$	−2977.87	−0.460693	−0.230347	+	0.973109i	$0.573986\pi$
$348$	1935.15	0.298088
$349$	9847.29	1.51035	0.755177	−	0.655521i	$-0.227551\pi$
$349$	9847.29	1.51035	0.755177	+	0.655521i	$0.227551\pi$
$350$	14925.4	2.27942
$351$	351.000	0.0533761
$352$	4288.62	0.649387
$353$	4687.34	0.706747	0.353374	−	0.935482i	$-0.385034\pi$
$353$	4687.34	0.706747	0.353374	+	0.935482i	$0.385034\pi$
$354$	2575.05	0.386616
$355$	3396.63	0.507816
$356$	6358.35	0.946606
$357$	−9163.38	−1.35848
$358$	−11858.7	−1.75070
$359$	−2069.88	−0.304301	−0.152151	−	0.988357i	$-0.548620\pi$
$359$	−2069.88	−0.304301	−0.152151	+	0.988357i	$0.548620\pi$
$360$	−268.812	−0.0393546
$361$	−4664.16	−0.680005
$362$	10180.8	1.47816
$363$	−2887.74	−0.417540
$364$	2818.38	0.405833
$365$	4294.91	0.615906
$366$	−1220.87	−0.174360
$367$	−7299.16	−1.03818	−0.519092	−	0.854719i	$-0.673730\pi$
$367$	−7299.16	−1.03818	−0.519092	+	0.854719i	$0.673730\pi$
$368$	−7915.70	−1.12129
$369$	2083.41	0.293924
$370$	−2335.76	−0.328191
$371$	−26686.3	−3.73446
$372$	−2635.16	−0.367277
$373$	−8964.32	−1.24438	−0.622192	−	0.782865i	$-0.713758\pi$
$373$	−8964.32	−1.24438	−0.622192	+	0.782865i	$0.713758\pi$
$374$	6014.48	0.831554
$375$	2751.80	0.378940
$376$	914.541	0.125436
$377$	1408.43	0.192408
$378$	−3672.54	−0.499723
$379$	−4399.26	−0.596239	−0.298120	−	0.954529i	$-0.596359\pi$
$379$	−4399.26	−0.596239	−0.298120	+	0.954529i	$0.596359\pi$
$380$	−1090.01	−0.147148
$381$	828.337	0.111383
$382$	−2931.94	−0.392700
$383$	3529.74	0.470917	0.235459	−	0.971884i	$-0.424341\pi$
$383$	3529.74	0.470917	0.235459	+	0.971884i	$0.424341\pi$
$384$	−2839.01	−0.377286
$385$	−2731.21	−0.361547
$386$	4691.28	0.618601
$387$	−3062.82	−0.402305
$388$	5113.68	0.669092
$389$	−3034.77	−0.395549	−0.197775	−	0.980248i	$-0.563371\pi$
$389$	−3034.77	−0.395549	−0.197775	+	0.980248i	$0.563371\pi$
$390$	569.299	0.0739169
$391$	−8715.93	−1.12732
$392$	7512.57	0.967964
$393$	−288.672	−0.0370523
$394$	10374.8	1.32658
$395$	−548.690	−0.0698927
$396$	1028.52	0.130518
$397$	−3997.36	−0.505344	−0.252672	−	0.967552i	$-0.581309\pi$
$397$	−3997.36	−0.505344	−0.252672	+	0.967552i	$0.581309\pi$
$398$	−5567.49	−0.701188
$399$	5117.75	0.642125
$400$	8359.44	1.04493
$401$	−9092.88	−1.13236	−0.566181	−	0.824281i	$-0.691580\pi$
$401$	−9092.88	−1.13236	−0.566181	+	0.824281i	$0.691580\pi$
$402$	−116.497	−0.0144536
$403$	−1917.92	−0.237067
$404$	−9372.38	−1.15419
$405$	−316.529	−0.0388357
$406$	−14736.5	−1.80138
$407$	−3071.32	−0.374053
$408$	−1923.44	−0.233393
$409$	7143.54	0.863631	0.431816	−	0.901962i	$-0.357873\pi$
$409$	7143.54	0.863631	0.431816	+	0.901962i	$0.357873\pi$
$410$	3379.15	0.407036
$411$	7855.13	0.942738
$412$	−772.361	−0.0923579
$413$	−8367.04	−0.996889
$414$	−3493.21	−0.414691
$415$	623.187	0.0737134
$416$	2904.62	0.342333
$417$	5890.02	0.691692
$418$	−3359.09	−0.393058
$419$	8213.84	0.957691	0.478845	−	0.877899i	$-0.341055\pi$
$419$	8213.84	0.957691	0.478845	+	0.877899i	$0.341055\pi$
$420$	−2541.59	−0.295278
$421$	−7997.40	−0.925818	−0.462909	−	0.886406i	$-0.653194\pi$
$421$	−7997.40	−0.925818	−0.462909	+	0.886406i	$0.653194\pi$
$422$	−8612.64	−0.993499
$423$	1076.88	0.123782
$424$	−5601.58	−0.641597
$425$	9204.53	1.05055
$426$	9740.68	1.10783
$427$	3966.94	0.449587
$428$	−11654.3	−1.31620
$429$	748.577	0.0842462
$430$	−4967.70	−0.557125
$431$	−13694.8	−1.53053	−0.765263	−	0.643718i	$-0.777391\pi$
$431$	−13694.8	−1.53053	−0.765263	+	0.643718i	$0.777391\pi$
$432$	−2056.92	−0.229083
$433$	6716.57	0.745445	0.372722	−	0.927943i	$-0.378424\pi$
$433$	6716.57	0.745445	0.372722	+	0.927943i	$0.378424\pi$
$434$	20067.3	2.21950
$435$	−1270.11	−0.139993
$436$	7315.97	0.803604
$437$	4867.84	0.532862
$438$	12316.7	1.34364
$439$	−5933.32	−0.645061	−0.322531	−	0.946559i	$-0.604534\pi$
$439$	−5933.32	−0.645061	−0.322531	+	0.946559i	$0.604534\pi$
$440$	−573.295	−0.0621154
$441$	8846.12	0.955201
$442$	4073.52	0.438365
$443$	−6923.40	−0.742530	−0.371265	−	0.928527i	$-0.621076\pi$
$443$	−6923.40	−0.742530	−0.371265	+	0.928527i	$0.621076\pi$
$444$	−2858.08	−0.305492
$445$	−4173.23	−0.444562
$446$	−4639.41	−0.492561
$447$	−903.333	−0.0955843
$448$	−8199.11	−0.864669
$449$	8886.78	0.934061	0.467030	−	0.884241i	$-0.345324\pi$
$449$	8886.78	0.934061	0.467030	+	0.884241i	$0.345324\pi$
$450$	3689.04	0.386451
$451$	4443.28	0.463916
$452$	9701.84	1.00959
$453$	1028.92	0.106717
$454$	6442.81	0.666026
$455$	−1849.81	−0.190594
$456$	1074.24	0.110320
$457$	10965.0	1.12237	0.561184	−	0.827691i	$-0.310346\pi$
$457$	10965.0	1.12237	0.561184	+	0.827691i	$0.310346\pi$
$458$	12228.9	1.24764
$459$	−2264.87	−0.230316
$460$	−2417.48	−0.245034
$461$	10069.2	1.01729	0.508644	−	0.860977i	$-0.330147\pi$
$461$	10069.2	1.01729	0.508644	+	0.860977i	$0.330147\pi$
$462$	−7832.42	−0.788739
$463$	5599.72	0.562076	0.281038	−	0.959697i	$-0.409321\pi$
$463$	5599.72	0.562076	0.281038	+	0.959697i	$0.409321\pi$
$464$	−8253.66	−0.825790
$465$	1729.56	0.172487
$466$	7954.78	0.790769
$467$	−13247.8	−1.31271	−0.656355	−	0.754452i	$-0.727903\pi$
$467$	−13247.8	−1.31271	−0.656355	+	0.754452i	$0.727903\pi$
$468$	696.604	0.0688046
$469$	378.532	0.0372686
$470$	1746.63	0.171417
$471$	−3860.90	−0.377709
$472$	−1756.28	−0.171270
$473$	−6532.08	−0.634979
$474$	−1573.50	−0.152476
$475$	−5140.73	−0.496575
$476$	−18185.9	−1.75115
$477$	−6595.92	−0.633137
$478$	18985.2	1.81666
$479$	16725.4	1.59541	0.797707	−	0.603045i	$-0.206046\pi$
$479$	16725.4	1.59541	0.797707	+	0.603045i	$0.206046\pi$
$480$	−2619.36	−0.249077
$481$	−2080.16	−0.197187
$482$	−17802.0	−1.68228
$483$	11350.4	1.06928
$484$	−5731.09	−0.538231
$485$	−3356.30	−0.314231
$486$	−907.724	−0.0847226
$487$	−5305.86	−0.493699	−0.246850	−	0.969054i	$-0.579395\pi$
$487$	−5305.86	−0.493699	−0.246850	+	0.969054i	$0.579395\pi$
$488$	832.679	0.0772410
$489$	1597.68	0.147750
$490$	14347.8	1.32279
$491$	16200.2	1.48901	0.744506	−	0.667616i	$-0.232685\pi$
$491$	16200.2	1.48901	0.744506	+	0.667616i	$0.232685\pi$
$492$	4134.79	0.378884
$493$	−9088.05	−0.830234
$494$	−2275.06	−0.207206
$495$	−675.060	−0.0612963
$496$	11239.3	1.01746
$497$	−31650.2	−2.85655
$498$	1787.14	0.160811
$499$	4392.70	0.394076	0.197038	−	0.980396i	$-0.436868\pi$
$499$	4392.70	0.394076	0.197038	+	0.980396i	$0.436868\pi$
$500$	5461.30	0.488473
$501$	125.863	0.0112238
$502$	16211.9	1.44138
$503$	−14955.2	−1.32568	−0.662841	−	0.748760i	$-0.730650\pi$
$503$	−14955.2	−1.32568	−0.662841	+	0.748760i	$0.730650\pi$
$504$	2504.82	0.221376
$505$	6151.46	0.542052
$506$	−7449.96	−0.654528
$507$	507.000	0.0444116
$508$	1643.94	0.143579
$509$	13403.4	1.16719	0.583593	−	0.812047i	$-0.301647\pi$
$509$	13403.4	1.16719	0.583593	+	0.812047i	$0.301647\pi$
$510$	−3673.46	−0.318948
$511$	−40020.4	−3.46458
$512$	−12363.4	−1.06716
$513$	1264.93	0.108865
$514$	−16284.8	−1.39746
$515$	506.930	0.0433748
$516$	−6078.57	−0.518593
$517$	2296.66	0.195371
$518$	21764.9	1.84613
$519$	−3199.49	−0.270601
$520$	−388.284	−0.0327450
$521$	19643.0	1.65178	0.825888	−	0.563834i	$-0.190674\pi$
$521$	19643.0	1.65178	0.825888	+	0.563834i	$0.190674\pi$
$522$	−3642.35	−0.305405
$523$	14657.4	1.22548	0.612738	−	0.790286i	$-0.290068\pi$
$523$	14657.4	1.22548	0.612738	+	0.790286i	$0.290068\pi$
$524$	−572.906	−0.0477624
$525$	−11986.7	−0.996462
$526$	−2271.46	−0.188290
$527$	12375.6	1.02294
$528$	−4386.79	−0.361573
$529$	−1370.83	−0.112668
$530$	−10698.1	−0.876788
$531$	−2068.04	−0.169012
$532$	10156.8	0.827733
$533$	3009.37	0.244560
$534$	−11967.8	−0.969842
$535$	7649.19	0.618137
$536$	79.4558	0.00640292
$537$	9523.82	0.765332
$538$	−12903.4	−1.03403
$539$	18866.1	1.50764
$540$	−628.192	−0.0500612
$541$	13921.3	1.10633	0.553164	−	0.833072i	$-0.313420\pi$
$541$	13921.3	1.10633	0.553164	+	0.833072i	$0.313420\pi$
$542$	−13835.2	−1.09645
$543$	−8176.30	−0.646185
$544$	−18742.4	−1.47716
$545$	−4801.75	−0.377403
$546$	−5304.79	−0.415795
$547$	−2324.11	−0.181667	−0.0908335	−	0.995866i	$-0.528953\pi$
$547$	−2324.11	−0.181667	−0.0908335	+	0.995866i	$0.528953\pi$
$548$	15589.5	1.21524
$549$	980.488	0.0762226
$550$	7867.60	0.609955
$551$	5075.68	0.392434
$552$	2382.51	0.183707
$553$	5112.75	0.393158
$554$	13324.1	1.02182
$555$	1875.87	0.143471
$556$	11689.5	0.891628
$557$	−16962.8	−1.29037	−0.645185	−	0.764027i	$-0.723220\pi$
$557$	−16962.8	−1.29037	−0.645185	+	0.764027i	$0.723220\pi$
$558$	4959.94	0.376292
$559$	−4424.08	−0.334738
$560$	10840.2	0.818006
$561$	−4830.27	−0.363519
$562$	438.823	0.0329370
$563$	−389.000	−0.0291197	−0.0145599	−	0.999894i	$-0.504635\pi$
$563$	−389.000	−0.0291197	−0.0145599	+	0.999894i	$0.504635\pi$
$564$	2137.21	0.159561
$565$	−6367.69	−0.474143
$566$	6490.85	0.482033
$567$	2949.45	0.218457
$568$	−6643.53	−0.490768
$569$	2217.56	0.163383	0.0816914	−	0.996658i	$-0.473968\pi$
$569$	2217.56	0.163383	0.0816914	+	0.996658i	$0.473968\pi$
$570$	2051.63	0.150760
$571$	−17087.3	−1.25233	−0.626167	−	0.779689i	$-0.715377\pi$
$571$	−17087.3	−1.25233	−0.626167	+	0.779689i	$0.715377\pi$
$572$	1485.65	0.108598
$573$	2354.67	0.171671
$574$	−31487.3	−2.28964
$575$	−11401.4	−0.826906
$576$	−2026.53	−0.146595
$577$	−3977.26	−0.286959	−0.143480	−	0.989653i	$-0.545829\pi$
$577$	−3977.26	−0.286959	−0.143480	+	0.989653i	$0.545829\pi$
$578$	−7932.35	−0.570835
$579$	−3767.61	−0.270425
$580$	−2520.70	−0.180459
$581$	−5806.92	−0.414650
$582$	−9625.02	−0.685516
$583$	−14067.1	−0.999312
$584$	−8400.48	−0.595230
$585$	−457.208	−0.0323132
$586$	−7112.54	−0.501393
$587$	−16880.3	−1.18693	−0.593463	−	0.804861i	$-0.702240\pi$
$587$	−16880.3	−1.18693	−0.593463	+	0.804861i	$0.702240\pi$
$588$	17556.2	1.23131
$589$	−6911.75	−0.483521
$590$	−3354.22	−0.234053
$591$	−8332.06	−0.579924
$592$	12190.1	0.846301
$593$	2423.25	0.167810	0.0839048	−	0.996474i	$-0.473261\pi$
$593$	2423.25	0.167810	0.0839048	+	0.996474i	$0.473261\pi$
$594$	−1935.90	−0.133722
$595$	11936.1	0.822408
$596$	−1792.78	−0.123213
$597$	4471.29	0.306529
$598$	−5045.75	−0.345044
$599$	−3900.55	−0.266064	−0.133032	−	0.991112i	$-0.542471\pi$
$599$	−3900.55	−0.266064	−0.133032	+	0.991112i	$0.542471\pi$
$600$	−2516.07	−0.171197
$601$	28653.4	1.94476	0.972378	−	0.233413i	$-0.0749893\pi$
$601$	28653.4	1.94476	0.972378	+	0.233413i	$0.0749893\pi$
$602$	46289.5	3.13392
$603$	93.5599	0.00631850
$604$	2042.02	0.137564
$605$	3761.54	0.252774
$606$	17640.8	1.18252
$607$	214.736	0.0143589	0.00717946	−	0.999974i	$-0.497715\pi$
$607$	214.736	0.0143589	0.00717946	+	0.999974i	$0.497715\pi$
$608$	10467.6	0.698220
$609$	11835.0	0.787487
$610$	1590.29	0.105555
$611$	1555.49	0.102993
$612$	−4494.91	−0.296889
$613$	26438.5	1.74199	0.870996	−	0.491290i	$-0.163475\pi$
$613$	26438.5	1.74199	0.870996	+	0.491290i	$0.163475\pi$
$614$	−10692.4	−0.702787
$615$	−2713.82	−0.177938
$616$	5342.02	0.349409
$617$	6700.96	0.437229	0.218615	−	0.975811i	$-0.429846\pi$
$617$	6700.96	0.437229	0.218615	+	0.975811i	$0.429846\pi$
$618$	1453.75	0.0946250
$619$	−27319.1	−1.77391	−0.886953	−	0.461860i	$-0.847182\pi$
$619$	−27319.1	−1.77391	−0.886953	+	0.461860i	$0.847182\pi$
$620$	3432.53	0.222345
$621$	2805.42	0.181285
$622$	−15694.9	−1.01175
$623$	38886.6	2.50074
$624$	−2971.11	−0.190608
$625$	10131.7	0.648429
$626$	−12804.3	−0.817513
$627$	2697.71	0.171828
$628$	−7662.45	−0.486887
$629$	13422.4	0.850855
$630$	4783.81	0.302526
$631$	−7126.87	−0.449629	−0.224815	−	0.974402i	$-0.572178\pi$
$631$	−7126.87	−0.449629	−0.224815	+	0.974402i	$0.572178\pi$
$632$	1073.19	0.0675463
$633$	6916.88	0.434315
$634$	−6261.00	−0.392202
$635$	−1078.98	−0.0674301
$636$	−13090.4	−0.816147
$637$	12777.7	0.794775
$638$	−7768.04	−0.482037
$639$	−7822.81	−0.484297
$640$	3698.06	0.228404
$641$	23615.0	1.45513	0.727565	−	0.686039i	$-0.240652\pi$
$641$	23615.0	1.45513	0.727565	+	0.686039i	$0.240652\pi$
$642$	21935.9	1.34851
$643$	−8144.41	−0.499509	−0.249755	−	0.968309i	$-0.580350\pi$
$643$	−8144.41	−0.499509	−0.249755	+	0.968309i	$0.580350\pi$
$644$	22526.3	1.37836
$645$	3989.60	0.243551
$646$	14680.1	0.894086
$647$	9682.00	0.588313	0.294157	−	0.955757i	$-0.404961\pi$
$647$	9682.00	0.588313	0.294157	+	0.955757i	$0.404961\pi$
$648$	619.103	0.0375319
$649$	−4410.50	−0.266760
$650$	5328.61	0.321546
$651$	−16116.2	−0.970268
$652$	3170.80	0.190457
$653$	−18193.6	−1.09030	−0.545152	−	0.838337i	$-0.683528\pi$
$653$	−18193.6	−1.09030	−0.545152	+	0.838337i	$0.683528\pi$
$654$	−13770.2	−0.823329
$655$	376.020	0.0224310
$656$	−17635.5	−1.04962
$657$	−9891.64	−0.587381
$658$	−16275.3	−0.964250
$659$	9300.88	0.549789	0.274895	−	0.961474i	$-0.411357\pi$
$659$	9300.88	0.549789	0.274895	+	0.961474i	$0.411357\pi$
$660$	−1339.74	−0.0790143
$661$	−5437.29	−0.319949	−0.159974	−	0.987121i	$-0.551141\pi$
$661$	−5437.29	−0.319949	−0.159974	+	0.987121i	$0.551141\pi$
$662$	−41675.4	−2.44677
$663$	−3271.47	−0.191634
$664$	−1218.90	−0.0712388
$665$	−6666.32	−0.388735
$666$	5379.51	0.312991
$667$	11257.1	0.653489
$668$	249.791	0.0144681
$669$	3725.94	0.215326
$670$	151.748	0.00875005
$671$	2091.08	0.120306
$672$	24407.5	1.40110
$673$	−8682.75	−0.497319	−0.248659	−	0.968591i	$-0.579990\pi$
$673$	−8682.75	−0.497319	−0.248659	+	0.968591i	$0.579990\pi$
$674$	−6112.89	−0.349347
$675$	−2962.69	−0.168939
$676$	1006.21	0.0572489
$677$	13300.1	0.755041	0.377521	−	0.926001i	$-0.376777\pi$
$677$	13300.1	0.755041	0.377521	+	0.926001i	$0.376777\pi$
$678$	−18260.9	−1.03437
$679$	31274.4	1.76760
$680$	2505.45	0.141293
$681$	−5174.27	−0.291158
$682$	10578.0	0.593921
$683$	−504.175	−0.0282455	−0.0141228	−	0.999900i	$-0.504496\pi$
$683$	−504.175	−0.0282455	−0.0141228	+	0.999900i	$0.504496\pi$
$684$	2510.41	0.140333
$685$	−10232.0	−0.570722
$686$	−87039.6	−4.84429
$687$	−9821.16	−0.545416
$688$	25925.9	1.43665
$689$	−9527.43	−0.526802
$690$	4550.21	0.251049
$691$	13443.8	0.740124	0.370062	−	0.929007i	$-0.379336\pi$
$691$	13443.8	0.740124	0.370062	+	0.929007i	$0.379336\pi$
$692$	−6349.79	−0.348819
$693$	6290.28	0.344802
$694$	11123.8	0.608435
$695$	−7672.27	−0.418742
$696$	2484.23	0.135294
$697$	−19418.3	−1.05527
$698$	−36784.4	−1.99472
$699$	−6388.55	−0.345690
$700$	−23789.1	−1.28449
$701$	28735.6	1.54826	0.774128	−	0.633030i	$-0.218189\pi$
$701$	28735.6	1.54826	0.774128	+	0.633030i	$0.218189\pi$
$702$	−1311.16	−0.0704935
$703$	−7496.44	−0.402181
$704$	−4321.98	−0.231379
$705$	−1402.73	−0.0749361
$706$	−17509.5	−0.933398
$707$	−57319.9	−3.04913
$708$	−4104.29	−0.217865
$709$	17610.2	0.932812	0.466406	−	0.884571i	$-0.345549\pi$
$709$	17610.2	0.932812	0.466406	+	0.884571i	$0.345549\pi$
$710$	−12688.1	−0.670670
$711$	1263.69	0.0666557
$712$	8162.48	0.429638
$713$	−15329.3	−0.805168
$714$	34229.7	1.79414
$715$	−975.087	−0.0510016
$716$	18901.2	0.986553
$717$	−15247.1	−0.794163
$718$	7732.02	0.401889
$719$	−9226.04	−0.478544	−0.239272	−	0.970953i	$-0.576909\pi$
$719$	−9226.04	−0.478544	−0.239272	+	0.970953i	$0.576909\pi$
$720$	2679.32	0.138684
$721$	−4723.63	−0.243990
$722$	17422.9	0.898079
$723$	14296.9	0.735420
$724$	−16226.9	−0.832967
$725$	−11888.2	−0.608987
$726$	10787.1	0.551443
$727$	33246.0	1.69604	0.848022	−	0.529961i	$-0.177793\pi$
$727$	33246.0	1.69604	0.848022	+	0.529961i	$0.177793\pi$
$728$	3618.07	0.184196
$729$	729.000	0.0370370
$730$	−16043.6	−0.813424
$731$	28546.9	1.44438
$732$	1945.90	0.0982549
$733$	−4423.26	−0.222888	−0.111444	−	0.993771i	$-0.535548\pi$
$733$	−4423.26	−0.222888	−0.111444	+	0.993771i	$0.535548\pi$
$734$	27266.0	1.37112
$735$	−11522.8	−0.578267
$736$	23215.6	1.16269
$737$	199.535	0.00997281
$738$	−7782.56	−0.388184
$739$	−4529.56	−0.225470	−0.112735	−	0.993625i	$-0.535961\pi$
$739$	−4529.56	−0.225470	−0.112735	+	0.993625i	$0.535961\pi$
$740$	3722.90	0.184941
$741$	1827.12	0.0905814
$742$	99686.4	4.93208
$743$	10851.5	0.535803	0.267901	−	0.963446i	$-0.413670\pi$
$743$	10851.5	0.535803	0.267901	+	0.963446i	$0.413670\pi$
$744$	−3382.87	−0.166696
$745$	1176.67	0.0578656
$746$	33486.1	1.64345
$747$	−1435.27	−0.0702994
$748$	−9586.29	−0.468595
$749$	−71275.9	−3.47712
$750$	−10279.3	−0.500464
$751$	−33022.6	−1.60454	−0.802272	−	0.596958i	$-0.796376\pi$
$751$	−33022.6	−1.60454	−0.802272	+	0.596958i	$0.796376\pi$
$752$	−9115.48	−0.442031
$753$	−13019.9	−0.630107
$754$	−5261.18	−0.254113
$755$	−1340.26	−0.0646053
$756$	5853.55	0.281603
$757$	−3443.77	−0.165345	−0.0826724	−	0.996577i	$-0.526346\pi$
$757$	−3443.77	−0.165345	−0.0826724	+	0.996577i	$0.526346\pi$
$758$	16433.4	0.787450
$759$	5983.12	0.286131
$760$	−1399.29	−0.0667864
$761$	19562.6	0.931858	0.465929	−	0.884822i	$-0.345720\pi$
$761$	19562.6	0.931858	0.465929	+	0.884822i	$0.345720\pi$
$762$	−3094.24	−0.147103
$763$	44743.2	2.12295
$764$	4673.13	0.221293
$765$	2950.19	0.139430
$766$	−13185.3	−0.621938
$767$	−2987.17	−0.140626
$768$	16009.2	0.752190
$769$	−17061.1	−0.800049	−0.400025	−	0.916504i	$-0.630998\pi$
$769$	−17061.1	−0.800049	−0.400025	+	0.916504i	$0.630998\pi$
$770$	10202.4	0.477493
$771$	13078.5	0.610908
$772$	−7477.29	−0.348593
$773$	10798.4	0.502448	0.251224	−	0.967929i	$-0.419167\pi$
$773$	10798.4	0.502448	0.251224	+	0.967929i	$0.419167\pi$
$774$	11441.1	0.531322
$775$	16188.6	0.750337
$776$	6564.64	0.303682
$777$	−17479.5	−0.807046
$778$	11336.3	0.522400
$779$	10845.1	0.498802
$780$	−907.388	−0.0416535
$781$	−16683.7	−0.764391
$782$	32558.2	1.48885
$783$	2925.20	0.133510
$784$	−74879.8	−3.41107
$785$	5029.16	0.228661
$786$	1078.33	0.0489348
$787$	−35607.0	−1.61277	−0.806386	−	0.591390i	$-0.798580\pi$
$787$	−35607.0	−1.61277	−0.806386	+	0.591390i	$0.798580\pi$
$788$	−16536.0	−0.747553
$789$	1824.23	0.0823122
$790$	2049.63	0.0923069
$791$	59334.8	2.66713
$792$	1320.36	0.0592386
$793$	1416.26	0.0634210
$794$	14932.1	0.667405
$795$	8591.76	0.383293
$796$	8873.85	0.395132
$797$	22155.3	0.984668	0.492334	−	0.870406i	$-0.336144\pi$
$797$	22155.3	0.984668	0.492334	+	0.870406i	$0.336144\pi$
$798$	−19117.3	−0.848051
$799$	−10037.0	−0.444410
$800$	−24517.1	−1.08351
$801$	9611.40	0.423973
$802$	33966.4	1.49550
$803$	−21095.9	−0.927094
$804$	185.681	0.00814488
$805$	−14784.9	−0.647329
$806$	7164.35	0.313094
$807$	10362.9	0.452032
$808$	−12031.7	−0.523855
$809$	−22524.6	−0.978889	−0.489445	−	0.872034i	$-0.662800\pi$
$809$	−22524.6	−0.978889	−0.489445	+	0.872034i	$0.662800\pi$
$810$	1182.39	0.0512901
$811$	4452.39	0.192780	0.0963900	−	0.995344i	$-0.469270\pi$
$811$	4452.39	0.192780	0.0963900	+	0.995344i	$0.469270\pi$
$812$	23488.1	1.01511
$813$	11111.2	0.479318
$814$	11472.9	0.494010
$815$	−2081.12	−0.0894460
$816$	19171.4	0.822468
$817$	−15943.4	−0.682729
$818$	−26684.6	−1.14059
$819$	4260.31	0.181767
$820$	−5385.93	−0.229372
$821$	−7097.27	−0.301701	−0.150851	−	0.988557i	$-0.548201\pi$
$821$	−7097.27	−0.301701	−0.150851	+	0.988557i	$0.548201\pi$
$822$	−29342.8	−1.24507
$823$	−12193.8	−0.516463	−0.258231	−	0.966083i	$-0.583140\pi$
$823$	−12193.8	−0.516463	−0.258231	+	0.966083i	$0.583140\pi$
$824$	−991.512	−0.0419187
$825$	−6318.53	−0.266646
$826$	31255.0	1.31659
$827$	7427.97	0.312329	0.156164	−	0.987731i	$-0.450087\pi$
$827$	7427.97	0.312329	0.156164	+	0.987731i	$0.450087\pi$
$828$	5567.72	0.233686
$829$	16966.2	0.710810	0.355405	−	0.934712i	$-0.384343\pi$
$829$	16966.2	0.710810	0.355405	+	0.934712i	$0.384343\pi$
$830$	−2327.91	−0.0973529
$831$	−10700.7	−0.446693
$832$	−2927.21	−0.121975
$833$	−82449.7	−3.42943
$834$	−22002.1	−0.913514
$835$	−163.947	−0.00679477
$836$	5353.94	0.221495
$837$	−3983.36	−0.164498
$838$	−30682.7	−1.26482
$839$	12025.7	0.494844	0.247422	−	0.968908i	$-0.420417\pi$
$839$	12025.7	0.494844	0.247422	+	0.968908i	$0.420417\pi$
$840$	−3262.75	−0.134018
$841$	−12651.3	−0.518728
$842$	29874.2	1.22272
$843$	−352.422	−0.0143986
$844$	13727.4	0.559855
$845$	−660.412	−0.0268862
$846$	−4022.68	−0.163478
$847$	−35050.4	−1.42189
$848$	55832.5	2.26096
$849$	−5212.85	−0.210724
$850$	−34383.4	−1.38746
$851$	−16626.0	−0.669720
$852$	−15525.4	−0.624284
$853$	−22187.2	−0.890593	−0.445297	−	0.895383i	$-0.646902\pi$
$853$	−22187.2	−0.890593	−0.445297	+	0.895383i	$0.646902\pi$
$854$	−14818.5	−0.593767
$855$	−1647.68	−0.0659058
$856$	−14961.2	−0.597385
$857$	5746.19	0.229038	0.114519	−	0.993421i	$-0.463467\pi$
$857$	5746.19	0.229038	0.114519	+	0.993421i	$0.463467\pi$
$858$	−2796.30	−0.111264
$859$	8305.66	0.329902	0.164951	−	0.986302i	$-0.447253\pi$
$859$	8305.66	0.329902	0.164951	+	0.986302i	$0.447253\pi$
$860$	7917.87	0.313950
$861$	25287.7	1.00093
$862$	51156.9	2.02136
$863$	38086.4	1.50229	0.751146	−	0.660137i	$-0.229502\pi$
$863$	38086.4	1.50229	0.751146	+	0.660137i	$0.229502\pi$
$864$	6032.67	0.237541
$865$	4167.61	0.163819
$866$	−25089.7	−0.984505
$867$	6370.53	0.249544
$868$	−31984.7	−1.25073
$869$	2695.07	0.105206
$870$	4744.49	0.184889
$871$	135.142	0.00525731
$872$	9391.82	0.364733
$873$	7729.93	0.299677
$874$	−18183.8	−0.703748
$875$	33400.4	1.29044
$876$	−19631.2	−0.757166
$877$	−2098.53	−0.0808009	−0.0404005	−	0.999184i	$-0.512863\pi$
$877$	−2098.53	−0.0808009	−0.0404005	+	0.999184i	$0.512863\pi$
$878$	22163.8	0.851929
$879$	5712.14	0.219187
$880$	5714.18	0.218892
$881$	14555.3	0.556619	0.278309	−	0.960491i	$-0.410226\pi$
$881$	14555.3	0.556619	0.278309	+	0.960491i	$0.410226\pi$
$882$	−33044.6	−1.26153
$883$	2122.88	0.0809066	0.0404533	−	0.999181i	$-0.487120\pi$
$883$	2122.88	0.0809066	0.0404533	+	0.999181i	$0.487120\pi$
$884$	−6492.65	−0.247027
$885$	2693.80	0.102318
$886$	25862.3	0.980656
$887$	−12487.3	−0.472696	−0.236348	−	0.971668i	$-0.575951\pi$
$887$	−12487.3	−0.472696	−0.236348	+	0.971668i	$0.575951\pi$
$888$	−3669.04	−0.138654
$889$	10054.1	0.379305
$890$	15589.1	0.587131
$891$	1554.74	0.0584575
$892$	7394.61	0.277567
$893$	5605.66	0.210063
$894$	3374.39	0.126238
$895$	−12405.6	−0.463323
$896$	−34458.9	−1.28481
$897$	4052.28	0.150838
$898$	−33196.5	−1.23361
$899$	−15983.7	−0.592978
$900$	−5879.84	−0.217772
$901$	61476.8	2.27313
$902$	−16597.8	−0.612691
$903$	−37175.5	−1.37001
$904$	12454.7	0.458226
$905$	10650.3	0.391193
$906$	−3843.52	−0.140941
$907$	29679.8	1.08655	0.543275	−	0.839555i	$-0.317184\pi$
$907$	29679.8	1.08655	0.543275	+	0.839555i	$0.317184\pi$
$908$	−10269.0	−0.375318
$909$	−14167.5	−0.516948
$910$	6909.95	0.251717
$911$	24800.0	0.901934	0.450967	−	0.892541i	$-0.351079\pi$
$911$	24800.0	0.901934	0.450967	+	0.892541i	$0.351079\pi$
$912$	−10707.2	−0.388763
$913$	−3060.99	−0.110957
$914$	−40959.7	−1.48230
$915$	−1277.17	−0.0461442
$916$	−19491.3	−0.703070
$917$	−3503.80	−0.126178
$918$	8460.38	0.304177
$919$	−6597.90	−0.236828	−0.118414	−	0.992964i	$-0.537781\pi$
$919$	−6597.90	−0.236828	−0.118414	+	0.992964i	$0.537781\pi$
$920$	−3103.43	−0.111214
$921$	8587.17	0.307228
$922$	−37613.4	−1.34353
$923$	−11299.6	−0.402959
$924$	12483.9	0.444468
$925$	17558.0	0.624113
$926$	−20917.7	−0.742331
$927$	−1167.51	−0.0413659
$928$	24206.8	0.856281
$929$	15056.0	0.531724	0.265862	−	0.964011i	$-0.414344\pi$
$929$	15056.0	0.531724	0.265862	+	0.964011i	$0.414344\pi$
$930$	−6460.75	−0.227803
$931$	46048.1	1.62102
$932$	−12678.9	−0.445612
$933$	12604.7	0.442291
$934$	49487.1	1.73369
$935$	6291.85	0.220070
$936$	894.261	0.0312284
$937$	−35777.0	−1.24737	−0.623683	−	0.781677i	$-0.714365\pi$
$937$	−35777.0	−1.24737	−0.623683	+	0.781677i	$0.714365\pi$
$938$	−1414.00	−0.0492205
$939$	10283.2	0.357381
$940$	−2783.90	−0.0965966
$941$	−22973.6	−0.795873	−0.397937	−	0.917413i	$-0.630274\pi$
$941$	−22973.6	−0.795873	−0.397937	+	0.917413i	$0.630274\pi$
$942$	14422.4	0.498838
$943$	24052.9	0.830615
$944$	17505.3	0.603549
$945$	−3841.92	−0.132251
$946$	24400.5	0.838614
$947$	−51038.3	−1.75134	−0.875671	−	0.482908i	$-0.839580\pi$
$947$	−51038.3	−1.75134	−0.875671	+	0.482908i	$0.839580\pi$
$948$	2507.96	0.0859227
$949$	−14287.9	−0.488731
$950$	19203.1	0.655823
$951$	5028.26	0.171454
$952$	−23346.0	−0.794799
$953$	−22586.5	−0.767733	−0.383866	−	0.923389i	$-0.625408\pi$
$953$	−22586.5	−0.767733	−0.383866	+	0.923389i	$0.625408\pi$
$954$	24639.0	0.836180
$955$	−3067.16	−0.103928
$956$	−30259.9	−1.02372
$957$	6238.57	0.210726
$958$	−62477.6	−2.10706
$959$	95342.8	3.21041
$960$	2639.74	0.0887470
$961$	−8025.32	−0.269387
$962$	7770.41	0.260424
$963$	−17616.9	−0.589509
$964$	28374.1	0.947996
$965$	4907.64	0.163712
$966$	−42399.4	−1.41219
$967$	−36678.7	−1.21976	−0.609880	−	0.792494i	$-0.708782\pi$
$967$	−36678.7	−1.21976	−0.609880	+	0.792494i	$0.708782\pi$
$968$	−7357.24	−0.244288
$969$	−11789.7	−0.390855
$970$	12537.4	0.415003
$971$	32635.2	1.07859	0.539296	−	0.842116i	$-0.318690\pi$
$971$	32635.2	1.07859	0.539296	+	0.842116i	$0.318690\pi$
$972$	1446.79	0.0477427
$973$	71491.0	2.35549
$974$	19820.0	0.652026
$975$	−4279.45	−0.140566
$976$	−8299.54	−0.272194
$977$	44432.6	1.45499	0.727496	−	0.686112i	$-0.240684\pi$
$977$	44432.6	1.45499	0.727496	+	0.686112i	$0.240684\pi$
$978$	−5968.12	−0.195133
$979$	20498.2	0.669178
$980$	−22868.6	−0.745418
$981$	11059.0	0.359924
$982$	−60515.6	−1.96653
$983$	484.485	0.0157199	0.00785996	−	0.999969i	$-0.497498\pi$
$983$	484.485	0.0157199	0.00785996	+	0.999969i	$0.497498\pi$
$984$	5308.01	0.171965
$985$	10853.2	0.351079
$986$	33948.3	1.09649
$987$	13070.8	0.421528
$988$	3626.15	0.116764
$989$	−35360.2	−1.13689
$990$	2521.68	0.0809538
$991$	−48017.1	−1.53917	−0.769583	−	0.638546i	$-0.779536\pi$
$991$	−48017.1	−1.53917	−0.769583	+	0.638546i	$0.779536\pi$
$992$	−32963.4	−1.05503
$993$	33469.8	1.06962
$994$	118229.	3.77263
$995$	−5824.25	−0.185569
$996$	−2848.47	−0.0906197
$997$	−26561.9	−0.843755	−0.421877	−	0.906653i	$-0.638629\pi$
$997$	−26561.9	−0.843755	−0.421877	+	0.906653i	$0.638629\pi$
$998$	−16408.9	−0.520455
$999$	−4320.33	−0.136826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.a.c.1.1	✓	3
3.2	odd	2		117.4.a.f.1.3		3
4.3	odd	2		624.4.a.t.1.2		3
5.4	even	2		975.4.a.l.1.3		3
7.6	odd	2		1911.4.a.k.1.1		3
8.3	odd	2		2496.4.a.bp.1.2		3
8.5	even	2		2496.4.a.bl.1.2		3
12.11	even	2		1872.4.a.bk.1.2		3
13.5	odd	4		507.4.b.g.337.5		6
13.8	odd	4		507.4.b.g.337.2		6
13.12	even	2		507.4.a.h.1.3		3
39.38	odd	2		1521.4.a.u.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.a.c.1.1	✓	3	1.1	even	1	trivial
117.4.a.f.1.3		3	3.2	odd	2
507.4.a.h.1.3		3	13.12	even	2
507.4.b.g.337.2		6	13.8	odd	4
507.4.b.g.337.5		6	13.5	odd	4
624.4.a.t.1.2		3	4.3	odd	2
975.4.a.l.1.3		3	5.4	even	2
1521.4.a.u.1.1		3	39.38	odd	2
1872.4.a.bk.1.2		3	12.11	even	2
1911.4.a.k.1.1		3	7.6	odd	2
2496.4.a.bl.1.2		3	8.5	even	2
2496.4.a.bp.1.2		3	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.a (trivial)

\(f(q)\)	\(=\)	\(q-3.73549 q^{2} +3.00000 q^{3} +5.95388 q^{4} -3.90776 q^{5} -11.2065 q^{6} +36.4129 q^{7} +7.64325 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.73549 q^{2} +3.00000 q^{3} +5.95388 q^{4} -3.90776 q^{5} -11.2065 q^{6} +36.4129 q^{7} +7.64325 q^{8} +9.00000 q^{9} +14.5974 q^{10} +19.1943 q^{11} +17.8616 q^{12} +13.0000 q^{13} -136.020 q^{14} -11.7233 q^{15} -76.1823 q^{16} -83.8839 q^{17} -33.6194 q^{18} +46.8492 q^{19} -23.2664 q^{20} +109.239 q^{21} -71.7000 q^{22} +103.905 q^{23} +22.9298 q^{24} -109.729 q^{25} -48.5614 q^{26} +27.0000 q^{27} +216.798 q^{28} +108.341 q^{29} +43.7922 q^{30} -147.532 q^{31} +223.432 q^{32} +57.5828 q^{33} +313.347 q^{34} -142.293 q^{35} +53.5849 q^{36} -160.012 q^{37} -175.005 q^{38} +39.0000 q^{39} -29.8680 q^{40} +231.490 q^{41} -408.060 q^{42} -340.314 q^{43} +114.280 q^{44} -35.1699 q^{45} -388.135 q^{46} +119.653 q^{47} -228.547 q^{48} +982.902 q^{49} +409.893 q^{50} -251.652 q^{51} +77.4005 q^{52} -732.879 q^{53} -100.858 q^{54} -75.0067 q^{55} +278.313 q^{56} +140.548 q^{57} -404.706 q^{58} -229.782 q^{59} -69.7991 q^{60} +108.943 q^{61} +551.104 q^{62} +327.716 q^{63} -225.170 q^{64} -50.8009 q^{65} -215.100 q^{66} +10.3955 q^{67} -499.435 q^{68} +311.714 q^{69} +531.535 q^{70} -869.201 q^{71} +68.7893 q^{72} -1099.07 q^{73} +597.724 q^{74} -329.188 q^{75} +278.934 q^{76} +698.920 q^{77} -145.684 q^{78} +140.410 q^{79} +297.703 q^{80} +81.0000 q^{81} -864.729 q^{82} -159.474 q^{83} +650.395 q^{84} +327.799 q^{85} +1271.24 q^{86} +325.023 q^{87} +146.707 q^{88} +1067.93 q^{89} +131.377 q^{90} +473.368 q^{91} +618.636 q^{92} -442.596 q^{93} -446.964 q^{94} -183.075 q^{95} +670.297 q^{96} +858.881 q^{97} -3671.62 q^{98} +172.748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 9 q^{3} + 10 q^{4} + 4 q^{5} + 6 q^{6} + 30 q^{7} - 6 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 9 * q^3 + 10 * q^4 + 4 * q^5 + 6 * q^6 + 30 * q^7 - 6 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 10 q^{4} + 4 q^{5} + 6 q^{6} + 30 q^{7} - 6 q^{8} + 27 q^{9} - 4 q^{10} - 16 q^{11} + 30 q^{12} + 39 q^{13} - 176 q^{14} + 12 q^{15} - 110 q^{16} - 146 q^{17} + 18 q^{18} + 94 q^{19} - 244 q^{20} + 90 q^{21} - 56 q^{22} - 48 q^{23} - 18 q^{24} + 145 q^{25} + 26 q^{26} + 81 q^{27} + 80 q^{28} - 2 q^{29} - 12 q^{30} + 302 q^{31} + 154 q^{32} - 48 q^{33} + 164 q^{34} + 80 q^{35} + 90 q^{36} + 374 q^{37} + 312 q^{38} + 117 q^{39} - 516 q^{40} + 480 q^{41} - 528 q^{42} - 260 q^{43} + 712 q^{44} + 36 q^{45} - 1104 q^{46} - 24 q^{47} - 330 q^{48} + 447 q^{49} + 814 q^{50} - 438 q^{51} + 130 q^{52} - 678 q^{53} + 54 q^{54} - 1552 q^{55} + 96 q^{56} + 282 q^{57} - 628 q^{58} - 1788 q^{59} - 732 q^{60} + 230 q^{61} + 1952 q^{62} + 270 q^{63} - 750 q^{64} + 52 q^{65} - 168 q^{66} + 74 q^{67} - 460 q^{68} - 144 q^{69} + 1216 q^{70} - 948 q^{71} - 54 q^{72} - 222 q^{73} + 1724 q^{74} + 435 q^{75} + 2392 q^{76} + 112 q^{77} + 78 q^{78} - 24 q^{79} + 1100 q^{80} + 243 q^{81} + 564 q^{82} - 796 q^{83} + 240 q^{84} - 248 q^{85} + 1800 q^{86} - 6 q^{87} + 1608 q^{88} + 1436 q^{89} - 36 q^{90} + 390 q^{91} - 1296 q^{92} + 906 q^{93} - 1920 q^{94} - 4032 q^{95} + 462 q^{96} + 3242 q^{97} - 5070 q^{98} - 144 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 10 * q^4 + 4 * q^5 + 6 * q^6 + 30 * q^7 - 6 * q^8 + 27 * q^9 - 4 * q^10 - 16 * q^11 + 30 * q^12 + 39 * q^13 - 176 * q^14 + 12 * q^15 - 110 * q^16 - 146 * q^17 + 18 * q^18 + 94 * q^19 - 244 * q^20 + 90 * q^21 - 56 * q^22 - 48 * q^23 - 18 * q^24 + 145 * q^25 + 26 * q^26 + 81 * q^27 + 80 * q^28 - 2 * q^29 - 12 * q^30 + 302 * q^31 + 154 * q^32 - 48 * q^33 + 164 * q^34 + 80 * q^35 + 90 * q^36 + 374 * q^37 + 312 * q^38 + 117 * q^39 - 516 * q^40 + 480 * q^41 - 528 * q^42 - 260 * q^43 + 712 * q^44 + 36 * q^45 - 1104 * q^46 - 24 * q^47 - 330 * q^48 + 447 * q^49 + 814 * q^50 - 438 * q^51 + 130 * q^52 - 678 * q^53 + 54 * q^54 - 1552 * q^55 + 96 * q^56 + 282 * q^57 - 628 * q^58 - 1788 * q^59 - 732 * q^60 + 230 * q^61 + 1952 * q^62 + 270 * q^63 - 750 * q^64 + 52 * q^65 - 168 * q^66 + 74 * q^67 - 460 * q^68 - 144 * q^69 + 1216 * q^70 - 948 * q^71 - 54 * q^72 - 222 * q^73 + 1724 * q^74 + 435 * q^75 + 2392 * q^76 + 112 * q^77 + 78 * q^78 - 24 * q^79 + 1100 * q^80 + 243 * q^81 + 564 * q^82 - 796 * q^83 + 240 * q^84 - 248 * q^85 + 1800 * q^86 - 6 * q^87 + 1608 * q^88 + 1436 * q^89 - 36 * q^90 + 390 * q^91 - 1296 * q^92 + 906 * q^93 - 1920 * q^94 - 4032 * q^95 + 462 * q^96 + 3242 * q^97 - 5070 * q^98 - 144 * q^99

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