LMFDB - Embedded newform 8002.2.a.d.1.65

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:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.65
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.53759 q^{3} +1.00000 q^{4} +0.622019 q^{5} +2.53759 q^{6} -2.73093 q^{7} +1.00000 q^{8} +3.43937 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.53759 q^{3} +1.00000 q^{4} +0.622019 q^{5} +2.53759 q^{6} -2.73093 q^{7} +1.00000 q^{8} +3.43937 q^{9} +0.622019 q^{10} -2.19764 q^{11} +2.53759 q^{12} -4.72758 q^{13} -2.73093 q^{14} +1.57843 q^{15} +1.00000 q^{16} -4.84420 q^{17} +3.43937 q^{18} +1.53647 q^{19} +0.622019 q^{20} -6.92998 q^{21} -2.19764 q^{22} -2.54871 q^{23} +2.53759 q^{24} -4.61309 q^{25} -4.72758 q^{26} +1.11495 q^{27} -2.73093 q^{28} +4.88461 q^{29} +1.57843 q^{30} -5.36331 q^{31} +1.00000 q^{32} -5.57672 q^{33} -4.84420 q^{34} -1.69869 q^{35} +3.43937 q^{36} +6.59523 q^{37} +1.53647 q^{38} -11.9967 q^{39} +0.622019 q^{40} +10.7368 q^{41} -6.92998 q^{42} -11.3380 q^{43} -2.19764 q^{44} +2.13936 q^{45} -2.54871 q^{46} +4.39378 q^{47} +2.53759 q^{48} +0.457958 q^{49} -4.61309 q^{50} -12.2926 q^{51} -4.72758 q^{52} -4.47673 q^{53} +1.11495 q^{54} -1.36698 q^{55} -2.73093 q^{56} +3.89895 q^{57} +4.88461 q^{58} +4.81462 q^{59} +1.57843 q^{60} -14.1378 q^{61} -5.36331 q^{62} -9.39267 q^{63} +1.00000 q^{64} -2.94065 q^{65} -5.57672 q^{66} -7.23353 q^{67} -4.84420 q^{68} -6.46758 q^{69} -1.69869 q^{70} +15.3218 q^{71} +3.43937 q^{72} -8.98873 q^{73} +6.59523 q^{74} -11.7061 q^{75} +1.53647 q^{76} +6.00160 q^{77} -11.9967 q^{78} -9.79071 q^{79} +0.622019 q^{80} -7.48883 q^{81} +10.7368 q^{82} +10.4209 q^{83} -6.92998 q^{84} -3.01319 q^{85} -11.3380 q^{86} +12.3952 q^{87} -2.19764 q^{88} +10.9827 q^{89} +2.13936 q^{90} +12.9107 q^{91} -2.54871 q^{92} -13.6099 q^{93} +4.39378 q^{94} +0.955717 q^{95} +2.53759 q^{96} -2.02109 q^{97} +0.457958 q^{98} -7.55851 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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
$3$	2.53759	1.46508	0.732540	−	0.680724i	$-0.238335\pi$
$3$	2.53759	1.46508	0.732540	+	0.680724i	$0.238335\pi$
$4$	1.00000	0.500000
$5$	0.622019	0.278175	0.139088	−	0.990280i	$-0.455583\pi$
$5$	0.622019	0.278175	0.139088	+	0.990280i	$0.455583\pi$
$6$	2.53759	1.03597
$7$	−2.73093	−1.03219	−0.516097	−	0.856530i	$-0.672615\pi$
$7$	−2.73093	−1.03219	−0.516097	+	0.856530i	$0.672615\pi$
$8$	1.00000	0.353553
$9$	3.43937	1.14646
$10$	0.622019	0.196700
$11$	−2.19764	−0.662614	−0.331307	−	0.943523i	$-0.607490\pi$
$11$	−2.19764	−0.662614	−0.331307	+	0.943523i	$0.607490\pi$
$12$	2.53759	0.732540
$13$	−4.72758	−1.31120	−0.655598	−	0.755110i	$-0.727583\pi$
$13$	−4.72758	−1.31120	−0.655598	+	0.755110i	$0.727583\pi$
$14$	−2.73093	−0.729871
$15$	1.57843	0.407549
$16$	1.00000	0.250000
$17$	−4.84420	−1.17489	−0.587446	−	0.809263i	$-0.699867\pi$
$17$	−4.84420	−1.17489	−0.587446	+	0.809263i	$0.699867\pi$
$18$	3.43937	0.810668
$19$	1.53647	0.352491	0.176246	−	0.984346i	$-0.443605\pi$
$19$	1.53647	0.352491	0.176246	+	0.984346i	$0.443605\pi$
$20$	0.622019	0.139088
$21$	−6.92998	−1.51224
$22$	−2.19764	−0.468539
$23$	−2.54871	−0.531442	−0.265721	−	0.964050i	$-0.585610\pi$
$23$	−2.54871	−0.531442	−0.265721	+	0.964050i	$0.585610\pi$
$24$	2.53759	0.517984
$25$	−4.61309	−0.922618
$26$	−4.72758	−0.927156
$27$	1.11495	0.214572
$28$	−2.73093	−0.516097
$29$	4.88461	0.907050	0.453525	−	0.891244i	$-0.350166\pi$
$29$	4.88461	0.907050	0.453525	+	0.891244i	$0.350166\pi$
$30$	1.57843	0.288181
$31$	−5.36331	−0.963278	−0.481639	−	0.876370i	$-0.659958\pi$
$31$	−5.36331	−0.963278	−0.481639	+	0.876370i	$0.659958\pi$
$32$	1.00000	0.176777
$33$	−5.57672	−0.970782
$34$	−4.84420	−0.830774
$35$	−1.69869	−0.287131
$36$	3.43937	0.573229
$37$	6.59523	1.08425	0.542124	−	0.840298i	$-0.317620\pi$
$37$	6.59523	1.08425	0.542124	+	0.840298i	$0.317620\pi$
$38$	1.53647	0.249249
$39$	−11.9967	−1.92101
$40$	0.622019	0.0983499
$41$	10.7368	1.67681	0.838406	−	0.545046i	$-0.183488\pi$
$41$	10.7368	1.67681	0.838406	+	0.545046i	$0.183488\pi$
$42$	−6.92998	−1.06932
$43$	−11.3380	−1.72902	−0.864512	−	0.502612i	$-0.832372\pi$
$43$	−11.3380	−1.72902	−0.864512	+	0.502612i	$0.832372\pi$
$44$	−2.19764	−0.331307
$45$	2.13936	0.318916
$46$	−2.54871	−0.375786
$47$	4.39378	0.640899	0.320449	−	0.947266i	$-0.396166\pi$
$47$	4.39378	0.640899	0.320449	+	0.947266i	$0.396166\pi$
$48$	2.53759	0.366270
$49$	0.457958	0.0654226
$50$	−4.61309	−0.652390
$51$	−12.2926	−1.72131
$52$	−4.72758	−0.655598
$53$	−4.47673	−0.614927	−0.307463	−	0.951560i	$-0.599480\pi$
$53$	−4.47673	−0.614927	−0.307463	+	0.951560i	$0.599480\pi$
$54$	1.11495	0.151725
$55$	−1.36698	−0.184323
$56$	−2.73093	−0.364935
$57$	3.89895	0.516428
$58$	4.88461	0.641381
$59$	4.81462	0.626811	0.313405	−	0.949619i	$-0.398530\pi$
$59$	4.81462	0.626811	0.313405	+	0.949619i	$0.398530\pi$
$60$	1.57843	0.203775
$61$	−14.1378	−1.81015	−0.905077	−	0.425248i	$-0.860187\pi$
$61$	−14.1378	−1.81015	−0.905077	+	0.425248i	$0.860187\pi$
$62$	−5.36331	−0.681141
$63$	−9.39267	−1.18337
$64$	1.00000	0.125000
$65$	−2.94065	−0.364743
$66$	−5.57672	−0.686447
$67$	−7.23353	−0.883716	−0.441858	−	0.897085i	$-0.645680\pi$
$67$	−7.23353	−0.883716	−0.441858	+	0.897085i	$0.645680\pi$
$68$	−4.84420	−0.587446
$69$	−6.46758	−0.778605
$70$	−1.69869	−0.203032
$71$	15.3218	1.81836	0.909182	−	0.416400i	$-0.136708\pi$
$71$	15.3218	1.81836	0.909182	+	0.416400i	$0.136708\pi$
$72$	3.43937	0.405334
$73$	−8.98873	−1.05205	−0.526026	−	0.850469i	$-0.676318\pi$
$73$	−8.98873	−1.05205	−0.526026	+	0.850469i	$0.676318\pi$
$74$	6.59523	0.766680
$75$	−11.7061	−1.35171
$76$	1.53647	0.176246
$77$	6.00160	0.683946
$78$	−11.9967	−1.35836
$79$	−9.79071	−1.10154	−0.550771	−	0.834657i	$-0.685666\pi$
$79$	−9.79071	−1.10154	−0.550771	+	0.834657i	$0.685666\pi$
$80$	0.622019	0.0695439
$81$	−7.48883	−0.832092
$82$	10.7368	1.18569
$83$	10.4209	1.14384	0.571920	−	0.820309i	$-0.306199\pi$
$83$	10.4209	1.14384	0.571920	+	0.820309i	$0.306199\pi$
$84$	−6.92998	−0.756122
$85$	−3.01319	−0.326826
$86$	−11.3380	−1.22260
$87$	12.3952	1.32890
$88$	−2.19764	−0.234269
$89$	10.9827	1.16417	0.582083	−	0.813129i	$-0.302238\pi$
$89$	10.9827	1.16417	0.582083	+	0.813129i	$0.302238\pi$
$90$	2.13936	0.225508
$91$	12.9107	1.35341
$92$	−2.54871	−0.265721
$93$	−13.6099	−1.41128
$94$	4.39378	0.453184
$95$	0.955717	0.0980545
$96$	2.53759	0.258992
$97$	−2.02109	−0.205210	−0.102605	−	0.994722i	$-0.532718\pi$
$97$	−2.02109	−0.205210	−0.102605	+	0.994722i	$0.532718\pi$
$98$	0.457958	0.0462607
$99$	−7.55851	−0.759659
$100$	−4.61309	−0.461309
$101$	−12.2377	−1.21769	−0.608847	−	0.793288i	$-0.708368\pi$
$101$	−12.2377	−1.21769	−0.608847	+	0.793288i	$0.708368\pi$
$102$	−12.2926	−1.21715
$103$	−0.596774	−0.0588019	−0.0294010	−	0.999568i	$-0.509360\pi$
$103$	−0.596774	−0.0588019	−0.0294010	+	0.999568i	$0.509360\pi$
$104$	−4.72758	−0.463578
$105$	−4.31058	−0.420669
$106$	−4.47673	−0.434819
$107$	−8.32179	−0.804498	−0.402249	−	0.915530i	$-0.631771\pi$
$107$	−8.32179	−0.804498	−0.402249	+	0.915530i	$0.631771\pi$
$108$	1.11495	0.107286
$109$	−6.36704	−0.609852	−0.304926	−	0.952376i	$-0.598632\pi$
$109$	−6.36704	−0.609852	−0.304926	+	0.952376i	$0.598632\pi$
$110$	−1.36698	−0.130336
$111$	16.7360	1.58851
$112$	−2.73093	−0.258048
$113$	2.69829	0.253834	0.126917	−	0.991913i	$-0.459492\pi$
$113$	2.69829	0.253834	0.126917	+	0.991913i	$0.459492\pi$
$114$	3.89895	0.365170
$115$	−1.58535	−0.147834
$116$	4.88461	0.453525
$117$	−16.2599	−1.50323
$118$	4.81462	0.443222
$119$	13.2292	1.21272
$120$	1.57843	0.144090
$121$	−6.17037	−0.560943
$122$	−14.1378	−1.27997
$123$	27.2457	2.45666
$124$	−5.36331	−0.481639
$125$	−5.97953	−0.534825
$126$	−9.39267	−0.836766
$127$	−15.1747	−1.34653	−0.673267	−	0.739399i	$-0.735110\pi$
$127$	−15.1747	−1.34653	−0.673267	+	0.739399i	$0.735110\pi$
$128$	1.00000	0.0883883
$129$	−28.7711	−2.53316
$130$	−2.94065	−0.257912
$131$	−13.2550	−1.15809	−0.579046	−	0.815295i	$-0.696575\pi$
$131$	−13.2550	−1.15809	−0.579046	+	0.815295i	$0.696575\pi$
$132$	−5.57672	−0.485391
$133$	−4.19600	−0.363839
$134$	−7.23353	−0.624881
$135$	0.693520	0.0596887
$136$	−4.84420	−0.415387
$137$	11.5851	0.989784	0.494892	−	0.868954i	$-0.335208\pi$
$137$	11.5851	0.989784	0.494892	+	0.868954i	$0.335208\pi$
$138$	−6.46758	−0.550557
$139$	−14.1105	−1.19683	−0.598417	−	0.801185i	$-0.704203\pi$
$139$	−14.1105	−1.19683	−0.598417	+	0.801185i	$0.704203\pi$
$140$	−1.69869	−0.143565
$141$	11.1496	0.938967
$142$	15.3218	1.28578
$143$	10.3895	0.868817
$144$	3.43937	0.286614
$145$	3.03832	0.252319
$146$	−8.98873	−0.743913
$147$	1.16211	0.0958492
$148$	6.59523	0.542124
$149$	−15.4811	−1.26826	−0.634132	−	0.773225i	$-0.718642\pi$
$149$	−15.4811	−1.26826	−0.634132	+	0.773225i	$0.718642\pi$
$150$	−11.7061	−0.955803
$151$	18.0158	1.46611	0.733054	−	0.680171i	$-0.238094\pi$
$151$	18.0158	1.46611	0.733054	+	0.680171i	$0.238094\pi$
$152$	1.53647	0.124625
$153$	−16.6610	−1.34696
$154$	6.00160	0.483623
$155$	−3.33608	−0.267960
$156$	−11.9967	−0.960503
$157$	−11.8263	−0.943840	−0.471920	−	0.881641i	$-0.656439\pi$
$157$	−11.8263	−0.943840	−0.471920	+	0.881641i	$0.656439\pi$
$158$	−9.79071	−0.778907
$159$	−11.3601	−0.900917
$160$	0.622019	0.0491749
$161$	6.96033	0.548551
$162$	−7.48883	−0.588378
$163$	−1.01631	−0.0796035	−0.0398017	−	0.999208i	$-0.512673\pi$
$163$	−1.01631	−0.0796035	−0.0398017	+	0.999208i	$0.512673\pi$
$164$	10.7368	0.838406
$165$	−3.46883	−0.270048
$166$	10.4209	0.808817
$167$	20.0590	1.55221	0.776107	−	0.630601i	$-0.217191\pi$
$167$	20.0590	1.55221	0.776107	+	0.630601i	$0.217191\pi$
$168$	−6.92998	−0.534659
$169$	9.35005	0.719235
$170$	−3.01319	−0.231101
$171$	5.28451	0.404116
$172$	−11.3380	−0.864512
$173$	12.3281	0.937286	0.468643	−	0.883388i	$-0.344743\pi$
$173$	12.3281	0.937286	0.468643	+	0.883388i	$0.344743\pi$
$174$	12.3952	0.939674
$175$	12.5980	0.952320
$176$	−2.19764	−0.165654
$177$	12.2175	0.918327
$178$	10.9827	0.823190
$179$	−21.1712	−1.58241	−0.791204	−	0.611552i	$-0.790546\pi$
$179$	−21.1712	−1.58241	−0.791204	+	0.611552i	$0.790546\pi$
$180$	2.13936	0.159458
$181$	9.68326	0.719751	0.359876	−	0.933000i	$-0.382819\pi$
$181$	9.68326	0.719751	0.359876	+	0.933000i	$0.382819\pi$
$182$	12.9107	0.957004
$183$	−35.8758	−2.65202
$184$	−2.54871	−0.187893
$185$	4.10236	0.301611
$186$	−13.6099	−0.997925
$187$	10.6458	0.778500
$188$	4.39378	0.320449
$189$	−3.04485	−0.221480
$190$	0.955717	0.0693350
$191$	24.2144	1.75210	0.876048	−	0.482224i	$-0.160171\pi$
$191$	24.2144	1.75210	0.876048	+	0.482224i	$0.160171\pi$
$192$	2.53759	0.183135
$193$	7.06659	0.508664	0.254332	−	0.967117i	$-0.418144\pi$
$193$	7.06659	0.508664	0.254332	+	0.967117i	$0.418144\pi$
$194$	−2.02109	−0.145105
$195$	−7.46217	−0.534377
$196$	0.457958	0.0327113
$197$	−7.09006	−0.505146	−0.252573	−	0.967578i	$-0.581277\pi$
$197$	−7.09006	−0.505146	−0.252573	+	0.967578i	$0.581277\pi$
$198$	−7.55851	−0.537160
$199$	27.1562	1.92506	0.962528	−	0.271183i	$-0.0874149\pi$
$199$	27.1562	1.92506	0.962528	+	0.271183i	$0.0874149\pi$
$200$	−4.61309	−0.326195
$201$	−18.3557	−1.29471
$202$	−12.2377	−0.861040
$203$	−13.3395	−0.936251
$204$	−12.2926	−0.860655
$205$	6.67852	0.466448
$206$	−0.596774	−0.0415792
$207$	−8.76596	−0.609276
$208$	−4.72758	−0.327799
$209$	−3.37662	−0.233566
$210$	−4.31058	−0.297458
$211$	16.3138	1.12309	0.561545	−	0.827447i	$-0.310207\pi$
$211$	16.3138	1.12309	0.561545	+	0.827447i	$0.310207\pi$
$212$	−4.47673	−0.307463
$213$	38.8805	2.66405
$214$	−8.32179	−0.568866
$215$	−7.05243	−0.480972
$216$	1.11495	0.0758627
$217$	14.6468	0.994289
$218$	−6.36704	−0.431231
$219$	−22.8097	−1.54134
$220$	−1.36698	−0.0921615
$221$	22.9014	1.54051
$222$	16.7360	1.12325
$223$	−11.8975	−0.796716	−0.398358	−	0.917230i	$-0.630420\pi$
$223$	−11.8975	−0.796716	−0.398358	+	0.917230i	$0.630420\pi$
$224$	−2.73093	−0.182468
$225$	−15.8661	−1.05774
$226$	2.69829	0.179488
$227$	1.01542	0.0673956	0.0336978	−	0.999432i	$-0.489272\pi$
$227$	1.01542	0.0673956	0.0336978	+	0.999432i	$0.489272\pi$
$228$	3.89895	0.258214
$229$	10.3112	0.681385	0.340693	−	0.940175i	$-0.389338\pi$
$229$	10.3112	0.681385	0.340693	+	0.940175i	$0.389338\pi$
$230$	−1.58535	−0.104535
$231$	15.2296	1.00203
$232$	4.88461	0.320691
$233$	4.94348	0.323858	0.161929	−	0.986802i	$-0.448228\pi$
$233$	4.94348	0.323858	0.161929	+	0.986802i	$0.448228\pi$
$234$	−16.2599	−1.06294
$235$	2.73302	0.178282
$236$	4.81462	0.313405
$237$	−24.8448	−1.61385
$238$	13.2292	0.857519
$239$	−23.5255	−1.52174	−0.760870	−	0.648904i	$-0.775228\pi$
$239$	−23.5255	−1.52174	−0.760870	+	0.648904i	$0.775228\pi$
$240$	1.57843	0.101887
$241$	15.3551	0.989106	0.494553	−	0.869147i	$-0.335332\pi$
$241$	15.3551	0.989106	0.494553	+	0.869147i	$0.335332\pi$
$242$	−6.17037	−0.396646
$243$	−22.3484	−1.43365
$244$	−14.1378	−0.905077
$245$	0.284859	0.0181989
$246$	27.2457	1.73712
$247$	−7.26381	−0.462185
$248$	−5.36331	−0.340570
$249$	26.4439	1.67582
$250$	−5.97953	−0.378179
$251$	−14.8730	−0.938774	−0.469387	−	0.882993i	$-0.655525\pi$
$251$	−14.8730	−0.938774	−0.469387	+	0.882993i	$0.655525\pi$
$252$	−9.39267	−0.591683
$253$	5.60115	0.352141
$254$	−15.1747	−0.952144
$255$	−7.64624	−0.478826
$256$	1.00000	0.0625000
$257$	8.63706	0.538765	0.269382	−	0.963033i	$-0.413180\pi$
$257$	8.63706	0.538765	0.269382	+	0.963033i	$0.413180\pi$
$258$	−28.7711	−1.79121
$259$	−18.0111	−1.11915
$260$	−2.94065	−0.182371
$261$	16.8000	1.03989
$262$	−13.2550	−0.818895
$263$	18.8587	1.16288	0.581438	−	0.813591i	$-0.302490\pi$
$263$	18.8587	1.16288	0.581438	+	0.813591i	$0.302490\pi$
$264$	−5.57672	−0.343223
$265$	−2.78461	−0.171058
$266$	−4.19600	−0.257273
$267$	27.8697	1.70560
$268$	−7.23353	−0.441858
$269$	−0.210385	−0.0128274	−0.00641370	−	0.999979i	$-0.502042\pi$
$269$	−0.210385	−0.0128274	−0.00641370	+	0.999979i	$0.502042\pi$
$270$	0.693520	0.0422063
$271$	−11.0619	−0.671964	−0.335982	−	0.941868i	$-0.609068\pi$
$271$	−11.0619	−0.671964	−0.335982	+	0.941868i	$0.609068\pi$
$272$	−4.84420	−0.293723
$273$	32.7620	1.98285
$274$	11.5851	0.699883
$275$	10.1379	0.611340
$276$	−6.46758	−0.389303
$277$	−13.2923	−0.798655	−0.399328	−	0.916808i	$-0.630756\pi$
$277$	−13.2923	−0.798655	−0.399328	+	0.916808i	$0.630756\pi$
$278$	−14.1105	−0.846290
$279$	−18.4464	−1.10436
$280$	−1.69869	−0.101516
$281$	3.31331	0.197655	0.0988277	−	0.995105i	$-0.468491\pi$
$281$	3.31331	0.197655	0.0988277	+	0.995105i	$0.468491\pi$
$282$	11.1496	0.663950
$283$	12.0637	0.717112	0.358556	−	0.933508i	$-0.383269\pi$
$283$	12.0637	0.717112	0.358556	+	0.933508i	$0.383269\pi$
$284$	15.3218	0.909182
$285$	2.42522	0.143658
$286$	10.3895	0.614346
$287$	−29.3215	−1.73079
$288$	3.43937	0.202667
$289$	6.46632	0.380372
$290$	3.03832	0.178416
$291$	−5.12869	−0.300649
$292$	−8.98873	−0.526026
$293$	11.3669	0.664062	0.332031	−	0.943268i	$-0.392266\pi$
$293$	11.3669	0.664062	0.332031	+	0.943268i	$0.392266\pi$
$294$	1.16211	0.0677756
$295$	2.99479	0.174363
$296$	6.59523	0.383340
$297$	−2.45026	−0.142179
$298$	−15.4811	−0.896797
$299$	12.0492	0.696825
$300$	−11.7061	−0.675855
$301$	30.9632	1.78469
$302$	18.0158	1.03669
$303$	−31.0542	−1.78402
$304$	1.53647	0.0881228
$305$	−8.79395	−0.503540
$306$	−16.6610	−0.952448
$307$	5.84588	0.333642	0.166821	−	0.985987i	$-0.446650\pi$
$307$	5.84588	0.333642	0.166821	+	0.985987i	$0.446650\pi$
$308$	6.00160	0.341973
$309$	−1.51437	−0.0861495
$310$	−3.33608	−0.189477
$311$	24.1318	1.36839	0.684194	−	0.729300i	$-0.260154\pi$
$311$	24.1318	1.36839	0.684194	+	0.729300i	$0.260154\pi$
$312$	−11.9967	−0.679178
$313$	−0.418902	−0.0236777	−0.0118389	−	0.999930i	$-0.503769\pi$
$313$	−0.418902	−0.0236777	−0.0118389	+	0.999930i	$0.503769\pi$
$314$	−11.8263	−0.667396
$315$	−5.84242	−0.329183
$316$	−9.79071	−0.550771
$317$	−11.1789	−0.627868	−0.313934	−	0.949445i	$-0.601647\pi$
$317$	−11.1789	−0.627868	−0.313934	+	0.949445i	$0.601647\pi$
$318$	−11.3601	−0.637044
$319$	−10.7346	−0.601024
$320$	0.622019	0.0347719
$321$	−21.1173	−1.17865
$322$	6.96033	0.387884
$323$	−7.44300	−0.414139
$324$	−7.48883	−0.416046
$325$	21.8088	1.20973
$326$	−1.01631	−0.0562882
$327$	−16.1570	−0.893482
$328$	10.7368	0.592843
$329$	−11.9991	−0.661531
$330$	−3.46883	−0.190953
$331$	−9.44549	−0.519171	−0.259586	−	0.965720i	$-0.583586\pi$
$331$	−9.44549	−0.519171	−0.259586	+	0.965720i	$0.583586\pi$
$332$	10.4209	0.571920
$333$	22.6834	1.24305
$334$	20.0590	1.09758
$335$	−4.49939	−0.245828
$336$	−6.92998	−0.378061
$337$	−7.30638	−0.398004	−0.199002	−	0.979999i	$-0.563770\pi$
$337$	−7.30638	−0.398004	−0.199002	+	0.979999i	$0.563770\pi$
$338$	9.35005	0.508576
$339$	6.84717	0.371887
$340$	−3.01319	−0.163413
$341$	11.7866	0.638282
$342$	5.28451	0.285754
$343$	17.8658	0.964664
$344$	−11.3380	−0.611302
$345$	−4.02296	−0.216589
$346$	12.3281	0.662761
$347$	−3.88483	−0.208549	−0.104274	−	0.994549i	$-0.533252\pi$
$347$	−3.88483	−0.208549	−0.104274	+	0.994549i	$0.533252\pi$
$348$	12.3952	0.664450
$349$	−31.0517	−1.66216	−0.831079	−	0.556154i	$-0.812276\pi$
$349$	−31.0517	−1.66216	−0.831079	+	0.556154i	$0.812276\pi$
$350$	12.5980	0.673392
$351$	−5.27102	−0.281346
$352$	−2.19764	−0.117135
$353$	−11.3193	−0.602467	−0.301233	−	0.953550i	$-0.597398\pi$
$353$	−11.3193	−0.602467	−0.301233	+	0.953550i	$0.597398\pi$
$354$	12.2175	0.649355
$355$	9.53045	0.505824
$356$	10.9827	0.582083
$357$	33.5702	1.77672
$358$	−21.1712	−1.11893
$359$	−2.73849	−0.144532	−0.0722660	−	0.997385i	$-0.523023\pi$
$359$	−2.73849	−0.144532	−0.0722660	+	0.997385i	$0.523023\pi$
$360$	2.13936	0.112754
$361$	−16.6392	−0.875750
$362$	9.68326	0.508941
$363$	−15.6579	−0.821825
$364$	12.9107	0.676704
$365$	−5.59116	−0.292655
$366$	−35.8758	−1.87526
$367$	25.1626	1.31348	0.656740	−	0.754117i	$-0.271935\pi$
$367$	25.1626	1.31348	0.656740	+	0.754117i	$0.271935\pi$
$368$	−2.54871	−0.132861
$369$	36.9280	1.92239
$370$	4.10236	0.213271
$371$	12.2256	0.634723
$372$	−13.6099	−0.705639
$373$	28.9585	1.49942	0.749708	−	0.661768i	$-0.230194\pi$
$373$	28.9585	1.49942	0.749708	+	0.661768i	$0.230194\pi$
$374$	10.6458	0.550483
$375$	−15.1736	−0.783561
$376$	4.39378	0.226592
$377$	−23.0924	−1.18932
$378$	−3.04485	−0.156610
$379$	2.06744	0.106197	0.0530985	−	0.998589i	$-0.483090\pi$
$379$	2.06744	0.106197	0.0530985	+	0.998589i	$0.483090\pi$
$380$	0.955717	0.0490272
$381$	−38.5071	−1.97278
$382$	24.2144	1.23892
$383$	−5.82726	−0.297759	−0.148880	−	0.988855i	$-0.547567\pi$
$383$	−5.82726	−0.297759	−0.148880	+	0.988855i	$0.547567\pi$
$384$	2.53759	0.129496
$385$	3.73311	0.190257
$386$	7.06659	0.359680
$387$	−38.9955	−1.98225
$388$	−2.02109	−0.102605
$389$	22.8784	1.15998	0.579991	−	0.814623i	$-0.303056\pi$
$389$	22.8784	1.15998	0.579991	+	0.814623i	$0.303056\pi$
$390$	−7.46217	−0.377861
$391$	12.3465	0.624387
$392$	0.457958	0.0231304
$393$	−33.6357	−1.69670
$394$	−7.09006	−0.357192
$395$	−6.09001	−0.306422
$396$	−7.55851	−0.379830
$397$	20.0294	1.00525	0.502624	−	0.864505i	$-0.332368\pi$
$397$	20.0294	1.00525	0.502624	+	0.864505i	$0.332368\pi$
$398$	27.1562	1.36122
$399$	−10.6477	−0.533053
$400$	−4.61309	−0.230655
$401$	17.3181	0.864826	0.432413	−	0.901676i	$-0.357662\pi$
$401$	17.3181	0.864826	0.432413	+	0.901676i	$0.357662\pi$
$402$	−18.3557	−0.915501
$403$	25.3555	1.26305
$404$	−12.2377	−0.608847
$405$	−4.65820	−0.231468
$406$	−13.3395	−0.662029
$407$	−14.4940	−0.718438
$408$	−12.2926	−0.608575
$409$	15.4454	0.763728	0.381864	−	0.924219i	$-0.375282\pi$
$409$	15.4454	0.763728	0.381864	+	0.924219i	$0.375282\pi$
$410$	6.67852	0.329829
$411$	29.3983	1.45011
$412$	−0.596774	−0.0294010
$413$	−13.1484	−0.646990
$414$	−8.76596	−0.430823
$415$	6.48199	0.318188
$416$	−4.72758	−0.231789
$417$	−35.8066	−1.75346
$418$	−3.37662	−0.165156
$419$	10.4276	0.509422	0.254711	−	0.967017i	$-0.418020\pi$
$419$	10.4276	0.509422	0.254711	+	0.967017i	$0.418020\pi$
$420$	−4.31058	−0.210335
$421$	−6.49035	−0.316320	−0.158160	−	0.987413i	$-0.550556\pi$
$421$	−6.49035	−0.316320	−0.158160	+	0.987413i	$0.550556\pi$
$422$	16.3138	0.794144
$423$	15.1118	0.734763
$424$	−4.47673	−0.217409
$425$	22.3468	1.08398
$426$	38.8805	1.88377
$427$	38.6092	1.86843
$428$	−8.32179	−0.402249
$429$	26.3644	1.27289
$430$	−7.05243	−0.340099
$431$	2.87772	0.138615	0.0693075	−	0.997595i	$-0.477921\pi$
$431$	2.87772	0.138615	0.0693075	+	0.997595i	$0.477921\pi$
$432$	1.11495	0.0536431
$433$	−17.7633	−0.853648	−0.426824	−	0.904335i	$-0.640368\pi$
$433$	−17.7633	−0.853648	−0.426824	+	0.904335i	$0.640368\pi$
$434$	14.6468	0.703069
$435$	7.71002	0.369667
$436$	−6.36704	−0.304926
$437$	−3.91602	−0.187329
$438$	−22.8097	−1.08989
$439$	−3.33472	−0.159157	−0.0795787	−	0.996829i	$-0.525358\pi$
$439$	−3.33472	−0.159157	−0.0795787	+	0.996829i	$0.525358\pi$
$440$	−1.36698	−0.0651680
$441$	1.57509	0.0750042
$442$	22.9014	1.08931
$443$	−6.05598	−0.287728	−0.143864	−	0.989597i	$-0.545953\pi$
$443$	−6.05598	−0.287728	−0.143864	+	0.989597i	$0.545953\pi$
$444$	16.7360	0.794255
$445$	6.83146	0.323842
$446$	−11.8975	−0.563364
$447$	−39.2848	−1.85811
$448$	−2.73093	−0.129024
$449$	2.26436	0.106862	0.0534308	−	0.998572i	$-0.482984\pi$
$449$	2.26436	0.106862	0.0534308	+	0.998572i	$0.482984\pi$
$450$	−15.8661	−0.747937
$451$	−23.5957	−1.11108
$452$	2.69829	0.126917
$453$	45.7168	2.14796
$454$	1.01542	0.0476559
$455$	8.03069	0.376485
$456$	3.89895	0.182585
$457$	−18.3316	−0.857518	−0.428759	−	0.903419i	$-0.641049\pi$
$457$	−18.3316	−0.857518	−0.428759	+	0.903419i	$0.641049\pi$
$458$	10.3112	0.481812
$459$	−5.40105	−0.252099
$460$	−1.58535	−0.0739171
$461$	−19.6672	−0.915993	−0.457997	−	0.888954i	$-0.651433\pi$
$461$	−19.6672	−0.915993	−0.457997	+	0.888954i	$0.651433\pi$
$462$	15.2296	0.708546
$463$	4.65105	0.216153	0.108076	−	0.994143i	$-0.465531\pi$
$463$	4.65105	0.216153	0.108076	+	0.994143i	$0.465531\pi$
$464$	4.88461	0.226762
$465$	−8.46561	−0.392583
$466$	4.94348	0.229002
$467$	36.3073	1.68010	0.840050	−	0.542509i	$-0.182526\pi$
$467$	36.3073	1.68010	0.840050	+	0.542509i	$0.182526\pi$
$468$	−16.2599	−0.751615
$469$	19.7542	0.912165
$470$	2.73302	0.126065
$471$	−30.0103	−1.38280
$472$	4.81462	0.221611
$473$	24.9168	1.14568
$474$	−24.8448	−1.14116
$475$	−7.08790	−0.325215
$476$	13.2292	0.606358
$477$	−15.3972	−0.704988
$478$	−23.5255	−1.07603
$479$	28.9259	1.32166	0.660830	−	0.750536i	$-0.270204\pi$
$479$	28.9259	1.32166	0.660830	+	0.750536i	$0.270204\pi$
$480$	1.57843	0.0720452
$481$	−31.1795	−1.42166
$482$	15.3551	0.699404
$483$	17.6625	0.803671
$484$	−6.17037	−0.280471
$485$	−1.25715	−0.0570844
$486$	−22.3484	−1.01375
$487$	−18.3684	−0.832354	−0.416177	−	0.909284i	$-0.636630\pi$
$487$	−18.3684	−0.832354	−0.416177	+	0.909284i	$0.636630\pi$
$488$	−14.1378	−0.639986
$489$	−2.57898	−0.116625
$490$	0.284859	0.0128686
$491$	−37.0555	−1.67229	−0.836147	−	0.548506i	$-0.815197\pi$
$491$	−37.0555	−1.67229	−0.836147	+	0.548506i	$0.815197\pi$
$492$	27.2457	1.22833
$493$	−23.6621	−1.06569
$494$	−7.26381	−0.326814
$495$	−4.70154	−0.211319
$496$	−5.36331	−0.240820
$497$	−41.8427	−1.87690
$498$	26.4439	1.18498
$499$	−1.95467	−0.0875029	−0.0437514	−	0.999042i	$-0.513931\pi$
$499$	−1.95467	−0.0875029	−0.0437514	+	0.999042i	$0.513931\pi$
$500$	−5.97953	−0.267413
$501$	50.9016	2.27412
$502$	−14.8730	−0.663813
$503$	10.0794	0.449420	0.224710	−	0.974426i	$-0.427857\pi$
$503$	10.0794	0.449420	0.224710	+	0.974426i	$0.427857\pi$
$504$	−9.39267	−0.418383
$505$	−7.61207	−0.338733
$506$	5.60115	0.249001
$507$	23.7266	1.05374
$508$	−15.1747	−0.673267
$509$	8.69248	0.385288	0.192644	−	0.981269i	$-0.438294\pi$
$509$	8.69248	0.385288	0.192644	+	0.981269i	$0.438294\pi$
$510$	−7.64624	−0.338581
$511$	24.5476	1.08592
$512$	1.00000	0.0441942
$513$	1.71309	0.0756349
$514$	8.63706	0.380964
$515$	−0.371205	−0.0163572
$516$	−28.7711	−1.26658
$517$	−9.65596	−0.424668
$518$	−18.0111	−0.791361
$519$	31.2836	1.37320
$520$	−2.94065	−0.128956
$521$	11.7013	0.512645	0.256322	−	0.966591i	$-0.417489\pi$
$521$	11.7013	0.512645	0.256322	+	0.966591i	$0.417489\pi$
$522$	16.8000	0.735316
$523$	−27.4285	−1.19936	−0.599681	−	0.800239i	$-0.704706\pi$
$523$	−27.4285	−1.19936	−0.599681	+	0.800239i	$0.704706\pi$
$524$	−13.2550	−0.579046
$525$	31.9686	1.39522
$526$	18.8587	0.822277
$527$	25.9810	1.13175
$528$	−5.57672	−0.242696
$529$	−16.5041	−0.717569
$530$	−2.78461	−0.120956
$531$	16.5593	0.718612
$532$	−4.19600	−0.181920
$533$	−50.7593	−2.19863
$534$	27.8697	1.20604
$535$	−5.17631	−0.223791
$536$	−7.23353	−0.312441
$537$	−53.7238	−2.31835
$538$	−0.210385	−0.00907034
$539$	−1.00643	−0.0433499
$540$	0.693520	0.0298444
$541$	12.8569	0.552760	0.276380	−	0.961048i	$-0.410865\pi$
$541$	12.8569	0.552760	0.276380	+	0.961048i	$0.410865\pi$
$542$	−11.0619	−0.475150
$543$	24.5722	1.05449
$544$	−4.84420	−0.207694
$545$	−3.96042	−0.169646
$546$	32.7620	1.40209
$547$	24.7325	1.05748	0.528742	−	0.848783i	$-0.322664\pi$
$547$	24.7325	1.05748	0.528742	+	0.848783i	$0.322664\pi$
$548$	11.5851	0.494892
$549$	−48.6250	−2.07526
$550$	10.1379	0.432283
$551$	7.50508	0.319727
$552$	−6.46758	−0.275278
$553$	26.7377	1.13700
$554$	−13.2923	−0.564734
$555$	10.4101	0.441885
$556$	−14.1105	−0.598417
$557$	−19.7325	−0.836092	−0.418046	−	0.908426i	$-0.637285\pi$
$557$	−19.7325	−0.836092	−0.418046	+	0.908426i	$0.637285\pi$
$558$	−18.4464	−0.780899
$559$	53.6012	2.26709
$560$	−1.69869	−0.0717827
$561$	27.0148	1.14056
$562$	3.31331	0.139763
$563$	−9.56024	−0.402916	−0.201458	−	0.979497i	$-0.564568\pi$
$563$	−9.56024	−0.402916	−0.201458	+	0.979497i	$0.564568\pi$
$564$	11.1496	0.469484
$565$	1.67839	0.0706104
$566$	12.0637	0.507075
$567$	20.4514	0.858880
$568$	15.3218	0.642888
$569$	38.1989	1.60138	0.800691	−	0.599078i	$-0.204466\pi$
$569$	38.1989	1.60138	0.800691	+	0.599078i	$0.204466\pi$
$570$	2.42522	0.101581
$571$	9.22957	0.386245	0.193123	−	0.981175i	$-0.438138\pi$
$571$	9.22957	0.386245	0.193123	+	0.981175i	$0.438138\pi$
$572$	10.3895	0.434408
$573$	61.4464	2.56696
$574$	−29.3215	−1.22386
$575$	11.7574	0.490318
$576$	3.43937	0.143307
$577$	9.16251	0.381440	0.190720	−	0.981644i	$-0.438918\pi$
$577$	9.16251	0.381440	0.190720	+	0.981644i	$0.438918\pi$
$578$	6.46632	0.268963
$579$	17.9321	0.745233
$580$	3.03832	0.126160
$581$	−28.4587	−1.18066
$582$	−5.12869	−0.212591
$583$	9.83826	0.407459
$584$	−8.98873	−0.371956
$585$	−10.1140	−0.418162
$586$	11.3669	0.469563
$587$	−29.3494	−1.21138	−0.605690	−	0.795701i	$-0.707103\pi$
$587$	−29.3494	−1.21138	−0.605690	+	0.795701i	$0.707103\pi$
$588$	1.16211	0.0479246
$589$	−8.24058	−0.339547
$590$	2.99479	0.123293
$591$	−17.9917	−0.740079
$592$	6.59523	0.271062
$593$	−6.28363	−0.258038	−0.129019	−	0.991642i	$-0.541183\pi$
$593$	−6.28363	−0.258038	−0.129019	+	0.991642i	$0.541183\pi$
$594$	−2.45026	−0.100535
$595$	8.22880	0.337348
$596$	−15.4811	−0.634132
$597$	68.9115	2.82036
$598$	12.0492	0.492730
$599$	6.07833	0.248354	0.124177	−	0.992260i	$-0.460371\pi$
$599$	6.07833	0.248354	0.124177	+	0.992260i	$0.460371\pi$
$600$	−11.7061	−0.477901
$601$	−42.4088	−1.72989	−0.864945	−	0.501867i	$-0.832647\pi$
$601$	−42.4088	−1.72989	−0.864945	+	0.501867i	$0.832647\pi$
$602$	30.9632	1.26196
$603$	−24.8788	−1.01314
$604$	18.0158	0.733054
$605$	−3.83809	−0.156040
$606$	−31.0542	−1.26149
$607$	1.25045	0.0507542	0.0253771	−	0.999678i	$-0.491921\pi$
$607$	1.25045	0.0507542	0.0253771	+	0.999678i	$0.491921\pi$
$608$	1.53647	0.0623123
$609$	−33.8503	−1.37168
$610$	−8.79395	−0.356057
$611$	−20.7720	−0.840344
$612$	−16.6610	−0.673482
$613$	9.17601	0.370616	0.185308	−	0.982681i	$-0.440672\pi$
$613$	9.17601	0.370616	0.185308	+	0.982681i	$0.440672\pi$
$614$	5.84588	0.235921
$615$	16.9474	0.683383
$616$	6.00160	0.241811
$617$	21.3837	0.860875	0.430437	−	0.902620i	$-0.358359\pi$
$617$	21.3837	0.860875	0.430437	+	0.902620i	$0.358359\pi$
$618$	−1.51437	−0.0609169
$619$	−4.06118	−0.163233	−0.0816164	−	0.996664i	$-0.526008\pi$
$619$	−4.06118	−0.163233	−0.0816164	+	0.996664i	$0.526008\pi$
$620$	−3.33608	−0.133980
$621$	−2.84168	−0.114033
$622$	24.1318	0.967597
$623$	−29.9930	−1.20164
$624$	−11.9967	−0.480252
$625$	19.3461	0.773843
$626$	−0.418902	−0.0167427
$627$	−8.56849	−0.342192
$628$	−11.8263	−0.471920
$629$	−31.9486	−1.27388
$630$	−5.84242	−0.232768
$631$	−37.0675	−1.47563	−0.737816	−	0.675002i	$-0.764143\pi$
$631$	−37.0675	−1.47563	−0.737816	+	0.675002i	$0.764143\pi$
$632$	−9.79071	−0.389454
$633$	41.3978	1.64541
$634$	−11.1789	−0.443970
$635$	−9.43894	−0.374573
$636$	−11.3601	−0.450458
$637$	−2.16503	−0.0857818
$638$	−10.7346	−0.424988
$639$	52.6974	2.08468
$640$	0.622019	0.0245875
$641$	23.0524	0.910514	0.455257	−	0.890360i	$-0.349547\pi$
$641$	23.0524	0.910514	0.455257	+	0.890360i	$0.349547\pi$
$642$	−21.1173	−0.833433
$643$	−22.1398	−0.873107	−0.436554	−	0.899678i	$-0.643801\pi$
$643$	−22.1398	−0.873107	−0.436554	+	0.899678i	$0.643801\pi$
$644$	6.96033	0.274276
$645$	−17.8962	−0.704662
$646$	−7.44300	−0.292841
$647$	−35.0012	−1.37604	−0.688020	−	0.725692i	$-0.741520\pi$
$647$	−35.0012	−1.37604	−0.688020	+	0.725692i	$0.741520\pi$
$648$	−7.48883	−0.294189
$649$	−10.5808	−0.415334
$650$	21.8088	0.855411
$651$	37.1676	1.45671
$652$	−1.01631	−0.0398017
$653$	−18.6413	−0.729489	−0.364744	−	0.931108i	$-0.618844\pi$
$653$	−18.6413	−0.729489	−0.364744	+	0.931108i	$0.618844\pi$
$654$	−16.1570	−0.631787
$655$	−8.24485	−0.322153
$656$	10.7368	0.419203
$657$	−30.9156	−1.20613
$658$	−11.9991	−0.467773
$659$	19.7523	0.769441	0.384721	−	0.923033i	$-0.374298\pi$
$659$	19.7523	0.769441	0.384721	+	0.923033i	$0.374298\pi$
$660$	−3.46883	−0.135024
$661$	40.8311	1.58814	0.794072	−	0.607823i	$-0.207957\pi$
$661$	40.8311	1.58814	0.794072	+	0.607823i	$0.207957\pi$
$662$	−9.44549	−0.367110
$663$	58.1144	2.25698
$664$	10.4209	0.404409
$665$	−2.60999	−0.101211
$666$	22.6834	0.878966
$667$	−12.4495	−0.482045
$668$	20.0590	0.776107
$669$	−30.1910	−1.16725
$670$	−4.49939	−0.173827
$671$	31.0697	1.19943
$672$	−6.92998	−0.267330
$673$	−31.9789	−1.23270	−0.616348	−	0.787474i	$-0.711388\pi$
$673$	−31.9789	−1.23270	−0.616348	+	0.787474i	$0.711388\pi$
$674$	−7.30638	−0.281431
$675$	−5.14337	−0.197968
$676$	9.35005	0.359617
$677$	−16.9949	−0.653166	−0.326583	−	0.945169i	$-0.605897\pi$
$677$	−16.9949	−0.653166	−0.326583	+	0.945169i	$0.605897\pi$
$678$	6.84717	0.262964
$679$	5.51943	0.211816
$680$	−3.01319	−0.115551
$681$	2.57671	0.0987399
$682$	11.7866	0.451333
$683$	3.00971	0.115163	0.0575817	−	0.998341i	$-0.481661\pi$
$683$	3.00971	0.115163	0.0575817	+	0.998341i	$0.481661\pi$
$684$	5.28451	0.202058
$685$	7.20617	0.275334
$686$	17.8658	0.682121
$687$	26.1657	0.998284
$688$	−11.3380	−0.432256
$689$	21.1641	0.806289
$690$	−4.02296	−0.153151
$691$	−7.19067	−0.273546	−0.136773	−	0.990602i	$-0.543673\pi$
$691$	−7.19067	−0.273546	−0.136773	+	0.990602i	$0.543673\pi$
$692$	12.3281	0.468643
$693$	20.6417	0.784115
$694$	−3.88483	−0.147466
$695$	−8.77698	−0.332930
$696$	12.3952	0.469837
$697$	−52.0114	−1.97007
$698$	−31.0517	−1.17532
$699$	12.5445	0.474478
$700$	12.5980	0.476160
$701$	18.1346	0.684936	0.342468	−	0.939529i	$-0.388737\pi$
$701$	18.1346	0.684936	0.342468	+	0.939529i	$0.388737\pi$
$702$	−5.27102	−0.198942
$703$	10.1334	0.382188
$704$	−2.19764	−0.0828268
$705$	6.93528	0.261198
$706$	−11.3193	−0.426008
$707$	33.4202	1.25690
$708$	12.2175	0.459164
$709$	−44.8723	−1.68522	−0.842608	−	0.538527i	$-0.818981\pi$
$709$	−44.8723	−1.68522	−0.842608	+	0.538527i	$0.818981\pi$
$710$	9.53045	0.357672
$711$	−33.6739	−1.26287
$712$	10.9827	0.411595
$713$	13.6695	0.511927
$714$	33.5702	1.25633
$715$	6.46249	0.241684
$716$	−21.1712	−0.791204
$717$	−59.6982	−2.22947
$718$	−2.73849	−0.102200
$719$	−48.7162	−1.81681	−0.908404	−	0.418095i	$-0.862698\pi$
$719$	−48.7162	−1.81681	−0.908404	+	0.418095i	$0.862698\pi$
$720$	2.13936	0.0797291
$721$	1.62975	0.0606949
$722$	−16.6392	−0.619249
$723$	38.9649	1.44912
$724$	9.68326	0.359876
$725$	−22.5332	−0.836861
$726$	−15.6579	−0.581118
$727$	−33.5303	−1.24357	−0.621786	−	0.783187i	$-0.713593\pi$
$727$	−33.5303	−1.24357	−0.621786	+	0.783187i	$0.713593\pi$
$728$	12.9107	0.478502
$729$	−34.2448	−1.26832
$730$	−5.59116	−0.206938
$731$	54.9234	2.03142
$732$	−35.8758	−1.32601
$733$	−11.1411	−0.411505	−0.205753	−	0.978604i	$-0.565964\pi$
$733$	−11.1411	−0.411505	−0.205753	+	0.978604i	$0.565964\pi$
$734$	25.1626	0.928770
$735$	0.722855	0.0266629
$736$	−2.54871	−0.0939466
$737$	15.8967	0.585563
$738$	36.9280	1.35934
$739$	−21.5480	−0.792656	−0.396328	−	0.918109i	$-0.629716\pi$
$739$	−21.5480	−0.792656	−0.396328	+	0.918109i	$0.629716\pi$
$740$	4.10236	0.150806
$741$	−18.4326	−0.677138
$742$	12.2256	0.448817
$743$	29.3968	1.07847	0.539233	−	0.842157i	$-0.318714\pi$
$743$	29.3968	1.07847	0.539233	+	0.842157i	$0.318714\pi$
$744$	−13.6099	−0.498962
$745$	−9.62956	−0.352800
$746$	28.9585	1.06025
$747$	35.8413	1.31136
$748$	10.6458	0.389250
$749$	22.7262	0.830397
$750$	−15.1736	−0.554062
$751$	10.8372	0.395454	0.197727	−	0.980257i	$-0.436644\pi$
$751$	10.8372	0.395454	0.197727	+	0.980257i	$0.436644\pi$
$752$	4.39378	0.160225
$753$	−37.7415	−1.37538
$754$	−23.0924	−0.840976
$755$	11.2062	0.407835
$756$	−3.04485	−0.110740
$757$	5.37578	0.195386	0.0976930	−	0.995217i	$-0.468854\pi$
$757$	5.37578	0.195386	0.0976930	+	0.995217i	$0.468854\pi$
$758$	2.06744	0.0750926
$759$	14.2134	0.515915
$760$	0.955717	0.0346675
$761$	−28.5833	−1.03614	−0.518071	−	0.855337i	$-0.673350\pi$
$761$	−28.5833	−1.03614	−0.518071	+	0.855337i	$0.673350\pi$
$762$	−38.5071	−1.39497
$763$	17.3879	0.629485
$764$	24.2144	0.876048
$765$	−10.3635	−0.374692
$766$	−5.82726	−0.210547
$767$	−22.7615	−0.821871
$768$	2.53759	0.0915675
$769$	−6.76154	−0.243827	−0.121914	−	0.992541i	$-0.538903\pi$
$769$	−6.76154	−0.243827	−0.121914	+	0.992541i	$0.538903\pi$
$770$	3.73311	0.134532
$771$	21.9173	0.789333
$772$	7.06659	0.254332
$773$	7.75159	0.278805	0.139403	−	0.990236i	$-0.455482\pi$
$773$	7.75159	0.278805	0.139403	+	0.990236i	$0.455482\pi$
$774$	−38.9955	−1.40166
$775$	24.7414	0.888738
$776$	−2.02109	−0.0725527
$777$	−45.7048	−1.63965
$778$	22.8784	0.820232
$779$	16.4969	0.591062
$780$	−7.46217	−0.267188
$781$	−33.6718	−1.20487
$782$	12.3465	0.441509
$783$	5.44610	0.194628
$784$	0.457958	0.0163556
$785$	−7.35618	−0.262553
$786$	−33.6357	−1.19975
$787$	−21.2830	−0.758655	−0.379328	−	0.925262i	$-0.623845\pi$
$787$	−21.2830	−0.758655	−0.379328	+	0.925262i	$0.623845\pi$
$788$	−7.09006	−0.252573
$789$	47.8556	1.70371
$790$	−6.09001	−0.216673
$791$	−7.36884	−0.262006
$792$	−7.55851	−0.268580
$793$	66.8374	2.37347
$794$	20.0294	0.710818
$795$	−7.06622	−0.250613
$796$	27.1562	0.962528
$797$	−17.0731	−0.604760	−0.302380	−	0.953187i	$-0.597781\pi$
$797$	−17.0731	−0.604760	−0.302380	+	0.953187i	$0.597781\pi$
$798$	−10.6477	−0.376926
$799$	−21.2844	−0.752987
$800$	−4.61309	−0.163097
$801$	37.7737	1.33467
$802$	17.3181	0.611525
$803$	19.7540	0.697104
$804$	−18.3557	−0.647357
$805$	4.32946	0.152593
$806$	25.3555	0.893109
$807$	−0.533871	−0.0187932
$808$	−12.2377	−0.430520
$809$	47.4718	1.66902	0.834509	−	0.550994i	$-0.185751\pi$
$809$	47.4718	1.66902	0.834509	+	0.550994i	$0.185751\pi$
$810$	−4.65820	−0.163672
$811$	9.32530	0.327456	0.163728	−	0.986506i	$-0.447648\pi$
$811$	9.32530	0.327456	0.163728	+	0.986506i	$0.447648\pi$
$812$	−13.3395	−0.468125
$813$	−28.0706	−0.984480
$814$	−14.4940	−0.508013
$815$	−0.632164	−0.0221437
$816$	−12.2926	−0.430328
$817$	−17.4205	−0.609466
$818$	15.4454	0.540037
$819$	44.4047	1.55162
$820$	6.67852	0.233224
$821$	−19.3648	−0.675835	−0.337918	−	0.941176i	$-0.609723\pi$
$821$	−19.3648	−0.675835	−0.337918	+	0.941176i	$0.609723\pi$
$822$	29.3983	1.02538
$823$	−13.7764	−0.480213	−0.240107	−	0.970746i	$-0.577182\pi$
$823$	−13.7764	−0.480213	−0.240107	+	0.970746i	$0.577182\pi$
$824$	−0.596774	−0.0207896
$825$	25.7259	0.895662
$826$	−13.1484	−0.457491
$827$	28.1194	0.977806	0.488903	−	0.872338i	$-0.337397\pi$
$827$	28.1194	0.977806	0.488903	+	0.872338i	$0.337397\pi$
$828$	−8.76596	−0.304638
$829$	−23.1401	−0.803689	−0.401845	−	0.915708i	$-0.631631\pi$
$829$	−23.1401	−0.803689	−0.401845	+	0.915708i	$0.631631\pi$
$830$	6.48199	0.224993
$831$	−33.7304	−1.17009
$832$	−4.72758	−0.163899
$833$	−2.21844	−0.0768645
$834$	−35.8066	−1.23988
$835$	12.4771	0.431788
$836$	−3.37662	−0.116783
$837$	−5.97982	−0.206693
$838$	10.4276	0.360216
$839$	14.2366	0.491501	0.245750	−	0.969333i	$-0.420966\pi$
$839$	14.2366	0.491501	0.245750	+	0.969333i	$0.420966\pi$
$840$	−4.31058	−0.148729
$841$	−5.14056	−0.177261
$842$	−6.49035	−0.223672
$843$	8.40782	0.289581
$844$	16.3138	0.561545
$845$	5.81591	0.200073
$846$	15.1118	0.519556
$847$	16.8508	0.579001
$848$	−4.47673	−0.153732
$849$	30.6127	1.05063
$850$	22.3468	0.766488
$851$	−16.8093	−0.576216
$852$	38.8805	1.33202
$853$	38.0863	1.30405	0.652025	−	0.758197i	$-0.273920\pi$
$853$	38.0863	1.30405	0.652025	+	0.758197i	$0.273920\pi$
$854$	38.6092	1.32118
$855$	3.28707	0.112415
$856$	−8.32179	−0.284433
$857$	−6.80437	−0.232433	−0.116217	−	0.993224i	$-0.537077\pi$
$857$	−6.80437	−0.232433	−0.116217	+	0.993224i	$0.537077\pi$
$858$	26.3644	0.900066
$859$	−0.738210	−0.0251874	−0.0125937	−	0.999921i	$-0.504009\pi$
$859$	−0.738210	−0.0251874	−0.0125937	+	0.999921i	$0.504009\pi$
$860$	−7.05243	−0.240486
$861$	−74.4060	−2.53575
$862$	2.87772	0.0980156
$863$	28.7002	0.976965	0.488482	−	0.872574i	$-0.337551\pi$
$863$	28.7002	0.976965	0.488482	+	0.872574i	$0.337551\pi$
$864$	1.11495	0.0379314
$865$	7.66830	0.260730
$866$	−17.7633	−0.603620
$867$	16.4089	0.557275
$868$	14.6468	0.497145
$869$	21.5165	0.729897
$870$	7.71002	0.261394
$871$	34.1971	1.15872
$872$	−6.36704	−0.215615
$873$	−6.95127	−0.235265
$874$	−3.91602	−0.132461
$875$	16.3297	0.552043
$876$	−22.8097	−0.770669
$877$	19.2030	0.648441	0.324220	−	0.945982i	$-0.394898\pi$
$877$	19.2030	0.648441	0.324220	+	0.945982i	$0.394898\pi$
$878$	−3.33472	−0.112541
$879$	28.8446	0.972903
$880$	−1.36698	−0.0460807
$881$	−6.64403	−0.223843	−0.111921	−	0.993717i	$-0.535701\pi$
$881$	−6.64403	−0.223843	−0.111921	+	0.993717i	$0.535701\pi$
$882$	1.57509	0.0530360
$883$	−23.2038	−0.780870	−0.390435	−	0.920630i	$-0.627675\pi$
$883$	−23.2038	−0.780870	−0.390435	+	0.920630i	$0.627675\pi$
$884$	22.9014	0.770257
$885$	7.59955	0.255456
$886$	−6.05598	−0.203455
$887$	−29.2191	−0.981081	−0.490541	−	0.871418i	$-0.663201\pi$
$887$	−29.2191	−0.981081	−0.490541	+	0.871418i	$0.663201\pi$
$888$	16.7360	0.561623
$889$	41.4409	1.38988
$890$	6.83146	0.228991
$891$	16.4578	0.551356
$892$	−11.8975	−0.398358
$893$	6.75093	0.225911
$894$	−39.2848	−1.31388
$895$	−13.1689	−0.440187
$896$	−2.73093	−0.0912338
$897$	30.5760	1.02090
$898$	2.26436	0.0755626
$899$	−26.1977	−0.873741
$900$	−15.8661	−0.528872
$901$	21.6862	0.722473
$902$	−23.5957	−0.785652
$903$	78.5719	2.61471
$904$	2.69829	0.0897439
$905$	6.02318	0.200217
$906$	45.7168	1.51884
$907$	−41.4778	−1.37725	−0.688623	−	0.725119i	$-0.741785\pi$
$907$	−41.4778	−1.37725	−0.688623	+	0.725119i	$0.741785\pi$
$908$	1.01542	0.0336978
$909$	−42.0899	−1.39603
$910$	8.03069	0.266215
$911$	34.7784	1.15226	0.576129	−	0.817359i	$-0.304562\pi$
$911$	34.7784	1.15226	0.576129	+	0.817359i	$0.304562\pi$
$912$	3.89895	0.129107
$913$	−22.9014	−0.757925
$914$	−18.3316	−0.606357
$915$	−22.3155	−0.737727
$916$	10.3112	0.340693
$917$	36.1983	1.19537
$918$	−5.40105	−0.178261
$919$	18.4117	0.607344	0.303672	−	0.952777i	$-0.401787\pi$
$919$	18.4117	0.607344	0.303672	+	0.952777i	$0.401787\pi$
$920$	−1.58535	−0.0522673
$921$	14.8345	0.488812
$922$	−19.6672	−0.647705
$923$	−72.4351	−2.38423
$924$	15.2296	0.501017
$925$	−30.4244	−1.00035
$926$	4.65105	0.152843
$927$	−2.05253	−0.0674139
$928$	4.88461	0.160345
$929$	−35.6600	−1.16997	−0.584984	−	0.811045i	$-0.698899\pi$
$929$	−35.6600	−1.16997	−0.584984	+	0.811045i	$0.698899\pi$
$930$	−8.46561	−0.277598
$931$	0.703641	0.0230609
$932$	4.94348	0.161929
$933$	61.2366	2.00480
$934$	36.3073	1.18801
$935$	6.62191	0.216560
$936$	−16.2599	−0.531472
$937$	−27.9544	−0.913231	−0.456615	−	0.889664i	$-0.650938\pi$
$937$	−27.9544	−0.913231	−0.456615	+	0.889664i	$0.650938\pi$
$938$	19.7542	0.644998
$939$	−1.06300	−0.0346897
$940$	2.73302	0.0891411
$941$	15.3546	0.500545	0.250272	−	0.968175i	$-0.419480\pi$
$941$	15.3546	0.500545	0.250272	+	0.968175i	$0.419480\pi$
$942$	−30.0103	−0.977788
$943$	−27.3651	−0.891129
$944$	4.81462	0.156703
$945$	−1.89395	−0.0616103
$946$	24.9168	0.810115
$947$	−41.4871	−1.34815	−0.674074	−	0.738664i	$-0.735457\pi$
$947$	−41.4871	−1.34815	−0.674074	+	0.738664i	$0.735457\pi$
$948$	−24.8448	−0.806923
$949$	42.4950	1.37945
$950$	−7.08790	−0.229962
$951$	−28.3674	−0.919877
$952$	13.2292	0.428760
$953$	−29.5377	−0.956821	−0.478410	−	0.878136i	$-0.658787\pi$
$953$	−29.5377	−0.956821	−0.478410	+	0.878136i	$0.658787\pi$
$954$	−15.3972	−0.498501
$955$	15.0619	0.487390
$956$	−23.5255	−0.760870
$957$	−27.2401	−0.880548
$958$	28.9259	0.934555
$959$	−31.6381	−1.02165
$960$	1.57843	0.0509436
$961$	−2.23495	−0.0720952
$962$	−31.1795	−1.00527
$963$	−28.6217	−0.922322
$964$	15.3551	0.494553
$965$	4.39555	0.141498
$966$	17.6625	0.568281
$967$	59.0703	1.89957	0.949786	−	0.312900i	$-0.101301\pi$
$967$	59.0703	1.89957	0.949786	+	0.312900i	$0.101301\pi$
$968$	−6.17037	−0.198323
$969$	−18.8873	−0.606747
$970$	−1.25715	−0.0403648
$971$	42.7836	1.37299	0.686495	−	0.727134i	$-0.259148\pi$
$971$	42.7836	1.37299	0.686495	+	0.727134i	$0.259148\pi$
$972$	−22.3484	−0.716827
$973$	38.5346	1.23536
$974$	−18.3684	−0.588563
$975$	55.3418	1.77236
$976$	−14.1378	−0.452538
$977$	2.07998	0.0665443	0.0332722	−	0.999446i	$-0.489407\pi$
$977$	2.07998	0.0665443	0.0332722	+	0.999446i	$0.489407\pi$
$978$	−2.57898	−0.0824666
$979$	−24.1361	−0.771393
$980$	0.284859	0.00909947
$981$	−21.8986	−0.699170
$982$	−37.0555	−1.18249
$983$	39.8773	1.27189	0.635944	−	0.771735i	$-0.280611\pi$
$983$	39.8773	1.27189	0.635944	+	0.771735i	$0.280611\pi$
$984$	27.2457	0.868562
$985$	−4.41015	−0.140519
$986$	−23.6621	−0.753554
$987$	−30.4488	−0.969196
$988$	−7.26381	−0.231093
$989$	28.8972	0.918876
$990$	−4.70154	−0.149425
$991$	−32.1235	−1.02044	−0.510219	−	0.860045i	$-0.670436\pi$
$991$	−32.1235	−1.02044	−0.510219	+	0.860045i	$0.670436\pi$
$992$	−5.36331	−0.170285
$993$	−23.9688	−0.760627
$994$	−41.8427	−1.32717
$995$	16.8917	0.535503
$996$	26.4439	0.837908
$997$	−38.5924	−1.22223	−0.611116	−	0.791541i	$-0.709279\pi$
$997$	−38.5924	−1.22223	−0.611116	+	0.791541i	$0.709279\pi$
$998$	−1.95467	−0.0618739
$999$	7.35335	0.232650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.65	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.65	✓	69	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.53759 q^{3} +1.00000 q^{4} +0.622019 q^{5} +2.53759 q^{6} -2.73093 q^{7} +1.00000 q^{8} +3.43937 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.53759 q^{3} +1.00000 q^{4} +0.622019 q^{5} +2.53759 q^{6} -2.73093 q^{7} +1.00000 q^{8} +3.43937 q^{9} +0.622019 q^{10} -2.19764 q^{11} +2.53759 q^{12} -4.72758 q^{13} -2.73093 q^{14} +1.57843 q^{15} +1.00000 q^{16} -4.84420 q^{17} +3.43937 q^{18} +1.53647 q^{19} +0.622019 q^{20} -6.92998 q^{21} -2.19764 q^{22} -2.54871 q^{23} +2.53759 q^{24} -4.61309 q^{25} -4.72758 q^{26} +1.11495 q^{27} -2.73093 q^{28} +4.88461 q^{29} +1.57843 q^{30} -5.36331 q^{31} +1.00000 q^{32} -5.57672 q^{33} -4.84420 q^{34} -1.69869 q^{35} +3.43937 q^{36} +6.59523 q^{37} +1.53647 q^{38} -11.9967 q^{39} +0.622019 q^{40} +10.7368 q^{41} -6.92998 q^{42} -11.3380 q^{43} -2.19764 q^{44} +2.13936 q^{45} -2.54871 q^{46} +4.39378 q^{47} +2.53759 q^{48} +0.457958 q^{49} -4.61309 q^{50} -12.2926 q^{51} -4.72758 q^{52} -4.47673 q^{53} +1.11495 q^{54} -1.36698 q^{55} -2.73093 q^{56} +3.89895 q^{57} +4.88461 q^{58} +4.81462 q^{59} +1.57843 q^{60} -14.1378 q^{61} -5.36331 q^{62} -9.39267 q^{63} +1.00000 q^{64} -2.94065 q^{65} -5.57672 q^{66} -7.23353 q^{67} -4.84420 q^{68} -6.46758 q^{69} -1.69869 q^{70} +15.3218 q^{71} +3.43937 q^{72} -8.98873 q^{73} +6.59523 q^{74} -11.7061 q^{75} +1.53647 q^{76} +6.00160 q^{77} -11.9967 q^{78} -9.79071 q^{79} +0.622019 q^{80} -7.48883 q^{81} +10.7368 q^{82} +10.4209 q^{83} -6.92998 q^{84} -3.01319 q^{85} -11.3380 q^{86} +12.3952 q^{87} -2.19764 q^{88} +10.9827 q^{89} +2.13936 q^{90} +12.9107 q^{91} -2.54871 q^{92} -13.6099 q^{93} +4.39378 q^{94} +0.955717 q^{95} +2.53759 q^{96} -2.02109 q^{97} +0.457958 q^{98} -7.55851 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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