LMFDB - Embedded newform 6002.2.a.d.1.17

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:	$0$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.02789 q^{3} +1.00000 q^{4} +2.83925 q^{5} -2.02789 q^{6} -1.41231 q^{7} +1.00000 q^{8} +1.11233 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.02789 q^{3} +1.00000 q^{4} +2.83925 q^{5} -2.02789 q^{6} -1.41231 q^{7} +1.00000 q^{8} +1.11233 q^{9} +2.83925 q^{10} -0.0407054 q^{11} -2.02789 q^{12} +6.11457 q^{13} -1.41231 q^{14} -5.75767 q^{15} +1.00000 q^{16} +5.55209 q^{17} +1.11233 q^{18} -6.14213 q^{19} +2.83925 q^{20} +2.86400 q^{21} -0.0407054 q^{22} -1.68818 q^{23} -2.02789 q^{24} +3.06132 q^{25} +6.11457 q^{26} +3.82799 q^{27} -1.41231 q^{28} +5.96760 q^{29} -5.75767 q^{30} +7.19936 q^{31} +1.00000 q^{32} +0.0825460 q^{33} +5.55209 q^{34} -4.00988 q^{35} +1.11233 q^{36} -1.07066 q^{37} -6.14213 q^{38} -12.3997 q^{39} +2.83925 q^{40} -2.34419 q^{41} +2.86400 q^{42} -9.94000 q^{43} -0.0407054 q^{44} +3.15817 q^{45} -1.68818 q^{46} +5.35306 q^{47} -2.02789 q^{48} -5.00539 q^{49} +3.06132 q^{50} -11.2590 q^{51} +6.11457 q^{52} -1.71195 q^{53} +3.82799 q^{54} -0.115573 q^{55} -1.41231 q^{56} +12.4556 q^{57} +5.96760 q^{58} +10.9295 q^{59} -5.75767 q^{60} -3.72128 q^{61} +7.19936 q^{62} -1.57095 q^{63} +1.00000 q^{64} +17.3608 q^{65} +0.0825460 q^{66} -2.34760 q^{67} +5.55209 q^{68} +3.42344 q^{69} -4.00988 q^{70} +0.0610912 q^{71} +1.11233 q^{72} +12.6800 q^{73} -1.07066 q^{74} -6.20802 q^{75} -6.14213 q^{76} +0.0574885 q^{77} -12.3997 q^{78} -11.6255 q^{79} +2.83925 q^{80} -11.0997 q^{81} -2.34419 q^{82} +2.71959 q^{83} +2.86400 q^{84} +15.7638 q^{85} -9.94000 q^{86} -12.1016 q^{87} -0.0407054 q^{88} +10.3146 q^{89} +3.15817 q^{90} -8.63564 q^{91} -1.68818 q^{92} -14.5995 q^{93} +5.35306 q^{94} -17.4390 q^{95} -2.02789 q^{96} -8.43980 q^{97} -5.00539 q^{98} -0.0452778 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) $ 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * 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
$3$	−2.02789	−1.17080	−0.585401	−	0.810744i	$-0.699063\pi$
$3$	−2.02789	−1.17080	−0.585401	+	0.810744i	$0.699063\pi$
$4$	1.00000	0.500000
$5$	2.83925	1.26975	0.634875	−	0.772615i	$-0.281052\pi$
$5$	2.83925	1.26975	0.634875	+	0.772615i	$0.281052\pi$
$6$	−2.02789	−0.827882
$7$	−1.41231	−0.533801	−0.266901	−	0.963724i	$-0.586000\pi$
$7$	−1.41231	−0.533801	−0.266901	+	0.963724i	$0.586000\pi$
$8$	1.00000	0.353553
$9$	1.11233	0.370776
$10$	2.83925	0.897849
$11$	−0.0407054	−0.0122731	−0.00613657	−	0.999981i	$-0.501953\pi$
$11$	−0.0407054	−0.0122731	−0.00613657	+	0.999981i	$0.501953\pi$
$12$	−2.02789	−0.585401
$13$	6.11457	1.69588	0.847938	−	0.530095i	$-0.177844\pi$
$13$	6.11457	1.69588	0.847938	+	0.530095i	$0.177844\pi$
$14$	−1.41231	−0.377454
$15$	−5.75767	−1.48662
$16$	1.00000	0.250000
$17$	5.55209	1.34658	0.673290	−	0.739379i	$-0.264881\pi$
$17$	5.55209	1.34658	0.673290	+	0.739379i	$0.264881\pi$
$18$	1.11233	0.262178
$19$	−6.14213	−1.40910	−0.704551	−	0.709654i	$-0.748851\pi$
$19$	−6.14213	−1.40910	−0.704551	+	0.709654i	$0.748851\pi$
$20$	2.83925	0.634875
$21$	2.86400	0.624975
$22$	−0.0407054	−0.00867843
$23$	−1.68818	−0.352010	−0.176005	−	0.984389i	$-0.556318\pi$
$23$	−1.68818	−0.352010	−0.176005	+	0.984389i	$0.556318\pi$
$24$	−2.02789	−0.413941
$25$	3.06132	0.612264
$26$	6.11457	1.19917
$27$	3.82799	0.736697
$28$	−1.41231	−0.266901
$29$	5.96760	1.10816	0.554078	−	0.832465i	$-0.313071\pi$
$29$	5.96760	1.10816	0.554078	+	0.832465i	$0.313071\pi$
$30$	−5.75767	−1.05120
$31$	7.19936	1.29304	0.646522	−	0.762895i	$-0.276223\pi$
$31$	7.19936	1.29304	0.646522	+	0.762895i	$0.276223\pi$
$32$	1.00000	0.176777
$33$	0.0825460	0.0143694
$34$	5.55209	0.952176
$35$	−4.00988	−0.677794
$36$	1.11233	0.185388
$37$	−1.07066	−0.176016	−0.0880078	−	0.996120i	$-0.528050\pi$
$37$	−1.07066	−0.176016	−0.0880078	+	0.996120i	$0.528050\pi$
$38$	−6.14213	−0.996385
$39$	−12.3997	−1.98554
$40$	2.83925	0.448924
$41$	−2.34419	−0.366101	−0.183051	−	0.983103i	$-0.558597\pi$
$41$	−2.34419	−0.366101	−0.183051	+	0.983103i	$0.558597\pi$
$42$	2.86400	0.441924
$43$	−9.94000	−1.51584	−0.757918	−	0.652350i	$-0.773783\pi$
$43$	−9.94000	−1.51584	−0.757918	+	0.652350i	$0.773783\pi$
$44$	−0.0407054	−0.00613657
$45$	3.15817	0.470793
$46$	−1.68818	−0.248909
$47$	5.35306	0.780824	0.390412	−	0.920640i	$-0.372332\pi$
$47$	5.35306	0.780824	0.390412	+	0.920640i	$0.372332\pi$
$48$	−2.02789	−0.292700
$49$	−5.00539	−0.715056
$50$	3.06132	0.432936
$51$	−11.2590	−1.57658
$52$	6.11457	0.847938
$53$	−1.71195	−0.235154	−0.117577	−	0.993064i	$-0.537513\pi$
$53$	−1.71195	−0.235154	−0.117577	+	0.993064i	$0.537513\pi$
$54$	3.82799	0.520923
$55$	−0.115573	−0.0155838
$56$	−1.41231	−0.188727
$57$	12.4556	1.64978
$58$	5.96760	0.783585
$59$	10.9295	1.42290	0.711449	−	0.702738i	$-0.248039\pi$
$59$	10.9295	1.42290	0.711449	+	0.702738i	$0.248039\pi$
$60$	−5.75767	−0.743312
$61$	−3.72128	−0.476461	−0.238231	−	0.971209i	$-0.576567\pi$
$61$	−3.72128	−0.476461	−0.238231	+	0.971209i	$0.576567\pi$
$62$	7.19936	0.914320
$63$	−1.57095	−0.197921
$64$	1.00000	0.125000
$65$	17.3608	2.15334
$66$	0.0825460	0.0101607
$67$	−2.34760	−0.286805	−0.143402	−	0.989664i	$-0.545804\pi$
$67$	−2.34760	−0.286805	−0.143402	+	0.989664i	$0.545804\pi$
$68$	5.55209	0.673290
$69$	3.42344	0.412134
$70$	−4.00988	−0.479273
$71$	0.0610912	0.00725019	0.00362509	−	0.999993i	$-0.498846\pi$
$71$	0.0610912	0.00725019	0.00362509	+	0.999993i	$0.498846\pi$
$72$	1.11233	0.131089
$73$	12.6800	1.48408	0.742039	−	0.670356i	$-0.233859\pi$
$73$	12.6800	1.48408	0.742039	+	0.670356i	$0.233859\pi$
$74$	−1.07066	−0.124462
$75$	−6.20802	−0.716840
$76$	−6.14213	−0.704551
$77$	0.0574885	0.00655142
$78$	−12.3997	−1.40399
$79$	−11.6255	−1.30797	−0.653987	−	0.756506i	$-0.726905\pi$
$79$	−11.6255	−1.30797	−0.653987	+	0.756506i	$0.726905\pi$
$80$	2.83925	0.317437
$81$	−11.0997	−1.23330
$82$	−2.34419	−0.258873
$83$	2.71959	0.298514	0.149257	−	0.988798i	$-0.452312\pi$
$83$	2.71959	0.298514	0.149257	+	0.988798i	$0.452312\pi$
$84$	2.86400	0.312488
$85$	15.7638	1.70982
$86$	−9.94000	−1.07186
$87$	−12.1016	−1.29743
$88$	−0.0407054	−0.00433921
$89$	10.3146	1.09335	0.546673	−	0.837346i	$-0.315894\pi$
$89$	10.3146	1.09335	0.546673	+	0.837346i	$0.315894\pi$
$90$	3.15817	0.332901
$91$	−8.63564	−0.905261
$92$	−1.68818	−0.176005
$93$	−14.5995	−1.51390
$94$	5.35306	0.552126
$95$	−17.4390	−1.78921
$96$	−2.02789	−0.206970
$97$	−8.43980	−0.856932	−0.428466	−	0.903558i	$-0.640946\pi$
$97$	−8.43980	−0.856932	−0.428466	+	0.903558i	$0.640946\pi$
$98$	−5.00539	−0.505621
$99$	−0.0452778	−0.00455059
$100$	3.06132	0.306132
$101$	14.8473	1.47736	0.738679	−	0.674057i	$-0.235450\pi$
$101$	14.8473	1.47736	0.738679	+	0.674057i	$0.235450\pi$
$102$	−11.2590	−1.11481
$103$	2.03701	0.200713	0.100356	−	0.994952i	$-0.468002\pi$
$103$	2.03701	0.200713	0.100356	+	0.994952i	$0.468002\pi$
$104$	6.11457	0.599583
$105$	8.13159	0.793562
$106$	−1.71195	−0.166279
$107$	3.81128	0.368451	0.184225	−	0.982884i	$-0.441022\pi$
$107$	3.81128	0.368451	0.184225	+	0.982884i	$0.441022\pi$
$108$	3.82799	0.368348
$109$	9.96304	0.954286	0.477143	−	0.878826i	$-0.341672\pi$
$109$	9.96304	0.954286	0.477143	+	0.878826i	$0.341672\pi$
$110$	−0.115573	−0.0110194
$111$	2.17118	0.206079
$112$	−1.41231	−0.133450
$113$	9.24167	0.869383	0.434692	−	0.900579i	$-0.356857\pi$
$113$	9.24167	0.869383	0.434692	+	0.900579i	$0.356857\pi$
$114$	12.4556	1.16657
$115$	−4.79316	−0.446965
$116$	5.96760	0.554078
$117$	6.80141	0.628790
$118$	10.9295	1.00614
$119$	−7.84125	−0.718806
$120$	−5.75767	−0.525601
$121$	−10.9983	−0.999849
$122$	−3.72128	−0.336909
$123$	4.75376	0.428632
$124$	7.19936	0.646522
$125$	−5.50438	−0.492327
$126$	−1.57095	−0.139951
$127$	−19.1085	−1.69560	−0.847802	−	0.530313i	$-0.822074\pi$
$127$	−19.1085	−1.69560	−0.847802	+	0.530313i	$0.822074\pi$
$128$	1.00000	0.0883883
$129$	20.1572	1.77474
$130$	17.3608	1.52264
$131$	9.60256	0.838979	0.419490	−	0.907760i	$-0.362209\pi$
$131$	9.60256	0.838979	0.419490	+	0.907760i	$0.362209\pi$
$132$	0.0825460	0.00718471
$133$	8.67456	0.752180
$134$	−2.34760	−0.202802
$135$	10.8686	0.935420
$136$	5.55209	0.476088
$137$	−9.63910	−0.823524	−0.411762	−	0.911291i	$-0.635087\pi$
$137$	−9.63910	−0.823524	−0.411762	+	0.911291i	$0.635087\pi$
$138$	3.42344	0.291423
$139$	11.5766	0.981914	0.490957	−	0.871184i	$-0.336647\pi$
$139$	11.5766	0.981914	0.490957	+	0.871184i	$0.336647\pi$
$140$	−4.00988	−0.338897
$141$	−10.8554	−0.914190
$142$	0.0610912	0.00512666
$143$	−0.248896	−0.0208137
$144$	1.11233	0.0926940
$145$	16.9435	1.40708
$146$	12.6800	1.04940
$147$	10.1504	0.837189
$148$	−1.07066	−0.0880078
$149$	−4.50246	−0.368856	−0.184428	−	0.982846i	$-0.559043\pi$
$149$	−4.50246	−0.368856	−0.184428	+	0.982846i	$0.559043\pi$
$150$	−6.20802	−0.506882
$151$	19.4497	1.58279	0.791395	−	0.611305i	$-0.209355\pi$
$151$	19.4497	1.58279	0.791395	+	0.611305i	$0.209355\pi$
$152$	−6.14213	−0.498193
$153$	6.17574	0.499279
$154$	0.0574885	0.00463255
$155$	20.4408	1.64184
$156$	−12.3997	−0.992768
$157$	−9.01867	−0.719768	−0.359884	−	0.932997i	$-0.617184\pi$
$157$	−9.01867	−0.719768	−0.359884	+	0.932997i	$0.617184\pi$
$158$	−11.6255	−0.924878
$159$	3.47163	0.275318
$160$	2.83925	0.224462
$161$	2.38423	0.187903
$162$	−11.0997	−0.872076
$163$	10.9562	0.858153	0.429076	−	0.903268i	$-0.358839\pi$
$163$	10.9562	0.858153	0.429076	+	0.903268i	$0.358839\pi$
$164$	−2.34419	−0.183051
$165$	0.234369	0.0182456
$166$	2.71959	0.211081
$167$	9.97514	0.771900	0.385950	−	0.922520i	$-0.373874\pi$
$167$	9.97514	0.771900	0.385950	+	0.922520i	$0.373874\pi$
$168$	2.86400	0.220962
$169$	24.3880	1.87600
$170$	15.7638	1.20902
$171$	−6.83206	−0.522461
$172$	−9.94000	−0.757918
$173$	2.17460	0.165332	0.0826658	−	0.996577i	$-0.473657\pi$
$173$	2.17460	0.165332	0.0826658	+	0.996577i	$0.473657\pi$
$174$	−12.1016	−0.917422
$175$	−4.32352	−0.326827
$176$	−0.0407054	−0.00306829
$177$	−22.1638	−1.66593
$178$	10.3146	0.773112
$179$	0.814626	0.0608880	0.0304440	−	0.999536i	$-0.490308\pi$
$179$	0.814626	0.0608880	0.0304440	+	0.999536i	$0.490308\pi$
$180$	3.15817	0.235396
$181$	7.36323	0.547305	0.273652	−	0.961829i	$-0.411768\pi$
$181$	7.36323	0.547305	0.273652	+	0.961829i	$0.411768\pi$
$182$	−8.63564	−0.640116
$183$	7.54634	0.557841
$184$	−1.68818	−0.124454
$185$	−3.03987	−0.223496
$186$	−14.5995	−1.07049
$187$	−0.226000	−0.0165268
$188$	5.35306	0.390412
$189$	−5.40629	−0.393249
$190$	−17.4390	−1.26516
$191$	−11.4620	−0.829362	−0.414681	−	0.909967i	$-0.636107\pi$
$191$	−11.4620	−0.829362	−0.414681	+	0.909967i	$0.636107\pi$
$192$	−2.02789	−0.146350
$193$	0.178021	0.0128142	0.00640712	−	0.999979i	$-0.497961\pi$
$193$	0.178021	0.0128142	0.00640712	+	0.999979i	$0.497961\pi$
$194$	−8.43980	−0.605942
$195$	−35.2057	−2.52113
$196$	−5.00539	−0.357528
$197$	−1.82439	−0.129982	−0.0649911	−	0.997886i	$-0.520702\pi$
$197$	−1.82439	−0.129982	−0.0649911	+	0.997886i	$0.520702\pi$
$198$	−0.0452778	−0.00321775
$199$	15.8259	1.12187	0.560936	−	0.827859i	$-0.310442\pi$
$199$	15.8259	1.12187	0.560936	+	0.827859i	$0.310442\pi$
$200$	3.06132	0.216468
$201$	4.76067	0.335792
$202$	14.8473	1.04465
$203$	−8.42808	−0.591535
$204$	−11.2590	−0.788289
$205$	−6.65574	−0.464857
$206$	2.03701	0.141925
$207$	−1.87781	−0.130517
$208$	6.11457	0.423969
$209$	0.250018	0.0172941
$210$	8.13159	0.561133
$211$	−9.77325	−0.672818	−0.336409	−	0.941716i	$-0.609212\pi$
$211$	−9.77325	−0.672818	−0.336409	+	0.941716i	$0.609212\pi$
$212$	−1.71195	−0.117577
$213$	−0.123886	−0.00848853
$214$	3.81128	0.260534
$215$	−28.2221	−1.92473
$216$	3.82799	0.260462
$217$	−10.1677	−0.690228
$218$	9.96304	0.674782
$219$	−25.7136	−1.73756
$220$	−0.115573	−0.00779191
$221$	33.9487	2.28363
$222$	2.17118	0.145720
$223$	−16.5519	−1.10840	−0.554199	−	0.832384i	$-0.686975\pi$
$223$	−16.5519	−1.10840	−0.554199	+	0.832384i	$0.686975\pi$
$224$	−1.41231	−0.0943636
$225$	3.40519	0.227013
$226$	9.24167	0.614747
$227$	−28.1704	−1.86974	−0.934868	−	0.354995i	$-0.884483\pi$
$227$	−28.1704	−1.86974	−0.934868	+	0.354995i	$0.884483\pi$
$228$	12.4556	0.824889
$229$	−6.53899	−0.432109	−0.216054	−	0.976381i	$-0.569319\pi$
$229$	−6.53899	−0.432109	−0.216054	+	0.976381i	$0.569319\pi$
$230$	−4.79316	−0.316052
$231$	−0.116580	−0.00767041
$232$	5.96760	0.391792
$233$	−8.93097	−0.585087	−0.292544	−	0.956252i	$-0.594502\pi$
$233$	−8.93097	−0.585087	−0.292544	+	0.956252i	$0.594502\pi$
$234$	6.80141	0.444622
$235$	15.1987	0.991452
$236$	10.9295	0.711449
$237$	23.5753	1.53138
$238$	−7.84125	−0.508273
$239$	24.5704	1.58933	0.794664	−	0.607049i	$-0.207647\pi$
$239$	24.5704	1.58933	0.794664	+	0.607049i	$0.207647\pi$
$240$	−5.75767	−0.371656
$241$	15.2522	0.982483	0.491241	−	0.871024i	$-0.336543\pi$
$241$	15.2522	0.982483	0.491241	+	0.871024i	$0.336543\pi$
$242$	−10.9983	−0.707000
$243$	11.0250	0.707254
$244$	−3.72128	−0.238231
$245$	−14.2115	−0.907943
$246$	4.75376	0.303089
$247$	−37.5565	−2.38966
$248$	7.19936	0.457160
$249$	−5.51503	−0.349501
$250$	−5.50438	−0.348128
$251$	−25.4092	−1.60381	−0.801906	−	0.597450i	$-0.796181\pi$
$251$	−25.4092	−1.60381	−0.801906	+	0.597450i	$0.796181\pi$
$252$	−1.57095	−0.0989603
$253$	0.0687182	0.00432027
$254$	−19.1085	−1.19897
$255$	−31.9671	−2.00186
$256$	1.00000	0.0625000
$257$	22.3239	1.39253	0.696264	−	0.717785i	$-0.254844\pi$
$257$	22.3239	1.39253	0.696264	+	0.717785i	$0.254844\pi$
$258$	20.1572	1.25493
$259$	1.51210	0.0939573
$260$	17.3608	1.07667
$261$	6.63793	0.410877
$262$	9.60256	0.593248
$263$	26.3253	1.62329	0.811644	−	0.584153i	$-0.198573\pi$
$263$	26.3253	1.62329	0.811644	+	0.584153i	$0.198573\pi$
$264$	0.0825460	0.00508036
$265$	−4.86064	−0.298587
$266$	8.67456	0.531872
$267$	−20.9169	−1.28009
$268$	−2.34760	−0.143402
$269$	13.0043	0.792884	0.396442	−	0.918060i	$-0.370245\pi$
$269$	13.0043	0.792884	0.396442	+	0.918060i	$0.370245\pi$
$270$	10.8686	0.661442
$271$	21.8702	1.32852	0.664260	−	0.747502i	$-0.268747\pi$
$271$	21.8702	1.32852	0.664260	+	0.747502i	$0.268747\pi$
$272$	5.55209	0.336645
$273$	17.5121	1.05988
$274$	−9.63910	−0.582320
$275$	−0.124612	−0.00751441
$276$	3.42344	0.206067
$277$	−0.863110	−0.0518592	−0.0259296	−	0.999664i	$-0.508255\pi$
$277$	−0.863110	−0.0518592	−0.0259296	+	0.999664i	$0.508255\pi$
$278$	11.5766	0.694318
$279$	8.00805	0.479429
$280$	−4.00988	−0.239636
$281$	14.8900	0.888262	0.444131	−	0.895962i	$-0.353512\pi$
$281$	14.8900	0.888262	0.444131	+	0.895962i	$0.353512\pi$
$282$	−10.8554	−0.646430
$283$	11.1983	0.665670	0.332835	−	0.942985i	$-0.391995\pi$
$283$	11.1983	0.665670	0.332835	+	0.942985i	$0.391995\pi$
$284$	0.0610912	0.00362509
$285$	35.3644	2.09481
$286$	−0.248896	−0.0147175
$287$	3.31072	0.195425
$288$	1.11233	0.0655445
$289$	13.8257	0.813277
$290$	16.9435	0.994956
$291$	17.1150	1.00330
$292$	12.6800	0.742039
$293$	23.1571	1.35285	0.676425	−	0.736511i	$-0.263528\pi$
$293$	23.1571	1.35285	0.676425	+	0.736511i	$0.263528\pi$
$294$	10.1504	0.591982
$295$	31.0315	1.80672
$296$	−1.07066	−0.0622309
$297$	−0.155820	−0.00904159
$298$	−4.50246	−0.260821
$299$	−10.3225	−0.596966
$300$	−6.20802	−0.358420
$301$	14.0383	0.809155
$302$	19.4497	1.11920
$303$	−30.1086	−1.72969
$304$	−6.14213	−0.352275
$305$	−10.5656	−0.604986
$306$	6.17574	0.353044
$307$	16.6980	0.953008	0.476504	−	0.879172i	$-0.341904\pi$
$307$	16.6980	0.953008	0.476504	+	0.879172i	$0.341904\pi$
$308$	0.0574885	0.00327571
$309$	−4.13083	−0.234995
$310$	20.4408	1.16096
$311$	8.18331	0.464033	0.232016	−	0.972712i	$-0.425468\pi$
$311$	8.18331	0.464033	0.232016	+	0.972712i	$0.425468\pi$
$312$	−12.3997	−0.701993
$313$	0.488370	0.0276043	0.0138022	−	0.999905i	$-0.495606\pi$
$313$	0.488370	0.0276043	0.0138022	+	0.999905i	$0.495606\pi$
$314$	−9.01867	−0.508953
$315$	−4.46030	−0.251310
$316$	−11.6255	−0.653987
$317$	15.3546	0.862398	0.431199	−	0.902257i	$-0.358091\pi$
$317$	15.3546	0.862398	0.431199	+	0.902257i	$0.358091\pi$
$318$	3.47163	0.194680
$319$	−0.242914	−0.0136006
$320$	2.83925	0.158719
$321$	−7.72885	−0.431383
$322$	2.38423	0.132868
$323$	−34.1017	−1.89747
$324$	−11.0997	−0.616651
$325$	18.7187	1.03833
$326$	10.9562	0.606806
$327$	−20.2039	−1.11728
$328$	−2.34419	−0.129436
$329$	−7.56016	−0.416805
$330$	0.234369	0.0129016
$331$	−15.7778	−0.867225	−0.433612	−	0.901099i	$-0.642761\pi$
$331$	−15.7778	−0.867225	−0.433612	+	0.901099i	$0.642761\pi$
$332$	2.71959	0.149257
$333$	−1.19093	−0.0652623
$334$	9.97514	0.545815
$335$	−6.66541	−0.364170
$336$	2.86400	0.156244
$337$	−34.4602	−1.87717	−0.938583	−	0.345054i	$-0.887861\pi$
$337$	−34.4602	−1.87717	−0.938583	+	0.345054i	$0.887861\pi$
$338$	24.3880	1.32653
$339$	−18.7411	−1.01788
$340$	15.7638	0.854910
$341$	−0.293053	−0.0158697
$342$	−6.83206	−0.369436
$343$	16.9553	0.915499
$344$	−9.94000	−0.535929
$345$	9.72000	0.523307
$346$	2.17460	0.116907
$347$	−19.1859	−1.02995	−0.514977	−	0.857204i	$-0.672199\pi$
$347$	−19.1859	−1.02995	−0.514977	+	0.857204i	$0.672199\pi$
$348$	−12.1016	−0.648715
$349$	−12.8355	−0.687070	−0.343535	−	0.939140i	$-0.611624\pi$
$349$	−12.8355	−0.687070	−0.343535	+	0.939140i	$0.611624\pi$
$350$	−4.32352	−0.231102
$351$	23.4065	1.24935
$352$	−0.0407054	−0.00216961
$353$	1.25440	0.0667651	0.0333825	−	0.999443i	$-0.489372\pi$
$353$	1.25440	0.0667651	0.0333825	+	0.999443i	$0.489372\pi$
$354$	−22.1638	−1.17799
$355$	0.173453	0.00920593
$356$	10.3146	0.546673
$357$	15.9012	0.841579
$358$	0.814626	0.0430543
$359$	22.9849	1.21310	0.606548	−	0.795047i	$-0.292554\pi$
$359$	22.9849	1.21310	0.606548	+	0.795047i	$0.292554\pi$
$360$	3.15817	0.166450
$361$	18.7258	0.985568
$362$	7.36323	0.387003
$363$	22.3034	1.17063
$364$	−8.63564	−0.452631
$365$	36.0016	1.88441
$366$	7.54634	0.394453
$367$	−13.2593	−0.692131	−0.346066	−	0.938210i	$-0.612483\pi$
$367$	−13.2593	−0.692131	−0.346066	+	0.938210i	$0.612483\pi$
$368$	−1.68818	−0.0880026
$369$	−2.60751	−0.135742
$370$	−3.03987	−0.158035
$371$	2.41779	0.125525
$372$	−14.5995	−0.756949
$373$	−17.0578	−0.883222	−0.441611	−	0.897207i	$-0.645593\pi$
$373$	−17.0578	−0.883222	−0.441611	+	0.897207i	$0.645593\pi$
$374$	−0.226000	−0.0116862
$375$	11.1623	0.576417
$376$	5.35306	0.276063
$377$	36.4893	1.87930
$378$	−5.40629	−0.278069
$379$	−29.5552	−1.51815	−0.759075	−	0.651003i	$-0.774349\pi$
$379$	−29.5552	−1.51815	−0.759075	+	0.651003i	$0.774349\pi$
$380$	−17.4390	−0.894603
$381$	38.7499	1.98522
$382$	−11.4620	−0.586447
$383$	8.35180	0.426757	0.213379	−	0.976970i	$-0.431553\pi$
$383$	8.35180	0.426757	0.213379	+	0.976970i	$0.431553\pi$
$384$	−2.02789	−0.103485
$385$	0.163224	0.00831866
$386$	0.178021	0.00906103
$387$	−11.0565	−0.562035
$388$	−8.43980	−0.428466
$389$	29.5053	1.49598	0.747989	−	0.663711i	$-0.231019\pi$
$389$	29.5053	1.49598	0.747989	+	0.663711i	$0.231019\pi$
$390$	−35.2057	−1.78271
$391$	−9.37294	−0.474010
$392$	−5.00539	−0.252811
$393$	−19.4729	−0.982278
$394$	−1.82439	−0.0919112
$395$	−33.0077	−1.66080
$396$	−0.0452778	−0.00227529
$397$	24.6661	1.23796	0.618978	−	0.785409i	$-0.287547\pi$
$397$	24.6661	1.23796	0.618978	+	0.785409i	$0.287547\pi$
$398$	15.8259	0.793283
$399$	−17.5910	−0.880654
$400$	3.06132	0.153066
$401$	−5.31012	−0.265175	−0.132587	−	0.991171i	$-0.542328\pi$
$401$	−5.31012	−0.265175	−0.132587	+	0.991171i	$0.542328\pi$
$402$	4.76067	0.237441
$403$	44.0210	2.19284
$404$	14.8473	0.738679
$405$	−31.5148	−1.56598
$406$	−8.42808	−0.418278
$407$	0.0435817	0.00216026
$408$	−11.2590	−0.557404
$409$	−17.5631	−0.868438	−0.434219	−	0.900807i	$-0.642976\pi$
$409$	−17.5631	−0.868438	−0.434219	+	0.900807i	$0.642976\pi$
$410$	−6.65574	−0.328704
$411$	19.5470	0.964183
$412$	2.03701	0.100356
$413$	−15.4358	−0.759545
$414$	−1.87781	−0.0922894
$415$	7.72160	0.379038
$416$	6.11457	0.299792
$417$	−23.4760	−1.14963
$418$	0.250018	0.0122288
$419$	36.2147	1.76921	0.884603	−	0.466345i	$-0.154430\pi$
$419$	36.2147	1.76921	0.884603	+	0.466345i	$0.154430\pi$
$420$	8.13159	0.396781
$421$	−28.5926	−1.39352	−0.696759	−	0.717306i	$-0.745375\pi$
$421$	−28.5926	−1.39352	−0.696759	+	0.717306i	$0.745375\pi$
$422$	−9.77325	−0.475754
$423$	5.95436	0.289511
$424$	−1.71195	−0.0831395
$425$	16.9967	0.824463
$426$	−0.123886	−0.00600230
$427$	5.25558	0.254335
$428$	3.81128	0.184225
$429$	0.504734	0.0243688
$430$	−28.2221	−1.36099
$431$	−11.6924	−0.563201	−0.281601	−	0.959532i	$-0.590865\pi$
$431$	−11.6924	−0.563201	−0.281601	+	0.959532i	$0.590865\pi$
$432$	3.82799	0.184174
$433$	−20.1696	−0.969289	−0.484644	−	0.874711i	$-0.661051\pi$
$433$	−20.1696	−0.969289	−0.484644	+	0.874711i	$0.661051\pi$
$434$	−10.1677	−0.488065
$435$	−34.3595	−1.64741
$436$	9.96304	0.477143
$437$	10.3690	0.496018
$438$	−25.7136	−1.22864
$439$	6.58028	0.314059	0.157030	−	0.987594i	$-0.449808\pi$
$439$	6.58028	0.314059	0.157030	+	0.987594i	$0.449808\pi$
$440$	−0.115573	−0.00550971
$441$	−5.56764	−0.265126
$442$	33.9487	1.61477
$443$	9.46662	0.449773	0.224886	−	0.974385i	$-0.427799\pi$
$443$	9.46662	0.449773	0.224886	+	0.974385i	$0.427799\pi$
$444$	2.17118	0.103040
$445$	29.2857	1.38828
$446$	−16.5519	−0.783755
$447$	9.13048	0.431857
$448$	−1.41231	−0.0667251
$449$	12.5120	0.590477	0.295239	−	0.955424i	$-0.404601\pi$
$449$	12.5120	0.590477	0.295239	+	0.955424i	$0.404601\pi$
$450$	3.40519	0.160522
$451$	0.0954214	0.00449322
$452$	9.24167	0.434692
$453$	−39.4417	−1.85313
$454$	−28.1704	−1.32210
$455$	−24.5187	−1.14946
$456$	12.4556	0.583285
$457$	13.9357	0.651884	0.325942	−	0.945390i	$-0.394319\pi$
$457$	13.9357	0.651884	0.325942	+	0.945390i	$0.394319\pi$
$458$	−6.53899	−0.305547
$459$	21.2533	0.992021
$460$	−4.79316	−0.223482
$461$	−0.410171	−0.0191036	−0.00955179	−	0.999954i	$-0.503040\pi$
$461$	−0.410171	−0.0191036	−0.00955179	+	0.999954i	$0.503040\pi$
$462$	−0.116580	−0.00542380
$463$	19.6099	0.911351	0.455675	−	0.890146i	$-0.349398\pi$
$463$	19.6099	0.911351	0.455675	+	0.890146i	$0.349398\pi$
$464$	5.96760	0.277039
$465$	−41.4516	−1.92227
$466$	−8.93097	−0.413719
$467$	35.9645	1.66424	0.832119	−	0.554597i	$-0.187128\pi$
$467$	35.9645	1.66424	0.832119	+	0.554597i	$0.187128\pi$
$468$	6.80141	0.314395
$469$	3.31553	0.153097
$470$	15.1987	0.701062
$471$	18.2888	0.842705
$472$	10.9295	0.503071
$473$	0.404612	0.0186041
$474$	23.5753	1.08285
$475$	−18.8030	−0.862743
$476$	−7.84125	−0.359403
$477$	−1.90424	−0.0871894
$478$	24.5704	1.12383
$479$	19.6321	0.897013	0.448506	−	0.893780i	$-0.351956\pi$
$479$	19.6321	0.897013	0.448506	+	0.893780i	$0.351956\pi$
$480$	−5.75767	−0.262801
$481$	−6.54663	−0.298501
$482$	15.2522	0.694720
$483$	−4.83495	−0.219998
$484$	−10.9983	−0.499925
$485$	−23.9627	−1.08809
$486$	11.0250	0.500104
$487$	−1.02112	−0.0462714	−0.0231357	−	0.999732i	$-0.507365\pi$
$487$	−1.02112	−0.0462714	−0.0231357	+	0.999732i	$0.507365\pi$
$488$	−3.72128	−0.168454
$489$	−22.2179	−1.00473
$490$	−14.2115	−0.642012
$491$	−4.11076	−0.185516	−0.0927579	−	0.995689i	$-0.529568\pi$
$491$	−4.11076	−0.185516	−0.0927579	+	0.995689i	$0.529568\pi$
$492$	4.75376	0.214316
$493$	33.1327	1.49222
$494$	−37.5565	−1.68975
$495$	−0.128555	−0.00577811
$496$	7.19936	0.323261
$497$	−0.0862794	−0.00387016
$498$	−5.51503	−0.247134
$499$	38.5914	1.72759	0.863795	−	0.503843i	$-0.168081\pi$
$499$	38.5914	1.72759	0.863795	+	0.503843i	$0.168081\pi$
$500$	−5.50438	−0.246164
$501$	−20.2285	−0.903741
$502$	−25.4092	−1.13407
$503$	13.7542	0.613269	0.306634	−	0.951827i	$-0.400797\pi$
$503$	13.7542	0.613269	0.306634	+	0.951827i	$0.400797\pi$
$504$	−1.57095	−0.0699755
$505$	42.1550	1.87588
$506$	0.0687182	0.00305489
$507$	−49.4561	−2.19642
$508$	−19.1085	−0.847802
$509$	−22.7517	−1.00845	−0.504225	−	0.863572i	$-0.668222\pi$
$509$	−22.7517	−1.00845	−0.504225	+	0.863572i	$0.668222\pi$
$510$	−31.9671	−1.41553
$511$	−17.9080	−0.792203
$512$	1.00000	0.0441942
$513$	−23.5120	−1.03808
$514$	22.3239	0.984666
$515$	5.78358	0.254855
$516$	20.1572	0.887371
$517$	−0.217899	−0.00958317
$518$	1.51210	0.0664378
$519$	−4.40984	−0.193570
$520$	17.3608	0.761320
$521$	−36.4519	−1.59699	−0.798494	−	0.602003i	$-0.794369\pi$
$521$	−36.4519	−1.59699	−0.798494	+	0.602003i	$0.794369\pi$
$522$	6.63793	0.290534
$523$	−23.3274	−1.02004	−0.510018	−	0.860164i	$-0.670361\pi$
$523$	−23.3274	−1.02004	−0.510018	+	0.860164i	$0.670361\pi$
$524$	9.60256	0.419490
$525$	8.76761	0.382650
$526$	26.3253	1.14784
$527$	39.9715	1.74119
$528$	0.0825460	0.00359235
$529$	−20.1500	−0.876089
$530$	−4.86064	−0.211133
$531$	12.1572	0.527576
$532$	8.67456	0.376090
$533$	−14.3337	−0.620863
$534$	−20.9169	−0.905161
$535$	10.8212	0.467840
$536$	−2.34760	−0.101401
$537$	−1.65197	−0.0712877
$538$	13.0043	0.560654
$539$	0.203747	0.00877599
$540$	10.8686	0.467710
$541$	−17.9935	−0.773603	−0.386802	−	0.922163i	$-0.626420\pi$
$541$	−17.9935	−0.773603	−0.386802	+	0.922163i	$0.626420\pi$
$542$	21.8702	0.939406
$543$	−14.9318	−0.640785
$544$	5.55209	0.238044
$545$	28.2875	1.21170
$546$	17.5121	0.749449
$547$	2.72117	0.116349	0.0581743	−	0.998306i	$-0.481472\pi$
$547$	2.72117	0.116349	0.0581743	+	0.998306i	$0.481472\pi$
$548$	−9.63910	−0.411762
$549$	−4.13928	−0.176660
$550$	−0.124612	−0.00531349
$551$	−36.6538	−1.56150
$552$	3.42344	0.145711
$553$	16.4188	0.698198
$554$	−0.863110	−0.0366700
$555$	6.16451	0.261669
$556$	11.5766	0.490957
$557$	−15.6939	−0.664972	−0.332486	−	0.943108i	$-0.607887\pi$
$557$	−15.6939	−0.664972	−0.332486	+	0.943108i	$0.607887\pi$
$558$	8.00805	0.339008
$559$	−60.7788	−2.57067
$560$	−4.00988	−0.169448
$561$	0.458303	0.0193496
$562$	14.8900	0.628096
$563$	10.0388	0.423083	0.211542	−	0.977369i	$-0.432152\pi$
$563$	10.0388	0.423083	0.211542	+	0.977369i	$0.432152\pi$
$564$	−10.8554	−0.457095
$565$	26.2394	1.10390
$566$	11.1983	0.470700
$567$	15.6762	0.658338
$568$	0.0610912	0.00256333
$569$	−29.5542	−1.23898	−0.619488	−	0.785006i	$-0.712660\pi$
$569$	−29.5542	−1.23898	−0.619488	+	0.785006i	$0.712660\pi$
$570$	35.3644	1.48125
$571$	−41.0552	−1.71810	−0.859052	−	0.511888i	$-0.828946\pi$
$571$	−41.0552	−1.71810	−0.859052	+	0.511888i	$0.828946\pi$
$572$	−0.248896	−0.0104069
$573$	23.2437	0.971018
$574$	3.31072	0.138187
$575$	−5.16807	−0.215523
$576$	1.11233	0.0463470
$577$	2.56935	0.106964	0.0534818	−	0.998569i	$-0.482968\pi$
$577$	2.56935	0.106964	0.0534818	+	0.998569i	$0.482968\pi$
$578$	13.8257	0.575074
$579$	−0.361007	−0.0150029
$580$	16.9435	0.703540
$581$	−3.84090	−0.159347
$582$	17.1150	0.709438
$583$	0.0696855	0.00288608
$584$	12.6800	0.524701
$585$	19.3109	0.798406
$586$	23.1571	0.956610
$587$	9.11252	0.376114	0.188057	−	0.982158i	$-0.439781\pi$
$587$	9.11252	0.376114	0.188057	+	0.982158i	$0.439781\pi$
$588$	10.1504	0.418594
$589$	−44.2194	−1.82203
$590$	31.0315	1.27755
$591$	3.69965	0.152183
$592$	−1.07066	−0.0440039
$593$	−21.8108	−0.895664	−0.447832	−	0.894118i	$-0.647804\pi$
$593$	−21.8108	−0.895664	−0.447832	+	0.894118i	$0.647804\pi$
$594$	−0.155820	−0.00639337
$595$	−22.2632	−0.912704
$596$	−4.50246	−0.184428
$597$	−32.0932	−1.31349
$598$	−10.3225	−0.422119
$599$	−16.4444	−0.671900	−0.335950	−	0.941880i	$-0.609057\pi$
$599$	−16.4444	−0.671900	−0.335950	+	0.941880i	$0.609057\pi$
$600$	−6.20802	−0.253441
$601$	40.2685	1.64259	0.821293	−	0.570507i	$-0.193253\pi$
$601$	40.2685	1.64259	0.821293	+	0.570507i	$0.193253\pi$
$602$	14.0383	0.572159
$603$	−2.61130	−0.106340
$604$	19.4497	0.791395
$605$	−31.2270	−1.26956
$606$	−30.1086	−1.22308
$607$	2.29527	0.0931621	0.0465810	−	0.998915i	$-0.485167\pi$
$607$	2.29527	0.0931621	0.0465810	+	0.998915i	$0.485167\pi$
$608$	−6.14213	−0.249096
$609$	17.0912	0.692570
$610$	−10.5656	−0.427790
$611$	32.7317	1.32418
$612$	6.17574	0.249640
$613$	9.18950	0.371161	0.185580	−	0.982629i	$-0.440584\pi$
$613$	9.18950	0.371161	0.185580	+	0.982629i	$0.440584\pi$
$614$	16.6980	0.673878
$615$	13.4971	0.544255
$616$	0.0574885	0.00231628
$617$	27.7932	1.11891	0.559457	−	0.828860i	$-0.311010\pi$
$617$	27.7932	1.11891	0.559457	+	0.828860i	$0.311010\pi$
$618$	−4.13083	−0.166166
$619$	25.8124	1.03749	0.518744	−	0.854929i	$-0.326400\pi$
$619$	25.8124	1.03749	0.518744	+	0.854929i	$0.326400\pi$
$620$	20.4408	0.820921
$621$	−6.46234	−0.259325
$622$	8.18331	0.328121
$623$	−14.5674	−0.583629
$624$	−12.3997	−0.496384
$625$	−30.9349	−1.23740
$626$	0.488370	0.0195192
$627$	−0.507009	−0.0202480
$628$	−9.01867	−0.359884
$629$	−5.94441	−0.237019
$630$	−4.46030	−0.177703
$631$	−28.3790	−1.12975	−0.564876	−	0.825176i	$-0.691076\pi$
$631$	−28.3790	−1.12975	−0.564876	+	0.825176i	$0.691076\pi$
$632$	−11.6255	−0.462439
$633$	19.8190	0.787736
$634$	15.3546	0.609808
$635$	−54.2537	−2.15299
$636$	3.47163	0.137659
$637$	−30.6058	−1.21265
$638$	−0.242914	−0.00961705
$639$	0.0679534	0.00268819
$640$	2.83925	0.112231
$641$	−27.8738	−1.10095	−0.550474	−	0.834853i	$-0.685553\pi$
$641$	−27.8738	−1.10095	−0.550474	+	0.834853i	$0.685553\pi$
$642$	−7.72885	−0.305034
$643$	18.9276	0.746434	0.373217	−	0.927744i	$-0.378255\pi$
$643$	18.9276	0.746434	0.373217	+	0.927744i	$0.378255\pi$
$644$	2.38423	0.0939517
$645$	57.2313	2.25348
$646$	−34.1017	−1.34171
$647$	−1.94302	−0.0763882	−0.0381941	−	0.999270i	$-0.512161\pi$
$647$	−1.94302	−0.0763882	−0.0381941	+	0.999270i	$0.512161\pi$
$648$	−11.0997	−0.436038
$649$	−0.444890	−0.0174634
$650$	18.7187	0.734207
$651$	20.6189	0.808120
$652$	10.9562	0.429076
$653$	11.6280	0.455039	0.227519	−	0.973774i	$-0.426938\pi$
$653$	11.6280	0.455039	0.227519	+	0.973774i	$0.426938\pi$
$654$	−20.2039	−0.790036
$655$	27.2640	1.06529
$656$	−2.34419	−0.0915253
$657$	14.1043	0.550260
$658$	−7.56016	−0.294726
$659$	−16.9509	−0.660315	−0.330158	−	0.943926i	$-0.607102\pi$
$659$	−16.9509	−0.660315	−0.330158	+	0.943926i	$0.607102\pi$
$660$	0.234369	0.00912278
$661$	−12.1596	−0.472954	−0.236477	−	0.971637i	$-0.575993\pi$
$661$	−12.1596	−0.472954	−0.236477	+	0.971637i	$0.575993\pi$
$662$	−15.7778	−0.613221
$663$	−68.8441	−2.67368
$664$	2.71959	0.105541
$665$	24.6292	0.955081
$666$	−1.19093	−0.0461474
$667$	−10.0744	−0.390082
$668$	9.97514	0.385950
$669$	33.5654	1.29771
$670$	−6.66541	−0.257507
$671$	0.151476	0.00584768
$672$	2.86400	0.110481
$673$	17.9237	0.690907	0.345454	−	0.938436i	$-0.387725\pi$
$673$	17.9237	0.690907	0.345454	+	0.938436i	$0.387725\pi$
$674$	−34.4602	−1.32736
$675$	11.7187	0.451053
$676$	24.3880	0.937999
$677$	40.8121	1.56854	0.784269	−	0.620421i	$-0.213038\pi$
$677$	40.8121	1.56854	0.784269	+	0.620421i	$0.213038\pi$
$678$	−18.7411	−0.719747
$679$	11.9196	0.457431
$680$	15.7638	0.604512
$681$	57.1264	2.18909
$682$	−0.293053	−0.0112216
$683$	2.77685	0.106253	0.0531267	−	0.998588i	$-0.483081\pi$
$683$	2.77685	0.106253	0.0531267	+	0.998588i	$0.483081\pi$
$684$	−6.83206	−0.261230
$685$	−27.3678	−1.04567
$686$	16.9553	0.647356
$687$	13.2603	0.505913
$688$	−9.94000	−0.378959
$689$	−10.4678	−0.398792
$690$	9.72000	0.370034
$691$	−46.1037	−1.75387	−0.876934	−	0.480610i	$-0.840415\pi$
$691$	−46.1037	−1.75387	−0.876934	+	0.480610i	$0.840415\pi$
$692$	2.17460	0.0826658
$693$	0.0639460	0.00242911
$694$	−19.1859	−0.728287
$695$	32.8688	1.24679
$696$	−12.1016	−0.458711
$697$	−13.0152	−0.492985
$698$	−12.8355	−0.485832
$699$	18.1110	0.685021
$700$	−4.32352	−0.163414
$701$	−10.8095	−0.408269	−0.204134	−	0.978943i	$-0.565438\pi$
$701$	−10.8095	−0.408269	−0.204134	+	0.978943i	$0.565438\pi$
$702$	23.4065	0.883422
$703$	6.57614	0.248024
$704$	−0.0407054	−0.00153414
$705$	−30.8212	−1.16079
$706$	1.25440	0.0472100
$707$	−20.9689	−0.788616
$708$	−22.1638	−0.832966
$709$	−16.6193	−0.624149	−0.312075	−	0.950058i	$-0.601024\pi$
$709$	−16.6193	−0.624149	−0.312075	+	0.950058i	$0.601024\pi$
$710$	0.173453	0.00650957
$711$	−12.9314	−0.484965
$712$	10.3146	0.386556
$713$	−12.1538	−0.455165
$714$	15.9012	0.595086
$715$	−0.706678	−0.0264283
$716$	0.814626	0.0304440
$717$	−49.8261	−1.86079
$718$	22.9849	0.857789
$719$	−51.2398	−1.91092	−0.955461	−	0.295116i	$-0.904642\pi$
$719$	−51.2398	−1.91092	−0.955461	+	0.295116i	$0.904642\pi$
$720$	3.15817	0.117698
$721$	−2.87688	−0.107141
$722$	18.7258	0.696902
$723$	−30.9298	−1.15029
$724$	7.36323	0.273652
$725$	18.2688	0.678485
$726$	22.3034	0.827757
$727$	−0.804497	−0.0298371	−0.0149186	−	0.999889i	$-0.504749\pi$
$727$	−0.804497	−0.0298371	−0.0149186	+	0.999889i	$0.504749\pi$
$728$	−8.63564	−0.320058
$729$	10.9417	0.405247
$730$	36.0016	1.33248
$731$	−55.1878	−2.04119
$732$	7.54634	0.278921
$733$	−16.8227	−0.621361	−0.310681	−	0.950514i	$-0.600557\pi$
$733$	−16.8227	−0.621361	−0.310681	+	0.950514i	$0.600557\pi$
$734$	−13.2593	−0.489411
$735$	28.8194	1.06302
$736$	−1.68818	−0.0622272
$737$	0.0955600	0.00352000
$738$	−2.60751	−0.0959838
$739$	−29.3579	−1.07995	−0.539973	−	0.841682i	$-0.681566\pi$
$739$	−29.3579	−1.07995	−0.539973	+	0.841682i	$0.681566\pi$
$740$	−3.03987	−0.111748
$741$	76.1604	2.79782
$742$	2.41779	0.0887599
$743$	8.37296	0.307174	0.153587	−	0.988135i	$-0.450917\pi$
$743$	8.37296	0.307174	0.153587	+	0.988135i	$0.450917\pi$
$744$	−14.5995	−0.535244
$745$	−12.7836	−0.468355
$746$	−17.0578	−0.624532
$747$	3.02508	0.110682
$748$	−0.226000	−0.00826339
$749$	−5.38270	−0.196679
$750$	11.1623	0.407589
$751$	10.5603	0.385351	0.192675	−	0.981263i	$-0.438284\pi$
$751$	10.5603	0.385351	0.192675	+	0.981263i	$0.438284\pi$
$752$	5.35306	0.195206
$753$	51.5269	1.87775
$754$	36.4893	1.32886
$755$	55.2224	2.00975
$756$	−5.40629	−0.196625
$757$	18.2748	0.664207	0.332104	−	0.943243i	$-0.392242\pi$
$757$	18.2748	0.664207	0.332104	+	0.943243i	$0.392242\pi$
$758$	−29.5552	−1.07349
$759$	−0.139353	−0.00505818
$760$	−17.4390	−0.632580
$761$	−2.04083	−0.0739800	−0.0369900	−	0.999316i	$-0.511777\pi$
$761$	−2.04083	−0.0739800	−0.0369900	+	0.999316i	$0.511777\pi$
$762$	38.7499	1.40376
$763$	−14.0709	−0.509399
$764$	−11.4620	−0.414681
$765$	17.5345	0.633960
$766$	8.35180	0.301763
$767$	66.8291	2.41306
$768$	−2.02789	−0.0731751
$769$	−1.50744	−0.0543597	−0.0271799	−	0.999631i	$-0.508653\pi$
$769$	−1.50744	−0.0543597	−0.0271799	+	0.999631i	$0.508653\pi$
$770$	0.163224	0.00588218
$771$	−45.2704	−1.63037
$772$	0.178021	0.00640712
$773$	−30.0010	−1.07906	−0.539530	−	0.841966i	$-0.681398\pi$
$773$	−30.0010	−1.07906	−0.539530	+	0.841966i	$0.681398\pi$
$774$	−11.0565	−0.397419
$775$	22.0396	0.791685
$776$	−8.43980	−0.302971
$777$	−3.06637	−0.110005
$778$	29.5053	1.05782
$779$	14.3983	0.515874
$780$	−35.2057	−1.26057
$781$	−0.00248674	−8.89826e−5 0
$782$	−9.37294	−0.335176
$783$	22.8439	0.816375
$784$	−5.00539	−0.178764
$785$	−25.6062	−0.913925
$786$	−19.4729	−0.694575
$787$	−0.294142	−0.0104850	−0.00524251	−	0.999986i	$-0.501669\pi$
$787$	−0.294142	−0.0104850	−0.00524251	+	0.999986i	$0.501669\pi$
$788$	−1.82439	−0.0649911
$789$	−53.3847	−1.90055
$790$	−33.0077	−1.17436
$791$	−13.0521	−0.464078
$792$	−0.0452778	−0.00160888
$793$	−22.7540	−0.808019
$794$	24.6661	0.875366
$795$	9.85683	0.349586
$796$	15.8259	0.560936
$797$	−43.6552	−1.54635	−0.773174	−	0.634194i	$-0.781332\pi$
$797$	−43.6552	−1.54635	−0.773174	+	0.634194i	$0.781332\pi$
$798$	−17.5910	−0.622716
$799$	29.7207	1.05144
$800$	3.06132	0.108234
$801$	11.4732	0.405386
$802$	−5.31012	−0.187507
$803$	−0.516144	−0.0182143
$804$	4.76067	0.167896
$805$	6.76941	0.238590
$806$	44.0210	1.55057
$807$	−26.3712	−0.928310
$808$	14.8473	0.522325
$809$	−48.1960	−1.69448	−0.847240	−	0.531210i	$-0.821737\pi$
$809$	−48.1960	−1.69448	−0.847240	+	0.531210i	$0.821737\pi$
$810$	−31.5148	−1.10732
$811$	−28.4019	−0.997327	−0.498664	−	0.866796i	$-0.666176\pi$
$811$	−28.4019	−0.997327	−0.498664	+	0.866796i	$0.666176\pi$
$812$	−8.42808	−0.295768
$813$	−44.3503	−1.55543
$814$	0.0435817	0.00152754
$815$	31.1072	1.08964
$816$	−11.2590	−0.394144
$817$	61.0528	2.13597
$818$	−17.5631	−0.614078
$819$	−9.60566	−0.335649
$820$	−6.65574	−0.232429
$821$	32.6297	1.13878	0.569392	−	0.822066i	$-0.307179\pi$
$821$	32.6297	1.13878	0.569392	+	0.822066i	$0.307179\pi$
$822$	19.5470	0.681781
$823$	−20.1141	−0.701133	−0.350566	−	0.936538i	$-0.614011\pi$
$823$	−20.1141	−0.701133	−0.350566	+	0.936538i	$0.614011\pi$
$824$	2.03701	0.0709626
$825$	0.252700	0.00879788
$826$	−15.4358	−0.537079
$827$	−13.4882	−0.469032	−0.234516	−	0.972112i	$-0.575351\pi$
$827$	−13.4882	−0.469032	−0.234516	+	0.972112i	$0.575351\pi$
$828$	−1.87781	−0.0652584
$829$	−22.0461	−0.765694	−0.382847	−	0.923812i	$-0.625056\pi$
$829$	−22.0461	−0.765694	−0.382847	+	0.923812i	$0.625056\pi$
$830$	7.72160	0.268021
$831$	1.75029	0.0607169
$832$	6.11457	0.211985
$833$	−27.7904	−0.962880
$834$	−23.4760	−0.812909
$835$	28.3219	0.980119
$836$	0.250018	0.00864706
$837$	27.5591	0.952581
$838$	36.2147	1.25102
$839$	39.3109	1.35716	0.678582	−	0.734524i	$-0.262595\pi$
$839$	39.3109	1.35716	0.678582	+	0.734524i	$0.262595\pi$
$840$	8.13159	0.280567
$841$	6.61229	0.228010
$842$	−28.5926	−0.985366
$843$	−30.1952	−1.03998
$844$	−9.77325	−0.336409
$845$	69.2435	2.38205
$846$	5.95436	0.204715
$847$	15.5330	0.533721
$848$	−1.71195	−0.0587885
$849$	−22.7089	−0.779367
$850$	16.9967	0.582983
$851$	1.80747	0.0619593
$852$	−0.123886	−0.00424427
$853$	−20.8078	−0.712444	−0.356222	−	0.934401i	$-0.615935\pi$
$853$	−20.8078	−0.712444	−0.356222	+	0.934401i	$0.615935\pi$
$854$	5.25558	0.179842
$855$	−19.3979	−0.663395
$856$	3.81128	0.130267
$857$	−39.5280	−1.35025	−0.675125	−	0.737703i	$-0.735910\pi$
$857$	−39.5280	−1.35025	−0.675125	+	0.737703i	$0.735910\pi$
$858$	0.504734	0.0172313
$859$	28.3761	0.968180	0.484090	−	0.875018i	$-0.339151\pi$
$859$	28.3761	0.968180	0.484090	+	0.875018i	$0.339151\pi$
$860$	−28.2221	−0.962366
$861$	−6.71376	−0.228804
$862$	−11.6924	−0.398243
$863$	−24.1922	−0.823512	−0.411756	−	0.911294i	$-0.635084\pi$
$863$	−24.1922	−0.823512	−0.411756	+	0.911294i	$0.635084\pi$
$864$	3.82799	0.130231
$865$	6.17422	0.209930
$866$	−20.1696	−0.685391
$867$	−28.0370	−0.952186
$868$	−10.1677	−0.345114
$869$	0.473222	0.0160530
$870$	−34.3595	−1.16490
$871$	−14.3546	−0.486386
$872$	9.96304	0.337391
$873$	−9.38782	−0.317730
$874$	10.3690	0.350738
$875$	7.77387	0.262805
$876$	−25.7136	−0.868781
$877$	16.4148	0.554287	0.277144	−	0.960828i	$-0.410612\pi$
$877$	16.4148	0.554287	0.277144	+	0.960828i	$0.410612\pi$
$878$	6.58028	0.222074
$879$	−46.9599	−1.58392
$880$	−0.115573	−0.00389596
$881$	−21.9992	−0.741173	−0.370586	−	0.928798i	$-0.620843\pi$
$881$	−21.9992	−0.741173	−0.370586	+	0.928798i	$0.620843\pi$
$882$	−5.56764	−0.187472
$883$	6.76865	0.227783	0.113892	−	0.993493i	$-0.463668\pi$
$883$	6.76865	0.227783	0.113892	+	0.993493i	$0.463668\pi$
$884$	33.9487	1.14182
$885$	−62.9284	−2.11532
$886$	9.46662	0.318037
$887$	24.2409	0.813928	0.406964	−	0.913444i	$-0.366587\pi$
$887$	24.2409	0.813928	0.406964	+	0.913444i	$0.366587\pi$
$888$	2.17118	0.0728600
$889$	26.9870	0.905115
$890$	29.2857	0.981659
$891$	0.451818	0.0151365
$892$	−16.5519	−0.554199
$893$	−32.8792	−1.10026
$894$	9.13048	0.305369
$895$	2.31292	0.0773125
$896$	−1.41231	−0.0471818
$897$	20.9329	0.698929
$898$	12.5120	0.417531
$899$	42.9629	1.43289
$900$	3.40519	0.113506
$901$	−9.50488	−0.316654
$902$	0.0954214	0.00317718
$903$	−28.4681	−0.947360
$904$	9.24167	0.307373
$905$	20.9060	0.694940
$906$	−39.4417	−1.31036
$907$	−20.6080	−0.684279	−0.342139	−	0.939649i	$-0.611152\pi$
$907$	−20.6080	−0.684279	−0.342139	+	0.939649i	$0.611152\pi$
$908$	−28.1704	−0.934868
$909$	16.5150	0.547769
$910$	−24.5187	−0.812788
$911$	−47.8480	−1.58528	−0.792638	−	0.609692i	$-0.791293\pi$
$911$	−47.8480	−1.58528	−0.792638	+	0.609692i	$0.791293\pi$
$912$	12.4556	0.412445
$913$	−0.110702	−0.00366371
$914$	13.9357	0.460952
$915$	21.4259	0.708319
$916$	−6.53899	−0.216054
$917$	−13.5617	−0.447848
$918$	21.2533	0.701465
$919$	22.8896	0.755057	0.377529	−	0.925998i	$-0.376774\pi$
$919$	22.8896	0.755057	0.377529	+	0.925998i	$0.376774\pi$
$920$	−4.79316	−0.158026
$921$	−33.8618	−1.11578
$922$	−0.410171	−0.0135083
$923$	0.373546	0.0122954
$924$	−0.116580	−0.00383521
$925$	−3.27764	−0.107768
$926$	19.6099	0.644422
$927$	2.26582	0.0744194
$928$	5.96760	0.195896
$929$	−3.56205	−0.116867	−0.0584335	−	0.998291i	$-0.518611\pi$
$929$	−3.56205	−0.116867	−0.0584335	+	0.998291i	$0.518611\pi$
$930$	−41.4516	−1.35925
$931$	30.7438	1.00759
$932$	−8.93097	−0.292544
$933$	−16.5948	−0.543290
$934$	35.9645	1.17679
$935$	−0.641670	−0.0209849
$936$	6.80141	0.222311
$937$	−25.7161	−0.840108	−0.420054	−	0.907499i	$-0.637989\pi$
$937$	−25.7161	−0.840108	−0.420054	+	0.907499i	$0.637989\pi$
$938$	3.31553	0.108256
$939$	−0.990359	−0.0323192
$940$	15.1987	0.495726
$941$	−1.67438	−0.0545832	−0.0272916	−	0.999628i	$-0.508688\pi$
$941$	−1.67438	−0.0545832	−0.0272916	+	0.999628i	$0.508688\pi$
$942$	18.2888	0.595883
$943$	3.95742	0.128871
$944$	10.9295	0.355725
$945$	−15.3498	−0.499328
$946$	0.404612	0.0131551
$947$	2.84012	0.0922915	0.0461457	−	0.998935i	$-0.485306\pi$
$947$	2.84012	0.0922915	0.0461457	+	0.998935i	$0.485306\pi$
$948$	23.5753	0.765689
$949$	77.5326	2.51681
$950$	−18.8030	−0.610051
$951$	−31.1373	−1.00970
$952$	−7.84125	−0.254136
$953$	57.4108	1.85972	0.929858	−	0.367918i	$-0.119929\pi$
$953$	57.4108	1.85972	0.929858	+	0.367918i	$0.119929\pi$
$954$	−1.90424	−0.0616522
$955$	−32.5435	−1.05308
$956$	24.5704	0.794664
$957$	0.492602	0.0159236
$958$	19.6321	0.634284
$959$	13.6134	0.439598
$960$	−5.75767	−0.185828
$961$	20.8308	0.671962
$962$	−6.54663	−0.211072
$963$	4.23940	0.136613
$964$	15.2522	0.491241
$965$	0.505445	0.0162709
$966$	−4.83495	−0.155562
$967$	−24.8697	−0.799756	−0.399878	−	0.916568i	$-0.630947\pi$
$967$	−24.8697	−0.799756	−0.399878	+	0.916568i	$0.630947\pi$
$968$	−10.9983	−0.353500
$969$	69.1544	2.22156
$970$	−23.9627	−0.769395
$971$	−34.2696	−1.09977	−0.549883	−	0.835242i	$-0.685328\pi$
$971$	−34.2696	−1.09977	−0.549883	+	0.835242i	$0.685328\pi$
$972$	11.0250	0.353627
$973$	−16.3497	−0.524147
$974$	−1.02112	−0.0327188
$975$	−37.9594	−1.21567
$976$	−3.72128	−0.119115
$977$	61.0659	1.95367	0.976836	−	0.213988i	$-0.0686454\pi$
$977$	61.0659	1.95367	0.976836	+	0.213988i	$0.0686454\pi$
$978$	−22.2179	−0.710449
$979$	−0.419860	−0.0134188
$980$	−14.2115	−0.453971
$981$	11.0822	0.353826
$982$	−4.11076	−0.131180
$983$	41.1466	1.31237	0.656187	−	0.754599i	$-0.272168\pi$
$983$	41.1466	1.31237	0.656187	+	0.754599i	$0.272168\pi$
$984$	4.75376	0.151544
$985$	−5.17988	−0.165045
$986$	33.1327	1.05516
$987$	15.3311	0.487996
$988$	−37.5565	−1.19483
$989$	16.7805	0.533590
$990$	−0.128555	−0.00408574
$991$	22.8814	0.726853	0.363427	−	0.931623i	$-0.381607\pi$
$991$	22.8814	0.726853	0.363427	+	0.931623i	$0.381607\pi$
$992$	7.19936	0.228580
$993$	31.9956	1.01535
$994$	−0.0862794	−0.00273662
$995$	44.9337	1.42450
$996$	−5.51503	−0.174750
$997$	6.02577	0.190838	0.0954191	−	0.995437i	$-0.469581\pi$
$997$	6.02577	0.190838	0.0954191	+	0.995437i	$0.469581\pi$
$998$	38.5914	1.22159
$999$	−4.09848	−0.129670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.d.1.17	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.d.1.17	✓	79	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.02789 q^{3} +1.00000 q^{4} +2.83925 q^{5} -2.02789 q^{6} -1.41231 q^{7} +1.00000 q^{8} +1.11233 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.02789 q^{3} +1.00000 q^{4} +2.83925 q^{5} -2.02789 q^{6} -1.41231 q^{7} +1.00000 q^{8} +1.11233 q^{9} +2.83925 q^{10} -0.0407054 q^{11} -2.02789 q^{12} +6.11457 q^{13} -1.41231 q^{14} -5.75767 q^{15} +1.00000 q^{16} +5.55209 q^{17} +1.11233 q^{18} -6.14213 q^{19} +2.83925 q^{20} +2.86400 q^{21} -0.0407054 q^{22} -1.68818 q^{23} -2.02789 q^{24} +3.06132 q^{25} +6.11457 q^{26} +3.82799 q^{27} -1.41231 q^{28} +5.96760 q^{29} -5.75767 q^{30} +7.19936 q^{31} +1.00000 q^{32} +0.0825460 q^{33} +5.55209 q^{34} -4.00988 q^{35} +1.11233 q^{36} -1.07066 q^{37} -6.14213 q^{38} -12.3997 q^{39} +2.83925 q^{40} -2.34419 q^{41} +2.86400 q^{42} -9.94000 q^{43} -0.0407054 q^{44} +3.15817 q^{45} -1.68818 q^{46} +5.35306 q^{47} -2.02789 q^{48} -5.00539 q^{49} +3.06132 q^{50} -11.2590 q^{51} +6.11457 q^{52} -1.71195 q^{53} +3.82799 q^{54} -0.115573 q^{55} -1.41231 q^{56} +12.4556 q^{57} +5.96760 q^{58} +10.9295 q^{59} -5.75767 q^{60} -3.72128 q^{61} +7.19936 q^{62} -1.57095 q^{63} +1.00000 q^{64} +17.3608 q^{65} +0.0825460 q^{66} -2.34760 q^{67} +5.55209 q^{68} +3.42344 q^{69} -4.00988 q^{70} +0.0610912 q^{71} +1.11233 q^{72} +12.6800 q^{73} -1.07066 q^{74} -6.20802 q^{75} -6.14213 q^{76} +0.0574885 q^{77} -12.3997 q^{78} -11.6255 q^{79} +2.83925 q^{80} -11.0997 q^{81} -2.34419 q^{82} +2.71959 q^{83} +2.86400 q^{84} +15.7638 q^{85} -9.94000 q^{86} -12.1016 q^{87} -0.0407054 q^{88} +10.3146 q^{89} +3.15817 q^{90} -8.63564 q^{91} -1.68818 q^{92} -14.5995 q^{93} +5.35306 q^{94} -17.4390 q^{95} -2.02789 q^{96} -8.43980 q^{97} -5.00539 q^{98} -0.0452778 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * q^99

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