LMFDB - Embedded newform 6015.2.a.e.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.04920 q^{2} -1.00000 q^{3} -0.899176 q^{4} -1.00000 q^{5} -1.04920 q^{6} +2.71724 q^{7} -3.04182 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.04920 q^{2} -1.00000 q^{3} -0.899176 q^{4} -1.00000 q^{5} -1.04920 q^{6} +2.71724 q^{7} -3.04182 q^{8} +1.00000 q^{9} -1.04920 q^{10} -2.08096 q^{11} +0.899176 q^{12} -3.62066 q^{13} +2.85093 q^{14} +1.00000 q^{15} -1.39313 q^{16} -4.07174 q^{17} +1.04920 q^{18} -2.18827 q^{19} +0.899176 q^{20} -2.71724 q^{21} -2.18334 q^{22} +5.90198 q^{23} +3.04182 q^{24} +1.00000 q^{25} -3.79881 q^{26} -1.00000 q^{27} -2.44328 q^{28} -8.57966 q^{29} +1.04920 q^{30} +9.22410 q^{31} +4.62197 q^{32} +2.08096 q^{33} -4.27207 q^{34} -2.71724 q^{35} -0.899176 q^{36} -10.2625 q^{37} -2.29593 q^{38} +3.62066 q^{39} +3.04182 q^{40} +3.31346 q^{41} -2.85093 q^{42} -10.2238 q^{43} +1.87115 q^{44} -1.00000 q^{45} +6.19237 q^{46} +0.367729 q^{47} +1.39313 q^{48} +0.383408 q^{49} +1.04920 q^{50} +4.07174 q^{51} +3.25562 q^{52} +12.1829 q^{53} -1.04920 q^{54} +2.08096 q^{55} -8.26536 q^{56} +2.18827 q^{57} -9.00180 q^{58} +3.49592 q^{59} -0.899176 q^{60} +7.66346 q^{61} +9.67794 q^{62} +2.71724 q^{63} +7.63563 q^{64} +3.62066 q^{65} +2.18334 q^{66} +15.0716 q^{67} +3.66121 q^{68} -5.90198 q^{69} -2.85093 q^{70} -11.7750 q^{71} -3.04182 q^{72} +1.27505 q^{73} -10.7674 q^{74} -1.00000 q^{75} +1.96764 q^{76} -5.65447 q^{77} +3.79881 q^{78} -3.59780 q^{79} +1.39313 q^{80} +1.00000 q^{81} +3.47649 q^{82} +6.11402 q^{83} +2.44328 q^{84} +4.07174 q^{85} -10.7268 q^{86} +8.57966 q^{87} +6.32990 q^{88} -3.68986 q^{89} -1.04920 q^{90} -9.83822 q^{91} -5.30692 q^{92} -9.22410 q^{93} +0.385822 q^{94} +2.18827 q^{95} -4.62197 q^{96} -8.02288 q^{97} +0.402272 q^{98} -2.08096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - 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 $

$2$	1.04920	0.741897	0.370949	−	0.928653i	$-0.379033\pi$
$2$	1.04920	0.741897	0.370949	+	0.928653i	$0.379033\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.899176	−0.449588
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.04920	−0.428335
$7$	2.71724	1.02702	0.513511	−	0.858083i	$-0.328345\pi$
$7$	2.71724	1.02702	0.513511	+	0.858083i	$0.328345\pi$
$8$	−3.04182	−1.07545
$9$	1.00000	0.333333
$10$	−1.04920	−0.331787
$11$	−2.08096	−0.627432	−0.313716	−	0.949517i	$-0.601574\pi$
$11$	−2.08096	−0.627432	−0.313716	+	0.949517i	$0.601574\pi$
$12$	0.899176	0.259570
$13$	−3.62066	−1.00419	−0.502096	−	0.864812i	$-0.667438\pi$
$13$	−3.62066	−1.00419	−0.502096	+	0.864812i	$0.667438\pi$
$14$	2.85093	0.761944
$15$	1.00000	0.258199
$16$	−1.39313	−0.348282
$17$	−4.07174	−0.987541	−0.493771	−	0.869592i	$-0.664382\pi$
$17$	−4.07174	−0.987541	−0.493771	+	0.869592i	$0.664382\pi$
$18$	1.04920	0.247299
$19$	−2.18827	−0.502023	−0.251012	−	0.967984i	$-0.580763\pi$
$19$	−2.18827	−0.502023	−0.251012	+	0.967984i	$0.580763\pi$
$20$	0.899176	0.201062
$21$	−2.71724	−0.592951
$22$	−2.18334	−0.465490
$23$	5.90198	1.23065	0.615324	−	0.788274i	$-0.289025\pi$
$23$	5.90198	1.23065	0.615324	+	0.788274i	$0.289025\pi$
$24$	3.04182	0.620909
$25$	1.00000	0.200000
$26$	−3.79881	−0.745007
$27$	−1.00000	−0.192450
$28$	−2.44328	−0.461737
$29$	−8.57966	−1.59320	−0.796602	−	0.604504i	$-0.793371\pi$
$29$	−8.57966	−1.59320	−0.796602	+	0.604504i	$0.793371\pi$
$30$	1.04920	0.191557
$31$	9.22410	1.65670	0.828349	−	0.560212i	$-0.189281\pi$
$31$	9.22410	1.65670	0.828349	+	0.560212i	$0.189281\pi$
$32$	4.62197	0.817056
$33$	2.08096	0.362248
$34$	−4.27207	−0.732654
$35$	−2.71724	−0.459298
$36$	−0.899176	−0.149863
$37$	−10.2625	−1.68714	−0.843571	−	0.537017i	$-0.819551\pi$
$37$	−10.2625	−1.68714	−0.843571	+	0.537017i	$0.819551\pi$
$38$	−2.29593	−0.372450
$39$	3.62066	0.579770
$40$	3.04182	0.480954
$41$	3.31346	0.517476	0.258738	−	0.965948i	$-0.416693\pi$
$41$	3.31346	0.517476	0.258738	+	0.965948i	$0.416693\pi$
$42$	−2.85093	−0.439909
$43$	−10.2238	−1.55912	−0.779558	−	0.626331i	$-0.784556\pi$
$43$	−10.2238	−1.55912	−0.779558	+	0.626331i	$0.784556\pi$
$44$	1.87115	0.282086
$45$	−1.00000	−0.149071
$46$	6.19237	0.913014
$47$	0.367729	0.0536389	0.0268194	−	0.999640i	$-0.491462\pi$
$47$	0.367729	0.0536389	0.0268194	+	0.999640i	$0.491462\pi$
$48$	1.39313	0.201081
$49$	0.383408	0.0547726
$50$	1.04920	0.148379
$51$	4.07174	0.570157
$52$	3.25562	0.451473
$53$	12.1829	1.67345	0.836724	−	0.547624i	$-0.184468\pi$
$53$	12.1829	1.67345	0.836724	+	0.547624i	$0.184468\pi$
$54$	−1.04920	−0.142778
$55$	2.08096	0.280596
$56$	−8.26536	−1.10451
$57$	2.18827	0.289843
$58$	−9.00180	−1.18199
$59$	3.49592	0.455130	0.227565	−	0.973763i	$-0.426924\pi$
$59$	3.49592	0.455130	0.227565	+	0.973763i	$0.426924\pi$
$60$	−0.899176	−0.116083
$61$	7.66346	0.981206	0.490603	−	0.871383i	$-0.336777\pi$
$61$	7.66346	0.981206	0.490603	+	0.871383i	$0.336777\pi$
$62$	9.67794	1.22910
$63$	2.71724	0.342340
$64$	7.63563	0.954454
$65$	3.62066	0.449088
$66$	2.18334	0.268751
$67$	15.0716	1.84128	0.920642	−	0.390408i	$-0.127666\pi$
$67$	15.0716	1.84128	0.920642	+	0.390408i	$0.127666\pi$
$68$	3.66121	0.443987
$69$	−5.90198	−0.710515
$70$	−2.85093	−0.340752
$71$	−11.7750	−1.39744	−0.698719	−	0.715396i	$-0.746246\pi$
$71$	−11.7750	−1.39744	−0.698719	+	0.715396i	$0.746246\pi$
$72$	−3.04182	−0.358482
$73$	1.27505	0.149234	0.0746169	−	0.997212i	$-0.476227\pi$
$73$	1.27505	0.149234	0.0746169	+	0.997212i	$0.476227\pi$
$74$	−10.7674	−1.25169
$75$	−1.00000	−0.115470
$76$	1.96764	0.225704
$77$	−5.65447	−0.644386
$78$	3.79881	0.430130
$79$	−3.59780	−0.404784	−0.202392	−	0.979305i	$-0.564871\pi$
$79$	−3.59780	−0.404784	−0.202392	+	0.979305i	$0.564871\pi$
$80$	1.39313	0.155757
$81$	1.00000	0.111111
$82$	3.47649	0.383914
$83$	6.11402	0.671101	0.335550	−	0.942022i	$-0.391078\pi$
$83$	6.11402	0.671101	0.335550	+	0.942022i	$0.391078\pi$
$84$	2.44328	0.266584
$85$	4.07174	0.441642
$86$	−10.7268	−1.15670
$87$	8.57966	0.919837
$88$	6.32990	0.674769
$89$	−3.68986	−0.391124	−0.195562	−	0.980691i	$-0.562653\pi$
$89$	−3.68986	−0.391124	−0.195562	+	0.980691i	$0.562653\pi$
$90$	−1.04920	−0.110596
$91$	−9.83822	−1.03133
$92$	−5.30692	−0.553285
$93$	−9.22410	−0.956495
$94$	0.385822	0.0397945
$95$	2.18827	0.224512
$96$	−4.62197	−0.471728
$97$	−8.02288	−0.814600	−0.407300	−	0.913294i	$-0.633530\pi$
$97$	−8.02288	−0.814600	−0.407300	+	0.913294i	$0.633530\pi$
$98$	0.402272	0.0406356
$99$	−2.08096	−0.209144
$100$	−0.899176	−0.0899176
$101$	−2.10857	−0.209811	−0.104905	−	0.994482i	$-0.533454\pi$
$101$	−2.10857	−0.209811	−0.104905	+	0.994482i	$0.533454\pi$
$102$	4.27207	0.422998
$103$	−16.5314	−1.62889	−0.814446	−	0.580240i	$-0.802959\pi$
$103$	−16.5314	−1.62889	−0.814446	+	0.580240i	$0.802959\pi$
$104$	11.0134	1.07995
$105$	2.71724	0.265176
$106$	12.7823	1.24153
$107$	13.5548	1.31040	0.655198	−	0.755457i	$-0.272585\pi$
$107$	13.5548	1.31040	0.655198	+	0.755457i	$0.272585\pi$
$108$	0.899176	0.0865233
$109$	−16.9589	−1.62437	−0.812183	−	0.583403i	$-0.801721\pi$
$109$	−16.9589	−1.62437	−0.812183	+	0.583403i	$0.801721\pi$
$110$	2.18334	0.208174
$111$	10.2625	0.974072
$112$	−3.78547	−0.357693
$113$	9.08723	0.854854	0.427427	−	0.904050i	$-0.359420\pi$
$113$	9.08723	0.854854	0.427427	+	0.904050i	$0.359420\pi$
$114$	2.29593	0.215034
$115$	−5.90198	−0.550362
$116$	7.71463	0.716286
$117$	−3.62066	−0.334731
$118$	3.66792	0.337659
$119$	−11.0639	−1.01423
$120$	−3.04182	−0.277679
$121$	−6.66962	−0.606329
$122$	8.04051	0.727954
$123$	−3.31346	−0.298765
$124$	−8.29410	−0.744832
$125$	−1.00000	−0.0894427
$126$	2.85093	0.253981
$127$	8.48940	0.753312	0.376656	−	0.926353i	$-0.377074\pi$
$127$	8.48940	0.753312	0.376656	+	0.926353i	$0.377074\pi$
$128$	−1.23262	−0.108949
$129$	10.2238	0.900155
$130$	3.79881	0.333177
$131$	11.6610	1.01883	0.509414	−	0.860522i	$-0.329862\pi$
$131$	11.6610	1.01883	0.509414	+	0.860522i	$0.329862\pi$
$132$	−1.87115	−0.162863
$133$	−5.94606	−0.515588
$134$	15.8131	1.36604
$135$	1.00000	0.0860663
$136$	12.3855	1.06205
$137$	20.7393	1.77188	0.885940	−	0.463799i	$-0.153514\pi$
$137$	20.7393	1.77188	0.885940	+	0.463799i	$0.153514\pi$
$138$	−6.19237	−0.527129
$139$	11.5560	0.980169	0.490085	−	0.871675i	$-0.336966\pi$
$139$	11.5560	0.980169	0.490085	+	0.871675i	$0.336966\pi$
$140$	2.44328	0.206495
$141$	−0.367729	−0.0309684
$142$	−12.3544	−1.03676
$143$	7.53445	0.630062
$144$	−1.39313	−0.116094
$145$	8.57966	0.712502
$146$	1.33779	0.110716
$147$	−0.383408	−0.0316229
$148$	9.22778	0.758519
$149$	4.88230	0.399973	0.199987	−	0.979799i	$-0.435910\pi$
$149$	4.88230	0.399973	0.199987	+	0.979799i	$0.435910\pi$
$150$	−1.04920	−0.0856669
$151$	20.5577	1.67296	0.836482	−	0.547995i	$-0.184609\pi$
$151$	20.5577	1.67296	0.836482	+	0.547995i	$0.184609\pi$
$152$	6.65632	0.539899
$153$	−4.07174	−0.329180
$154$	−5.93267	−0.478068
$155$	−9.22410	−0.740898
$156$	−3.25562	−0.260658
$157$	−17.6938	−1.41212	−0.706058	−	0.708154i	$-0.749528\pi$
$157$	−17.6938	−1.41212	−0.706058	+	0.708154i	$0.749528\pi$
$158$	−3.77481	−0.300308
$159$	−12.1829	−0.966166
$160$	−4.62197	−0.365399
$161$	16.0371	1.26390
$162$	1.04920	0.0824330
$163$	−0.00395981	−0.000310157 0	−0.000155078	−	1.00000i	$-0.500049\pi$
$163$	−0.00395981	−0.000310157 0	−0.000155078		1.00000i	$0.500049\pi$
$164$	−2.97939	−0.232651
$165$	−2.08096	−0.162002
$166$	6.41484	0.497888
$167$	21.4244	1.65787	0.828934	−	0.559347i	$-0.188948\pi$
$167$	21.4244	1.65787	0.828934	+	0.559347i	$0.188948\pi$
$168$	8.26536	0.637687
$169$	0.109213	0.00840096
$170$	4.27207	0.327653
$171$	−2.18827	−0.167341
$172$	9.19300	0.700960
$173$	−16.5710	−1.25987	−0.629936	−	0.776647i	$-0.716919\pi$
$173$	−16.5710	−1.25987	−0.629936	+	0.776647i	$0.716919\pi$
$174$	9.00180	0.682424
$175$	2.71724	0.205404
$176$	2.89904	0.218524
$177$	−3.49592	−0.262769
$178$	−3.87140	−0.290174
$179$	13.9708	1.04423	0.522115	−	0.852875i	$-0.325143\pi$
$179$	13.9708	1.04423	0.522115	+	0.852875i	$0.325143\pi$
$180$	0.899176	0.0670207
$181$	14.8429	1.10326	0.551630	−	0.834089i	$-0.314006\pi$
$181$	14.8429	1.10326	0.551630	+	0.834089i	$0.314006\pi$
$182$	−10.3223	−0.765138
$183$	−7.66346	−0.566499
$184$	−17.9528	−1.32350
$185$	10.2625	0.754513
$186$	−9.67794	−0.709621
$187$	8.47311	0.619615
$188$	−0.330654	−0.0241154
$189$	−2.71724	−0.197650
$190$	2.29593	0.166565
$191$	25.2165	1.82460	0.912302	−	0.409517i	$-0.134303\pi$
$191$	25.2165	1.82460	0.912302	+	0.409517i	$0.134303\pi$
$192$	−7.63563	−0.551054
$193$	5.93756	0.427395	0.213698	−	0.976900i	$-0.431449\pi$
$193$	5.93756	0.427395	0.213698	+	0.976900i	$0.431449\pi$
$194$	−8.41761	−0.604349
$195$	−3.62066	−0.259281
$196$	−0.344751	−0.0246251
$197$	−12.5579	−0.894716	−0.447358	−	0.894355i	$-0.647635\pi$
$197$	−12.5579	−0.894716	−0.447358	+	0.894355i	$0.647635\pi$
$198$	−2.18334	−0.155163
$199$	8.46650	0.600174	0.300087	−	0.953912i	$-0.402984\pi$
$199$	8.46650	0.600174	0.300087	+	0.953912i	$0.402984\pi$
$200$	−3.04182	−0.215089
$201$	−15.0716	−1.06307
$202$	−2.21232	−0.155658
$203$	−23.3130	−1.63625
$204$	−3.66121	−0.256336
$205$	−3.31346	−0.231422
$206$	−17.3448	−1.20847
$207$	5.90198	0.410216
$208$	5.04405	0.349742
$209$	4.55369	0.314986
$210$	2.85093	0.196733
$211$	24.9651	1.71867	0.859333	−	0.511417i	$-0.170879\pi$
$211$	24.9651	1.71867	0.859333	+	0.511417i	$0.170879\pi$
$212$	−10.9546	−0.752363
$213$	11.7750	0.806812
$214$	14.2218	0.972180
$215$	10.2238	0.697257
$216$	3.04182	0.206970
$217$	25.0641	1.70146
$218$	−17.7933	−1.20511
$219$	−1.27505	−0.0861602
$220$	−1.87115	−0.126153
$221$	14.7424	0.991681
$222$	10.7674	0.722662
$223$	−20.0675	−1.34382	−0.671910	−	0.740633i	$-0.734526\pi$
$223$	−20.0675	−1.34382	−0.671910	+	0.740633i	$0.734526\pi$
$224$	12.5590	0.839134
$225$	1.00000	0.0666667
$226$	9.53433	0.634214
$227$	−8.69707	−0.577245	−0.288622	−	0.957443i	$-0.593197\pi$
$227$	−8.69707	−0.577245	−0.288622	+	0.957443i	$0.593197\pi$
$228$	−1.96764	−0.130310
$229$	−9.93625	−0.656606	−0.328303	−	0.944572i	$-0.606477\pi$
$229$	−9.93625	−0.656606	−0.328303	+	0.944572i	$0.606477\pi$
$230$	−6.19237	−0.408312
$231$	5.65447	0.372037
$232$	26.0978	1.71340
$233$	20.5188	1.34423	0.672115	−	0.740447i	$-0.265386\pi$
$233$	20.5188	1.34423	0.672115	+	0.740447i	$0.265386\pi$
$234$	−3.79881	−0.248336
$235$	−0.367729	−0.0239880
$236$	−3.14345	−0.204621
$237$	3.59780	0.233702
$238$	−11.6083	−0.752451
$239$	−16.9916	−1.09909	−0.549547	−	0.835463i	$-0.685200\pi$
$239$	−16.9916	−1.09909	−0.549547	+	0.835463i	$0.685200\pi$
$240$	−1.39313	−0.0899261
$241$	−0.224586	−0.0144668	−0.00723341	−	0.999974i	$-0.502302\pi$
$241$	−0.224586	−0.0144668	−0.00723341	+	0.999974i	$0.502302\pi$
$242$	−6.99777	−0.449834
$243$	−1.00000	−0.0641500
$244$	−6.89080	−0.441138
$245$	−0.383408	−0.0244950
$246$	−3.47649	−0.221653
$247$	7.92299	0.504128
$248$	−28.0581	−1.78169
$249$	−6.11402	−0.387460
$250$	−1.04920	−0.0663573
$251$	27.8092	1.75530	0.877652	−	0.479299i	$-0.159109\pi$
$251$	27.8092	1.75530	0.877652	+	0.479299i	$0.159109\pi$
$252$	−2.44328	−0.153912
$253$	−12.2818	−0.772148
$254$	8.90709	0.558880
$255$	−4.07174	−0.254982
$256$	−16.5645	−1.03528
$257$	3.33444	0.207997	0.103998	−	0.994577i	$-0.466836\pi$
$257$	3.33444	0.207997	0.103998	+	0.994577i	$0.466836\pi$
$258$	10.7268	0.667823
$259$	−27.8857	−1.73273
$260$	−3.25562	−0.201905
$261$	−8.57966	−0.531068
$262$	12.2348	0.755865
$263$	21.2976	1.31327	0.656634	−	0.754210i	$-0.271980\pi$
$263$	21.2976	1.31327	0.656634	+	0.754210i	$0.271980\pi$
$264$	−6.32990	−0.389578
$265$	−12.1829	−0.748389
$266$	−6.23861	−0.382514
$267$	3.68986	0.225816
$268$	−13.5520	−0.827819
$269$	10.4299	0.635921	0.317960	−	0.948104i	$-0.397002\pi$
$269$	10.4299	0.635921	0.317960	+	0.948104i	$0.397002\pi$
$270$	1.04920	0.0638524
$271$	−10.6250	−0.645424	−0.322712	−	0.946497i	$-0.604595\pi$
$271$	−10.6250	−0.645424	−0.322712	+	0.946497i	$0.604595\pi$
$272$	5.67245	0.343943
$273$	9.83822	0.595436
$274$	21.7597	1.31455
$275$	−2.08096	−0.125486
$276$	5.30692	0.319439
$277$	26.0111	1.56286	0.781428	−	0.623995i	$-0.214492\pi$
$277$	26.0111	1.56286	0.781428	+	0.623995i	$0.214492\pi$
$278$	12.1246	0.727185
$279$	9.22410	0.552233
$280$	8.26536	0.493950
$281$	−15.3016	−0.912816	−0.456408	−	0.889771i	$-0.650864\pi$
$281$	−15.3016	−0.912816	−0.456408	+	0.889771i	$0.650864\pi$
$282$	−0.385822	−0.0229754
$283$	16.5355	0.982936	0.491468	−	0.870896i	$-0.336460\pi$
$283$	16.5355	0.982936	0.491468	+	0.870896i	$0.336460\pi$
$284$	10.5878	0.628272
$285$	−2.18827	−0.129622
$286$	7.90515	0.467442
$287$	9.00348	0.531459
$288$	4.62197	0.272352
$289$	−0.420965	−0.0247627
$290$	9.00180	0.528604
$291$	8.02288	0.470309
$292$	−1.14650	−0.0670938
$293$	6.79657	0.397060	0.198530	−	0.980095i	$-0.436383\pi$
$293$	6.79657	0.397060	0.198530	+	0.980095i	$0.436383\pi$
$294$	−0.402272	−0.0234610
$295$	−3.49592	−0.203540
$296$	31.2166	1.81443
$297$	2.08096	0.120749
$298$	5.12251	0.296739
$299$	−21.3691	−1.23581
$300$	0.899176	0.0519140
$301$	−27.7805	−1.60124
$302$	21.5692	1.24117
$303$	2.10857	0.121134
$304$	3.04854	0.174846
$305$	−7.66346	−0.438809
$306$	−4.27207	−0.244218
$307$	5.15383	0.294145	0.147072	−	0.989126i	$-0.453015\pi$
$307$	5.15383	0.294145	0.147072	+	0.989126i	$0.453015\pi$
$308$	5.08436	0.289708
$309$	16.5314	0.940441
$310$	−9.67794	−0.549670
$311$	24.0369	1.36301	0.681503	−	0.731815i	$-0.261327\pi$
$311$	24.0369	1.36301	0.681503	+	0.731815i	$0.261327\pi$
$312$	−11.0134	−0.623512
$313$	−8.61277	−0.486823	−0.243411	−	0.969923i	$-0.578267\pi$
$313$	−8.61277	−0.486823	−0.243411	+	0.969923i	$0.578267\pi$
$314$	−18.5643	−1.04765
$315$	−2.71724	−0.153099
$316$	3.23505	0.181986
$317$	8.42446	0.473165	0.236582	−	0.971611i	$-0.423973\pi$
$317$	8.42446	0.473165	0.236582	+	0.971611i	$0.423973\pi$
$318$	−12.7823	−0.716796
$319$	17.8539	0.999627
$320$	−7.63563	−0.426845
$321$	−13.5548	−0.756558
$322$	16.8262	0.937685
$323$	8.91005	0.495769
$324$	−0.899176	−0.0499542
$325$	−3.62066	−0.200838
$326$	−0.00415464	−0.000230104 0
$327$	16.9589	0.937828
$328$	−10.0790	−0.556517
$329$	0.999210	0.0550882
$330$	−2.18334	−0.120189
$331$	10.4541	0.574609	0.287305	−	0.957839i	$-0.407241\pi$
$331$	10.4541	0.574609	0.287305	+	0.957839i	$0.407241\pi$
$332$	−5.49758	−0.301719
$333$	−10.2625	−0.562381
$334$	22.4785	1.22997
$335$	−15.0716	−0.823447
$336$	3.78547	0.206514
$337$	13.5709	0.739254	0.369627	−	0.929180i	$-0.379486\pi$
$337$	13.5709	0.739254	0.369627	+	0.929180i	$0.379486\pi$
$338$	0.114586	0.00623265
$339$	−9.08723	−0.493550
$340$	−3.66121	−0.198557
$341$	−19.1950	−1.03947
$342$	−2.29593	−0.124150
$343$	−17.9789	−0.970769
$344$	31.0990	1.67674
$345$	5.90198	0.317752
$346$	−17.3864	−0.934696
$347$	−5.83782	−0.313391	−0.156695	−	0.987647i	$-0.550084\pi$
$347$	−5.83782	−0.313391	−0.156695	+	0.987647i	$0.550084\pi$
$348$	−7.71463	−0.413548
$349$	16.6062	0.888912	0.444456	−	0.895801i	$-0.353397\pi$
$349$	16.6062	0.888912	0.444456	+	0.895801i	$0.353397\pi$
$350$	2.85093	0.152389
$351$	3.62066	0.193257
$352$	−9.61812	−0.512647
$353$	−4.66359	−0.248218	−0.124109	−	0.992269i	$-0.539607\pi$
$353$	−4.66359	−0.248218	−0.124109	+	0.992269i	$0.539607\pi$
$354$	−3.66792	−0.194948
$355$	11.7750	0.624954
$356$	3.31783	0.175845
$357$	11.0639	0.585563
$358$	14.6582	0.774711
$359$	5.12174	0.270315	0.135157	−	0.990824i	$-0.456846\pi$
$359$	5.12174	0.270315	0.135157	+	0.990824i	$0.456846\pi$
$360$	3.04182	0.160318
$361$	−14.2115	−0.747973
$362$	15.5731	0.818506
$363$	6.66962	0.350064
$364$	8.84630	0.463672
$365$	−1.27505	−0.0667394
$366$	−8.04051	−0.420284
$367$	18.1763	0.948795	0.474397	−	0.880311i	$-0.342666\pi$
$367$	18.1763	0.948795	0.474397	+	0.880311i	$0.342666\pi$
$368$	−8.22222	−0.428613
$369$	3.31346	0.172492
$370$	10.7674	0.559771
$371$	33.1039	1.71867
$372$	8.29410	0.430029
$373$	−1.93980	−0.100439	−0.0502196	−	0.998738i	$-0.515992\pi$
$373$	−1.93980	−0.100439	−0.0502196	+	0.998738i	$0.515992\pi$
$374$	8.89000	0.459691
$375$	1.00000	0.0516398
$376$	−1.11857	−0.0576857
$377$	31.0641	1.59988
$378$	−2.85093	−0.146636
$379$	−19.5298	−1.00318	−0.501590	−	0.865106i	$-0.667251\pi$
$379$	−19.5298	−1.00318	−0.501590	+	0.865106i	$0.667251\pi$
$380$	−1.96764	−0.100938
$381$	−8.48940	−0.434925
$382$	26.4572	1.35367
$383$	7.04870	0.360172	0.180086	−	0.983651i	$-0.442362\pi$
$383$	7.04870	0.360172	0.180086	+	0.983651i	$0.442362\pi$
$384$	1.23262	0.0629018
$385$	5.65447	0.288178
$386$	6.22970	0.317083
$387$	−10.2238	−0.519705
$388$	7.21398	0.366234
$389$	−12.3665	−0.627005	−0.313502	−	0.949587i	$-0.601502\pi$
$389$	−12.3665	−0.627005	−0.313502	+	0.949587i	$0.601502\pi$
$390$	−3.79881	−0.192360
$391$	−24.0313	−1.21532
$392$	−1.16626	−0.0589049
$393$	−11.6610	−0.588220
$394$	−13.1758	−0.663788
$395$	3.59780	0.181025
$396$	1.87115	0.0940287
$397$	−9.41601	−0.472576	−0.236288	−	0.971683i	$-0.575931\pi$
$397$	−9.41601	−0.472576	−0.236288	+	0.971683i	$0.575931\pi$
$398$	8.88306	0.445268
$399$	5.94606	0.297675
$400$	−1.39313	−0.0696565
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−15.8131	−0.788686
$403$	−33.3974	−1.66364
$404$	1.89598	0.0943284
$405$	−1.00000	−0.0496904
$406$	−24.4601	−1.21393
$407$	21.3558	1.05857
$408$	−12.3855	−0.613173
$409$	−8.36080	−0.413415	−0.206707	−	0.978403i	$-0.566275\pi$
$409$	−8.36080	−0.413415	−0.206707	+	0.978403i	$0.566275\pi$
$410$	−3.47649	−0.171692
$411$	−20.7393	−1.02300
$412$	14.8647	0.732330
$413$	9.49925	0.467428
$414$	6.19237	0.304338
$415$	−6.11402	−0.300125
$416$	−16.7346	−0.820481
$417$	−11.5560	−0.565901
$418$	4.77774	0.233687
$419$	7.44484	0.363704	0.181852	−	0.983326i	$-0.441791\pi$
$419$	7.44484	0.363704	0.181852	+	0.983326i	$0.441791\pi$
$420$	−2.44328	−0.119220
$421$	−19.0006	−0.926033	−0.463016	−	0.886350i	$-0.653233\pi$
$421$	−19.0006	−0.926033	−0.463016	+	0.886350i	$0.653233\pi$
$422$	26.1934	1.27507
$423$	0.367729	0.0178796
$424$	−37.0582	−1.79970
$425$	−4.07174	−0.197508
$426$	12.3544	0.598571
$427$	20.8235	1.00772
$428$	−12.1882	−0.589139
$429$	−7.53445	−0.363767
$430$	10.7268	0.517294
$431$	−0.464928	−0.0223948	−0.0111974	−	0.999937i	$-0.503564\pi$
$431$	−0.464928	−0.0223948	−0.0111974	+	0.999937i	$0.503564\pi$
$432$	1.39313	0.0670270
$433$	31.5884	1.51804	0.759021	−	0.651067i	$-0.225678\pi$
$433$	31.5884	1.51804	0.759021	+	0.651067i	$0.225678\pi$
$434$	26.2973	1.26231
$435$	−8.57966	−0.411363
$436$	15.2490	0.730295
$437$	−12.9151	−0.617814
$438$	−1.33779	−0.0639220
$439$	21.6112	1.03145	0.515724	−	0.856755i	$-0.327523\pi$
$439$	21.6112	1.03145	0.515724	+	0.856755i	$0.327523\pi$
$440$	−6.32990	−0.301766
$441$	0.383408	0.0182575
$442$	15.4677	0.735725
$443$	−20.3313	−0.965969	−0.482984	−	0.875629i	$-0.660447\pi$
$443$	−20.3313	−0.965969	−0.482984	+	0.875629i	$0.660447\pi$
$444$	−9.22778	−0.437931
$445$	3.68986	0.174916
$446$	−21.0549	−0.996977
$447$	−4.88230	−0.230925
$448$	20.7479	0.980245
$449$	−11.6865	−0.551522	−0.275761	−	0.961226i	$-0.588930\pi$
$449$	−11.6865	−0.551522	−0.275761	+	0.961226i	$0.588930\pi$
$450$	1.04920	0.0494598
$451$	−6.89517	−0.324681
$452$	−8.17102	−0.384332
$453$	−20.5577	−0.965886
$454$	−9.12497	−0.428256
$455$	9.83822	0.461223
$456$	−6.65632	−0.311711
$457$	−22.0823	−1.03297	−0.516483	−	0.856298i	$-0.672759\pi$
$457$	−22.0823	−1.03297	−0.516483	+	0.856298i	$0.672759\pi$
$458$	−10.4251	−0.487134
$459$	4.07174	0.190052
$460$	5.30692	0.247436
$461$	−25.7376	−1.19872	−0.599359	−	0.800481i	$-0.704578\pi$
$461$	−25.7376	−1.19872	−0.599359	+	0.800481i	$0.704578\pi$
$462$	5.93267	0.276013
$463$	40.5886	1.88631	0.943155	−	0.332352i	$-0.107842\pi$
$463$	40.5886	1.88631	0.943155	+	0.332352i	$0.107842\pi$
$464$	11.9526	0.554885
$465$	9.22410	0.427758
$466$	21.5283	0.997280
$467$	8.89365	0.411549	0.205774	−	0.978599i	$-0.434029\pi$
$467$	8.89365	0.411549	0.205774	+	0.978599i	$0.434029\pi$
$468$	3.25562	0.150491
$469$	40.9531	1.89104
$470$	−0.385822	−0.0177967
$471$	17.6938	0.815286
$472$	−10.6339	−0.489467
$473$	21.2753	0.978239
$474$	3.77481	0.173383
$475$	−2.18827	−0.100405
$476$	9.94839	0.455984
$477$	12.1829	0.557816
$478$	−17.8276	−0.815416
$479$	−13.4749	−0.615682	−0.307841	−	0.951438i	$-0.599606\pi$
$479$	−13.4749	−0.615682	−0.307841	+	0.951438i	$0.599606\pi$
$480$	4.62197	0.210963
$481$	37.1570	1.69421
$482$	−0.235635	−0.0107329
$483$	−16.0371	−0.729714
$484$	5.99716	0.272598
$485$	8.02288	0.364300
$486$	−1.04920	−0.0475927
$487$	−21.1160	−0.956858	−0.478429	−	0.878126i	$-0.658794\pi$
$487$	−21.1160	−0.956858	−0.478429	+	0.878126i	$0.658794\pi$
$488$	−23.3109	−1.05523
$489$	0.00395981	0.000179069 0
$490$	−0.402272	−0.0181728
$491$	−32.1411	−1.45051	−0.725253	−	0.688482i	$-0.758277\pi$
$491$	−32.1411	−1.45051	−0.725253	+	0.688482i	$0.758277\pi$
$492$	2.97939	0.134321
$493$	34.9341	1.57335
$494$	8.31281	0.374011
$495$	2.08096	0.0935321
$496$	−12.8504	−0.576998
$497$	−31.9956	−1.43520
$498$	−6.41484	−0.287456
$499$	7.41870	0.332107	0.166053	−	0.986117i	$-0.446898\pi$
$499$	7.41870	0.332107	0.166053	+	0.986117i	$0.446898\pi$
$500$	0.899176	0.0402124
$501$	−21.4244	−0.957170
$502$	29.1775	1.30226
$503$	17.4208	0.776755	0.388378	−	0.921500i	$-0.373036\pi$
$503$	17.4208	0.776755	0.388378	+	0.921500i	$0.373036\pi$
$504$	−8.26536	−0.368169
$505$	2.10857	0.0938302
$506$	−12.8860	−0.572855
$507$	−0.109213	−0.00485030
$508$	−7.63347	−0.338680
$509$	33.2214	1.47251	0.736256	−	0.676703i	$-0.236592\pi$
$509$	33.2214	1.47251	0.736256	+	0.676703i	$0.236592\pi$
$510$	−4.27207	−0.189170
$511$	3.46463	0.153266
$512$	−14.9143	−0.659125
$513$	2.18827	0.0966144
$514$	3.49850	0.154312
$515$	16.5314	0.728463
$516$	−9.19300	−0.404699
$517$	−0.765229	−0.0336547
$518$	−29.2577	−1.28551
$519$	16.5710	0.727388
$520$	−11.0134	−0.482970
$521$	−14.9509	−0.655012	−0.327506	−	0.944849i	$-0.606208\pi$
$521$	−14.9509	−0.655012	−0.327506	+	0.944849i	$0.606208\pi$
$522$	−9.00180	−0.393998
$523$	6.70451	0.293168	0.146584	−	0.989198i	$-0.453172\pi$
$523$	6.70451	0.293168	0.146584	+	0.989198i	$0.453172\pi$
$524$	−10.4853	−0.458053
$525$	−2.71724	−0.118590
$526$	22.3455	0.974310
$527$	−37.5581	−1.63606
$528$	−2.89904	−0.126165
$529$	11.8334	0.514494
$530$	−12.7823	−0.555228
$531$	3.49592	0.151710
$532$	5.34655	0.231802
$533$	−11.9969	−0.519645
$534$	3.87140	0.167532
$535$	−13.5548	−0.586027
$536$	−45.8450	−1.98020
$537$	−13.9708	−0.602886
$538$	10.9430	0.471788
$539$	−0.797855	−0.0343661
$540$	−0.899176	−0.0386944
$541$	−12.5333	−0.538850	−0.269425	−	0.963021i	$-0.586834\pi$
$541$	−12.5333	−0.538850	−0.269425	+	0.963021i	$0.586834\pi$
$542$	−11.1478	−0.478839
$543$	−14.8429	−0.636968
$544$	−18.8194	−0.806876
$545$	16.9589	0.726438
$546$	10.3223	0.441753
$547$	2.42342	0.103618	0.0518089	−	0.998657i	$-0.483501\pi$
$547$	2.42342	0.103618	0.0518089	+	0.998657i	$0.483501\pi$
$548$	−18.6483	−0.796617
$549$	7.66346	0.327069
$550$	−2.18334	−0.0930981
$551$	18.7746	0.799825
$552$	17.9528	0.764120
$553$	−9.77608	−0.415721
$554$	27.2909	1.15948
$555$	−10.2625	−0.435618
$556$	−10.3909	−0.440672
$557$	7.79747	0.330389	0.165195	−	0.986261i	$-0.447175\pi$
$557$	7.79747	0.330389	0.165195	+	0.986261i	$0.447175\pi$
$558$	9.67794	0.409700
$559$	37.0170	1.56565
$560$	3.78547	0.159965
$561$	−8.47311	−0.357735
$562$	−16.0544	−0.677216
$563$	−12.3990	−0.522555	−0.261277	−	0.965264i	$-0.584144\pi$
$563$	−12.3990	−0.522555	−0.261277	+	0.965264i	$0.584144\pi$
$564$	0.330654	0.0139230
$565$	−9.08723	−0.382303
$566$	17.3491	0.729238
$567$	2.71724	0.114113
$568$	35.8175	1.50287
$569$	12.7298	0.533662	0.266831	−	0.963743i	$-0.414023\pi$
$569$	12.7298	0.533662	0.266831	+	0.963743i	$0.414023\pi$
$570$	−2.29593	−0.0961661
$571$	−18.7212	−0.783458	−0.391729	−	0.920081i	$-0.628123\pi$
$571$	−18.7212	−0.783458	−0.391729	+	0.920081i	$0.628123\pi$
$572$	−6.77480	−0.283269
$573$	−25.2165	−1.05344
$574$	9.44646	0.394288
$575$	5.90198	0.246130
$576$	7.63563	0.318151
$577$	26.1510	1.08868	0.544340	−	0.838865i	$-0.316780\pi$
$577$	26.1510	1.08868	0.544340	+	0.838865i	$0.316780\pi$
$578$	−0.441677	−0.0183714
$579$	−5.93756	−0.246757
$580$	−7.71463	−0.320333
$581$	16.6133	0.689235
$582$	8.41761	0.348921
$583$	−25.3521	−1.04998
$584$	−3.87849	−0.160493
$585$	3.62066	0.149696
$586$	7.13097	0.294578
$587$	−45.0663	−1.86008	−0.930042	−	0.367452i	$-0.880230\pi$
$587$	−45.0663	−1.86008	−0.930042	+	0.367452i	$0.880230\pi$
$588$	0.344751	0.0142173
$589$	−20.1848	−0.831701
$590$	−3.66792	−0.151006
$591$	12.5579	0.516565
$592$	14.2970	0.587602
$593$	20.9455	0.860127	0.430063	−	0.902799i	$-0.358491\pi$
$593$	20.9455	0.860127	0.430063	+	0.902799i	$0.358491\pi$
$594$	2.18334	0.0895837
$595$	11.0639	0.453575
$596$	−4.39005	−0.179823
$597$	−8.46650	−0.346511
$598$	−22.4205	−0.916842
$599$	26.3311	1.07586	0.537929	−	0.842990i	$-0.319207\pi$
$599$	26.3311	1.07586	0.537929	+	0.842990i	$0.319207\pi$
$600$	3.04182	0.124182
$601$	40.4229	1.64889	0.824443	−	0.565946i	$-0.191489\pi$
$601$	40.4229	1.64889	0.824443	+	0.565946i	$0.191489\pi$
$602$	−29.1474	−1.18796
$603$	15.0716	0.613761
$604$	−18.4850	−0.752145
$605$	6.66962	0.271158
$606$	2.21232	0.0898692
$607$	−0.480609	−0.0195073	−0.00975366	−	0.999952i	$-0.503105\pi$
$607$	−0.480609	−0.0195073	−0.00975366	+	0.999952i	$0.503105\pi$
$608$	−10.1141	−0.410181
$609$	23.3130	0.944692
$610$	−8.04051	−0.325551
$611$	−1.33143	−0.0538637
$612$	3.66121	0.147996
$613$	−7.60653	−0.307225	−0.153612	−	0.988131i	$-0.549091\pi$
$613$	−7.60653	−0.307225	−0.153612	+	0.988131i	$0.549091\pi$
$614$	5.40741	0.218225
$615$	3.31346	0.133612
$616$	17.1999	0.693002
$617$	−17.4043	−0.700669	−0.350334	−	0.936625i	$-0.613932\pi$
$617$	−17.4043	−0.700669	−0.350334	+	0.936625i	$0.613932\pi$
$618$	17.3448	0.697711
$619$	−13.9889	−0.562261	−0.281131	−	0.959669i	$-0.590709\pi$
$619$	−13.9889	−0.562261	−0.281131	+	0.959669i	$0.590709\pi$
$620$	8.29410	0.333099
$621$	−5.90198	−0.236838
$622$	25.2195	1.01121
$623$	−10.0262	−0.401693
$624$	−5.04405	−0.201924
$625$	1.00000	0.0400000
$626$	−9.03653	−0.361173
$627$	−4.55369	−0.181857
$628$	15.9098	0.634871
$629$	41.7861	1.66612
$630$	−2.85093	−0.113584
$631$	−16.3455	−0.650703	−0.325351	−	0.945593i	$-0.605483\pi$
$631$	−16.3455	−0.650703	−0.325351	+	0.945593i	$0.605483\pi$
$632$	10.9438	0.435323
$633$	−24.9651	−0.992272
$634$	8.83896	0.351040
$635$	−8.48940	−0.336891
$636$	10.9546	0.434377
$637$	−1.38819	−0.0550021
$638$	18.7324	0.741621
$639$	−11.7750	−0.465813
$640$	1.23262	0.0487235
$641$	−13.1669	−0.520061	−0.260031	−	0.965600i	$-0.583733\pi$
$641$	−13.1669	−0.520061	−0.260031	+	0.965600i	$0.583733\pi$
$642$	−14.2218	−0.561288
$643$	6.41322	0.252913	0.126456	−	0.991972i	$-0.459640\pi$
$643$	6.41322	0.252913	0.126456	+	0.991972i	$0.459640\pi$
$644$	−14.4202	−0.568235
$645$	−10.2238	−0.402562
$646$	9.34844	0.367809
$647$	4.41884	0.173723	0.0868613	−	0.996220i	$-0.472316\pi$
$647$	4.41884	0.173723	0.0868613	+	0.996220i	$0.472316\pi$
$648$	−3.04182	−0.119494
$649$	−7.27485	−0.285563
$650$	−3.79881	−0.149001
$651$	−25.0641	−0.982341
$652$	0.00356057	0.000139443 0
$653$	−11.5218	−0.450883	−0.225441	−	0.974257i	$-0.572382\pi$
$653$	−11.5218	−0.450883	−0.225441	+	0.974257i	$0.572382\pi$
$654$	17.7933	0.695772
$655$	−11.6610	−0.455633
$656$	−4.61608	−0.180228
$657$	1.27505	0.0497446
$658$	1.04837	0.0408698
$659$	12.0219	0.468308	0.234154	−	0.972199i	$-0.424768\pi$
$659$	12.0219	0.468308	0.234154	+	0.972199i	$0.424768\pi$
$660$	1.87115	0.0728343
$661$	−19.2679	−0.749434	−0.374717	−	0.927139i	$-0.622260\pi$
$661$	−19.2679	−0.749434	−0.374717	+	0.927139i	$0.622260\pi$
$662$	10.9685	0.426301
$663$	−14.7424	−0.572547
$664$	−18.5977	−0.721733
$665$	5.94606	0.230578
$666$	−10.7674	−0.417229
$667$	−50.6370	−1.96067
$668$	−19.2643	−0.745358
$669$	20.0675	0.775855
$670$	−15.8131	−0.610913
$671$	−15.9473	−0.615640
$672$	−12.5590	−0.484474
$673$	−0.368704	−0.0142125	−0.00710624	−	0.999975i	$-0.502262\pi$
$673$	−0.368704	−0.0142125	−0.00710624	+	0.999975i	$0.502262\pi$
$674$	14.2386	0.548450
$675$	−1.00000	−0.0384900
$676$	−0.0982013	−0.00377697
$677$	23.0790	0.886998	0.443499	−	0.896275i	$-0.353737\pi$
$677$	23.0790	0.886998	0.443499	+	0.896275i	$0.353737\pi$
$678$	−9.53433	−0.366164
$679$	−21.8001	−0.836611
$680$	−12.3855	−0.474962
$681$	8.69707	0.333272
$682$	−20.1394	−0.771177
$683$	−36.6180	−1.40115	−0.700575	−	0.713579i	$-0.747073\pi$
$683$	−36.6180	−1.40115	−0.700575	+	0.713579i	$0.747073\pi$
$684$	1.96764	0.0752346
$685$	−20.7393	−0.792409
$686$	−18.8635	−0.720211
$687$	9.93625	0.379092
$688$	14.2431	0.543012
$689$	−44.1102	−1.68046
$690$	6.19237	0.235739
$691$	−17.3515	−0.660084	−0.330042	−	0.943966i	$-0.607063\pi$
$691$	−17.3515	−0.660084	−0.330042	+	0.943966i	$0.607063\pi$
$692$	14.9003	0.566424
$693$	−5.65447	−0.214795
$694$	−6.12505	−0.232504
$695$	−11.5560	−0.438345
$696$	−26.0978	−0.989234
$697$	−13.4915	−0.511029
$698$	17.4233	0.659481
$699$	−20.5188	−0.776091
$700$	−2.44328	−0.0923473
$701$	34.9233	1.31904	0.659518	−	0.751689i	$-0.270760\pi$
$701$	34.9233	1.31904	0.659518	+	0.751689i	$0.270760\pi$
$702$	3.79881	0.143377
$703$	22.4571	0.846985
$704$	−15.8894	−0.598855
$705$	0.367729	0.0138495
$706$	−4.89305	−0.184152
$707$	−5.72950	−0.215480
$708$	3.14345	0.118138
$709$	24.3728	0.915340	0.457670	−	0.889122i	$-0.348684\pi$
$709$	24.3728	0.915340	0.457670	+	0.889122i	$0.348684\pi$
$710$	12.3544	0.463651
$711$	−3.59780	−0.134928
$712$	11.2239	0.420633
$713$	54.4405	2.03881
$714$	11.6083	0.434428
$715$	−7.53445	−0.281772
$716$	−12.5622	−0.469473
$717$	16.9916	0.634563
$718$	5.37373	0.200546
$719$	−7.54297	−0.281305	−0.140653	−	0.990059i	$-0.544920\pi$
$719$	−7.54297	−0.281305	−0.140653	+	0.990059i	$0.544920\pi$
$720$	1.39313	0.0519189
$721$	−44.9199	−1.67291
$722$	−14.9107	−0.554919
$723$	0.224586	0.00835243
$724$	−13.3463	−0.496013
$725$	−8.57966	−0.318641
$726$	6.99777	0.259712
$727$	47.2152	1.75111	0.875557	−	0.483114i	$-0.160494\pi$
$727$	47.2152	1.75111	0.875557	+	0.483114i	$0.160494\pi$
$728$	29.9261	1.10914
$729$	1.00000	0.0370370
$730$	−1.33779	−0.0495138
$731$	41.6286	1.53969
$732$	6.89080	0.254691
$733$	−10.8819	−0.401932	−0.200966	−	0.979598i	$-0.564408\pi$
$733$	−10.8819	−0.401932	−0.200966	+	0.979598i	$0.564408\pi$
$734$	19.0706	0.703908
$735$	0.383408	0.0141422
$736$	27.2788	1.00551
$737$	−31.3633	−1.15528
$738$	3.47649	0.127971
$739$	16.3684	0.602121	0.301061	−	0.953605i	$-0.402659\pi$
$739$	16.3684	0.602121	0.301061	+	0.953605i	$0.402659\pi$
$740$	−9.22778	−0.339220
$741$	−7.92299	−0.291058
$742$	34.7326	1.27507
$743$	−34.5191	−1.26638	−0.633192	−	0.773995i	$-0.718255\pi$
$743$	−34.5191	−1.26638	−0.633192	+	0.773995i	$0.718255\pi$
$744$	28.0581	1.02866
$745$	−4.88230	−0.178874
$746$	−2.03524	−0.0745155
$747$	6.11402	0.223700
$748$	−7.61882	−0.278572
$749$	36.8318	1.34580
$750$	1.04920	0.0383114
$751$	10.1436	0.370143	0.185072	−	0.982725i	$-0.440748\pi$
$751$	10.1436	0.370143	0.185072	+	0.982725i	$0.440748\pi$
$752$	−0.512295	−0.0186815
$753$	−27.8092	−1.01342
$754$	32.5925	1.18695
$755$	−20.5577	−0.748172
$756$	2.44328	0.0888613
$757$	−26.8370	−0.975406	−0.487703	−	0.873010i	$-0.662165\pi$
$757$	−26.8370	−0.975406	−0.487703	+	0.873010i	$0.662165\pi$
$758$	−20.4907	−0.744256
$759$	12.2818	0.445800
$760$	−6.65632	−0.241450
$761$	−9.67005	−0.350539	−0.175269	−	0.984520i	$-0.556080\pi$
$761$	−9.67005	−0.350539	−0.175269	+	0.984520i	$0.556080\pi$
$762$	−8.90709	−0.322670
$763$	−46.0814	−1.66826
$764$	−22.6741	−0.820321
$765$	4.07174	0.147214
$766$	7.39550	0.267210
$767$	−12.6575	−0.457037
$768$	16.5645	0.597721
$769$	−9.48252	−0.341948	−0.170974	−	0.985276i	$-0.554691\pi$
$769$	−9.48252	−0.341948	−0.170974	+	0.985276i	$0.554691\pi$
$770$	5.93267	0.213799
$771$	−3.33444	−0.120087
$772$	−5.33892	−0.192152
$773$	21.1025	0.759005	0.379502	−	0.925191i	$-0.376095\pi$
$773$	21.1025	0.759005	0.379502	+	0.925191i	$0.376095\pi$
$774$	−10.7268	−0.385568
$775$	9.22410	0.331340
$776$	24.4041	0.876058
$777$	27.8857	1.00039
$778$	−12.9749	−0.465173
$779$	−7.25074	−0.259785
$780$	3.25562	0.116570
$781$	24.5033	0.876798
$782$	−25.2137	−0.901639
$783$	8.57966	0.306612
$784$	−0.534137	−0.0190763
$785$	17.6938	0.631518
$786$	−12.2348	−0.436399
$787$	−53.5688	−1.90952	−0.954760	−	0.297376i	$-0.903889\pi$
$787$	−53.5688	−1.90952	−0.954760	+	0.297376i	$0.903889\pi$
$788$	11.2918	0.402254
$789$	−21.2976	−0.758215
$790$	3.77481	0.134302
$791$	24.6922	0.877954
$792$	6.32990	0.224923
$793$	−27.7468	−0.985319
$794$	−9.87929	−0.350603
$795$	12.1829	0.432083
$796$	−7.61287	−0.269831
$797$	−26.6847	−0.945221	−0.472610	−	0.881272i	$-0.656688\pi$
$797$	−26.6847	−0.945221	−0.472610	+	0.881272i	$0.656688\pi$
$798$	6.23861	0.220844
$799$	−1.49730	−0.0529706
$800$	4.62197	0.163411
$801$	−3.68986	−0.130375
$802$	1.04920	0.0370486
$803$	−2.65333	−0.0936341
$804$	13.5520	0.477942
$805$	−16.0371	−0.565234
$806$	−35.0406	−1.23425
$807$	−10.4299	−0.367149
$808$	6.41389	0.225640
$809$	−41.4774	−1.45827	−0.729134	−	0.684371i	$-0.760077\pi$
$809$	−41.4774	−1.45827	−0.729134	+	0.684371i	$0.760077\pi$
$810$	−1.04920	−0.0368652
$811$	−18.0077	−0.632335	−0.316168	−	0.948703i	$-0.602396\pi$
$811$	−18.0077	−0.632335	−0.316168	+	0.948703i	$0.602396\pi$
$812$	20.9625	0.735640
$813$	10.6250	0.372636
$814$	22.4065	0.785348
$815$	0.00395981	0.000138706 0
$816$	−5.67245	−0.198576
$817$	22.3724	0.782712
$818$	−8.77216	−0.306711
$819$	−9.83822	−0.343775
$820$	2.97939	0.104045
$821$	−9.99523	−0.348836	−0.174418	−	0.984672i	$-0.555804\pi$
$821$	−9.99523	−0.348836	−0.174418	+	0.984672i	$0.555804\pi$
$822$	−21.7597	−0.758958
$823$	13.6278	0.475036	0.237518	−	0.971383i	$-0.423666\pi$
$823$	13.6278	0.475036	0.237518	+	0.971383i	$0.423666\pi$
$824$	50.2857	1.75178
$825$	2.08096	0.0724496
$826$	9.96663	0.346783
$827$	4.43189	0.154112	0.0770559	−	0.997027i	$-0.475448\pi$
$827$	4.43189	0.154112	0.0770559	+	0.997027i	$0.475448\pi$
$828$	−5.30692	−0.184428
$829$	−21.3473	−0.741421	−0.370710	−	0.928749i	$-0.620886\pi$
$829$	−21.3473	−0.741421	−0.370710	+	0.928749i	$0.620886\pi$
$830$	−6.41484	−0.222662
$831$	−26.0111	−0.902315
$832$	−27.6461	−0.958455
$833$	−1.56114	−0.0540901
$834$	−12.1246	−0.419840
$835$	−21.4244	−0.741421
$836$	−4.09457	−0.141614
$837$	−9.22410	−0.318832
$838$	7.81113	0.269831
$839$	−25.4315	−0.877992	−0.438996	−	0.898489i	$-0.644666\pi$
$839$	−25.4315	−0.877992	−0.438996	+	0.898489i	$0.644666\pi$
$840$	−8.26536	−0.285182
$841$	44.6106	1.53830
$842$	−19.9355	−0.687021
$843$	15.3016	0.527014
$844$	−22.4480	−0.772692
$845$	−0.109213	−0.00375702
$846$	0.385822	0.0132648
$847$	−18.1230	−0.622713
$848$	−16.9723	−0.582833
$849$	−16.5355	−0.567498
$850$	−4.27207	−0.146531
$851$	−60.5690	−2.07628
$852$	−10.5878	−0.362733
$853$	43.9482	1.50476	0.752378	−	0.658731i	$-0.228907\pi$
$853$	43.9482	1.50476	0.752378	+	0.658731i	$0.228907\pi$
$854$	21.8480	0.747624
$855$	2.18827	0.0748372
$856$	−41.2314	−1.40926
$857$	−13.2080	−0.451178	−0.225589	−	0.974223i	$-0.572431\pi$
$857$	−13.2080	−0.451178	−0.225589	+	0.974223i	$0.572431\pi$
$858$	−7.90515	−0.269878
$859$	−2.39116	−0.0815853	−0.0407927	−	0.999168i	$-0.512988\pi$
$859$	−2.39116	−0.0815853	−0.0407927	+	0.999168i	$0.512988\pi$
$860$	−9.19300	−0.313479
$861$	−9.00348	−0.306838
$862$	−0.487803	−0.0166146
$863$	19.3151	0.657493	0.328746	−	0.944418i	$-0.393374\pi$
$863$	19.3151	0.657493	0.328746	+	0.944418i	$0.393374\pi$
$864$	−4.62197	−0.157243
$865$	16.5710	0.563432
$866$	33.1426	1.12623
$867$	0.420965	0.0142967
$868$	−22.5371	−0.764958
$869$	7.48686	0.253974
$870$	−9.00180	−0.305189
$871$	−54.5690	−1.84900
$872$	51.5858	1.74692
$873$	−8.02288	−0.271533
$874$	−13.5506	−0.458354
$875$	−2.71724	−0.0918596
$876$	1.14650	0.0387366
$877$	2.13402	0.0720607	0.0360304	−	0.999351i	$-0.488529\pi$
$877$	2.13402	0.0720607	0.0360304	+	0.999351i	$0.488529\pi$
$878$	22.6745	0.765228
$879$	−6.79657	−0.229243
$880$	−2.89904	−0.0977267
$881$	1.15688	0.0389763	0.0194881	−	0.999810i	$-0.493796\pi$
$881$	1.15688	0.0389763	0.0194881	+	0.999810i	$0.493796\pi$
$882$	0.402272	0.0135452
$883$	−41.3318	−1.39093	−0.695464	−	0.718561i	$-0.744801\pi$
$883$	−41.3318	−1.39093	−0.695464	+	0.718561i	$0.744801\pi$
$884$	−13.2560	−0.445848
$885$	3.49592	0.117514
$886$	−21.3316	−0.716650
$887$	41.9286	1.40782	0.703912	−	0.710288i	$-0.251435\pi$
$887$	41.9286	1.40782	0.703912	+	0.710288i	$0.251435\pi$
$888$	−31.2166	−1.04756
$889$	23.0678	0.773668
$890$	3.87140	0.129770
$891$	−2.08096	−0.0697147
$892$	18.0442	0.604166
$893$	−0.804691	−0.0269279
$894$	−5.12251	−0.171322
$895$	−13.9708	−0.466993
$896$	−3.34932	−0.111893
$897$	21.3691	0.713493
$898$	−12.2615	−0.409172
$899$	−79.1397	−2.63946
$900$	−0.899176	−0.0299725
$901$	−49.6055	−1.65260
$902$	−7.23443	−0.240880
$903$	27.7805	0.924479
$904$	−27.6417	−0.919350
$905$	−14.8429	−0.493393
$906$	−21.5692	−0.716588
$907$	−17.5579	−0.583001	−0.291501	−	0.956571i	$-0.594155\pi$
$907$	−17.5579	−0.583001	−0.291501	+	0.956571i	$0.594155\pi$
$908$	7.82020	0.259522
$909$	−2.10857	−0.0699369
$910$	10.3223	0.342180
$911$	−25.4004	−0.841553	−0.420777	−	0.907164i	$-0.638242\pi$
$911$	−25.4004	−0.841553	−0.420777	+	0.907164i	$0.638242\pi$
$912$	−3.04854	−0.100947
$913$	−12.7230	−0.421070
$914$	−23.1688	−0.766355
$915$	7.66346	0.253346
$916$	8.93444	0.295202
$917$	31.6858	1.04636
$918$	4.27207	0.140999
$919$	37.9186	1.25082	0.625410	−	0.780297i	$-0.284932\pi$
$919$	37.9186	1.25082	0.625410	+	0.780297i	$0.284932\pi$
$920$	17.9528	0.591885
$921$	−5.15383	−0.169825
$922$	−27.0039	−0.889325
$923$	42.6334	1.40330
$924$	−5.08436	−0.167263
$925$	−10.2625	−0.337428
$926$	42.5856	1.39945
$927$	−16.5314	−0.542964
$928$	−39.6549	−1.30174
$929$	10.4480	0.342787	0.171393	−	0.985203i	$-0.445173\pi$
$929$	10.4480	0.342787	0.171393	+	0.985203i	$0.445173\pi$
$930$	9.67794	0.317352
$931$	−0.838999	−0.0274971
$932$	−18.4500	−0.604350
$933$	−24.0369	−0.786932
$934$	9.33123	0.305327
$935$	−8.47311	−0.277100
$936$	11.0134	0.359985
$937$	−11.0504	−0.361002	−0.180501	−	0.983575i	$-0.557772\pi$
$937$	−11.0504	−0.361002	−0.180501	+	0.983575i	$0.557772\pi$
$938$	42.9680	1.40296
$939$	8.61277	0.281067
$940$	0.330654	0.0107847
$941$	11.4672	0.373819	0.186909	−	0.982377i	$-0.440153\pi$
$941$	11.4672	0.373819	0.186909	+	0.982377i	$0.440153\pi$
$942$	18.5643	0.604859
$943$	19.5560	0.636831
$944$	−4.87026	−0.158514
$945$	2.71724	0.0883919
$946$	22.3221	0.725753
$947$	3.57823	0.116277	0.0581384	−	0.998309i	$-0.481484\pi$
$947$	3.57823	0.116277	0.0581384	+	0.998309i	$0.481484\pi$
$948$	−3.23505	−0.105070
$949$	−4.61654	−0.149859
$950$	−2.29593	−0.0744899
$951$	−8.42446	−0.273182
$952$	33.6544	1.09074
$953$	15.2775	0.494886	0.247443	−	0.968902i	$-0.420410\pi$
$953$	15.2775	0.494886	0.247443	+	0.968902i	$0.420410\pi$
$954$	12.7823	0.413842
$955$	−25.2165	−0.815988
$956$	15.2784	0.494140
$957$	−17.8539	−0.577135
$958$	−14.1378	−0.456773
$959$	56.3538	1.81976
$960$	7.63563	0.246439
$961$	54.0841	1.74465
$962$	38.9852	1.25693
$963$	13.5548	0.436799
$964$	0.201942	0.00650411
$965$	−5.93756	−0.191137
$966$	−16.8262	−0.541373
$967$	31.7006	1.01942	0.509712	−	0.860345i	$-0.329752\pi$
$967$	31.7006	1.01942	0.509712	+	0.860345i	$0.329752\pi$
$968$	20.2878	0.652074
$969$	−8.91005	−0.286232
$970$	8.41761	0.270273
$971$	−32.7730	−1.05174	−0.525868	−	0.850566i	$-0.676259\pi$
$971$	−32.7730	−1.05174	−0.525868	+	0.850566i	$0.676259\pi$
$972$	0.899176	0.0288411
$973$	31.4005	1.00665
$974$	−22.1549	−0.709890
$975$	3.62066	0.115954
$976$	−10.6762	−0.341737
$977$	26.8636	0.859443	0.429722	−	0.902961i	$-0.358612\pi$
$977$	26.8636	0.859443	0.429722	+	0.902961i	$0.358612\pi$
$978$	0.00415464	0.000132851 0
$979$	7.67843	0.245404
$980$	0.344751	0.0110127
$981$	−16.9589	−0.541455
$982$	−33.7225	−1.07613
$983$	51.0855	1.62937	0.814687	−	0.579901i	$-0.196909\pi$
$983$	51.0855	1.62937	0.814687	+	0.579901i	$0.196909\pi$
$984$	10.0790	0.321305
$985$	12.5579	0.400129
$986$	36.6529	1.16727
$987$	−0.999210	−0.0318052
$988$	−7.12416	−0.226650
$989$	−60.3407	−1.91872
$990$	2.18334	0.0693912
$991$	−58.6315	−1.86249	−0.931246	−	0.364392i	$-0.881277\pi$
$991$	−58.6315	−1.86249	−0.931246	+	0.364392i	$0.881277\pi$
$992$	42.6335	1.35362
$993$	−10.4541	−0.331751
$994$	−33.5698	−1.06477
$995$	−8.46650	−0.268406
$996$	5.49758	0.174198
$997$	−13.4697	−0.426591	−0.213296	−	0.976988i	$-0.568420\pi$
$997$	−13.4697	−0.426591	−0.213296	+	0.976988i	$0.568420\pi$
$998$	7.78371	0.246389
$999$	10.2625	0.324691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.20	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.20	✓	31	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.04920 q^{2} -1.00000 q^{3} -0.899176 q^{4} -1.00000 q^{5} -1.04920 q^{6} +2.71724 q^{7} -3.04182 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.04920 q^{2} -1.00000 q^{3} -0.899176 q^{4} -1.00000 q^{5} -1.04920 q^{6} +2.71724 q^{7} -3.04182 q^{8} +1.00000 q^{9} -1.04920 q^{10} -2.08096 q^{11} +0.899176 q^{12} -3.62066 q^{13} +2.85093 q^{14} +1.00000 q^{15} -1.39313 q^{16} -4.07174 q^{17} +1.04920 q^{18} -2.18827 q^{19} +0.899176 q^{20} -2.71724 q^{21} -2.18334 q^{22} +5.90198 q^{23} +3.04182 q^{24} +1.00000 q^{25} -3.79881 q^{26} -1.00000 q^{27} -2.44328 q^{28} -8.57966 q^{29} +1.04920 q^{30} +9.22410 q^{31} +4.62197 q^{32} +2.08096 q^{33} -4.27207 q^{34} -2.71724 q^{35} -0.899176 q^{36} -10.2625 q^{37} -2.29593 q^{38} +3.62066 q^{39} +3.04182 q^{40} +3.31346 q^{41} -2.85093 q^{42} -10.2238 q^{43} +1.87115 q^{44} -1.00000 q^{45} +6.19237 q^{46} +0.367729 q^{47} +1.39313 q^{48} +0.383408 q^{49} +1.04920 q^{50} +4.07174 q^{51} +3.25562 q^{52} +12.1829 q^{53} -1.04920 q^{54} +2.08096 q^{55} -8.26536 q^{56} +2.18827 q^{57} -9.00180 q^{58} +3.49592 q^{59} -0.899176 q^{60} +7.66346 q^{61} +9.67794 q^{62} +2.71724 q^{63} +7.63563 q^{64} +3.62066 q^{65} +2.18334 q^{66} +15.0716 q^{67} +3.66121 q^{68} -5.90198 q^{69} -2.85093 q^{70} -11.7750 q^{71} -3.04182 q^{72} +1.27505 q^{73} -10.7674 q^{74} -1.00000 q^{75} +1.96764 q^{76} -5.65447 q^{77} +3.79881 q^{78} -3.59780 q^{79} +1.39313 q^{80} +1.00000 q^{81} +3.47649 q^{82} +6.11402 q^{83} +2.44328 q^{84} +4.07174 q^{85} -10.7268 q^{86} +8.57966 q^{87} +6.32990 q^{88} -3.68986 q^{89} -1.04920 q^{90} -9.83822 q^{91} -5.30692 q^{92} -9.22410 q^{93} +0.385822 q^{94} +2.18827 q^{95} -4.62197 q^{96} -8.02288 q^{97} +0.402272 q^{98} -2.08096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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