LMFDB - Embedded newform 8002.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.37543 q^{3} +1.00000 q^{4} -2.94724 q^{5} -2.37543 q^{6} -3.40112 q^{7} +1.00000 q^{8} +2.64268 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.37543 q^{3} +1.00000 q^{4} -2.94724 q^{5} -2.37543 q^{6} -3.40112 q^{7} +1.00000 q^{8} +2.64268 q^{9} -2.94724 q^{10} -0.702823 q^{11} -2.37543 q^{12} -2.54404 q^{13} -3.40112 q^{14} +7.00098 q^{15} +1.00000 q^{16} +7.55347 q^{17} +2.64268 q^{18} -2.61667 q^{19} -2.94724 q^{20} +8.07912 q^{21} -0.702823 q^{22} -5.93787 q^{23} -2.37543 q^{24} +3.68625 q^{25} -2.54404 q^{26} +0.848790 q^{27} -3.40112 q^{28} -7.06259 q^{29} +7.00098 q^{30} -10.0484 q^{31} +1.00000 q^{32} +1.66951 q^{33} +7.55347 q^{34} +10.0239 q^{35} +2.64268 q^{36} -1.73950 q^{37} -2.61667 q^{38} +6.04319 q^{39} -2.94724 q^{40} -5.89424 q^{41} +8.07912 q^{42} -4.25793 q^{43} -0.702823 q^{44} -7.78862 q^{45} -5.93787 q^{46} -8.32574 q^{47} -2.37543 q^{48} +4.56759 q^{49} +3.68625 q^{50} -17.9428 q^{51} -2.54404 q^{52} -13.1427 q^{53} +0.848790 q^{54} +2.07139 q^{55} -3.40112 q^{56} +6.21572 q^{57} -7.06259 q^{58} +0.741030 q^{59} +7.00098 q^{60} +3.66672 q^{61} -10.0484 q^{62} -8.98806 q^{63} +1.00000 q^{64} +7.49791 q^{65} +1.66951 q^{66} -7.42588 q^{67} +7.55347 q^{68} +14.1050 q^{69} +10.0239 q^{70} +5.10943 q^{71} +2.64268 q^{72} +1.69315 q^{73} -1.73950 q^{74} -8.75644 q^{75} -2.61667 q^{76} +2.39038 q^{77} +6.04319 q^{78} -6.17516 q^{79} -2.94724 q^{80} -9.94428 q^{81} -5.89424 q^{82} -14.1998 q^{83} +8.07912 q^{84} -22.2619 q^{85} -4.25793 q^{86} +16.7767 q^{87} -0.702823 q^{88} -0.269865 q^{89} -7.78862 q^{90} +8.65257 q^{91} -5.93787 q^{92} +23.8694 q^{93} -8.32574 q^{94} +7.71197 q^{95} -2.37543 q^{96} +12.6756 q^{97} +4.56759 q^{98} -1.85733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) $ 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * 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
$3$	−2.37543	−1.37146	−0.685728	−	0.727858i	$-0.740516\pi$
$3$	−2.37543	−1.37146	−0.685728	+	0.727858i	$0.740516\pi$
$4$	1.00000	0.500000
$5$	−2.94724	−1.31805	−0.659024	−	0.752122i	$-0.729030\pi$
$5$	−2.94724	−1.31805	−0.659024	+	0.752122i	$0.729030\pi$
$6$	−2.37543	−0.969766
$7$	−3.40112	−1.28550	−0.642751	−	0.766076i	$-0.722207\pi$
$7$	−3.40112	−1.28550	−0.642751	+	0.766076i	$0.722207\pi$
$8$	1.00000	0.353553
$9$	2.64268	0.880893
$10$	−2.94724	−0.932001
$11$	−0.702823	−0.211909	−0.105954	−	0.994371i	$-0.533790\pi$
$11$	−0.702823	−0.211909	−0.105954	+	0.994371i	$0.533790\pi$
$12$	−2.37543	−0.685728
$13$	−2.54404	−0.705590	−0.352795	−	0.935701i	$-0.614769\pi$
$13$	−2.54404	−0.705590	−0.352795	+	0.935701i	$0.614769\pi$
$14$	−3.40112	−0.908987
$15$	7.00098	1.80765
$16$	1.00000	0.250000
$17$	7.55347	1.83199	0.915993	−	0.401194i	$-0.131405\pi$
$17$	7.55347	1.83199	0.915993	+	0.401194i	$0.131405\pi$
$18$	2.64268	0.622886
$19$	−2.61667	−0.600305	−0.300153	−	0.953891i	$-0.597038\pi$
$19$	−2.61667	−0.600305	−0.300153	+	0.953891i	$0.597038\pi$
$20$	−2.94724	−0.659024
$21$	8.07912	1.76301
$22$	−0.702823	−0.149842
$23$	−5.93787	−1.23813	−0.619066	−	0.785339i	$-0.712488\pi$
$23$	−5.93787	−1.23813	−0.619066	+	0.785339i	$0.712488\pi$
$24$	−2.37543	−0.484883
$25$	3.68625	0.737250
$26$	−2.54404	−0.498927
$27$	0.848790	0.163350
$28$	−3.40112	−0.642751
$29$	−7.06259	−1.31149	−0.655745	−	0.754982i	$-0.727646\pi$
$29$	−7.06259	−1.31149	−0.655745	+	0.754982i	$0.727646\pi$
$30$	7.00098	1.27820
$31$	−10.0484	−1.80475	−0.902376	−	0.430949i	$-0.858179\pi$
$31$	−10.0484	−1.80475	−0.902376	+	0.430949i	$0.858179\pi$
$32$	1.00000	0.176777
$33$	1.66951	0.290624
$34$	7.55347	1.29541
$35$	10.0239	1.69435
$36$	2.64268	0.440447
$37$	−1.73950	−0.285972	−0.142986	−	0.989725i	$-0.545670\pi$
$37$	−1.73950	−0.285972	−0.142986	+	0.989725i	$0.545670\pi$
$38$	−2.61667	−0.424480
$39$	6.04319	0.967685
$40$	−2.94724	−0.466000
$41$	−5.89424	−0.920525	−0.460263	−	0.887783i	$-0.652245\pi$
$41$	−5.89424	−0.920525	−0.460263	+	0.887783i	$0.652245\pi$
$42$	8.07912	1.24664
$43$	−4.25793	−0.649328	−0.324664	−	0.945829i	$-0.605251\pi$
$43$	−4.25793	−0.649328	−0.324664	+	0.945829i	$0.605251\pi$
$44$	−0.702823	−0.105954
$45$	−7.78862	−1.16106
$46$	−5.93787	−0.875491
$47$	−8.32574	−1.21443	−0.607217	−	0.794536i	$-0.707714\pi$
$47$	−8.32574	−1.21443	−0.607217	+	0.794536i	$0.707714\pi$
$48$	−2.37543	−0.342864
$49$	4.56759	0.652513
$50$	3.68625	0.521314
$51$	−17.9428	−2.51249
$52$	−2.54404	−0.352795
$53$	−13.1427	−1.80529	−0.902645	−	0.430386i	$-0.858377\pi$
$53$	−13.1427	−1.80529	−0.902645	+	0.430386i	$0.858377\pi$
$54$	0.848790	0.115506
$55$	2.07139	0.279306
$56$	−3.40112	−0.454493
$57$	6.21572	0.823293
$58$	−7.06259	−0.927364
$59$	0.741030	0.0964739	0.0482369	−	0.998836i	$-0.484640\pi$
$59$	0.741030	0.0964739	0.0482369	+	0.998836i	$0.484640\pi$
$60$	7.00098	0.903823
$61$	3.66672	0.469475	0.234738	−	0.972059i	$-0.424577\pi$
$61$	3.66672	0.469475	0.234738	+	0.972059i	$0.424577\pi$
$62$	−10.0484	−1.27615
$63$	−8.98806	−1.13239
$64$	1.00000	0.125000
$65$	7.49791	0.930001
$66$	1.66951	0.205502
$67$	−7.42588	−0.907216	−0.453608	−	0.891201i	$-0.649863\pi$
$67$	−7.42588	−0.907216	−0.453608	+	0.891201i	$0.649863\pi$
$68$	7.55347	0.915993
$69$	14.1050	1.69804
$70$	10.0239	1.19809
$71$	5.10943	0.606378	0.303189	−	0.952930i	$-0.401949\pi$
$71$	5.10943	0.606378	0.303189	+	0.952930i	$0.401949\pi$
$72$	2.64268	0.311443
$73$	1.69315	0.198168	0.0990839	−	0.995079i	$-0.468409\pi$
$73$	1.69315	0.198168	0.0990839	+	0.995079i	$0.468409\pi$
$74$	−1.73950	−0.202213
$75$	−8.75644	−1.01111
$76$	−2.61667	−0.300153
$77$	2.39038	0.272409
$78$	6.04319	0.684257
$79$	−6.17516	−0.694760	−0.347380	−	0.937724i	$-0.612929\pi$
$79$	−6.17516	−0.694760	−0.347380	+	0.937724i	$0.612929\pi$
$80$	−2.94724	−0.329512
$81$	−9.94428	−1.10492
$82$	−5.89424	−0.650910
$83$	−14.1998	−1.55863	−0.779317	−	0.626629i	$-0.784434\pi$
$83$	−14.1998	−1.55863	−0.779317	+	0.626629i	$0.784434\pi$
$84$	8.07912	0.881504
$85$	−22.2619	−2.41465
$86$	−4.25793	−0.459144
$87$	16.7767	1.79865
$88$	−0.702823	−0.0749211
$89$	−0.269865	−0.0286056	−0.0143028	−	0.999898i	$-0.504553\pi$
$89$	−0.269865	−0.0286056	−0.0143028	+	0.999898i	$0.504553\pi$
$90$	−7.78862	−0.820993
$91$	8.65257	0.907036
$92$	−5.93787	−0.619066
$93$	23.8694	2.47514
$94$	−8.32574	−0.858735
$95$	7.71197	0.791231
$96$	−2.37543	−0.242442
$97$	12.6756	1.28701	0.643506	−	0.765441i	$-0.277479\pi$
$97$	12.6756	1.28701	0.643506	+	0.765441i	$0.277479\pi$
$98$	4.56759	0.461396
$99$	−1.85733	−0.186669
$100$	3.68625	0.368625
$101$	−12.6044	−1.25418	−0.627091	−	0.778946i	$-0.715755\pi$
$101$	−12.6044	−1.25418	−0.627091	+	0.778946i	$0.715755\pi$
$102$	−17.9428	−1.77660
$103$	−17.6315	−1.73728	−0.868642	−	0.495440i	$-0.835007\pi$
$103$	−17.6315	−1.73728	−0.868642	+	0.495440i	$0.835007\pi$
$104$	−2.54404	−0.249464
$105$	−23.8111	−2.32373
$106$	−13.1427	−1.27653
$107$	18.8319	1.82054	0.910272	−	0.414011i	$-0.135872\pi$
$107$	18.8319	1.82054	0.910272	+	0.414011i	$0.135872\pi$
$108$	0.848790	0.0816749
$109$	12.1675	1.16543	0.582715	−	0.812676i	$-0.301990\pi$
$109$	12.1675	1.16543	0.582715	+	0.812676i	$0.301990\pi$
$110$	2.07139	0.197499
$111$	4.13207	0.392198
$112$	−3.40112	−0.321375
$113$	−16.2903	−1.53247	−0.766233	−	0.642563i	$-0.777871\pi$
$113$	−16.2903	−1.53247	−0.766233	+	0.642563i	$0.777871\pi$
$114$	6.21572	0.582156
$115$	17.5003	1.63192
$116$	−7.06259	−0.655745
$117$	−6.72308	−0.621549
$118$	0.741030	0.0682173
$119$	−25.6902	−2.35502
$120$	7.00098	0.639099
$121$	−10.5060	−0.955095
$122$	3.66672	0.331969
$123$	14.0014	1.26246
$124$	−10.0484	−0.902376
$125$	3.87194	0.346317
$126$	−8.98806	−0.800720
$127$	−10.2926	−0.913318	−0.456659	−	0.889642i	$-0.650954\pi$
$127$	−10.2926	−0.913318	−0.456659	+	0.889642i	$0.650954\pi$
$128$	1.00000	0.0883883
$129$	10.1144	0.890525
$130$	7.49791	0.657610
$131$	−8.36062	−0.730471	−0.365236	−	0.930915i	$-0.619012\pi$
$131$	−8.36062	−0.730471	−0.365236	+	0.930915i	$0.619012\pi$
$132$	1.66951	0.145312
$133$	8.89960	0.771693
$134$	−7.42588	−0.641498
$135$	−2.50159	−0.215303
$136$	7.55347	0.647705
$137$	−7.31016	−0.624549	−0.312275	−	0.949992i	$-0.601091\pi$
$137$	−7.31016	−0.624549	−0.312275	+	0.949992i	$0.601091\pi$
$138$	14.1050	1.20070
$139$	12.9099	1.09500	0.547502	−	0.836804i	$-0.315579\pi$
$139$	12.9099	1.09500	0.547502	+	0.836804i	$0.315579\pi$
$140$	10.0239	0.847176
$141$	19.7772	1.66554
$142$	5.10943	0.428774
$143$	1.78801	0.149521
$144$	2.64268	0.220223
$145$	20.8152	1.72861
$146$	1.69315	0.140126
$147$	−10.8500	−0.894893
$148$	−1.73950	−0.142986
$149$	12.2605	1.00442	0.502210	−	0.864746i	$-0.332520\pi$
$149$	12.2605	1.00442	0.502210	+	0.864746i	$0.332520\pi$
$150$	−8.75644	−0.714960
$151$	−19.6380	−1.59811	−0.799057	−	0.601255i	$-0.794667\pi$
$151$	−19.6380	−1.59811	−0.799057	+	0.601255i	$0.794667\pi$
$152$	−2.61667	−0.212240
$153$	19.9614	1.61378
$154$	2.39038	0.192622
$155$	29.6152	2.37875
$156$	6.04319	0.483843
$157$	5.91021	0.471686	0.235843	−	0.971791i	$-0.424215\pi$
$157$	5.91021	0.471686	0.235843	+	0.971791i	$0.424215\pi$
$158$	−6.17516	−0.491269
$159$	31.2196	2.47588
$160$	−2.94724	−0.233000
$161$	20.1954	1.59162
$162$	−9.94428	−0.781297
$163$	12.7123	0.995700	0.497850	−	0.867263i	$-0.334123\pi$
$163$	12.7123	0.995700	0.497850	+	0.867263i	$0.334123\pi$
$164$	−5.89424	−0.460263
$165$	−4.92045	−0.383056
$166$	−14.1998	−1.10212
$167$	7.32792	0.567052	0.283526	−	0.958965i	$-0.408496\pi$
$167$	7.32792	0.567052	0.283526	+	0.958965i	$0.408496\pi$
$168$	8.07912	0.623318
$169$	−6.52786	−0.502143
$170$	−22.2619	−1.70741
$171$	−6.91502	−0.528805
$172$	−4.25793	−0.324664
$173$	20.0911	1.52750	0.763750	−	0.645513i	$-0.223356\pi$
$173$	20.0911	1.52750	0.763750	+	0.645513i	$0.223356\pi$
$174$	16.7767	1.27184
$175$	−12.5374	−0.947736
$176$	−0.702823	−0.0529772
$177$	−1.76027	−0.132310
$178$	−0.269865	−0.0202272
$179$	−1.68979	−0.126301	−0.0631504	−	0.998004i	$-0.520115\pi$
$179$	−1.68979	−0.126301	−0.0631504	+	0.998004i	$0.520115\pi$
$180$	−7.78862	−0.580530
$181$	21.5011	1.59817	0.799083	−	0.601221i	$-0.205319\pi$
$181$	21.5011	1.59817	0.799083	+	0.601221i	$0.205319\pi$
$182$	8.65257	0.641371
$183$	−8.71004	−0.643865
$184$	−5.93787	−0.437745
$185$	5.12673	0.376925
$186$	23.8694	1.75019
$187$	−5.30875	−0.388214
$188$	−8.32574	−0.607217
$189$	−2.88684	−0.209986
$190$	7.71197	0.559485
$191$	3.46247	0.250536	0.125268	−	0.992123i	$-0.460021\pi$
$191$	3.46247	0.250536	0.125268	+	0.992123i	$0.460021\pi$
$192$	−2.37543	−0.171432
$193$	10.9120	0.785466	0.392733	−	0.919653i	$-0.371530\pi$
$193$	10.9120	0.785466	0.392733	+	0.919653i	$0.371530\pi$
$194$	12.6756	0.910056
$195$	−17.8108	−1.27546
$196$	4.56759	0.326257
$197$	12.9885	0.925395	0.462697	−	0.886516i	$-0.346882\pi$
$197$	12.9885	0.925395	0.462697	+	0.886516i	$0.346882\pi$
$198$	−1.85733	−0.131995
$199$	6.45636	0.457679	0.228840	−	0.973464i	$-0.426507\pi$
$199$	6.45636	0.457679	0.228840	+	0.973464i	$0.426507\pi$
$200$	3.68625	0.260657
$201$	17.6397	1.24421
$202$	−12.6044	−0.886841
$203$	24.0207	1.68592
$204$	−17.9428	−1.25624
$205$	17.3718	1.21330
$206$	−17.6315	−1.22845
$207$	−15.6919	−1.09066
$208$	−2.54404	−0.176397
$209$	1.83906	0.127210
$210$	−23.8111	−1.64313
$211$	−20.3242	−1.39917	−0.699587	−	0.714548i	$-0.746633\pi$
$211$	−20.3242	−1.39917	−0.699587	+	0.714548i	$0.746633\pi$
$212$	−13.1427	−0.902645
$213$	−12.1371	−0.831621
$214$	18.8319	1.28732
$215$	12.5492	0.855846
$216$	0.848790	0.0577529
$217$	34.1759	2.32001
$218$	12.1675	0.824084
$219$	−4.02196	−0.271779
$220$	2.07139	0.139653
$221$	−19.2163	−1.29263
$222$	4.13207	0.277326
$223$	−3.03498	−0.203238	−0.101619	−	0.994823i	$-0.532402\pi$
$223$	−3.03498	−0.203238	−0.101619	+	0.994823i	$0.532402\pi$
$224$	−3.40112	−0.227247
$225$	9.74158	0.649438
$226$	−16.2903	−1.08362
$227$	−5.64874	−0.374920	−0.187460	−	0.982272i	$-0.560026\pi$
$227$	−5.64874	−0.374920	−0.187460	+	0.982272i	$0.560026\pi$
$228$	6.21572	0.411646
$229$	17.1594	1.13392	0.566961	−	0.823744i	$-0.308119\pi$
$229$	17.1594	1.13392	0.566961	+	0.823744i	$0.308119\pi$
$230$	17.5003	1.15394
$231$	−5.67819	−0.373597
$232$	−7.06259	−0.463682
$233$	−22.3126	−1.46175	−0.730874	−	0.682513i	$-0.760887\pi$
$233$	−22.3126	−1.46175	−0.730874	+	0.682513i	$0.760887\pi$
$234$	−6.72308	−0.439502
$235$	24.5380	1.60068
$236$	0.741030	0.0482369
$237$	14.6687	0.952833
$238$	−25.6902	−1.66525
$239$	−20.1467	−1.30318	−0.651590	−	0.758571i	$-0.725898\pi$
$239$	−20.1467	−1.30318	−0.651590	+	0.758571i	$0.725898\pi$
$240$	7.00098	0.451911
$241$	−17.1953	−1.10765	−0.553823	−	0.832634i	$-0.686832\pi$
$241$	−17.1953	−1.10765	−0.553823	+	0.832634i	$0.686832\pi$
$242$	−10.5060	−0.675354
$243$	21.0756	1.35200
$244$	3.66672	0.234738
$245$	−13.4618	−0.860043
$246$	14.0014	0.892694
$247$	6.65691	0.423569
$248$	−10.0484	−0.638077
$249$	33.7308	2.13760
$250$	3.87194	0.244883
$251$	25.2815	1.59576	0.797879	−	0.602818i	$-0.205956\pi$
$251$	25.2815	1.59576	0.797879	+	0.602818i	$0.205956\pi$
$252$	−8.98806	−0.566195
$253$	4.17327	0.262371
$254$	−10.2926	−0.645813
$255$	52.8817	3.31158
$256$	1.00000	0.0625000
$257$	−27.4743	−1.71380	−0.856901	−	0.515482i	$-0.827613\pi$
$257$	−27.4743	−1.71380	−0.856901	+	0.515482i	$0.827613\pi$
$258$	10.1144	0.629697
$259$	5.91624	0.367617
$260$	7.49791	0.465000
$261$	−18.6642	−1.15528
$262$	−8.36062	−0.516521
$263$	25.3579	1.56363	0.781817	−	0.623508i	$-0.214293\pi$
$263$	25.3579	1.56363	0.781817	+	0.623508i	$0.214293\pi$
$264$	1.66951	0.102751
$265$	38.7348	2.37946
$266$	8.89960	0.545669
$267$	0.641045	0.0392313
$268$	−7.42588	−0.453608
$269$	−23.8400	−1.45355	−0.726776	−	0.686874i	$-0.758982\pi$
$269$	−23.8400	−1.45355	−0.726776	+	0.686874i	$0.758982\pi$
$270$	−2.50159	−0.152242
$271$	−23.9308	−1.45369	−0.726847	−	0.686799i	$-0.759015\pi$
$271$	−23.9308	−1.45369	−0.726847	+	0.686799i	$0.759015\pi$
$272$	7.55347	0.457997
$273$	−20.5536	−1.24396
$274$	−7.31016	−0.441623
$275$	−2.59078	−0.156230
$276$	14.1050	0.849022
$277$	−0.794588	−0.0477421	−0.0238711	−	0.999715i	$-0.507599\pi$
$277$	−0.794588	−0.0477421	−0.0238711	+	0.999715i	$0.507599\pi$
$278$	12.9099	0.774285
$279$	−26.5548	−1.58979
$280$	10.0239	0.599044
$281$	24.3961	1.45535	0.727675	−	0.685922i	$-0.240601\pi$
$281$	24.3961	1.45535	0.727675	+	0.685922i	$0.240601\pi$
$282$	19.7772	1.17772
$283$	3.11840	0.185370	0.0926848	−	0.995696i	$-0.470455\pi$
$283$	3.11840	0.185370	0.0926848	+	0.995696i	$0.470455\pi$
$284$	5.10943	0.303189
$285$	−18.3193	−1.08514
$286$	1.78801	0.105727
$287$	20.0470	1.18334
$288$	2.64268	0.155721
$289$	40.0550	2.35617
$290$	20.8152	1.22231
$291$	−30.1100	−1.76508
$292$	1.69315	0.0990839
$293$	3.81360	0.222793	0.111396	−	0.993776i	$-0.464468\pi$
$293$	3.81360	0.222793	0.111396	+	0.993776i	$0.464468\pi$
$294$	−10.8500	−0.632785
$295$	−2.18400	−0.127157
$296$	−1.73950	−0.101106
$297$	−0.596549	−0.0346153
$298$	12.2605	0.710232
$299$	15.1062	0.873612
$300$	−8.75644	−0.505553
$301$	14.4817	0.834712
$302$	−19.6380	−1.13004
$303$	29.9408	1.72006
$304$	−2.61667	−0.150076
$305$	−10.8067	−0.618791
$306$	19.9614	1.14112
$307$	17.4417	0.995449	0.497725	−	0.867335i	$-0.334169\pi$
$307$	17.4417	0.995449	0.497725	+	0.867335i	$0.334169\pi$
$308$	2.39038	0.136205
$309$	41.8825	2.38261
$310$	29.6152	1.68203
$311$	−14.7651	−0.837249	−0.418625	−	0.908159i	$-0.637488\pi$
$311$	−14.7651	−0.837249	−0.418625	+	0.908159i	$0.637488\pi$
$312$	6.04319	0.342128
$313$	−30.6805	−1.73417	−0.867083	−	0.498165i	$-0.834008\pi$
$313$	−30.6805	−1.73417	−0.867083	+	0.498165i	$0.834008\pi$
$314$	5.91021	0.333532
$315$	26.4900	1.49254
$316$	−6.17516	−0.347380
$317$	12.1008	0.679649	0.339825	−	0.940489i	$-0.389632\pi$
$317$	12.1008	0.679649	0.339825	+	0.940489i	$0.389632\pi$
$318$	31.2196	1.75071
$319$	4.96375	0.277917
$320$	−2.94724	−0.164756
$321$	−44.7338	−2.49680
$322$	20.1954	1.12544
$323$	−19.7649	−1.09975
$324$	−9.94428	−0.552460
$325$	−9.37796	−0.520196
$326$	12.7123	0.704067
$327$	−28.9030	−1.59834
$328$	−5.89424	−0.325455
$329$	28.3168	1.56116
$330$	−4.92045	−0.270862
$331$	5.50706	0.302695	0.151348	−	0.988481i	$-0.451639\pi$
$331$	5.50706	0.302695	0.151348	+	0.988481i	$0.451639\pi$
$332$	−14.1998	−0.779317
$333$	−4.59694	−0.251911
$334$	7.32792	0.400966
$335$	21.8859	1.19575
$336$	8.07912	0.440752
$337$	−8.79669	−0.479186	−0.239593	−	0.970873i	$-0.577014\pi$
$337$	−8.79669	−0.479186	−0.239593	+	0.970873i	$0.577014\pi$
$338$	−6.52786	−0.355069
$339$	38.6966	2.10171
$340$	−22.2619	−1.20732
$341$	7.06227	0.382443
$342$	−6.91502	−0.373922
$343$	8.27290	0.446695
$344$	−4.25793	−0.229572
$345$	−41.5709	−2.23810
$346$	20.0911	1.08011
$347$	−13.4446	−0.721745	−0.360872	−	0.932615i	$-0.617521\pi$
$347$	−13.4446	−0.721745	−0.360872	+	0.932615i	$0.617521\pi$
$348$	16.7767	0.899326
$349$	8.64749	0.462889	0.231445	−	0.972848i	$-0.425655\pi$
$349$	8.64749	0.462889	0.231445	+	0.972848i	$0.425655\pi$
$350$	−12.5374	−0.670150
$351$	−2.15936	−0.115258
$352$	−0.702823	−0.0374606
$353$	30.6683	1.63231	0.816155	−	0.577833i	$-0.196102\pi$
$353$	30.6683	1.63231	0.816155	+	0.577833i	$0.196102\pi$
$354$	−1.76027	−0.0935571
$355$	−15.0587	−0.799235
$356$	−0.269865	−0.0143028
$357$	61.0254	3.22981
$358$	−1.68979	−0.0893081
$359$	−33.8157	−1.78473	−0.892363	−	0.451318i	$-0.850954\pi$
$359$	−33.8157	−1.78473	−0.892363	+	0.451318i	$0.850954\pi$
$360$	−7.78862	−0.410496
$361$	−12.1530	−0.639633
$362$	21.5011	1.13007
$363$	24.9564	1.30987
$364$	8.65257	0.453518
$365$	−4.99012	−0.261195
$366$	−8.71004	−0.455281
$367$	6.02894	0.314708	0.157354	−	0.987542i	$-0.449704\pi$
$367$	6.02894	0.314708	0.157354	+	0.987542i	$0.449704\pi$
$368$	−5.93787	−0.309533
$369$	−15.5766	−0.810884
$370$	5.12673	0.266526
$371$	44.6999	2.32070
$372$	23.8694	1.23757
$373$	7.36067	0.381121	0.190561	−	0.981675i	$-0.438969\pi$
$373$	7.36067	0.381121	0.190561	+	0.981675i	$0.438969\pi$
$374$	−5.30875	−0.274509
$375$	−9.19754	−0.474959
$376$	−8.32574	−0.429368
$377$	17.9675	0.925374
$378$	−2.88684	−0.148483
$379$	7.47913	0.384177	0.192089	−	0.981378i	$-0.438474\pi$
$379$	7.47913	0.384177	0.192089	+	0.981378i	$0.438474\pi$
$380$	7.71197	0.395616
$381$	24.4493	1.25258
$382$	3.46247	0.177156
$383$	14.9852	0.765709	0.382855	−	0.923809i	$-0.374941\pi$
$383$	14.9852	0.765709	0.382855	+	0.923809i	$0.374941\pi$
$384$	−2.37543	−0.121221
$385$	−7.04504	−0.359048
$386$	10.9120	0.555408
$387$	−11.2523	−0.571989
$388$	12.6756	0.643506
$389$	−31.6756	−1.60602	−0.803009	−	0.595967i	$-0.796769\pi$
$389$	−31.6756	−1.60602	−0.803009	+	0.595967i	$0.796769\pi$
$390$	−17.8108	−0.901883
$391$	−44.8515	−2.26824
$392$	4.56759	0.230698
$393$	19.8601	1.00181
$394$	12.9885	0.654353
$395$	18.1997	0.915727
$396$	−1.85733	−0.0933346
$397$	−35.2978	−1.77155	−0.885773	−	0.464119i	$-0.846371\pi$
$397$	−35.2978	−1.77155	−0.885773	+	0.464119i	$0.846371\pi$
$398$	6.45636	0.323628
$399$	−21.1404	−1.05834
$400$	3.68625	0.184312
$401$	−7.48980	−0.374023	−0.187011	−	0.982358i	$-0.559880\pi$
$401$	−7.48980	−0.374023	−0.187011	+	0.982358i	$0.559880\pi$
$402$	17.6397	0.879787
$403$	25.5636	1.27341
$404$	−12.6044	−0.627091
$405$	29.3082	1.45634
$406$	24.0207	1.19213
$407$	1.22256	0.0606001
$408$	−17.9428	−0.888299
$409$	1.29911	0.0642368	0.0321184	−	0.999484i	$-0.489775\pi$
$409$	1.29911	0.0642368	0.0321184	+	0.999484i	$0.489775\pi$
$410$	17.3718	0.857930
$411$	17.3648	0.856542
$412$	−17.6315	−0.868642
$413$	−2.52033	−0.124017
$414$	−15.6919	−0.771214
$415$	41.8504	2.05436
$416$	−2.54404	−0.124732
$417$	−30.6666	−1.50175
$418$	1.83906	0.0899511
$419$	−14.1470	−0.691126	−0.345563	−	0.938395i	$-0.612312\pi$
$419$	−14.1470	−0.691126	−0.345563	+	0.938395i	$0.612312\pi$
$420$	−23.8111	−1.16187
$421$	−36.8034	−1.79369	−0.896844	−	0.442347i	$-0.854146\pi$
$421$	−36.8034	−1.79369	−0.896844	+	0.442347i	$0.854146\pi$
$422$	−20.3242	−0.989365
$423$	−22.0023	−1.06979
$424$	−13.1427	−0.638266
$425$	27.8440	1.35063
$426$	−12.1371	−0.588045
$427$	−12.4709	−0.603511
$428$	18.8319	0.910272
$429$	−4.24729	−0.205061
$430$	12.5492	0.605174
$431$	−14.7276	−0.709403	−0.354701	−	0.934980i	$-0.615417\pi$
$431$	−14.7276	−0.709403	−0.354701	+	0.934980i	$0.615417\pi$
$432$	0.848790	0.0408375
$433$	26.9358	1.29445	0.647225	−	0.762299i	$-0.275930\pi$
$433$	26.9358	1.29445	0.647225	+	0.762299i	$0.275930\pi$
$434$	34.1759	1.64050
$435$	−49.4451	−2.37071
$436$	12.1675	0.582715
$437$	15.5374	0.743257
$438$	−4.02196	−0.192177
$439$	11.2838	0.538547	0.269274	−	0.963064i	$-0.413216\pi$
$439$	11.2838	0.538547	0.269274	+	0.963064i	$0.413216\pi$
$440$	2.07139	0.0987496
$441$	12.0707	0.574794
$442$	−19.2163	−0.914028
$443$	−29.9375	−1.42237	−0.711186	−	0.703004i	$-0.751842\pi$
$443$	−29.9375	−1.42237	−0.711186	+	0.703004i	$0.751842\pi$
$444$	4.13207	0.196099
$445$	0.795357	0.0377035
$446$	−3.03498	−0.143711
$447$	−29.1240	−1.37752
$448$	−3.40112	−0.160688
$449$	−12.2719	−0.579147	−0.289574	−	0.957156i	$-0.593513\pi$
$449$	−12.2719	−0.579147	−0.289574	+	0.957156i	$0.593513\pi$
$450$	9.74158	0.459222
$451$	4.14260	0.195068
$452$	−16.2903	−0.766233
$453$	46.6486	2.19174
$454$	−5.64874	−0.265109
$455$	−25.5012	−1.19552
$456$	6.21572	0.291078
$457$	−0.0358637	−0.00167763	−0.000838816	−	1.00000i	$-0.500267\pi$
$457$	−0.0358637	−0.00167763	−0.000838816		1.00000i	$0.500267\pi$
$458$	17.1594	0.801804
$459$	6.41132	0.299255
$460$	17.5003	0.815958
$461$	7.11039	0.331164	0.165582	−	0.986196i	$-0.447050\pi$
$461$	7.11039	0.331164	0.165582	+	0.986196i	$0.447050\pi$
$462$	−5.67819	−0.264173
$463$	3.03553	0.141073	0.0705366	−	0.997509i	$-0.477529\pi$
$463$	3.03553	0.141073	0.0705366	+	0.997509i	$0.477529\pi$
$464$	−7.06259	−0.327873
$465$	−70.3489	−3.26235
$466$	−22.3126	−1.03361
$467$	21.5699	0.998135	0.499067	−	0.866563i	$-0.333676\pi$
$467$	21.5699	0.998135	0.499067	+	0.866563i	$0.333676\pi$
$468$	−6.72308	−0.310775
$469$	25.2563	1.16623
$470$	24.5380	1.13185
$471$	−14.0393	−0.646897
$472$	0.741030	0.0341087
$473$	2.99257	0.137598
$474$	14.6687	0.673755
$475$	−9.64570	−0.442575
$476$	−25.6902	−1.17751
$477$	−34.7320	−1.59027
$478$	−20.1467	−0.921488
$479$	−21.7831	−0.995294	−0.497647	−	0.867380i	$-0.665802\pi$
$479$	−21.7831	−0.995294	−0.497647	+	0.867380i	$0.665802\pi$
$480$	7.00098	0.319550
$481$	4.42536	0.201779
$482$	−17.1953	−0.783225
$483$	−47.9728	−2.18284
$484$	−10.5060	−0.477547
$485$	−37.3581	−1.69634
$486$	21.0756	0.956009
$487$	−11.1982	−0.507437	−0.253719	−	0.967278i	$-0.581654\pi$
$487$	−11.1982	−0.507437	−0.253719	+	0.967278i	$0.581654\pi$
$488$	3.66672	0.165985
$489$	−30.1971	−1.36556
$490$	−13.4618	−0.608143
$491$	−1.57003	−0.0708545	−0.0354272	−	0.999372i	$-0.511279\pi$
$491$	−1.57003	−0.0708545	−0.0354272	+	0.999372i	$0.511279\pi$
$492$	14.0014	0.631230
$493$	−53.3471	−2.40263
$494$	6.65691	0.299509
$495$	5.47402	0.246039
$496$	−10.0484	−0.451188
$497$	−17.3778	−0.779499
$498$	33.7308	1.51151
$499$	−17.7507	−0.794630	−0.397315	−	0.917682i	$-0.630058\pi$
$499$	−17.7507	−0.794630	−0.397315	+	0.917682i	$0.630058\pi$
$500$	3.87194	0.173159
$501$	−17.4070	−0.777687
$502$	25.2815	1.12837
$503$	−12.5451	−0.559357	−0.279679	−	0.960094i	$-0.590228\pi$
$503$	−12.5451	−0.559357	−0.279679	+	0.960094i	$0.590228\pi$
$504$	−8.98806	−0.400360
$505$	37.1482	1.65307
$506$	4.17327	0.185524
$507$	15.5065	0.688668
$508$	−10.2926	−0.456659
$509$	9.86408	0.437218	0.218609	−	0.975813i	$-0.429848\pi$
$509$	9.86408	0.437218	0.218609	+	0.975813i	$0.429848\pi$
$510$	52.8817	2.34164
$511$	−5.75859	−0.254745
$512$	1.00000	0.0441942
$513$	−2.22100	−0.0980598
$514$	−27.4743	−1.21184
$515$	51.9644	2.28982
$516$	10.1144	0.445263
$517$	5.85152	0.257350
$518$	5.91624	0.259945
$519$	−47.7251	−2.09490
$520$	7.49791	0.328805
$521$	−35.2407	−1.54392	−0.771961	−	0.635669i	$-0.780724\pi$
$521$	−35.2407	−1.54392	−0.771961	+	0.635669i	$0.780724\pi$
$522$	−18.6642	−0.816909
$523$	5.24694	0.229433	0.114716	−	0.993398i	$-0.463404\pi$
$523$	5.24694	0.229433	0.114716	+	0.993398i	$0.463404\pi$
$524$	−8.36062	−0.365236
$525$	29.7817	1.29978
$526$	25.3579	1.10566
$527$	−75.9006	−3.30628
$528$	1.66951	0.0726560
$529$	12.2583	0.532969
$530$	38.7348	1.68253
$531$	1.95830	0.0849832
$532$	8.89960	0.385847
$533$	14.9952	0.649513
$534$	0.641045	0.0277407
$535$	−55.5021	−2.39956
$536$	−7.42588	−0.320749
$537$	4.01398	0.173216
$538$	−23.8400	−1.02782
$539$	−3.21021	−0.138273
$540$	−2.50159	−0.107651
$541$	14.6421	0.629514	0.314757	−	0.949172i	$-0.398077\pi$
$541$	14.6421	0.629514	0.314757	+	0.949172i	$0.398077\pi$
$542$	−23.9308	−1.02792
$543$	−51.0745	−2.19182
$544$	7.55347	0.323852
$545$	−35.8605	−1.53609
$546$	−20.5536	−0.879613
$547$	20.4916	0.876158	0.438079	−	0.898936i	$-0.355659\pi$
$547$	20.4916	0.876158	0.438079	+	0.898936i	$0.355659\pi$
$548$	−7.31016	−0.312275
$549$	9.68996	0.413558
$550$	−2.59078	−0.110471
$551$	18.4805	0.787295
$552$	14.1050	0.600349
$553$	21.0024	0.893115
$554$	−0.794588	−0.0337588
$555$	−12.1782	−0.516936
$556$	12.9099	0.547502
$557$	23.0788	0.977882	0.488941	−	0.872317i	$-0.337383\pi$
$557$	23.0788	0.977882	0.488941	+	0.872317i	$0.337383\pi$
$558$	−26.5548	−1.12415
$559$	10.8323	0.458159
$560$	10.0239	0.423588
$561$	12.6106	0.532419
$562$	24.3961	1.02909
$563$	−2.61285	−0.110119	−0.0550593	−	0.998483i	$-0.517535\pi$
$563$	−2.61285	−0.110119	−0.0550593	+	0.998483i	$0.517535\pi$
$564$	19.7772	0.832772
$565$	48.0116	2.01986
$566$	3.11840	0.131076
$567$	33.8217	1.42038
$568$	5.10943	0.214387
$569$	47.2336	1.98014	0.990068	−	0.140588i	$-0.0448992\pi$
$569$	47.2336	1.98014	0.990068	+	0.140588i	$0.0448992\pi$
$570$	−18.3193	−0.767309
$571$	−7.37985	−0.308837	−0.154418	−	0.988006i	$-0.549350\pi$
$571$	−7.37985	−0.308837	−0.154418	+	0.988006i	$0.549350\pi$
$572$	1.78801	0.0747604
$573$	−8.22487	−0.343599
$574$	20.0470	0.836745
$575$	−21.8885	−0.912812
$576$	2.64268	0.110112
$577$	36.7291	1.52905	0.764527	−	0.644592i	$-0.222973\pi$
$577$	36.7291	1.52905	0.764527	+	0.644592i	$0.222973\pi$
$578$	40.0550	1.66607
$579$	−25.9208	−1.07723
$580$	20.8152	0.864304
$581$	48.2953	2.00363
$582$	−30.1100	−1.24810
$583$	9.23699	0.382557
$584$	1.69315	0.0700629
$585$	19.8146	0.819231
$586$	3.81360	0.157538
$587$	15.7894	0.651696	0.325848	−	0.945422i	$-0.394350\pi$
$587$	15.7894	0.651696	0.325848	+	0.945422i	$0.394350\pi$
$588$	−10.8500	−0.447447
$589$	26.2935	1.08340
$590$	−2.18400	−0.0899137
$591$	−30.8534	−1.26914
$592$	−1.73950	−0.0714930
$593$	12.2352	0.502439	0.251220	−	0.967930i	$-0.419168\pi$
$593$	12.2352	0.502439	0.251220	+	0.967930i	$0.419168\pi$
$594$	−0.596549	−0.0244767
$595$	75.7154	3.10403
$596$	12.2605	0.502210
$597$	−15.3366	−0.627687
$598$	15.1062	0.617737
$599$	2.19129	0.0895335	0.0447668	−	0.998997i	$-0.485746\pi$
$599$	2.19129	0.0895335	0.0447668	+	0.998997i	$0.485746\pi$
$600$	−8.75644	−0.357480
$601$	8.72082	0.355730	0.177865	−	0.984055i	$-0.443081\pi$
$601$	8.72082	0.355730	0.177865	+	0.984055i	$0.443081\pi$
$602$	14.4817	0.590231
$603$	−19.6242	−0.799160
$604$	−19.6380	−0.799057
$605$	30.9639	1.25886
$606$	29.9408	1.21626
$607$	38.6058	1.56696	0.783481	−	0.621416i	$-0.213442\pi$
$607$	38.6058	1.56696	0.783481	+	0.621416i	$0.213442\pi$
$608$	−2.61667	−0.106120
$609$	−57.0596	−2.31217
$610$	−10.8067	−0.437551
$611$	21.1810	0.856892
$612$	19.9614	0.806892
$613$	−30.7946	−1.24378	−0.621890	−	0.783104i	$-0.713635\pi$
$613$	−30.7946	−1.24378	−0.621890	+	0.783104i	$0.713635\pi$
$614$	17.4417	0.703889
$615$	−41.2654	−1.66398
$616$	2.39038	0.0963112
$617$	40.0787	1.61351	0.806754	−	0.590888i	$-0.201222\pi$
$617$	40.0787	1.61351	0.806754	+	0.590888i	$0.201222\pi$
$618$	41.8825	1.68476
$619$	10.4766	0.421092	0.210546	−	0.977584i	$-0.432476\pi$
$619$	10.4766	0.421092	0.210546	+	0.977584i	$0.432476\pi$
$620$	29.6152	1.18938
$621$	−5.04001	−0.202248
$622$	−14.7651	−0.592025
$623$	0.917841	0.0367725
$624$	6.04319	0.241921
$625$	−29.8428	−1.19371
$626$	−30.6805	−1.22624
$627$	−4.36855	−0.174463
$628$	5.91021	0.235843
$629$	−13.1393	−0.523897
$630$	26.4900	1.05539
$631$	15.5991	0.620992	0.310496	−	0.950575i	$-0.399505\pi$
$631$	15.5991	0.620992	0.310496	+	0.950575i	$0.399505\pi$
$632$	−6.17516	−0.245635
$633$	48.2787	1.91891
$634$	12.1008	0.480584
$635$	30.3347	1.20380
$636$	31.2196	1.23794
$637$	−11.6201	−0.460406
$638$	4.96375	0.196517
$639$	13.5026	0.534154
$640$	−2.94724	−0.116500
$641$	−16.7365	−0.661051	−0.330525	−	0.943797i	$-0.607226\pi$
$641$	−16.7365	−0.661051	−0.330525	+	0.943797i	$0.607226\pi$
$642$	−44.7338	−1.76550
$643$	−13.9119	−0.548630	−0.274315	−	0.961640i	$-0.588451\pi$
$643$	−13.9119	−0.548630	−0.274315	+	0.961640i	$0.588451\pi$
$644$	20.1954	0.795809
$645$	−29.8097	−1.17375
$646$	−19.7649	−0.777641
$647$	20.9658	0.824252	0.412126	−	0.911127i	$-0.364786\pi$
$647$	20.9658	0.824252	0.412126	+	0.911127i	$0.364786\pi$
$648$	−9.94428	−0.390648
$649$	−0.520813	−0.0204437
$650$	−9.37796	−0.367834
$651$	−81.1826	−3.18180
$652$	12.7123	0.497850
$653$	−25.2223	−0.987025	−0.493512	−	0.869739i	$-0.664287\pi$
$653$	−25.2223	−0.987025	−0.493512	+	0.869739i	$0.664287\pi$
$654$	−28.9030	−1.13020
$655$	24.6408	0.962796
$656$	−5.89424	−0.230131
$657$	4.47444	0.174565
$658$	28.3168	1.10390
$659$	−49.0670	−1.91138	−0.955690	−	0.294376i	$-0.904888\pi$
$659$	−49.0670	−1.91138	−0.955690	+	0.294376i	$0.904888\pi$
$660$	−4.92045	−0.191528
$661$	31.2515	1.21554	0.607772	−	0.794112i	$-0.292064\pi$
$661$	31.2515	1.21554	0.607772	+	0.794112i	$0.292064\pi$
$662$	5.50706	0.214038
$663$	45.6471	1.77279
$664$	−14.1998	−0.551061
$665$	−26.2293	−1.01713
$666$	−4.59694	−0.178128
$667$	41.9368	1.62380
$668$	7.32792	0.283526
$669$	7.20940	0.278732
$670$	21.8859	0.845526
$671$	−2.57705	−0.0994860
$672$	8.07912	0.311659
$673$	−19.5884	−0.755077	−0.377539	−	0.925994i	$-0.623229\pi$
$673$	−19.5884	−0.755077	−0.377539	+	0.925994i	$0.623229\pi$
$674$	−8.79669	−0.338836
$675$	3.12885	0.120430
$676$	−6.52786	−0.251072
$677$	11.9790	0.460391	0.230195	−	0.973144i	$-0.426063\pi$
$677$	11.9790	0.460391	0.230195	+	0.973144i	$0.426063\pi$
$678$	38.6966	1.48613
$679$	−43.1112	−1.65446
$680$	−22.2619	−0.853706
$681$	13.4182	0.514187
$682$	7.06227	0.270428
$683$	39.8427	1.52454	0.762269	−	0.647260i	$-0.224085\pi$
$683$	39.8427	1.52454	0.762269	+	0.647260i	$0.224085\pi$
$684$	−6.91502	−0.264402
$685$	21.5448	0.823186
$686$	8.27290	0.315861
$687$	−40.7609	−1.55513
$688$	−4.25793	−0.162332
$689$	33.4356	1.27379
$690$	−41.5709	−1.58258
$691$	37.1603	1.41365	0.706823	−	0.707391i	$-0.250128\pi$
$691$	37.1603	1.41365	0.706823	+	0.707391i	$0.250128\pi$
$692$	20.0911	0.763750
$693$	6.31701	0.239963
$694$	−13.4446	−0.510351
$695$	−38.0487	−1.44327
$696$	16.7767	0.635920
$697$	−44.5220	−1.68639
$698$	8.64749	0.327312
$699$	53.0021	2.00472
$700$	−12.5374	−0.473868
$701$	−20.9758	−0.792246	−0.396123	−	0.918197i	$-0.629645\pi$
$701$	−20.9758	−0.792246	−0.396123	+	0.918197i	$0.629645\pi$
$702$	−2.15936	−0.0814997
$703$	4.55170	0.171671
$704$	−0.702823	−0.0264886
$705$	−58.2884	−2.19527
$706$	30.6683	1.15422
$707$	42.8690	1.61225
$708$	−1.76027	−0.0661549
$709$	−45.5162	−1.70940	−0.854698	−	0.519126i	$-0.826258\pi$
$709$	−45.5162	−1.70940	−0.854698	+	0.519126i	$0.826258\pi$
$710$	−15.0587	−0.565145
$711$	−16.3190	−0.612009
$712$	−0.269865	−0.0101136
$713$	59.6663	2.23452
$714$	61.0254	2.28382
$715$	−5.26970	−0.197076
$716$	−1.68979	−0.0631504
$717$	47.8571	1.78726
$718$	−33.8157	−1.26199
$719$	−0.329129	−0.0122745	−0.00613723	−	0.999981i	$-0.501954\pi$
$719$	−0.329129	−0.0122745	−0.00613723	+	0.999981i	$0.501954\pi$
$720$	−7.78862	−0.290265
$721$	59.9668	2.23328
$722$	−12.1530	−0.452289
$723$	40.8463	1.51909
$724$	21.5011	0.799083
$725$	−26.0345	−0.966897
$726$	24.9564	0.926218
$727$	−27.1112	−1.00550	−0.502749	−	0.864433i	$-0.667678\pi$
$727$	−27.1112	−1.00550	−0.502749	+	0.864433i	$0.667678\pi$
$728$	8.65257	0.320686
$729$	−20.2308	−0.749290
$730$	−4.99012	−0.184693
$731$	−32.1622	−1.18956
$732$	−8.71004	−0.321932
$733$	−6.20322	−0.229121	−0.114560	−	0.993416i	$-0.536546\pi$
$733$	−6.20322	−0.229121	−0.114560	+	0.993416i	$0.536546\pi$
$734$	6.02894	0.222532
$735$	31.9776	1.17951
$736$	−5.93787	−0.218873
$737$	5.21908	0.192247
$738$	−15.5766	−0.573382
$739$	−48.0961	−1.76925	−0.884623	−	0.466308i	$-0.845584\pi$
$739$	−48.0961	−1.76925	−0.884623	+	0.466308i	$0.845584\pi$
$740$	5.12673	0.188462
$741$	−15.8130	−0.580907
$742$	44.6999	1.64098
$743$	−20.6093	−0.756083	−0.378041	−	0.925789i	$-0.623402\pi$
$743$	−20.6093	−0.756083	−0.378041	+	0.925789i	$0.623402\pi$
$744$	23.8694	0.875094
$745$	−36.1347	−1.32387
$746$	7.36067	0.269493
$747$	−37.5256	−1.37299
$748$	−5.30875	−0.194107
$749$	−64.0493	−2.34031
$750$	−9.19754	−0.335847
$751$	46.8211	1.70853	0.854263	−	0.519841i	$-0.174009\pi$
$751$	46.8211	1.70853	0.854263	+	0.519841i	$0.174009\pi$
$752$	−8.32574	−0.303609
$753$	−60.0546	−2.18851
$754$	17.9675	0.654338
$755$	57.8778	2.10639
$756$	−2.88684	−0.104993
$757$	−6.50091	−0.236280	−0.118140	−	0.992997i	$-0.537693\pi$
$757$	−6.50091	−0.236280	−0.118140	+	0.992997i	$0.537693\pi$
$758$	7.47913	0.271654
$759$	−9.91332	−0.359831
$760$	7.71197	0.279742
$761$	−7.16841	−0.259855	−0.129927	−	0.991524i	$-0.541474\pi$
$761$	−7.16841	−0.259855	−0.129927	+	0.991524i	$0.541474\pi$
$762$	24.4493	0.885705
$763$	−41.3829	−1.49816
$764$	3.46247	0.125268
$765$	−58.8312	−2.12704
$766$	14.9852	0.541438
$767$	−1.88521	−0.0680710
$768$	−2.37543	−0.0857160
$769$	2.80053	0.100990	0.0504949	−	0.998724i	$-0.483920\pi$
$769$	2.80053	0.100990	0.0504949	+	0.998724i	$0.483920\pi$
$770$	−7.04504	−0.253886
$771$	65.2634	2.35040
$772$	10.9120	0.392733
$773$	−33.0581	−1.18902	−0.594508	−	0.804090i	$-0.702653\pi$
$773$	−33.0581	−1.18902	−0.594508	+	0.804090i	$0.702653\pi$
$774$	−11.2523	−0.404457
$775$	−37.0411	−1.33055
$776$	12.6756	0.455028
$777$	−14.0536	−0.504171
$778$	−31.6756	−1.13563
$779$	15.4233	0.552596
$780$	−17.8108	−0.637728
$781$	−3.59102	−0.128497
$782$	−44.8515	−1.60389
$783$	−5.99466	−0.214232
$784$	4.56759	0.163128
$785$	−17.4188	−0.621704
$786$	19.8601	0.708386
$787$	6.79596	0.242250	0.121125	−	0.992637i	$-0.461350\pi$
$787$	6.79596	0.242250	0.121125	+	0.992637i	$0.461350\pi$
$788$	12.9885	0.462697
$789$	−60.2359	−2.14446
$790$	18.1997	0.647517
$791$	55.4053	1.96999
$792$	−1.85733	−0.0659975
$793$	−9.32828	−0.331257
$794$	−35.2978	−1.25267
$795$	−92.0118	−3.26332
$796$	6.45636	0.228840
$797$	−4.44015	−0.157278	−0.0786391	−	0.996903i	$-0.525057\pi$
$797$	−4.44015	−0.157278	−0.0786391	+	0.996903i	$0.525057\pi$
$798$	−21.1404	−0.748362
$799$	−62.8883	−2.22483
$800$	3.68625	0.130329
$801$	−0.713166	−0.0251985
$802$	−7.48980	−0.264474
$803$	−1.18998	−0.0419936
$804$	17.6397	0.622103
$805$	−59.5207	−2.09783
$806$	25.5636	0.900440
$807$	56.6304	1.99348
$808$	−12.6044	−0.443420
$809$	45.1914	1.58884	0.794422	−	0.607367i	$-0.207774\pi$
$809$	45.1914	1.58884	0.794422	+	0.607367i	$0.207774\pi$
$810$	29.3082	1.02979
$811$	−41.8439	−1.46934	−0.734669	−	0.678426i	$-0.762662\pi$
$811$	−41.8439	−1.46934	−0.734669	+	0.678426i	$0.762662\pi$
$812$	24.0207	0.842961
$813$	56.8461	1.99368
$814$	1.22256	0.0428507
$815$	−37.4661	−1.31238
$816$	−17.9428	−0.628122
$817$	11.1416	0.389795
$818$	1.29911	0.0454223
$819$	22.8660	0.799002
$820$	17.3718	0.606648
$821$	46.5256	1.62376	0.811878	−	0.583827i	$-0.198445\pi$
$821$	46.5256	1.62376	0.811878	+	0.583827i	$0.198445\pi$
$822$	17.3648	0.605667
$823$	−56.4897	−1.96911	−0.984554	−	0.175081i	$-0.943981\pi$
$823$	−56.4897	−1.96911	−0.984554	+	0.175081i	$0.943981\pi$
$824$	−17.6315	−0.614223
$825$	6.15422	0.214263
$826$	−2.52033	−0.0876935
$827$	−7.03343	−0.244576	−0.122288	−	0.992495i	$-0.539023\pi$
$827$	−7.03343	−0.244576	−0.122288	+	0.992495i	$0.539023\pi$
$828$	−15.6919	−0.545331
$829$	19.5013	0.677306	0.338653	−	0.940911i	$-0.390029\pi$
$829$	19.5013	0.677306	0.338653	+	0.940911i	$0.390029\pi$
$830$	41.8504	1.45265
$831$	1.88749	0.0654763
$832$	−2.54404	−0.0881987
$833$	34.5012	1.19540
$834$	−30.6666	−1.06190
$835$	−21.5972	−0.747401
$836$	1.83906	0.0636050
$837$	−8.52902	−0.294806
$838$	−14.1470	−0.488700
$839$	42.1826	1.45631	0.728153	−	0.685415i	$-0.240379\pi$
$839$	42.1826	1.45631	0.728153	+	0.685415i	$0.240379\pi$
$840$	−23.8111	−0.821563
$841$	20.8802	0.720008
$842$	−36.8034	−1.26833
$843$	−57.9513	−1.99595
$844$	−20.3242	−0.699587
$845$	19.2392	0.661849
$846$	−22.0023	−0.756454
$847$	35.7323	1.22778
$848$	−13.1427	−0.451322
$849$	−7.40754	−0.254226
$850$	27.8440	0.955041
$851$	10.3289	0.354071
$852$	−12.1371	−0.415810
$853$	−10.2692	−0.351611	−0.175805	−	0.984425i	$-0.556253\pi$
$853$	−10.2692	−0.351611	−0.175805	+	0.984425i	$0.556253\pi$
$854$	−12.4709	−0.426747
$855$	20.3803	0.696990
$856$	18.8319	0.643660
$857$	−36.4397	−1.24475	−0.622377	−	0.782717i	$-0.713833\pi$
$857$	−36.4397	−1.24475	−0.622377	+	0.782717i	$0.713833\pi$
$858$	−4.24729	−0.145000
$859$	22.8269	0.778845	0.389422	−	0.921059i	$-0.372675\pi$
$859$	22.8269	0.778845	0.389422	+	0.921059i	$0.372675\pi$
$860$	12.5492	0.427923
$861$	−47.6203	−1.62289
$862$	−14.7276	−0.501623
$863$	−33.9297	−1.15498	−0.577489	−	0.816398i	$-0.695968\pi$
$863$	−33.9297	−1.15498	−0.577489	+	0.816398i	$0.695968\pi$
$864$	0.848790	0.0288764
$865$	−59.2134	−2.01332
$866$	26.9358	0.915314
$867$	−95.1478	−3.23139
$868$	34.1759	1.16001
$869$	4.34004	0.147226
$870$	−49.4451	−1.67635
$871$	18.8917	0.640122
$872$	12.1675	0.412042
$873$	33.4976	1.13372
$874$	15.5374	0.525562
$875$	−13.1689	−0.445191
$876$	−4.02196	−0.135889
$877$	18.5429	0.626149	0.313074	−	0.949729i	$-0.398641\pi$
$877$	18.5429	0.626149	0.313074	+	0.949729i	$0.398641\pi$
$878$	11.2838	0.380810
$879$	−9.05895	−0.305551
$880$	2.07139	0.0698265
$881$	15.0545	0.507199	0.253599	−	0.967309i	$-0.418386\pi$
$881$	15.0545	0.507199	0.253599	+	0.967309i	$0.418386\pi$
$882$	12.0707	0.406441
$883$	19.5390	0.657539	0.328769	−	0.944410i	$-0.393366\pi$
$883$	19.5390	0.657539	0.328769	+	0.944410i	$0.393366\pi$
$884$	−19.2163	−0.646315
$885$	5.18794	0.174391
$886$	−29.9375	−1.00577
$887$	38.7097	1.29974	0.649872	−	0.760044i	$-0.274823\pi$
$887$	38.7097	1.29974	0.649872	+	0.760044i	$0.274823\pi$
$888$	4.13207	0.138663
$889$	35.0062	1.17407
$890$	0.795357	0.0266604
$891$	6.98907	0.234143
$892$	−3.03498	−0.101619
$893$	21.7857	0.729032
$894$	−29.1240	−0.974053
$895$	4.98022	0.166470
$896$	−3.40112	−0.113623
$897$	−35.8837	−1.19812
$898$	−12.2719	−0.409519
$899$	70.9681	2.36692
$900$	9.74158	0.324719
$901$	−99.2731	−3.30727
$902$	4.14260	0.137934
$903$	−34.4003	−1.14477
$904$	−16.2903	−0.541808
$905$	−63.3691	−2.10646
$906$	46.6486	1.54980
$907$	27.8084	0.923363	0.461682	−	0.887046i	$-0.347246\pi$
$907$	27.8084	0.923363	0.461682	+	0.887046i	$0.347246\pi$
$908$	−5.64874	−0.187460
$909$	−33.3093	−1.10480
$910$	−25.5012	−0.845358
$911$	−4.76952	−0.158021	−0.0790106	−	0.996874i	$-0.525176\pi$
$911$	−4.76952	−0.158021	−0.0790106	+	0.996874i	$0.525176\pi$
$912$	6.21572	0.205823
$913$	9.97997	0.330289
$914$	−0.0358637	−0.00118626
$915$	25.6706	0.848645
$916$	17.1594	0.566961
$917$	28.4354	0.939021
$918$	6.41132	0.211605
$919$	24.6381	0.812737	0.406368	−	0.913709i	$-0.366795\pi$
$919$	24.6381	0.812737	0.406368	+	0.913709i	$0.366795\pi$
$920$	17.5003	0.576969
$921$	−41.4315	−1.36522
$922$	7.11039	0.234168
$923$	−12.9986	−0.427854
$924$	−5.67819	−0.186799
$925$	−6.41223	−0.210833
$926$	3.03553	0.0997538
$927$	−46.5944	−1.53036
$928$	−7.06259	−0.231841
$929$	−30.4785	−0.999967	−0.499984	−	0.866035i	$-0.666661\pi$
$929$	−30.4785	−0.999967	−0.499984	+	0.866035i	$0.666661\pi$
$930$	−70.3489	−2.30683
$931$	−11.9519	−0.391707
$932$	−22.3126	−0.730874
$933$	35.0734	1.14825
$934$	21.5699	0.705788
$935$	15.6462	0.511685
$936$	−6.72308	−0.219751
$937$	−2.80943	−0.0917800	−0.0458900	−	0.998946i	$-0.514612\pi$
$937$	−2.80943	−0.0917800	−0.0458900	+	0.998946i	$0.514612\pi$
$938$	25.2563	0.824647
$939$	72.8795	2.37833
$940$	24.5380	0.800341
$941$	6.45238	0.210342	0.105171	−	0.994454i	$-0.466461\pi$
$941$	6.45238	0.210342	0.105171	+	0.994454i	$0.466461\pi$
$942$	−14.0393	−0.457425
$943$	34.9992	1.13973
$944$	0.741030	0.0241185
$945$	8.50821	0.276772
$946$	2.99257	0.0972968
$947$	−24.9130	−0.809564	−0.404782	−	0.914413i	$-0.632653\pi$
$947$	−24.9130	−0.809564	−0.404782	+	0.914413i	$0.632653\pi$
$948$	14.6687	0.476417
$949$	−4.30743	−0.139825
$950$	−9.64570	−0.312948
$951$	−28.7447	−0.932109
$952$	−25.6902	−0.832625
$953$	27.2812	0.883723	0.441862	−	0.897083i	$-0.354318\pi$
$953$	27.2812	0.883723	0.441862	+	0.897083i	$0.354318\pi$
$954$	−34.7320	−1.12449
$955$	−10.2048	−0.330218
$956$	−20.1467	−0.651590
$957$	−11.7911	−0.381151
$958$	−21.7831	−0.703779
$959$	24.8627	0.802859
$960$	7.00098	0.225956
$961$	69.9711	2.25713
$962$	4.42536	0.142679
$963$	49.7666	1.60370
$964$	−17.1953	−0.553823
$965$	−32.1604	−1.03528
$966$	−47.9728	−1.54350
$967$	−17.2522	−0.554793	−0.277397	−	0.960755i	$-0.589472\pi$
$967$	−17.2522	−0.554793	−0.277397	+	0.960755i	$0.589472\pi$
$968$	−10.5060	−0.337677
$969$	46.9503	1.50826
$970$	−37.3581	−1.19950
$971$	25.8757	0.830391	0.415195	−	0.909732i	$-0.363713\pi$
$971$	25.8757	0.830391	0.415195	+	0.909732i	$0.363713\pi$
$972$	21.0756	0.676000
$973$	−43.9081	−1.40763
$974$	−11.1982	−0.358812
$975$	22.2767	0.713426
$976$	3.66672	0.117369
$977$	−23.2105	−0.742570	−0.371285	−	0.928519i	$-0.621083\pi$
$977$	−23.2105	−0.742570	−0.371285	+	0.928519i	$0.621083\pi$
$978$	−30.1971	−0.965597
$979$	0.189667	0.00606178
$980$	−13.4618	−0.430022
$981$	32.1547	1.02662
$982$	−1.57003	−0.0501017
$983$	−22.4107	−0.714790	−0.357395	−	0.933953i	$-0.616335\pi$
$983$	−22.4107	−0.714790	−0.357395	+	0.933953i	$0.616335\pi$
$984$	14.0014	0.446347
$985$	−38.2804	−1.21971
$986$	−53.3471	−1.69892
$987$	−67.2647	−2.14106
$988$	6.65691	0.211785
$989$	25.2830	0.803953
$990$	5.47402	0.173976
$991$	−19.2580	−0.611751	−0.305875	−	0.952072i	$-0.598949\pi$
$991$	−19.2580	−0.611751	−0.305875	+	0.952072i	$0.598949\pi$
$992$	−10.0484	−0.319038
$993$	−13.0816	−0.415133
$994$	−17.3778	−0.551189
$995$	−19.0285	−0.603243
$996$	33.7308	1.06880
$997$	−43.1019	−1.36505	−0.682525	−	0.730862i	$-0.739118\pi$
$997$	−43.1019	−1.36505	−0.682525	+	0.730862i	$0.739118\pi$
$998$	−17.7507	−0.561888
$999$	−1.47647	−0.0467135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.13	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.13	✓	95	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.37543 q^{3} +1.00000 q^{4} -2.94724 q^{5} -2.37543 q^{6} -3.40112 q^{7} +1.00000 q^{8} +2.64268 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.37543 q^{3} +1.00000 q^{4} -2.94724 q^{5} -2.37543 q^{6} -3.40112 q^{7} +1.00000 q^{8} +2.64268 q^{9} -2.94724 q^{10} -0.702823 q^{11} -2.37543 q^{12} -2.54404 q^{13} -3.40112 q^{14} +7.00098 q^{15} +1.00000 q^{16} +7.55347 q^{17} +2.64268 q^{18} -2.61667 q^{19} -2.94724 q^{20} +8.07912 q^{21} -0.702823 q^{22} -5.93787 q^{23} -2.37543 q^{24} +3.68625 q^{25} -2.54404 q^{26} +0.848790 q^{27} -3.40112 q^{28} -7.06259 q^{29} +7.00098 q^{30} -10.0484 q^{31} +1.00000 q^{32} +1.66951 q^{33} +7.55347 q^{34} +10.0239 q^{35} +2.64268 q^{36} -1.73950 q^{37} -2.61667 q^{38} +6.04319 q^{39} -2.94724 q^{40} -5.89424 q^{41} +8.07912 q^{42} -4.25793 q^{43} -0.702823 q^{44} -7.78862 q^{45} -5.93787 q^{46} -8.32574 q^{47} -2.37543 q^{48} +4.56759 q^{49} +3.68625 q^{50} -17.9428 q^{51} -2.54404 q^{52} -13.1427 q^{53} +0.848790 q^{54} +2.07139 q^{55} -3.40112 q^{56} +6.21572 q^{57} -7.06259 q^{58} +0.741030 q^{59} +7.00098 q^{60} +3.66672 q^{61} -10.0484 q^{62} -8.98806 q^{63} +1.00000 q^{64} +7.49791 q^{65} +1.66951 q^{66} -7.42588 q^{67} +7.55347 q^{68} +14.1050 q^{69} +10.0239 q^{70} +5.10943 q^{71} +2.64268 q^{72} +1.69315 q^{73} -1.73950 q^{74} -8.75644 q^{75} -2.61667 q^{76} +2.39038 q^{77} +6.04319 q^{78} -6.17516 q^{79} -2.94724 q^{80} -9.94428 q^{81} -5.89424 q^{82} -14.1998 q^{83} +8.07912 q^{84} -22.2619 q^{85} -4.25793 q^{86} +16.7767 q^{87} -0.702823 q^{88} -0.269865 q^{89} -7.78862 q^{90} +8.65257 q^{91} -5.93787 q^{92} +23.8694 q^{93} -8.32574 q^{94} +7.71197 q^{95} -2.37543 q^{96} +12.6756 q^{97} +4.56759 q^{98} -1.85733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

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