LMFDB - Embedded newform 6002.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.03423 q^{3} +1.00000 q^{4} -3.81435 q^{5} -2.03423 q^{6} -2.54300 q^{7} +1.00000 q^{8} +1.13810 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.03423 q^{3} +1.00000 q^{4} -3.81435 q^{5} -2.03423 q^{6} -2.54300 q^{7} +1.00000 q^{8} +1.13810 q^{9} -3.81435 q^{10} -0.317399 q^{11} -2.03423 q^{12} -0.346540 q^{13} -2.54300 q^{14} +7.75927 q^{15} +1.00000 q^{16} +4.84440 q^{17} +1.13810 q^{18} -2.98980 q^{19} -3.81435 q^{20} +5.17304 q^{21} -0.317399 q^{22} +3.42117 q^{23} -2.03423 q^{24} +9.54925 q^{25} -0.346540 q^{26} +3.78754 q^{27} -2.54300 q^{28} -9.15213 q^{29} +7.75927 q^{30} +1.66034 q^{31} +1.00000 q^{32} +0.645663 q^{33} +4.84440 q^{34} +9.69987 q^{35} +1.13810 q^{36} +2.87444 q^{37} -2.98980 q^{38} +0.704944 q^{39} -3.81435 q^{40} +8.19668 q^{41} +5.17304 q^{42} +4.34464 q^{43} -0.317399 q^{44} -4.34110 q^{45} +3.42117 q^{46} +9.29070 q^{47} -2.03423 q^{48} -0.533171 q^{49} +9.54925 q^{50} -9.85463 q^{51} -0.346540 q^{52} -1.38016 q^{53} +3.78754 q^{54} +1.21067 q^{55} -2.54300 q^{56} +6.08194 q^{57} -9.15213 q^{58} -2.71772 q^{59} +7.75927 q^{60} +11.4121 q^{61} +1.66034 q^{62} -2.89418 q^{63} +1.00000 q^{64} +1.32183 q^{65} +0.645663 q^{66} -10.6955 q^{67} +4.84440 q^{68} -6.95945 q^{69} +9.69987 q^{70} -0.686555 q^{71} +1.13810 q^{72} -6.25003 q^{73} +2.87444 q^{74} -19.4254 q^{75} -2.98980 q^{76} +0.807144 q^{77} +0.704944 q^{78} -0.621057 q^{79} -3.81435 q^{80} -11.1190 q^{81} +8.19668 q^{82} -7.24657 q^{83} +5.17304 q^{84} -18.4782 q^{85} +4.34464 q^{86} +18.6175 q^{87} -0.317399 q^{88} -14.6999 q^{89} -4.34110 q^{90} +0.881251 q^{91} +3.42117 q^{92} -3.37751 q^{93} +9.29070 q^{94} +11.4041 q^{95} -2.03423 q^{96} +12.8744 q^{97} -0.533171 q^{98} -0.361231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.03423	−1.17446	−0.587232	−	0.809419i	$-0.699782\pi$
$3$	−2.03423	−1.17446	−0.587232	+	0.809419i	$0.699782\pi$
$4$	1.00000	0.500000
$5$	−3.81435	−1.70583	−0.852914	−	0.522051i	$-0.825167\pi$
$5$	−3.81435	−1.70583	−0.852914	+	0.522051i	$0.825167\pi$
$6$	−2.03423	−0.830472
$7$	−2.54300	−0.961162	−0.480581	−	0.876950i	$-0.659574\pi$
$7$	−2.54300	−0.961162	−0.480581	+	0.876950i	$0.659574\pi$
$8$	1.00000	0.353553
$9$	1.13810	0.379366
$10$	−3.81435	−1.20620
$11$	−0.317399	−0.0956993	−0.0478497	−	0.998855i	$-0.515237\pi$
$11$	−0.317399	−0.0956993	−0.0478497	+	0.998855i	$0.515237\pi$
$12$	−2.03423	−0.587232
$13$	−0.346540	−0.0961130	−0.0480565	−	0.998845i	$-0.515303\pi$
$13$	−0.346540	−0.0961130	−0.0480565	+	0.998845i	$0.515303\pi$
$14$	−2.54300	−0.679644
$15$	7.75927	2.00343
$16$	1.00000	0.250000
$17$	4.84440	1.17494	0.587470	−	0.809246i	$-0.300124\pi$
$17$	4.84440	1.17494	0.587470	+	0.809246i	$0.300124\pi$
$18$	1.13810	0.268252
$19$	−2.98980	−0.685906	−0.342953	−	0.939353i	$-0.611427\pi$
$19$	−2.98980	−0.685906	−0.342953	+	0.939353i	$0.611427\pi$
$20$	−3.81435	−0.852914
$21$	5.17304	1.12885
$22$	−0.317399	−0.0676697
$23$	3.42117	0.713363	0.356682	−	0.934226i	$-0.383908\pi$
$23$	3.42117	0.713363	0.356682	+	0.934226i	$0.383908\pi$
$24$	−2.03423	−0.415236
$25$	9.54925	1.90985
$26$	−0.346540	−0.0679622
$27$	3.78754	0.728912
$28$	−2.54300	−0.480581
$29$	−9.15213	−1.69951	−0.849754	−	0.527180i	$-0.823249\pi$
$29$	−9.15213	−1.69951	−0.849754	+	0.527180i	$0.823249\pi$
$30$	7.75927	1.41664
$31$	1.66034	0.298206	0.149103	−	0.988822i	$-0.452361\pi$
$31$	1.66034	0.298206	0.149103	+	0.988822i	$0.452361\pi$
$32$	1.00000	0.176777
$33$	0.645663	0.112395
$34$	4.84440	0.830808
$35$	9.69987	1.63958
$36$	1.13810	0.189683
$37$	2.87444	0.472555	0.236278	−	0.971686i	$-0.424072\pi$
$37$	2.87444	0.472555	0.236278	+	0.971686i	$0.424072\pi$
$38$	−2.98980	−0.485009
$39$	0.704944	0.112881
$40$	−3.81435	−0.603101
$41$	8.19668	1.28011	0.640053	−	0.768331i	$-0.278912\pi$
$41$	8.19668	1.28011	0.640053	+	0.768331i	$0.278912\pi$
$42$	5.17304	0.798218
$43$	4.34464	0.662552	0.331276	−	0.943534i	$-0.392521\pi$
$43$	4.34464	0.662552	0.331276	+	0.943534i	$0.392521\pi$
$44$	−0.317399	−0.0478497
$45$	−4.34110	−0.647133
$46$	3.42117	0.504424
$47$	9.29070	1.35519	0.677594	−	0.735436i	$-0.263023\pi$
$47$	9.29070	1.35519	0.677594	+	0.735436i	$0.263023\pi$
$48$	−2.03423	−0.293616
$49$	−0.533171	−0.0761673
$50$	9.54925	1.35047
$51$	−9.85463	−1.37992
$52$	−0.346540	−0.0480565
$53$	−1.38016	−0.189580	−0.0947900	−	0.995497i	$-0.530218\pi$
$53$	−1.38016	−0.189580	−0.0947900	+	0.995497i	$0.530218\pi$
$54$	3.78754	0.515419
$55$	1.21067	0.163247
$56$	−2.54300	−0.339822
$57$	6.08194	0.805572
$58$	−9.15213	−1.20173
$59$	−2.71772	−0.353817	−0.176909	−	0.984227i	$-0.556610\pi$
$59$	−2.71772	−0.353817	−0.176909	+	0.984227i	$0.556610\pi$
$60$	7.75927	1.00172
$61$	11.4121	1.46117	0.730587	−	0.682820i	$-0.239247\pi$
$61$	11.4121	1.46117	0.730587	+	0.682820i	$0.239247\pi$
$62$	1.66034	0.210863
$63$	−2.89418	−0.364632
$64$	1.00000	0.125000
$65$	1.32183	0.163952
$66$	0.645663	0.0794756
$67$	−10.6955	−1.30667	−0.653333	−	0.757071i	$-0.726630\pi$
$67$	−10.6955	−1.30667	−0.653333	+	0.757071i	$0.726630\pi$
$68$	4.84440	0.587470
$69$	−6.95945	−0.837820
$70$	9.69987	1.15936
$71$	−0.686555	−0.0814791	−0.0407395	−	0.999170i	$-0.512971\pi$
$71$	−0.686555	−0.0814791	−0.0407395	+	0.999170i	$0.512971\pi$
$72$	1.13810	0.134126
$73$	−6.25003	−0.731511	−0.365755	−	0.930711i	$-0.619189\pi$
$73$	−6.25003	−0.731511	−0.365755	+	0.930711i	$0.619189\pi$
$74$	2.87444	0.334147
$75$	−19.4254	−2.24305
$76$	−2.98980	−0.342953
$77$	0.807144	0.0919826
$78$	0.704944	0.0798191
$79$	−0.621057	−0.0698743	−0.0349372	−	0.999390i	$-0.511123\pi$
$79$	−0.621057	−0.0698743	−0.0349372	+	0.999390i	$0.511123\pi$
$80$	−3.81435	−0.426457
$81$	−11.1190	−1.23545
$82$	8.19668	0.905172
$83$	−7.24657	−0.795415	−0.397707	−	0.917512i	$-0.630194\pi$
$83$	−7.24657	−0.795415	−0.397707	+	0.917512i	$0.630194\pi$
$84$	5.17304	0.564425
$85$	−18.4782	−2.00424
$86$	4.34464	0.468495
$87$	18.6175	1.99601
$88$	−0.317399	−0.0338348
$89$	−14.6999	−1.55818	−0.779092	−	0.626909i	$-0.784320\pi$
$89$	−14.6999	−1.55818	−0.779092	+	0.626909i	$0.784320\pi$
$90$	−4.34110	−0.457592
$91$	0.881251	0.0923802
$92$	3.42117	0.356682
$93$	−3.37751	−0.350232
$94$	9.29070	0.958262
$95$	11.4041	1.17004
$96$	−2.03423	−0.207618
$97$	12.8744	1.30720	0.653601	−	0.756839i	$-0.273257\pi$
$97$	12.8744	1.30720	0.653601	+	0.756839i	$0.273257\pi$
$98$	−0.533171	−0.0538584
$99$	−0.361231	−0.0363051
$100$	9.54925	0.954925
$101$	4.11092	0.409052	0.204526	−	0.978861i	$-0.434435\pi$
$101$	4.11092	0.409052	0.204526	+	0.978861i	$0.434435\pi$
$102$	−9.85463	−0.975754
$103$	1.61855	0.159480	0.0797401	−	0.996816i	$-0.474591\pi$
$103$	1.61855	0.159480	0.0797401	+	0.996816i	$0.474591\pi$
$104$	−0.346540	−0.0339811
$105$	−19.7318	−1.92562
$106$	−1.38016	−0.134053
$107$	−5.60729	−0.542078	−0.271039	−	0.962568i	$-0.587367\pi$
$107$	−5.60729	−0.542078	−0.271039	+	0.962568i	$0.587367\pi$
$108$	3.78754	0.364456
$109$	8.83708	0.846439	0.423219	−	0.906027i	$-0.360900\pi$
$109$	8.83708	0.846439	0.423219	+	0.906027i	$0.360900\pi$
$110$	1.21067	0.115433
$111$	−5.84728	−0.554999
$112$	−2.54300	−0.240291
$113$	−3.88509	−0.365479	−0.182739	−	0.983161i	$-0.558496\pi$
$113$	−3.88509	−0.365479	−0.182739	+	0.983161i	$0.558496\pi$
$114$	6.08194	0.569626
$115$	−13.0495	−1.21687
$116$	−9.15213	−0.849754
$117$	−0.394397	−0.0364620
$118$	−2.71772	−0.250187
$119$	−12.3193	−1.12931
$120$	7.75927	0.708321
$121$	−10.8993	−0.990842
$122$	11.4121	1.03321
$123$	−16.6739	−1.50344
$124$	1.66034	0.149103
$125$	−17.3524	−1.55205
$126$	−2.89418	−0.257834
$127$	9.74607	0.864824	0.432412	−	0.901676i	$-0.357663\pi$
$127$	9.74607	0.864824	0.432412	+	0.901676i	$0.357663\pi$
$128$	1.00000	0.0883883
$129$	−8.83801	−0.778143
$130$	1.32183	0.115932
$131$	13.7552	1.20180	0.600899	−	0.799325i	$-0.294809\pi$
$131$	13.7552	1.20180	0.600899	+	0.799325i	$0.294809\pi$
$132$	0.645663	0.0561977
$133$	7.60304	0.659267
$134$	−10.6955	−0.923952
$135$	−14.4470	−1.24340
$136$	4.84440	0.415404
$137$	18.8097	1.60702	0.803510	−	0.595291i	$-0.202963\pi$
$137$	18.8097	1.60702	0.803510	+	0.595291i	$0.202963\pi$
$138$	−6.95945	−0.592428
$139$	7.26629	0.616318	0.308159	−	0.951335i	$-0.400287\pi$
$139$	7.26629	0.616318	0.308159	+	0.951335i	$0.400287\pi$
$140$	9.69987	0.819789
$141$	−18.8994	−1.59162
$142$	−0.686555	−0.0576144
$143$	0.109992	0.00919795
$144$	1.13810	0.0948415
$145$	34.9094	2.89907
$146$	−6.25003	−0.517256
$147$	1.08459	0.0894558
$148$	2.87444	0.236278
$149$	−16.2613	−1.33217	−0.666087	−	0.745874i	$-0.732032\pi$
$149$	−16.2613	−1.33217	−0.666087	+	0.745874i	$0.732032\pi$
$150$	−19.4254	−1.58608
$151$	6.34160	0.516072	0.258036	−	0.966135i	$-0.416925\pi$
$151$	6.34160	0.516072	0.258036	+	0.966135i	$0.416925\pi$
$152$	−2.98980	−0.242504
$153$	5.51340	0.445732
$154$	0.807144	0.0650415
$155$	−6.33311	−0.508688
$156$	0.704944	0.0564407
$157$	−20.1505	−1.60819	−0.804093	−	0.594503i	$-0.797349\pi$
$157$	−20.1505	−1.60819	−0.804093	+	0.594503i	$0.797349\pi$
$158$	−0.621057	−0.0494086
$159$	2.80757	0.222655
$160$	−3.81435	−0.301551
$161$	−8.70002	−0.685658
$162$	−11.1190	−0.873593
$163$	−0.319380	−0.0250158	−0.0125079	−	0.999922i	$-0.503981\pi$
$163$	−0.319380	−0.0250158	−0.0125079	+	0.999922i	$0.503981\pi$
$164$	8.19668	0.640053
$165$	−2.46278	−0.191727
$166$	−7.24657	−0.562443
$167$	5.94072	0.459707	0.229853	−	0.973225i	$-0.426175\pi$
$167$	5.94072	0.459707	0.229853	+	0.973225i	$0.426175\pi$
$168$	5.17304	0.399109
$169$	−12.8799	−0.990762
$170$	−18.4782	−1.41721
$171$	−3.40268	−0.260210
$172$	4.34464	0.331276
$173$	−8.21904	−0.624882	−0.312441	−	0.949937i	$-0.601147\pi$
$173$	−8.21904	−0.624882	−0.312441	+	0.949937i	$0.601147\pi$
$174$	18.6175	1.41139
$175$	−24.2837	−1.83567
$176$	−0.317399	−0.0239248
$177$	5.52847	0.415546
$178$	−14.6999	−1.10180
$179$	2.66620	0.199281	0.0996407	−	0.995023i	$-0.468231\pi$
$179$	2.66620	0.199281	0.0996407	+	0.995023i	$0.468231\pi$
$180$	−4.34110	−0.323567
$181$	−10.3938	−0.772562	−0.386281	−	0.922381i	$-0.626240\pi$
$181$	−10.3938	−0.772562	−0.386281	+	0.922381i	$0.626240\pi$
$182$	0.881251	0.0653227
$183$	−23.2149	−1.71610
$184$	3.42117	0.252212
$185$	−10.9641	−0.806098
$186$	−3.37751	−0.247651
$187$	−1.53761	−0.112441
$188$	9.29070	0.677594
$189$	−9.63170	−0.700603
$190$	11.4041	0.827342
$191$	−9.55402	−0.691305	−0.345652	−	0.938363i	$-0.612342\pi$
$191$	−9.55402	−0.691305	−0.345652	+	0.938363i	$0.612342\pi$
$192$	−2.03423	−0.146808
$193$	−20.1462	−1.45015	−0.725077	−	0.688667i	$-0.758196\pi$
$193$	−20.1462	−1.45015	−0.725077	+	0.688667i	$0.758196\pi$
$194$	12.8744	0.924331
$195$	−2.68890	−0.192556
$196$	−0.533171	−0.0380837
$197$	6.71408	0.478358	0.239179	−	0.970975i	$-0.423122\pi$
$197$	6.71408	0.478358	0.239179	+	0.970975i	$0.423122\pi$
$198$	−0.361231	−0.0256716
$199$	−5.72309	−0.405699	−0.202849	−	0.979210i	$-0.565020\pi$
$199$	−5.72309	−0.405699	−0.202849	+	0.979210i	$0.565020\pi$
$200$	9.54925	0.675234
$201$	21.7572	1.53463
$202$	4.11092	0.289243
$203$	23.2738	1.63350
$204$	−9.85463	−0.689962
$205$	−31.2650	−2.18364
$206$	1.61855	0.112770
$207$	3.89363	0.270626
$208$	−0.346540	−0.0240283
$209$	0.948958	0.0656408
$210$	−19.7318	−1.36162
$211$	−23.3615	−1.60827	−0.804136	−	0.594446i	$-0.797371\pi$
$211$	−23.3615	−1.60827	−0.804136	+	0.594446i	$0.797371\pi$
$212$	−1.38016	−0.0947900
$213$	1.39661	0.0956943
$214$	−5.60729	−0.383307
$215$	−16.5720	−1.13020
$216$	3.78754	0.257709
$217$	−4.22223	−0.286624
$218$	8.83708	0.598523
$219$	12.7140	0.859133
$220$	1.21067	0.0816233
$221$	−1.67878	−0.112927
$222$	−5.84728	−0.392444
$223$	−18.4097	−1.23281	−0.616403	−	0.787431i	$-0.711411\pi$
$223$	−18.4097	−1.23281	−0.616403	+	0.787431i	$0.711411\pi$
$224$	−2.54300	−0.169911
$225$	10.8680	0.724532
$226$	−3.88509	−0.258433
$227$	−16.8957	−1.12141	−0.560705	−	0.828016i	$-0.689470\pi$
$227$	−16.8957	−1.12141	−0.560705	+	0.828016i	$0.689470\pi$
$228$	6.08194	0.402786
$229$	17.8376	1.17874	0.589370	−	0.807864i	$-0.299376\pi$
$229$	17.8376	1.17874	0.589370	+	0.807864i	$0.299376\pi$
$230$	−13.0495	−0.860460
$231$	−1.64192	−0.108030
$232$	−9.15213	−0.600867
$233$	−6.36697	−0.417114	−0.208557	−	0.978010i	$-0.566877\pi$
$233$	−6.36697	−0.417114	−0.208557	+	0.978010i	$0.566877\pi$
$234$	−0.394397	−0.0257826
$235$	−35.4379	−2.31172
$236$	−2.71772	−0.176909
$237$	1.26337	0.0820649
$238$	−12.3193	−0.798541
$239$	0.100899	0.00652664	0.00326332	−	0.999995i	$-0.498961\pi$
$239$	0.100899	0.00652664	0.00326332	+	0.999995i	$0.498961\pi$
$240$	7.75927	0.500858
$241$	14.8424	0.956082	0.478041	−	0.878338i	$-0.341347\pi$
$241$	14.8424	0.956082	0.478041	+	0.878338i	$0.341347\pi$
$242$	−10.8993	−0.700631
$243$	11.2561	0.722077
$244$	11.4121	0.730587
$245$	2.03370	0.129928
$246$	−16.6739	−1.06309
$247$	1.03609	0.0659245
$248$	1.66034	0.105432
$249$	14.7412	0.934186
$250$	−17.3524	−1.09746
$251$	−7.59554	−0.479426	−0.239713	−	0.970844i	$-0.577053\pi$
$251$	−7.59554	−0.479426	−0.239713	+	0.970844i	$0.577053\pi$
$252$	−2.89418	−0.182316
$253$	−1.08588	−0.0682684
$254$	9.74607	0.611523
$255$	37.5890	2.35391
$256$	1.00000	0.0625000
$257$	8.37700	0.522543	0.261272	−	0.965265i	$-0.415858\pi$
$257$	8.37700	0.522543	0.261272	+	0.965265i	$0.415858\pi$
$258$	−8.83801	−0.550230
$259$	−7.30970	−0.454202
$260$	1.32183	0.0819762
$261$	−10.4160	−0.644736
$262$	13.7552	0.849800
$263$	9.50328	0.585997	0.292999	−	0.956113i	$-0.405347\pi$
$263$	9.50328	0.585997	0.292999	+	0.956113i	$0.405347\pi$
$264$	0.645663	0.0397378
$265$	5.26442	0.323391
$266$	7.60304	0.466172
$267$	29.9030	1.83003
$268$	−10.6955	−0.653333
$269$	−7.11694	−0.433927	−0.216964	−	0.976180i	$-0.569615\pi$
$269$	−7.11694	−0.433927	−0.216964	+	0.976180i	$0.569615\pi$
$270$	−14.4470	−0.879216
$271$	−3.71253	−0.225520	−0.112760	−	0.993622i	$-0.535969\pi$
$271$	−3.71253	−0.225520	−0.112760	+	0.993622i	$0.535969\pi$
$272$	4.84440	0.293735
$273$	−1.79267	−0.108497
$274$	18.8097	1.13634
$275$	−3.03092	−0.182771
$276$	−6.95945	−0.418910
$277$	−8.22774	−0.494357	−0.247178	−	0.968970i	$-0.579503\pi$
$277$	−8.22774	−0.494357	−0.247178	+	0.968970i	$0.579503\pi$
$278$	7.26629	0.435803
$279$	1.88963	0.113129
$280$	9.69987	0.579678
$281$	10.0346	0.598613	0.299306	−	0.954157i	$-0.403245\pi$
$281$	10.0346	0.598613	0.299306	+	0.954157i	$0.403245\pi$
$282$	−18.8994	−1.12544
$283$	9.07656	0.539546	0.269773	−	0.962924i	$-0.413051\pi$
$283$	9.07656	0.539546	0.269773	+	0.962924i	$0.413051\pi$
$284$	−0.686555	−0.0407395
$285$	−23.1986	−1.37417
$286$	0.109992	0.00650394
$287$	−20.8441	−1.23039
$288$	1.13810	0.0670631
$289$	6.46820	0.380483
$290$	34.9094	2.04995
$291$	−26.1896	−1.53526
$292$	−6.25003	−0.365755
$293$	−15.1195	−0.883292	−0.441646	−	0.897190i	$-0.645605\pi$
$293$	−15.1195	−0.883292	−0.441646	+	0.897190i	$0.645605\pi$
$294$	1.08459	0.0632548
$295$	10.3663	0.603551
$296$	2.87444	0.167074
$297$	−1.20216	−0.0697564
$298$	−16.2613	−0.941990
$299$	−1.18557	−0.0685635
$300$	−19.4254	−1.12152
$301$	−11.0484	−0.636820
$302$	6.34160	0.364918
$303$	−8.36256	−0.480417
$304$	−2.98980	−0.171477
$305$	−43.5298	−2.49251
$306$	5.51340	0.315180
$307$	−23.6049	−1.34720	−0.673601	−	0.739095i	$-0.735253\pi$
$307$	−23.6049	−1.34720	−0.673601	+	0.739095i	$0.735253\pi$
$308$	0.807144	0.0459913
$309$	−3.29250	−0.187304
$310$	−6.33311	−0.359696
$311$	28.4888	1.61545	0.807726	−	0.589557i	$-0.200698\pi$
$311$	28.4888	1.61545	0.807726	+	0.589557i	$0.200698\pi$
$312$	0.704944	0.0399096
$313$	−9.66921	−0.546536	−0.273268	−	0.961938i	$-0.588105\pi$
$313$	−9.66921	−0.546536	−0.273268	+	0.961938i	$0.588105\pi$
$314$	−20.1505	−1.13716
$315$	11.0394	0.622000
$316$	−0.621057	−0.0349372
$317$	−19.6352	−1.10282	−0.551412	−	0.834233i	$-0.685911\pi$
$317$	−19.6352	−1.10282	−0.551412	+	0.834233i	$0.685911\pi$
$318$	2.80757	0.157441
$319$	2.90487	0.162642
$320$	−3.81435	−0.213229
$321$	11.4065	0.636651
$322$	−8.70002	−0.484833
$323$	−14.4838	−0.805898
$324$	−11.1190	−0.617724
$325$	−3.30920	−0.183561
$326$	−0.319380	−0.0176888
$327$	−17.9767	−0.994112
$328$	8.19668	0.452586
$329$	−23.6262	−1.30255
$330$	−2.46278	−0.135572
$331$	23.8723	1.31214	0.656071	−	0.754699i	$-0.272217\pi$
$331$	23.8723	1.31214	0.656071	+	0.754699i	$0.272217\pi$
$332$	−7.24657	−0.397707
$333$	3.27140	0.179272
$334$	5.94072	0.325062
$335$	40.7964	2.22895
$336$	5.17304	0.282213
$337$	5.59037	0.304527	0.152263	−	0.988340i	$-0.451344\pi$
$337$	5.59037	0.304527	0.152263	+	0.988340i	$0.451344\pi$
$338$	−12.8799	−0.700575
$339$	7.90318	0.429242
$340$	−18.4782	−1.00212
$341$	−0.526990	−0.0285381
$342$	−3.40268	−0.183996
$343$	19.1568	1.03437
$344$	4.34464	0.234247
$345$	26.5458	1.42918
$346$	−8.21904	−0.441858
$347$	5.54386	0.297610	0.148805	−	0.988867i	$-0.452457\pi$
$347$	5.54386	0.297610	0.148805	+	0.988867i	$0.452457\pi$
$348$	18.6175	0.998005
$349$	5.61241	0.300425	0.150213	−	0.988654i	$-0.452004\pi$
$349$	5.61241	0.300425	0.150213	+	0.988654i	$0.452004\pi$
$350$	−24.2837	−1.29802
$351$	−1.31254	−0.0700580
$352$	−0.317399	−0.0169174
$353$	−0.0133269	−0.000709319 0	−0.000354659	−	1.00000i	$-0.500113\pi$
$353$	−0.0133269	−0.000709319 0	−0.000354659		1.00000i	$0.500113\pi$
$354$	5.52847	0.293835
$355$	2.61876	0.138989
$356$	−14.6999	−0.779092
$357$	25.0603	1.32633
$358$	2.66620	0.140913
$359$	33.1929	1.75185	0.875927	−	0.482443i	$-0.160250\pi$
$359$	33.1929	1.75185	0.875927	+	0.482443i	$0.160250\pi$
$360$	−4.34110	−0.228796
$361$	−10.0611	−0.529533
$362$	−10.3938	−0.546284
$363$	22.1716	1.16371
$364$	0.881251	0.0461901
$365$	23.8398	1.24783
$366$	−23.2149	−1.21346
$367$	24.9837	1.30414	0.652068	−	0.758160i	$-0.273901\pi$
$367$	24.9837	1.30414	0.652068	+	0.758160i	$0.273901\pi$
$368$	3.42117	0.178341
$369$	9.32863	0.485629
$370$	−10.9641	−0.569998
$371$	3.50975	0.182217
$372$	−3.37751	−0.175116
$373$	21.4045	1.10828	0.554142	−	0.832422i	$-0.313046\pi$
$373$	21.4045	1.10828	0.554142	+	0.832422i	$0.313046\pi$
$374$	−1.53761	−0.0795077
$375$	35.2988	1.82282
$376$	9.29070	0.479131
$377$	3.17158	0.163345
$378$	−9.63170	−0.495401
$379$	−8.48836	−0.436018	−0.218009	−	0.975947i	$-0.569956\pi$
$379$	−8.48836	−0.436018	−0.218009	+	0.975947i	$0.569956\pi$
$380$	11.4041	0.585019
$381$	−19.8258	−1.01570
$382$	−9.55402	−0.488826
$383$	22.9394	1.17215	0.586073	−	0.810258i	$-0.300673\pi$
$383$	22.9394	1.17215	0.586073	+	0.810258i	$0.300673\pi$
$384$	−2.03423	−0.103809
$385$	−3.07873	−0.156906
$386$	−20.1462	−1.02541
$387$	4.94463	0.251350
$388$	12.8744	0.653601
$389$	−30.0337	−1.52277	−0.761385	−	0.648300i	$-0.775480\pi$
$389$	−30.0337	−1.52277	−0.761385	+	0.648300i	$0.775480\pi$
$390$	−2.68890	−0.136158
$391$	16.5735	0.838158
$392$	−0.533171	−0.0269292
$393$	−27.9813	−1.41147
$394$	6.71408	0.338250
$395$	2.36893	0.119194
$396$	−0.361231	−0.0181525
$397$	13.5128	0.678190	0.339095	−	0.940752i	$-0.389879\pi$
$397$	13.5128	0.678190	0.339095	+	0.940752i	$0.389879\pi$
$398$	−5.72309	−0.286872
$399$	−15.4663	−0.774286
$400$	9.54925	0.477462
$401$	7.09079	0.354097	0.177049	−	0.984202i	$-0.443345\pi$
$401$	7.09079	0.354097	0.177049	+	0.984202i	$0.443345\pi$
$402$	21.7572	1.08515
$403$	−0.575375	−0.0286614
$404$	4.11092	0.204526
$405$	42.4118	2.10746
$406$	23.2738	1.15506
$407$	−0.912345	−0.0452232
$408$	−9.85463	−0.487877
$409$	3.22482	0.159457	0.0797286	−	0.996817i	$-0.474595\pi$
$409$	3.22482	0.159457	0.0797286	+	0.996817i	$0.474595\pi$
$410$	−31.2650	−1.54407
$411$	−38.2633	−1.88739
$412$	1.61855	0.0797401
$413$	6.91115	0.340076
$414$	3.89363	0.191361
$415$	27.6410	1.35684
$416$	−0.346540	−0.0169905
$417$	−14.7813	−0.723844
$418$	0.948958	0.0464150
$419$	−24.3391	−1.18904	−0.594522	−	0.804080i	$-0.702659\pi$
$419$	−24.3391	−1.18904	−0.594522	+	0.804080i	$0.702659\pi$
$420$	−19.7318	−0.962812
$421$	11.7078	0.570602	0.285301	−	0.958438i	$-0.407906\pi$
$421$	11.7078	0.570602	0.285301	+	0.958438i	$0.407906\pi$
$422$	−23.3615	−1.13722
$423$	10.5737	0.514112
$424$	−1.38016	−0.0670267
$425$	46.2604	2.24396
$426$	1.39661	0.0676661
$427$	−29.0210	−1.40442
$428$	−5.60729	−0.271039
$429$	−0.223748	−0.0108027
$430$	−16.5720	−0.799172
$431$	−19.7035	−0.949084	−0.474542	−	0.880233i	$-0.657386\pi$
$431$	−19.7035	−0.949084	−0.474542	+	0.880233i	$0.657386\pi$
$432$	3.78754	0.182228
$433$	−24.6550	−1.18484	−0.592422	−	0.805628i	$-0.701828\pi$
$433$	−24.6550	−1.18484	−0.592422	+	0.805628i	$0.701828\pi$
$434$	−4.22223	−0.202674
$435$	−71.0138	−3.40485
$436$	8.83708	0.423219
$437$	−10.2286	−0.489300
$438$	12.7140	0.607499
$439$	6.51202	0.310802	0.155401	−	0.987851i	$-0.450333\pi$
$439$	6.51202	0.310802	0.155401	+	0.987851i	$0.450333\pi$
$440$	1.21067	0.0577164
$441$	−0.606801	−0.0288953
$442$	−1.67878	−0.0798514
$443$	−14.2421	−0.676663	−0.338332	−	0.941027i	$-0.609863\pi$
$443$	−14.2421	−0.676663	−0.338332	+	0.941027i	$0.609863\pi$
$444$	−5.84728	−0.277500
$445$	56.0705	2.65799
$446$	−18.4097	−0.871726
$447$	33.0792	1.56459
$448$	−2.54300	−0.120145
$449$	−2.99085	−0.141147	−0.0705734	−	0.997507i	$-0.522483\pi$
$449$	−2.99085	−0.141147	−0.0705734	+	0.997507i	$0.522483\pi$
$450$	10.8680	0.512322
$451$	−2.60162	−0.122505
$452$	−3.88509	−0.182739
$453$	−12.9003	−0.606108
$454$	−16.8957	−0.792957
$455$	−3.36140	−0.157585
$456$	6.08194	0.284813
$457$	−38.9237	−1.82078	−0.910388	−	0.413757i	$-0.864216\pi$
$457$	−38.9237	−1.82078	−0.910388	+	0.413757i	$0.864216\pi$
$458$	17.8376	0.833494
$459$	18.3484	0.856428
$460$	−13.0495	−0.608437
$461$	33.1764	1.54518	0.772590	−	0.634905i	$-0.218961\pi$
$461$	33.1764	1.54518	0.772590	+	0.634905i	$0.218961\pi$
$462$	−1.64192	−0.0763889
$463$	−34.3536	−1.59655	−0.798274	−	0.602294i	$-0.794253\pi$
$463$	−34.3536	−1.59655	−0.798274	+	0.602294i	$0.794253\pi$
$464$	−9.15213	−0.424877
$465$	12.8830	0.597435
$466$	−6.36697	−0.294944
$467$	39.3704	1.82185	0.910923	−	0.412576i	$-0.135371\pi$
$467$	39.3704	1.82185	0.910923	+	0.412576i	$0.135371\pi$
$468$	−0.394397	−0.0182310
$469$	27.1987	1.25592
$470$	−35.4379	−1.63463
$471$	40.9908	1.88876
$472$	−2.71772	−0.125093
$473$	−1.37898	−0.0634058
$474$	1.26337	0.0580287
$475$	−28.5503	−1.30998
$476$	−12.3193	−0.564654
$477$	−1.57076	−0.0719203
$478$	0.100899	0.00461503
$479$	−25.3820	−1.15973	−0.579867	−	0.814711i	$-0.696895\pi$
$479$	−25.3820	−1.15973	−0.579867	+	0.814711i	$0.696895\pi$
$480$	7.75927	0.354160
$481$	−0.996111	−0.0454187
$482$	14.8424	0.676052
$483$	17.6979	0.805280
$484$	−10.8993	−0.495421
$485$	−49.1076	−2.22986
$486$	11.2561	0.510585
$487$	−15.1642	−0.687157	−0.343579	−	0.939124i	$-0.611639\pi$
$487$	−15.1642	−0.687157	−0.343579	+	0.939124i	$0.611639\pi$
$488$	11.4121	0.516603
$489$	0.649693	0.0293801
$490$	2.03370	0.0918732
$491$	−8.32128	−0.375534	−0.187767	−	0.982214i	$-0.560125\pi$
$491$	−8.32128	−0.375534	−0.187767	+	0.982214i	$0.560125\pi$
$492$	−16.6739	−0.751719
$493$	−44.3366	−1.99682
$494$	1.03609	0.0466157
$495$	1.37786	0.0619302
$496$	1.66034	0.0745514
$497$	1.74591	0.0783146
$498$	14.7412	0.660569
$499$	8.69026	0.389029	0.194515	−	0.980900i	$-0.437687\pi$
$499$	8.69026	0.389029	0.194515	+	0.980900i	$0.437687\pi$
$500$	−17.3524	−0.776023
$501$	−12.0848	−0.539909
$502$	−7.59554	−0.339006
$503$	10.1600	0.453014	0.226507	−	0.974010i	$-0.427269\pi$
$503$	10.1600	0.453014	0.226507	+	0.974010i	$0.427269\pi$
$504$	−2.89418	−0.128917
$505$	−15.6805	−0.697772
$506$	−1.08588	−0.0482730
$507$	26.2007	1.16361
$508$	9.74607	0.432412
$509$	19.2561	0.853513	0.426757	−	0.904366i	$-0.359656\pi$
$509$	19.2561	0.853513	0.426757	+	0.904366i	$0.359656\pi$
$510$	37.5890	1.66447
$511$	15.8938	0.703101
$512$	1.00000	0.0441942
$513$	−11.3240	−0.499965
$514$	8.37700	0.369494
$515$	−6.17371	−0.272046
$516$	−8.83801	−0.389072
$517$	−2.94886	−0.129691
$518$	−7.30970	−0.321170
$519$	16.7194	0.733902
$520$	1.32183	0.0579659
$521$	−25.9756	−1.13801	−0.569007	−	0.822333i	$-0.692672\pi$
$521$	−25.9756	−1.13801	−0.569007	+	0.822333i	$0.692672\pi$
$522$	−10.4160	−0.455897
$523$	−4.37403	−0.191263	−0.0956315	−	0.995417i	$-0.530487\pi$
$523$	−4.37403	−0.191263	−0.0956315	+	0.995417i	$0.530487\pi$
$524$	13.7552	0.600899
$525$	49.3987	2.15593
$526$	9.50328	0.414363
$527$	8.04334	0.350374
$528$	0.645663	0.0280989
$529$	−11.2956	−0.491113
$530$	5.26442	0.228672
$531$	−3.09303	−0.134226
$532$	7.60304	0.329634
$533$	−2.84048	−0.123035
$534$	29.9030	1.29403
$535$	21.3882	0.924691
$536$	−10.6955	−0.461976
$537$	−5.42368	−0.234049
$538$	−7.11694	−0.306833
$539$	0.169228	0.00728916
$540$	−14.4470	−0.621699
$541$	−2.46095	−0.105805	−0.0529024	−	0.998600i	$-0.516847\pi$
$541$	−2.46095	−0.105805	−0.0529024	+	0.998600i	$0.516847\pi$
$542$	−3.71253	−0.159467
$543$	21.1433	0.907346
$544$	4.84440	0.207702
$545$	−33.7077	−1.44388
$546$	−1.79267	−0.0767191
$547$	−30.4968	−1.30395	−0.651974	−	0.758241i	$-0.726059\pi$
$547$	−30.4968	−1.30395	−0.651974	+	0.758241i	$0.726059\pi$
$548$	18.8097	0.803510
$549$	12.9881	0.554320
$550$	−3.03092	−0.129239
$551$	27.3630	1.16570
$552$	−6.95945	−0.296214
$553$	1.57934	0.0671606
$554$	−8.22774	−0.349563
$555$	22.3036	0.946734
$556$	7.26629	0.308159
$557$	−17.4617	−0.739876	−0.369938	−	0.929056i	$-0.620621\pi$
$557$	−17.4617	−0.739876	−0.369938	+	0.929056i	$0.620621\pi$
$558$	1.88963	0.0799944
$559$	−1.50559	−0.0636799
$560$	9.69987	0.409894
$561$	3.12785	0.132058
$562$	10.0346	0.423283
$563$	10.7502	0.453068	0.226534	−	0.974003i	$-0.427261\pi$
$563$	10.7502	0.453068	0.226534	+	0.974003i	$0.427261\pi$
$564$	−18.8994	−0.795809
$565$	14.8191	0.623444
$566$	9.07656	0.381516
$567$	28.2756	1.18747
$568$	−0.686555	−0.0288072
$569$	0.0464089	0.00194556	0.000972780	−	1.00000i	$-0.499690\pi$
$569$	0.0464089	0.00194556	0.000972780		1.00000i	$0.499690\pi$
$570$	−23.1986	−0.971683
$571$	−35.9212	−1.50326	−0.751628	−	0.659587i	$-0.770731\pi$
$571$	−35.9212	−1.50326	−0.751628	+	0.659587i	$0.770731\pi$
$572$	0.109992	0.00459898
$573$	19.4351	0.811913
$574$	−20.8441	−0.870017
$575$	32.6696	1.36242
$576$	1.13810	0.0474208
$577$	25.3693	1.05614	0.528068	−	0.849202i	$-0.322916\pi$
$577$	25.3693	1.05614	0.528068	+	0.849202i	$0.322916\pi$
$578$	6.46820	0.269042
$579$	40.9820	1.70316
$580$	34.9094	1.44953
$581$	18.4280	0.764523
$582$	−26.1896	−1.08559
$583$	0.438062	0.0181427
$584$	−6.25003	−0.258628
$585$	1.50437	0.0621980
$586$	−15.1195	−0.624581
$587$	−5.54445	−0.228844	−0.114422	−	0.993432i	$-0.536502\pi$
$587$	−5.54445	−0.228844	−0.114422	+	0.993432i	$0.536502\pi$
$588$	1.08459	0.0447279
$589$	−4.96407	−0.204541
$590$	10.3663	0.426775
$591$	−13.6580	−0.561814
$592$	2.87444	0.118139
$593$	−22.9889	−0.944043	−0.472021	−	0.881587i	$-0.656475\pi$
$593$	−22.9889	−0.944043	−0.472021	+	0.881587i	$0.656475\pi$
$594$	−1.20216	−0.0493252
$595$	46.9900	1.92640
$596$	−16.2613	−0.666087
$597$	11.6421	0.476479
$598$	−1.18557	−0.0484817
$599$	−21.1296	−0.863332	−0.431666	−	0.902034i	$-0.642074\pi$
$599$	−21.1296	−0.863332	−0.431666	+	0.902034i	$0.642074\pi$
$600$	−19.4254	−0.793038
$601$	−30.2093	−1.23226	−0.616131	−	0.787644i	$-0.711301\pi$
$601$	−30.2093	−1.23226	−0.616131	+	0.787644i	$0.711301\pi$
$602$	−11.0484	−0.450299
$603$	−12.1726	−0.495705
$604$	6.34160	0.258036
$605$	41.5736	1.69021
$606$	−8.36256	−0.339706
$607$	4.80110	0.194871	0.0974353	−	0.995242i	$-0.468936\pi$
$607$	4.80110	0.194871	0.0974353	+	0.995242i	$0.468936\pi$
$608$	−2.98980	−0.121252
$609$	−47.3444	−1.91849
$610$	−43.5298	−1.76247
$611$	−3.21960	−0.130251
$612$	5.51340	0.222866
$613$	−11.8858	−0.480062	−0.240031	−	0.970765i	$-0.577158\pi$
$613$	−11.8858	−0.480062	−0.240031	+	0.970765i	$0.577158\pi$
$614$	−23.6049	−0.952616
$615$	63.6002	2.56461
$616$	0.807144	0.0325208
$617$	19.2666	0.775645	0.387823	−	0.921734i	$-0.373227\pi$
$617$	19.2666	0.775645	0.387823	+	0.921734i	$0.373227\pi$
$618$	−3.29250	−0.132444
$619$	21.3322	0.857413	0.428707	−	0.903444i	$-0.358969\pi$
$619$	21.3322	0.857413	0.428707	+	0.903444i	$0.358969\pi$
$620$	−6.33311	−0.254344
$621$	12.9578	0.519979
$622$	28.4888	1.14230
$623$	37.3817	1.49767
$624$	0.704944	0.0282203
$625$	18.4419	0.737675
$626$	−9.66921	−0.386459
$627$	−1.93040	−0.0770927
$628$	−20.1505	−0.804093
$629$	13.9249	0.555224
$630$	11.0394	0.439821
$631$	−34.3038	−1.36561	−0.682807	−	0.730599i	$-0.739241\pi$
$631$	−34.3038	−1.36561	−0.682807	+	0.730599i	$0.739241\pi$
$632$	−0.621057	−0.0247043
$633$	47.5227	1.88886
$634$	−19.6352	−0.779814
$635$	−37.1749	−1.47524
$636$	2.80757	0.111328
$637$	0.184765	0.00732067
$638$	2.90487	0.115005
$639$	−0.781367	−0.0309104
$640$	−3.81435	−0.150775
$641$	24.8882	0.983025	0.491513	−	0.870870i	$-0.336444\pi$
$641$	24.8882	0.983025	0.491513	+	0.870870i	$0.336444\pi$
$642$	11.4065	0.450180
$643$	12.9284	0.509845	0.254922	−	0.966962i	$-0.417950\pi$
$643$	12.9284	0.509845	0.254922	+	0.966962i	$0.417950\pi$
$644$	−8.70002	−0.342829
$645$	33.7112	1.32738
$646$	−14.4838	−0.569856
$647$	−1.44550	−0.0568284	−0.0284142	−	0.999596i	$-0.509046\pi$
$647$	−1.44550	−0.0568284	−0.0284142	+	0.999596i	$0.509046\pi$
$648$	−11.1190	−0.436797
$649$	0.862602	0.0338601
$650$	−3.30920	−0.129798
$651$	8.58900	0.336630
$652$	−0.319380	−0.0125079
$653$	−7.39727	−0.289477	−0.144739	−	0.989470i	$-0.546234\pi$
$653$	−7.39727	−0.289477	−0.144739	+	0.989470i	$0.546234\pi$
$654$	−17.9767	−0.702943
$655$	−52.4672	−2.05006
$656$	8.19668	0.320027
$657$	−7.11315	−0.277510
$658$	−23.6262	−0.921045
$659$	22.9527	0.894110	0.447055	−	0.894506i	$-0.352473\pi$
$659$	22.9527	0.894110	0.447055	+	0.894506i	$0.352473\pi$
$660$	−2.46278	−0.0958637
$661$	−31.1480	−1.21152	−0.605759	−	0.795648i	$-0.707131\pi$
$661$	−31.1480	−1.21152	−0.605759	+	0.795648i	$0.707131\pi$
$662$	23.8723	0.927824
$663$	3.41503	0.132629
$664$	−7.24657	−0.281222
$665$	−29.0006	−1.12460
$666$	3.27140	0.126764
$667$	−31.3110	−1.21237
$668$	5.94072	0.229853
$669$	37.4496	1.44789
$670$	40.7964	1.57610
$671$	−3.62220	−0.139833
$672$	5.17304	0.199554
$673$	−1.95081	−0.0751983	−0.0375991	−	0.999293i	$-0.511971\pi$
$673$	−1.95081	−0.0751983	−0.0375991	+	0.999293i	$0.511971\pi$
$674$	5.59037	0.215333
$675$	36.1681	1.39211
$676$	−12.8799	−0.495381
$677$	4.11377	0.158105	0.0790524	−	0.996870i	$-0.474811\pi$
$677$	4.11377	0.158105	0.0790524	+	0.996870i	$0.474811\pi$
$678$	7.90318	0.303520
$679$	−32.7397	−1.25643
$680$	−18.4782	−0.708607
$681$	34.3699	1.31706
$682$	−0.526990	−0.0201795
$683$	22.6278	0.865828	0.432914	−	0.901435i	$-0.357485\pi$
$683$	22.6278	0.865828	0.432914	+	0.901435i	$0.357485\pi$
$684$	−3.40268	−0.130105
$685$	−71.7467	−2.74130
$686$	19.1568	0.731411
$687$	−36.2857	−1.38439
$688$	4.34464	0.165638
$689$	0.478283	0.0182211
$690$	26.5458	1.01058
$691$	5.91153	0.224885	0.112443	−	0.993658i	$-0.464133\pi$
$691$	5.91153	0.224885	0.112443	+	0.993658i	$0.464133\pi$
$692$	−8.21904	−0.312441
$693$	0.918609	0.0348951
$694$	5.54386	0.210442
$695$	−27.7161	−1.05133
$696$	18.6175	0.705696
$697$	39.7080	1.50405
$698$	5.61241	0.212433
$699$	12.9519	0.489885
$700$	−24.2837	−0.917837
$701$	−17.0563	−0.644207	−0.322103	−	0.946704i	$-0.604390\pi$
$701$	−17.0563	−0.644207	−0.322103	+	0.946704i	$0.604390\pi$
$702$	−1.31254	−0.0495385
$703$	−8.59400	−0.324129
$704$	−0.317399	−0.0119624
$705$	72.0890	2.71503
$706$	−0.0133269	−0.000501564 0
$707$	−10.4541	−0.393165
$708$	5.52847	0.207773
$709$	18.9749	0.712618	0.356309	−	0.934368i	$-0.384035\pi$
$709$	18.9749	0.712618	0.356309	+	0.934368i	$0.384035\pi$
$710$	2.61876	0.0982803
$711$	−0.706824	−0.0265080
$712$	−14.6999	−0.550901
$713$	5.68030	0.212729
$714$	25.0603	0.937858
$715$	−0.419546	−0.0156901
$716$	2.66620	0.0996407
$717$	−0.205253	−0.00766531
$718$	33.1929	1.23875
$719$	12.7324	0.474838	0.237419	−	0.971407i	$-0.423699\pi$
$719$	12.7324	0.474838	0.237419	+	0.971407i	$0.423699\pi$
$720$	−4.34110	−0.161783
$721$	−4.11596	−0.153286
$722$	−10.0611	−0.374436
$723$	−30.1928	−1.12288
$724$	−10.3938	−0.386281
$725$	−87.3959	−3.24580
$726$	22.1716	0.822866
$727$	1.54266	0.0572140	0.0286070	−	0.999591i	$-0.490893\pi$
$727$	1.54266	0.0572140	0.0286070	+	0.999591i	$0.490893\pi$
$728$	0.881251	0.0326613
$729$	10.4596	0.387394
$730$	23.8398	0.882350
$731$	21.0472	0.778458
$732$	−23.2149	−0.858048
$733$	19.8089	0.731660	0.365830	−	0.930682i	$-0.380785\pi$
$733$	19.8089	0.731660	0.365830	+	0.930682i	$0.380785\pi$
$734$	24.9837	0.922164
$735$	−4.13702	−0.152596
$736$	3.42117	0.126106
$737$	3.39474	0.125047
$738$	9.32863	0.343391
$739$	−40.2397	−1.48024	−0.740121	−	0.672474i	$-0.765232\pi$
$739$	−40.2397	−1.48024	−0.740121	+	0.672474i	$0.765232\pi$
$740$	−10.9641	−0.403049
$741$	−2.10764	−0.0774260
$742$	3.50975	0.128847
$743$	49.0056	1.79784	0.898920	−	0.438113i	$-0.144353\pi$
$743$	49.0056	1.79784	0.898920	+	0.438113i	$0.144353\pi$
$744$	−3.37751	−0.123826
$745$	62.0261	2.27246
$746$	21.4045	0.783675
$747$	−8.24732	−0.301753
$748$	−1.53761	−0.0562205
$749$	14.2593	0.521024
$750$	35.2988	1.28893
$751$	37.5080	1.36869	0.684343	−	0.729160i	$-0.260089\pi$
$751$	37.5080	1.36869	0.684343	+	0.729160i	$0.260089\pi$
$752$	9.29070	0.338797
$753$	15.4511	0.563069
$754$	3.17158	0.115502
$755$	−24.1890	−0.880330
$756$	−9.63170	−0.350301
$757$	14.5536	0.528958	0.264479	−	0.964391i	$-0.414800\pi$
$757$	14.5536	0.528958	0.264479	+	0.964391i	$0.414800\pi$
$758$	−8.48836	−0.308311
$759$	2.20892	0.0801788
$760$	11.4041	0.413671
$761$	4.62640	0.167707	0.0838535	−	0.996478i	$-0.473277\pi$
$761$	4.62640	0.167707	0.0838535	+	0.996478i	$0.473277\pi$
$762$	−19.8258	−0.718212
$763$	−22.4727	−0.813565
$764$	−9.55402	−0.345652
$765$	−21.0300	−0.760343
$766$	22.9394	0.828833
$767$	0.941800	0.0340064
$768$	−2.03423	−0.0734040
$769$	−37.0767	−1.33702	−0.668510	−	0.743703i	$-0.733068\pi$
$769$	−37.0767	−1.33702	−0.668510	+	0.743703i	$0.733068\pi$
$770$	−3.07873	−0.110950
$771$	−17.0408	−0.613708
$772$	−20.1462	−0.725077
$773$	9.20779	0.331181	0.165591	−	0.986195i	$-0.447047\pi$
$773$	9.20779	0.331181	0.165591	+	0.986195i	$0.447047\pi$
$774$	4.94463	0.177731
$775$	15.8550	0.569528
$776$	12.8744	0.462166
$777$	14.8696	0.533445
$778$	−30.0337	−1.07676
$779$	−24.5064	−0.878033
$780$	−2.68890	−0.0962781
$781$	0.217912	0.00779750
$782$	16.5735	0.592668
$783$	−34.6640	−1.23879
$784$	−0.533171	−0.0190418
$785$	76.8611	2.74329
$786$	−27.9813	−0.998060
$787$	−11.1907	−0.398906	−0.199453	−	0.979907i	$-0.563917\pi$
$787$	−11.1907	−0.398906	−0.199453	+	0.979907i	$0.563917\pi$
$788$	6.71408	0.239179
$789$	−19.3319	−0.688233
$790$	2.36893	0.0842826
$791$	9.87978	0.351284
$792$	−0.361231	−0.0128358
$793$	−3.95476	−0.140438
$794$	13.5128	0.479553
$795$	−10.7091	−0.379811
$796$	−5.72309	−0.202849
$797$	−12.6285	−0.447326	−0.223663	−	0.974667i	$-0.571802\pi$
$797$	−12.6285	−0.447326	−0.223663	+	0.974667i	$0.571802\pi$
$798$	−15.4663	−0.547503
$799$	45.0078	1.59226
$800$	9.54925	0.337617
$801$	−16.7299	−0.591122
$802$	7.09079	0.250384
$803$	1.98375	0.0700051
$804$	21.7572	0.767316
$805$	33.1849	1.16961
$806$	−0.575375	−0.0202667
$807$	14.4775	0.509632
$808$	4.11092	0.144622
$809$	−55.4071	−1.94801	−0.974004	−	0.226530i	$-0.927262\pi$
$809$	−55.4071	−1.94801	−0.974004	+	0.226530i	$0.927262\pi$
$810$	42.4118	1.49020
$811$	7.25483	0.254752	0.127376	−	0.991855i	$-0.459345\pi$
$811$	7.25483	0.254752	0.127376	+	0.991855i	$0.459345\pi$
$812$	23.2738	0.816751
$813$	7.55214	0.264865
$814$	−0.912345	−0.0319777
$815$	1.21823	0.0426726
$816$	−9.85463	−0.344981
$817$	−12.9896	−0.454448
$818$	3.22482	0.112753
$819$	1.00295	0.0350459
$820$	−31.2650	−1.09182
$821$	−26.2914	−0.917577	−0.458789	−	0.888545i	$-0.651716\pi$
$821$	−26.2914	−0.917577	−0.458789	+	0.888545i	$0.651716\pi$
$822$	−38.2633	−1.33459
$823$	10.8621	0.378628	0.189314	−	0.981917i	$-0.439374\pi$
$823$	10.8621	0.378628	0.189314	+	0.981917i	$0.439374\pi$
$824$	1.61855	0.0563848
$825$	6.16559	0.214658
$826$	6.91115	0.240470
$827$	29.4853	1.02531	0.512653	−	0.858596i	$-0.328663\pi$
$827$	29.4853	1.02531	0.512653	+	0.858596i	$0.328663\pi$
$828$	3.89363	0.135313
$829$	25.2176	0.875844	0.437922	−	0.899013i	$-0.355715\pi$
$829$	25.2176	0.875844	0.437922	+	0.899013i	$0.355715\pi$
$830$	27.6410	0.959431
$831$	16.7371	0.580604
$832$	−0.346540	−0.0120141
$833$	−2.58289	−0.0894920
$834$	−14.7813	−0.511835
$835$	−22.6600	−0.784180
$836$	0.948958	0.0328204
$837$	6.28860	0.217366
$838$	−24.3391	−0.840781
$839$	46.2543	1.59688	0.798438	−	0.602077i	$-0.205660\pi$
$839$	46.2543	1.59688	0.798438	+	0.602077i	$0.205660\pi$
$840$	−19.7318	−0.680811
$841$	54.7615	1.88833
$842$	11.7078	0.403477
$843$	−20.4127	−0.703049
$844$	−23.3615	−0.804136
$845$	49.1284	1.69007
$846$	10.5737	0.363532
$847$	27.7168	0.952359
$848$	−1.38016	−0.0473950
$849$	−18.4638	−0.633677
$850$	46.2604	1.58672
$851$	9.83396	0.337104
$852$	1.39661	0.0478471
$853$	14.6135	0.500357	0.250178	−	0.968200i	$-0.419511\pi$
$853$	14.6135	0.500357	0.250178	+	0.968200i	$0.419511\pi$
$854$	−29.0210	−0.993078
$855$	12.9790	0.443873
$856$	−5.60729	−0.191653
$857$	−50.3686	−1.72056	−0.860279	−	0.509823i	$-0.829711\pi$
$857$	−50.3686	−1.72056	−0.860279	+	0.509823i	$0.829711\pi$
$858$	−0.223748	−0.00763864
$859$	−3.07795	−0.105018	−0.0525092	−	0.998620i	$-0.516722\pi$
$859$	−3.07795	−0.105018	−0.0525092	+	0.998620i	$0.516722\pi$
$860$	−16.5720	−0.565100
$861$	42.4018	1.44505
$862$	−19.7035	−0.671104
$863$	13.0268	0.443437	0.221719	−	0.975111i	$-0.428833\pi$
$863$	13.0268	0.443437	0.221719	+	0.975111i	$0.428833\pi$
$864$	3.78754	0.128855
$865$	31.3503	1.06594
$866$	−24.6550	−0.837812
$867$	−13.1578	−0.446863
$868$	−4.22223	−0.143312
$869$	0.197123	0.00668693
$870$	−71.0138	−2.40759
$871$	3.70643	0.125588
$872$	8.83708	0.299261
$873$	14.6524	0.495908
$874$	−10.2286	−0.345988
$875$	44.1271	1.49177
$876$	12.7140	0.429567
$877$	34.1448	1.15299	0.576494	−	0.817102i	$-0.304421\pi$
$877$	34.1448	1.15299	0.576494	+	0.817102i	$0.304421\pi$
$878$	6.51202	0.219770
$879$	30.7566	1.03739
$880$	1.21067	0.0408117
$881$	37.9503	1.27858	0.639289	−	0.768966i	$-0.279229\pi$
$881$	37.9503	1.27858	0.639289	+	0.768966i	$0.279229\pi$
$882$	−0.606801	−0.0204321
$883$	−47.7408	−1.60661	−0.803303	−	0.595570i	$-0.796926\pi$
$883$	−47.7408	−1.60661	−0.803303	+	0.595570i	$0.796926\pi$
$884$	−1.67878	−0.0564635
$885$	−21.0875	−0.708849
$886$	−14.2421	−0.478473
$887$	−58.1048	−1.95097	−0.975484	−	0.220072i	$-0.929371\pi$
$887$	−58.1048	−1.95097	−0.975484	+	0.220072i	$0.929371\pi$
$888$	−5.84728	−0.196222
$889$	−24.7842	−0.831236
$890$	56.0705	1.87949
$891$	3.52917	0.118232
$892$	−18.4097	−0.616403
$893$	−27.7773	−0.929531
$894$	33.0792	1.10633
$895$	−10.1698	−0.339940
$896$	−2.54300	−0.0849555
$897$	2.41173	0.0805254
$898$	−2.99085	−0.0998059
$899$	−15.1956	−0.506803
$900$	10.8680	0.362266
$901$	−6.68606	−0.222745
$902$	−2.60162	−0.0866243
$903$	22.4750	0.747922
$904$	−3.88509	−0.129216
$905$	39.6454	1.31786
$906$	−12.9003	−0.428583
$907$	−41.8724	−1.39035	−0.695175	−	0.718840i	$-0.744673\pi$
$907$	−41.8724	−1.39035	−0.695175	+	0.718840i	$0.744673\pi$
$908$	−16.8957	−0.560705
$909$	4.67863	0.155180
$910$	−3.36140	−0.111429
$911$	−0.395731	−0.0131112	−0.00655558	−	0.999979i	$-0.502087\pi$
$911$	−0.395731	−0.0131112	−0.00655558	+	0.999979i	$0.502087\pi$
$912$	6.08194	0.201393
$913$	2.30005	0.0761207
$914$	−38.9237	−1.28748
$915$	88.5497	2.92736
$916$	17.8376	0.589370
$917$	−34.9795	−1.15512
$918$	18.3484	0.605586
$919$	−32.6315	−1.07641	−0.538207	−	0.842812i	$-0.680898\pi$
$919$	−32.6315	−1.07641	−0.538207	+	0.842812i	$0.680898\pi$
$920$	−13.0495	−0.430230
$921$	48.0178	1.58224
$922$	33.1764	1.09261
$923$	0.237919	0.00783120
$924$	−1.64192	−0.0540151
$925$	27.4488	0.902510
$926$	−34.3536	−1.12893
$927$	1.84207	0.0605014
$928$	−9.15213	−0.300433
$929$	17.7539	0.582486	0.291243	−	0.956649i	$-0.405931\pi$
$929$	17.7539	0.582486	0.291243	+	0.956649i	$0.405931\pi$
$930$	12.8830	0.422451
$931$	1.59407	0.0522436
$932$	−6.36697	−0.208557
$933$	−57.9529	−1.89729
$934$	39.3704	1.28824
$935$	5.86497	0.191805
$936$	−0.394397	−0.0128913
$937$	−46.7195	−1.52626	−0.763130	−	0.646245i	$-0.776339\pi$
$937$	−46.7195	−1.52626	−0.763130	+	0.646245i	$0.776339\pi$
$938$	27.1987	0.888068
$939$	19.6694	0.641887
$940$	−35.4379	−1.15586
$941$	6.02202	0.196312	0.0981562	−	0.995171i	$-0.468706\pi$
$941$	6.02202	0.196312	0.0981562	+	0.995171i	$0.468706\pi$
$942$	40.9908	1.33555
$943$	28.0422	0.913181
$944$	−2.71772	−0.0884543
$945$	36.7386	1.19511
$946$	−1.37898	−0.0448346
$947$	20.6880	0.672271	0.336136	−	0.941814i	$-0.390880\pi$
$947$	20.6880	0.672271	0.336136	+	0.941814i	$0.390880\pi$
$948$	1.26337	0.0410325
$949$	2.16589	0.0703077
$950$	−28.5503	−0.926294
$951$	39.9426	1.29523
$952$	−12.3193	−0.399270
$953$	−43.7264	−1.41644	−0.708219	−	0.705993i	$-0.750501\pi$
$953$	−43.7264	−1.41644	−0.708219	+	0.705993i	$0.750501\pi$
$954$	−1.57076	−0.0508553
$955$	36.4424	1.17925
$956$	0.100899	0.00326332
$957$	−5.90919	−0.191017
$958$	−25.3820	−0.820055
$959$	−47.8330	−1.54461
$960$	7.75927	0.250429
$961$	−28.2433	−0.911073
$962$	−0.996111	−0.0321159
$963$	−6.38165	−0.205646
$964$	14.8424	0.478041
$965$	76.8446	2.47371
$966$	17.6979	0.569419
$967$	−41.8486	−1.34576	−0.672881	−	0.739751i	$-0.734943\pi$
$967$	−41.8486	−1.34576	−0.672881	+	0.739751i	$0.734943\pi$
$968$	−10.8993	−0.350315
$969$	29.4633	0.946499
$970$	−49.1076	−1.57675
$971$	25.0434	0.803681	0.401841	−	0.915710i	$-0.368371\pi$
$971$	25.0434	0.803681	0.401841	+	0.915710i	$0.368371\pi$
$972$	11.2561	0.361038
$973$	−18.4781	−0.592382
$974$	−15.1642	−0.485894
$975$	6.73168	0.215586
$976$	11.4121	0.365293
$977$	−22.3744	−0.715821	−0.357910	−	0.933756i	$-0.616511\pi$
$977$	−22.3744	−0.715821	−0.357910	+	0.933756i	$0.616511\pi$
$978$	0.649693	0.0207749
$979$	4.66572	0.149117
$980$	2.03370	0.0649642
$981$	10.0575	0.321110
$982$	−8.32128	−0.265543
$983$	4.23873	0.135194	0.0675972	−	0.997713i	$-0.478467\pi$
$983$	4.23873	0.135194	0.0675972	+	0.997713i	$0.478467\pi$
$984$	−16.6739	−0.531546
$985$	−25.6098	−0.815997
$986$	−44.3366	−1.41196
$987$	48.0612	1.52980
$988$	1.03609	0.0329623
$989$	14.8638	0.472640
$990$	1.37786	0.0437913
$991$	−33.7293	−1.07145	−0.535724	−	0.844393i	$-0.679961\pi$
$991$	−33.7293	−1.07145	−0.535724	+	0.844393i	$0.679961\pi$
$992$	1.66034	0.0527158
$993$	−48.5618	−1.54106
$994$	1.74591	0.0553768
$995$	21.8298	0.692053
$996$	14.7412	0.467093
$997$	−16.6015	−0.525774	−0.262887	−	0.964827i	$-0.584675\pi$
$997$	−16.6015	−0.525774	−0.262887	+	0.964827i	$0.584675\pi$
$998$	8.69026	0.275085
$999$	10.8871	0.344451

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.10	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.10	✓	47	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.03423 q^{3} +1.00000 q^{4} -3.81435 q^{5} -2.03423 q^{6} -2.54300 q^{7} +1.00000 q^{8} +1.13810 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.03423 q^{3} +1.00000 q^{4} -3.81435 q^{5} -2.03423 q^{6} -2.54300 q^{7} +1.00000 q^{8} +1.13810 q^{9} -3.81435 q^{10} -0.317399 q^{11} -2.03423 q^{12} -0.346540 q^{13} -2.54300 q^{14} +7.75927 q^{15} +1.00000 q^{16} +4.84440 q^{17} +1.13810 q^{18} -2.98980 q^{19} -3.81435 q^{20} +5.17304 q^{21} -0.317399 q^{22} +3.42117 q^{23} -2.03423 q^{24} +9.54925 q^{25} -0.346540 q^{26} +3.78754 q^{27} -2.54300 q^{28} -9.15213 q^{29} +7.75927 q^{30} +1.66034 q^{31} +1.00000 q^{32} +0.645663 q^{33} +4.84440 q^{34} +9.69987 q^{35} +1.13810 q^{36} +2.87444 q^{37} -2.98980 q^{38} +0.704944 q^{39} -3.81435 q^{40} +8.19668 q^{41} +5.17304 q^{42} +4.34464 q^{43} -0.317399 q^{44} -4.34110 q^{45} +3.42117 q^{46} +9.29070 q^{47} -2.03423 q^{48} -0.533171 q^{49} +9.54925 q^{50} -9.85463 q^{51} -0.346540 q^{52} -1.38016 q^{53} +3.78754 q^{54} +1.21067 q^{55} -2.54300 q^{56} +6.08194 q^{57} -9.15213 q^{58} -2.71772 q^{59} +7.75927 q^{60} +11.4121 q^{61} +1.66034 q^{62} -2.89418 q^{63} +1.00000 q^{64} +1.32183 q^{65} +0.645663 q^{66} -10.6955 q^{67} +4.84440 q^{68} -6.95945 q^{69} +9.69987 q^{70} -0.686555 q^{71} +1.13810 q^{72} -6.25003 q^{73} +2.87444 q^{74} -19.4254 q^{75} -2.98980 q^{76} +0.807144 q^{77} +0.704944 q^{78} -0.621057 q^{79} -3.81435 q^{80} -11.1190 q^{81} +8.19668 q^{82} -7.24657 q^{83} +5.17304 q^{84} -18.4782 q^{85} +4.34464 q^{86} +18.6175 q^{87} -0.317399 q^{88} -14.6999 q^{89} -4.34110 q^{90} +0.881251 q^{91} +3.42117 q^{92} -3.37751 q^{93} +9.29070 q^{94} +11.4041 q^{95} -2.03423 q^{96} +12.8744 q^{97} -0.533171 q^{98} -0.361231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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