LMFDB - Embedded newform 8015.2.a.n.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33656 q^{2} +2.32181 q^{3} +3.45950 q^{4} -1.00000 q^{5} -5.42504 q^{6} +1.00000 q^{7} -3.41021 q^{8} +2.39080 q^{9} +O(q^{10})$	\(q-2.33656 q^{2} +2.32181 q^{3} +3.45950 q^{4} -1.00000 q^{5} -5.42504 q^{6} +1.00000 q^{7} -3.41021 q^{8} +2.39080 q^{9} +2.33656 q^{10} -3.95042 q^{11} +8.03231 q^{12} +5.74399 q^{13} -2.33656 q^{14} -2.32181 q^{15} +1.04916 q^{16} +2.68932 q^{17} -5.58624 q^{18} +3.53123 q^{19} -3.45950 q^{20} +2.32181 q^{21} +9.23039 q^{22} +1.72570 q^{23} -7.91787 q^{24} +1.00000 q^{25} -13.4212 q^{26} -1.41445 q^{27} +3.45950 q^{28} +7.53432 q^{29} +5.42504 q^{30} +8.88224 q^{31} +4.36901 q^{32} -9.17213 q^{33} -6.28376 q^{34} -1.00000 q^{35} +8.27097 q^{36} +1.66084 q^{37} -8.25093 q^{38} +13.3364 q^{39} +3.41021 q^{40} +2.36380 q^{41} -5.42504 q^{42} -2.28025 q^{43} -13.6665 q^{44} -2.39080 q^{45} -4.03220 q^{46} -0.691683 q^{47} +2.43594 q^{48} +1.00000 q^{49} -2.33656 q^{50} +6.24409 q^{51} +19.8713 q^{52} -2.10426 q^{53} +3.30494 q^{54} +3.95042 q^{55} -3.41021 q^{56} +8.19885 q^{57} -17.6044 q^{58} -6.67054 q^{59} -8.03231 q^{60} +11.5827 q^{61} -20.7539 q^{62} +2.39080 q^{63} -12.3068 q^{64} -5.74399 q^{65} +21.4312 q^{66} -6.99263 q^{67} +9.30372 q^{68} +4.00674 q^{69} +2.33656 q^{70} +8.85202 q^{71} -8.15313 q^{72} +2.05400 q^{73} -3.88066 q^{74} +2.32181 q^{75} +12.2163 q^{76} -3.95042 q^{77} -31.1614 q^{78} -9.47921 q^{79} -1.04916 q^{80} -10.4565 q^{81} -5.52316 q^{82} -6.11997 q^{83} +8.03231 q^{84} -2.68932 q^{85} +5.32794 q^{86} +17.4933 q^{87} +13.4718 q^{88} -0.379613 q^{89} +5.58624 q^{90} +5.74399 q^{91} +5.97006 q^{92} +20.6229 q^{93} +1.61616 q^{94} -3.53123 q^{95} +10.1440 q^{96} -1.02753 q^{97} -2.33656 q^{98} -9.44466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) $ 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * 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 $

$2$	−2.33656	−1.65220	−0.826098	−	0.563526i	$-0.809444\pi$
$2$	−2.33656	−1.65220	−0.826098	+	0.563526i	$0.809444\pi$
$3$	2.32181	1.34050	0.670249	−	0.742137i	$-0.266187\pi$
$3$	2.32181	1.34050	0.670249	+	0.742137i	$0.266187\pi$
$4$	3.45950	1.72975
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.42504	−2.21476
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.41021	−1.20569
$9$	2.39080	0.796933
$10$	2.33656	0.738885
$11$	−3.95042	−1.19110	−0.595549	−	0.803319i	$-0.703065\pi$
$11$	−3.95042	−1.19110	−0.595549	+	0.803319i	$0.703065\pi$
$12$	8.03231	2.31873
$13$	5.74399	1.59310	0.796548	−	0.604576i	$-0.206657\pi$
$13$	5.74399	1.59310	0.796548	+	0.604576i	$0.206657\pi$
$14$	−2.33656	−0.624471
$15$	−2.32181	−0.599489
$16$	1.04916	0.262289
$17$	2.68932	0.652257	0.326128	−	0.945326i	$-0.394256\pi$
$17$	2.68932	0.652257	0.326128	+	0.945326i	$0.394256\pi$
$18$	−5.58624	−1.31669
$19$	3.53123	0.810120	0.405060	−	0.914290i	$-0.367251\pi$
$19$	3.53123	0.810120	0.405060	+	0.914290i	$0.367251\pi$
$20$	−3.45950	−0.773568
$21$	2.32181	0.506660
$22$	9.23039	1.96793
$23$	1.72570	0.359833	0.179917	−	0.983682i	$-0.442417\pi$
$23$	1.72570	0.359833	0.179917	+	0.983682i	$0.442417\pi$
$24$	−7.91787	−1.61623
$25$	1.00000	0.200000
$26$	−13.4212	−2.63211
$27$	−1.41445	−0.272211
$28$	3.45950	0.653785
$29$	7.53432	1.39909	0.699544	−	0.714589i	$-0.253386\pi$
$29$	7.53432	1.39909	0.699544	+	0.714589i	$0.253386\pi$
$30$	5.42504	0.990473
$31$	8.88224	1.59530	0.797649	−	0.603122i	$-0.206077\pi$
$31$	8.88224	1.59530	0.797649	+	0.603122i	$0.206077\pi$
$32$	4.36901	0.772340
$33$	−9.17213	−1.59666
$34$	−6.28376	−1.07766
$35$	−1.00000	−0.169031
$36$	8.27097	1.37850
$37$	1.66084	0.273041	0.136521	−	0.990637i	$-0.456408\pi$
$37$	1.66084	0.273041	0.136521	+	0.990637i	$0.456408\pi$
$38$	−8.25093	−1.33848
$39$	13.3364	2.13554
$40$	3.41021	0.539202
$41$	2.36380	0.369164	0.184582	−	0.982817i	$-0.440907\pi$
$41$	2.36380	0.369164	0.184582	+	0.982817i	$0.440907\pi$
$42$	−5.42504	−0.837102
$43$	−2.28025	−0.347735	−0.173868	−	0.984769i	$-0.555626\pi$
$43$	−2.28025	−0.347735	−0.173868	+	0.984769i	$0.555626\pi$
$44$	−13.6665	−2.06030
$45$	−2.39080	−0.356399
$46$	−4.03220	−0.594515
$47$	−0.691683	−0.100892	−0.0504461	−	0.998727i	$-0.516064\pi$
$47$	−0.691683	−0.100892	−0.0504461	+	0.998727i	$0.516064\pi$
$48$	2.43594	0.351598
$49$	1.00000	0.142857
$50$	−2.33656	−0.330439
$51$	6.24409	0.874348
$52$	19.8713	2.75566
$53$	−2.10426	−0.289042	−0.144521	−	0.989502i	$-0.546164\pi$
$53$	−2.10426	−0.289042	−0.144521	+	0.989502i	$0.546164\pi$
$54$	3.30494	0.449746
$55$	3.95042	0.532675
$56$	−3.41021	−0.455709
$57$	8.19885	1.08596
$58$	−17.6044	−2.31157
$59$	−6.67054	−0.868430	−0.434215	−	0.900809i	$-0.642974\pi$
$59$	−6.67054	−0.868430	−0.434215	+	0.900809i	$0.642974\pi$
$60$	−8.03231	−1.03697
$61$	11.5827	1.48301	0.741506	−	0.670946i	$-0.234112\pi$
$61$	11.5827	1.48301	0.741506	+	0.670946i	$0.234112\pi$
$62$	−20.7539	−2.63575
$63$	2.39080	0.301212
$64$	−12.3068	−1.53835
$65$	−5.74399	−0.712454
$66$	21.4312	2.63800
$67$	−6.99263	−0.854286	−0.427143	−	0.904184i	$-0.640480\pi$
$67$	−6.99263	−0.854286	−0.427143	+	0.904184i	$0.640480\pi$
$68$	9.30372	1.12824
$69$	4.00674	0.482355
$70$	2.33656	0.279272
$71$	8.85202	1.05054	0.525271	−	0.850935i	$-0.323964\pi$
$71$	8.85202	1.05054	0.525271	+	0.850935i	$0.323964\pi$
$72$	−8.15313	−0.960856
$73$	2.05400	0.240402	0.120201	−	0.992750i	$-0.461646\pi$
$73$	2.05400	0.240402	0.120201	+	0.992750i	$0.461646\pi$
$74$	−3.88066	−0.451117
$75$	2.32181	0.268099
$76$	12.2163	1.40131
$77$	−3.95042	−0.450192
$78$	−31.1614	−3.52833
$79$	−9.47921	−1.06649	−0.533247	−	0.845959i	$-0.679029\pi$
$79$	−9.47921	−1.06649	−0.533247	+	0.845959i	$0.679029\pi$
$80$	−1.04916	−0.117299
$81$	−10.4565	−1.16183
$82$	−5.52316	−0.609931
$83$	−6.11997	−0.671753	−0.335877	−	0.941906i	$-0.609033\pi$
$83$	−6.11997	−0.671753	−0.335877	+	0.941906i	$0.609033\pi$
$84$	8.03231	0.876397
$85$	−2.68932	−0.291698
$86$	5.32794	0.574527
$87$	17.4933	1.87547
$88$	13.4718	1.43610
$89$	−0.379613	−0.0402389	−0.0201194	−	0.999798i	$-0.506405\pi$
$89$	−0.379613	−0.0402389	−0.0201194	+	0.999798i	$0.506405\pi$
$90$	5.58624	0.588841
$91$	5.74399	0.602133
$92$	5.97006	0.622422
$93$	20.6229	2.13849
$94$	1.61616	0.166694
$95$	−3.53123	−0.362297
$96$	10.1440	1.03532
$97$	−1.02753	−0.104330	−0.0521650	−	0.998638i	$-0.516612\pi$
$97$	−1.02753	−0.104330	−0.0521650	+	0.998638i	$0.516612\pi$
$98$	−2.33656	−0.236028
$99$	−9.44466	−0.949224
$100$	3.45950	0.345950
$101$	−6.11944	−0.608907	−0.304453	−	0.952527i	$-0.598474\pi$
$101$	−6.11944	−0.608907	−0.304453	+	0.952527i	$0.598474\pi$
$102$	−14.5897	−1.44459
$103$	−5.99921	−0.591120	−0.295560	−	0.955324i	$-0.595506\pi$
$103$	−5.99921	−0.591120	−0.295560	+	0.955324i	$0.595506\pi$
$104$	−19.5882	−1.92078
$105$	−2.32181	−0.226585
$106$	4.91672	0.477554
$107$	−0.935760	−0.0904633	−0.0452317	−	0.998977i	$-0.514403\pi$
$107$	−0.935760	−0.0904633	−0.0452317	+	0.998977i	$0.514403\pi$
$108$	−4.89329	−0.470858
$109$	5.15657	0.493910	0.246955	−	0.969027i	$-0.420570\pi$
$109$	5.15657	0.493910	0.246955	+	0.969027i	$0.420570\pi$
$110$	−9.23039	−0.880083
$111$	3.85616	0.366011
$112$	1.04916	0.0991359
$113$	−8.71295	−0.819645	−0.409822	−	0.912165i	$-0.634409\pi$
$113$	−8.71295	−0.819645	−0.409822	+	0.912165i	$0.634409\pi$
$114$	−19.1571	−1.79423
$115$	−1.72570	−0.160922
$116$	26.0650	2.42008
$117$	13.7327	1.26959
$118$	15.5861	1.43482
$119$	2.68932	0.246530
$120$	7.91787	0.722799
$121$	4.60584	0.418713
$122$	−27.0636	−2.45023
$123$	5.48830	0.494863
$124$	30.7282	2.75947
$125$	−1.00000	−0.0894427
$126$	−5.58624	−0.497662
$127$	14.8264	1.31563	0.657816	−	0.753179i	$-0.271481\pi$
$127$	14.8264	1.31563	0.657816	+	0.753179i	$0.271481\pi$
$128$	20.0174	1.76931
$129$	−5.29431	−0.466138
$130$	13.4212	1.17711
$131$	−4.38586	−0.383194	−0.191597	−	0.981474i	$-0.561367\pi$
$131$	−4.38586	−0.383194	−0.191597	+	0.981474i	$0.561367\pi$
$132$	−31.7310	−2.76183
$133$	3.53123	0.306197
$134$	16.3387	1.41145
$135$	1.41445	0.121736
$136$	−9.17117	−0.786421
$137$	−3.80036	−0.324686	−0.162343	−	0.986734i	$-0.551905\pi$
$137$	−3.80036	−0.324686	−0.162343	+	0.986734i	$0.551905\pi$
$138$	−9.36199	−0.796945
$139$	−7.12163	−0.604048	−0.302024	−	0.953300i	$-0.597662\pi$
$139$	−7.12163	−0.604048	−0.302024	+	0.953300i	$0.597662\pi$
$140$	−3.45950	−0.292381
$141$	−1.60596	−0.135246
$142$	−20.6833	−1.73570
$143$	−22.6912	−1.89753
$144$	2.50832	0.209027
$145$	−7.53432	−0.625691
$146$	−4.79928	−0.397192
$147$	2.32181	0.191500
$148$	5.74570	0.472293
$149$	−18.9138	−1.54948	−0.774740	−	0.632280i	$-0.782119\pi$
$149$	−18.9138	−1.54948	−0.774740	+	0.632280i	$0.782119\pi$
$150$	−5.42504	−0.442953
$151$	16.5783	1.34912	0.674562	−	0.738218i	$-0.264333\pi$
$151$	16.5783	1.34912	0.674562	+	0.738218i	$0.264333\pi$
$152$	−12.0423	−0.976756
$153$	6.42963	0.519805
$154$	9.23039	0.743806
$155$	−8.88224	−0.713439
$156$	46.1375	3.69395
$157$	−2.16463	−0.172756	−0.0863780	−	0.996262i	$-0.527529\pi$
$157$	−2.16463	−0.172756	−0.0863780	+	0.996262i	$0.527529\pi$
$158$	22.1487	1.76206
$159$	−4.88569	−0.387460
$160$	−4.36901	−0.345401
$161$	1.72570	0.136004
$162$	24.4322	1.91957
$163$	−14.8764	−1.16521	−0.582605	−	0.812755i	$-0.697967\pi$
$163$	−14.8764	−1.16521	−0.582605	+	0.812755i	$0.697967\pi$
$164$	8.17758	0.638562
$165$	9.17213	0.714049
$166$	14.2997	1.10987
$167$	14.7159	1.13875	0.569374	−	0.822079i	$-0.307186\pi$
$167$	14.7159	1.13875	0.569374	+	0.822079i	$0.307186\pi$
$168$	−7.91787	−0.610877
$169$	19.9934	1.53795
$170$	6.28376	0.481942
$171$	8.44247	0.645611
$172$	−7.88854	−0.601495
$173$	−13.3548	−1.01534	−0.507672	−	0.861550i	$-0.669494\pi$
$173$	−13.3548	−1.01534	−0.507672	+	0.861550i	$0.669494\pi$
$174$	−40.8740	−3.09865
$175$	1.00000	0.0755929
$176$	−4.14461	−0.312412
$177$	−15.4877	−1.16413
$178$	0.886988	0.0664825
$179$	−24.9400	−1.86410	−0.932050	−	0.362329i	$-0.881982\pi$
$179$	−24.9400	−1.86410	−0.932050	+	0.362329i	$0.881982\pi$
$180$	−8.27097	−0.616482
$181$	20.1478	1.49758	0.748788	−	0.662809i	$-0.230636\pi$
$181$	20.1478	1.49758	0.748788	+	0.662809i	$0.230636\pi$
$182$	−13.4212	−0.994842
$183$	26.8928	1.98797
$184$	−5.88500	−0.433848
$185$	−1.66084	−0.122108
$186$	−48.1866	−3.53321
$187$	−10.6240	−0.776901
$188$	−2.39288	−0.174519
$189$	−1.41445	−0.102886
$190$	8.25093	0.598585
$191$	3.49669	0.253012	0.126506	−	0.991966i	$-0.459624\pi$
$191$	3.49669	0.253012	0.126506	+	0.991966i	$0.459624\pi$
$192$	−28.5740	−2.06215
$193$	−0.996474	−0.0717278	−0.0358639	−	0.999357i	$-0.511418\pi$
$193$	−0.996474	−0.0717278	−0.0358639	+	0.999357i	$0.511418\pi$
$194$	2.40088	0.172373
$195$	−13.3364	−0.955042
$196$	3.45950	0.247107
$197$	10.9175	0.777839	0.388920	−	0.921272i	$-0.372848\pi$
$197$	10.9175	0.777839	0.388920	+	0.921272i	$0.372848\pi$
$198$	22.0680	1.56830
$199$	26.6517	1.88929	0.944646	−	0.328091i	$-0.106405\pi$
$199$	26.6517	1.88929	0.944646	+	0.328091i	$0.106405\pi$
$200$	−3.41021	−0.241139
$201$	−16.2356	−1.14517
$202$	14.2984	1.00603
$203$	7.53432	0.528806
$204$	21.6015	1.51241
$205$	−2.36380	−0.165095
$206$	14.0175	0.976645
$207$	4.12580	0.286763
$208$	6.02634	0.417852
$209$	−13.9499	−0.964932
$210$	5.42504	0.374363
$211$	1.56176	0.107516	0.0537580	−	0.998554i	$-0.482880\pi$
$211$	1.56176	0.107516	0.0537580	+	0.998554i	$0.482880\pi$
$212$	−7.27969	−0.499971
$213$	20.5527	1.40825
$214$	2.18646	0.149463
$215$	2.28025	0.155512
$216$	4.82358	0.328203
$217$	8.88224	0.602966
$218$	−12.0486	−0.816036
$219$	4.76899	0.322259
$220$	13.6665	0.921395
$221$	15.4474	1.03911
$222$	−9.01015	−0.604722
$223$	−8.28466	−0.554782	−0.277391	−	0.960757i	$-0.589470\pi$
$223$	−8.28466	−0.554782	−0.277391	+	0.960757i	$0.589470\pi$
$224$	4.36901	0.291917
$225$	2.39080	0.159387
$226$	20.3583	1.35421
$227$	17.2912	1.14766	0.573830	−	0.818975i	$-0.305457\pi$
$227$	17.2912	1.14766	0.573830	+	0.818975i	$0.305457\pi$
$228$	28.3639	1.87845
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	4.03220	0.265875
$231$	−9.17213	−0.603482
$232$	−25.6936	−1.68687
$233$	28.3492	1.85722	0.928609	−	0.371061i	$-0.121006\pi$
$233$	28.3492	1.85722	0.928609	+	0.371061i	$0.121006\pi$
$234$	−32.0873	−2.09761
$235$	0.691683	0.0451204
$236$	−23.0767	−1.50217
$237$	−22.0089	−1.42963
$238$	−6.28376	−0.407316
$239$	−5.55439	−0.359283	−0.179642	−	0.983732i	$-0.557494\pi$
$239$	−5.55439	−0.359283	−0.179642	+	0.983732i	$0.557494\pi$
$240$	−2.43594	−0.157239
$241$	28.1153	1.81107	0.905533	−	0.424276i	$-0.139471\pi$
$241$	28.1153	1.81107	0.905533	+	0.424276i	$0.139471\pi$
$242$	−10.7618	−0.691795
$243$	−20.0346	−1.28522
$244$	40.0704	2.56524
$245$	−1.00000	−0.0638877
$246$	−12.8237	−0.817611
$247$	20.2834	1.29060
$248$	−30.2904	−1.92344
$249$	−14.2094	−0.900484
$250$	2.33656	0.147777
$251$	−21.7596	−1.37346	−0.686728	−	0.726915i	$-0.740954\pi$
$251$	−21.7596	−1.37346	−0.686728	+	0.726915i	$0.740954\pi$
$252$	8.27097	0.521022
$253$	−6.81724	−0.428596
$254$	−34.6428	−2.17368
$255$	−6.24409	−0.391020
$256$	−22.1584	−1.38490
$257$	−2.75780	−0.172027	−0.0860135	−	0.996294i	$-0.527413\pi$
$257$	−2.75780	−0.172027	−0.0860135	+	0.996294i	$0.527413\pi$
$258$	12.3705	0.770151
$259$	1.66084	0.103200
$260$	−19.8713	−1.23237
$261$	18.0130	1.11498
$262$	10.2478	0.633112
$263$	6.56597	0.404875	0.202438	−	0.979295i	$-0.435114\pi$
$263$	6.56597	0.404875	0.202438	+	0.979295i	$0.435114\pi$
$264$	31.2789	1.92508
$265$	2.10426	0.129264
$266$	−8.25093	−0.505897
$267$	−0.881389	−0.0539401
$268$	−24.1910	−1.47770
$269$	3.43328	0.209331	0.104665	−	0.994508i	$-0.466623\pi$
$269$	3.43328	0.209331	0.104665	+	0.994508i	$0.466623\pi$
$270$	−3.30494	−0.201133
$271$	−1.79752	−0.109191	−0.0545957	−	0.998509i	$-0.517387\pi$
$271$	−1.79752	−0.109191	−0.0545957	+	0.998509i	$0.517387\pi$
$272$	2.82152	0.171080
$273$	13.3364	0.807158
$274$	8.87976	0.536446
$275$	−3.95042	−0.238219
$276$	13.8613	0.834355
$277$	15.9758	0.959896	0.479948	−	0.877297i	$-0.340656\pi$
$277$	15.9758	0.959896	0.479948	+	0.877297i	$0.340656\pi$
$278$	16.6401	0.998006
$279$	21.2357	1.27135
$280$	3.41021	0.203799
$281$	24.9136	1.48622	0.743110	−	0.669169i	$-0.233350\pi$
$281$	24.9136	1.48622	0.743110	+	0.669169i	$0.233350\pi$
$282$	3.75241	0.223453
$283$	9.60876	0.571181	0.285591	−	0.958352i	$-0.407810\pi$
$283$	9.60876	0.571181	0.285591	+	0.958352i	$0.407810\pi$
$284$	30.6236	1.81718
$285$	−8.19885	−0.485658
$286$	53.0192	3.13509
$287$	2.36380	0.139531
$288$	10.4454	0.615503
$289$	−9.76754	−0.574561
$290$	17.6044	1.03376
$291$	−2.38573	−0.139854
$292$	7.10581	0.415836
$293$	28.5931	1.67043	0.835213	−	0.549927i	$-0.185344\pi$
$293$	28.5931	1.67043	0.835213	+	0.549927i	$0.185344\pi$
$294$	−5.42504	−0.316395
$295$	6.67054	0.388374
$296$	−5.66383	−0.329204
$297$	5.58768	0.324230
$298$	44.1932	2.56004
$299$	9.91239	0.573248
$300$	8.03231	0.463745
$301$	−2.28025	−0.131432
$302$	−38.7362	−2.22902
$303$	−14.2082	−0.816238
$304$	3.70481	0.212486
$305$	−11.5827	−0.663223
$306$	−15.0232	−0.858819
$307$	34.7612	1.98393	0.991963	−	0.126531i	$-0.0403844\pi$
$307$	34.7612	1.98393	0.991963	+	0.126531i	$0.0403844\pi$
$308$	−13.6665	−0.778721
$309$	−13.9290	−0.792394
$310$	20.7539	1.17874
$311$	−1.35437	−0.0767992	−0.0383996	−	0.999262i	$-0.512226\pi$
$311$	−1.35437	−0.0767992	−0.0383996	+	0.999262i	$0.512226\pi$
$312$	−45.4801	−2.57480
$313$	−13.3685	−0.755634	−0.377817	−	0.925880i	$-0.623325\pi$
$313$	−13.3685	−0.755634	−0.377817	+	0.925880i	$0.623325\pi$
$314$	5.05777	0.285427
$315$	−2.39080	−0.134706
$316$	−32.7934	−1.84477
$317$	11.8045	0.663007	0.331503	−	0.943454i	$-0.392444\pi$
$317$	11.8045	0.663007	0.331503	+	0.943454i	$0.392444\pi$
$318$	11.4157	0.640160
$319$	−29.7638	−1.66645
$320$	12.3068	0.687969
$321$	−2.17266	−0.121266
$322$	−4.03220	−0.224705
$323$	9.49662	0.528406
$324$	−36.1742	−2.00968
$325$	5.74399	0.318619
$326$	34.7596	1.92516
$327$	11.9726	0.662085
$328$	−8.06107	−0.445098
$329$	−0.691683	−0.0381337
$330$	−21.4312	−1.17975
$331$	−14.2874	−0.785306	−0.392653	−	0.919687i	$-0.628443\pi$
$331$	−14.2874	−0.785306	−0.392653	+	0.919687i	$0.628443\pi$
$332$	−21.1720	−1.16197
$333$	3.97074	0.217595
$334$	−34.3845	−1.88143
$335$	6.99263	0.382048
$336$	2.43594	0.132891
$337$	−0.0608750	−0.00331607	−0.00165804	−	0.999999i	$-0.500528\pi$
$337$	−0.0608750	−0.00331607	−0.00165804	+	0.999999i	$0.500528\pi$
$338$	−46.7157	−2.54100
$339$	−20.2298	−1.09873
$340$	−9.30372	−0.504565
$341$	−35.0886	−1.90016
$342$	−19.7263	−1.06668
$343$	1.00000	0.0539949
$344$	7.77615	0.419262
$345$	−4.00674	−0.215716
$346$	31.2042	1.67755
$347$	−6.37247	−0.342092	−0.171046	−	0.985263i	$-0.554715\pi$
$347$	−6.37247	−0.342092	−0.171046	+	0.985263i	$0.554715\pi$
$348$	60.5180	3.24410
$349$	15.8032	0.845927	0.422964	−	0.906147i	$-0.360990\pi$
$349$	15.8032	0.845927	0.422964	+	0.906147i	$0.360990\pi$
$350$	−2.33656	−0.124894
$351$	−8.12458	−0.433658
$352$	−17.2594	−0.919932
$353$	25.9374	1.38051	0.690255	−	0.723566i	$-0.257498\pi$
$353$	25.9374	1.38051	0.690255	+	0.723566i	$0.257498\pi$
$354$	36.1879	1.92337
$355$	−8.85202	−0.469817
$356$	−1.31327	−0.0696033
$357$	6.24409	0.330473
$358$	58.2737	3.07986
$359$	−14.5252	−0.766611	−0.383305	−	0.923622i	$-0.625214\pi$
$359$	−14.5252	−0.766611	−0.383305	+	0.923622i	$0.625214\pi$
$360$	8.15313	0.429708
$361$	−6.53040	−0.343705
$362$	−47.0766	−2.47429
$363$	10.6939	0.561283
$364$	19.8713	1.04154
$365$	−2.05400	−0.107511
$366$	−62.8366	−3.28452
$367$	27.2925	1.42466	0.712329	−	0.701845i	$-0.247640\pi$
$367$	27.2925	1.42466	0.712329	+	0.701845i	$0.247640\pi$
$368$	1.81053	0.0943803
$369$	5.65138	0.294199
$370$	3.88066	0.201746
$371$	−2.10426	−0.109248
$372$	71.3449	3.69906
$373$	−11.4792	−0.594370	−0.297185	−	0.954820i	$-0.596048\pi$
$373$	−11.4792	−0.594370	−0.297185	+	0.954820i	$0.596048\pi$
$374$	24.8235	1.28359
$375$	−2.32181	−0.119898
$376$	2.35879	0.121645
$377$	43.2770	2.22888
$378$	3.30494	0.169988
$379$	−17.1082	−0.878792	−0.439396	−	0.898294i	$-0.644807\pi$
$379$	−17.1082	−0.878792	−0.439396	+	0.898294i	$0.644807\pi$
$380$	−12.2163	−0.626684
$381$	34.4241	1.76360
$382$	−8.17023	−0.418025
$383$	23.7039	1.21121	0.605606	−	0.795765i	$-0.292931\pi$
$383$	23.7039	1.21121	0.605606	+	0.795765i	$0.292931\pi$
$384$	46.4767	2.37175
$385$	3.95042	0.201332
$386$	2.32832	0.118508
$387$	−5.45162	−0.277121
$388$	−3.55475	−0.180465
$389$	2.38922	0.121138	0.0605691	−	0.998164i	$-0.480708\pi$
$389$	2.38922	0.121138	0.0605691	+	0.998164i	$0.480708\pi$
$390$	31.1614	1.57792
$391$	4.64096	0.234703
$392$	−3.41021	−0.172242
$393$	−10.1831	−0.513671
$394$	−25.5094	−1.28514
$395$	9.47921	0.476951
$396$	−32.6738	−1.64192
$397$	32.9364	1.65303	0.826516	−	0.562914i	$-0.190320\pi$
$397$	32.9364	1.65303	0.826516	+	0.562914i	$0.190320\pi$
$398$	−62.2734	−3.12148
$399$	8.19885	0.410456
$400$	1.04916	0.0524578
$401$	−15.8339	−0.790709	−0.395354	−	0.918529i	$-0.629378\pi$
$401$	−15.8339	−0.790709	−0.395354	+	0.918529i	$0.629378\pi$
$402$	37.9353	1.89204
$403$	51.0195	2.54146
$404$	−21.1702	−1.05326
$405$	10.4565	0.519587
$406$	−17.6044	−0.873691
$407$	−6.56104	−0.325218
$408$	−21.2937	−1.05420
$409$	14.0841	0.696415	0.348208	−	0.937417i	$-0.386790\pi$
$409$	14.0841	0.696415	0.348208	+	0.937417i	$0.386790\pi$
$410$	5.52316	0.272770
$411$	−8.82371	−0.435241
$412$	−20.7543	−1.02249
$413$	−6.67054	−0.328236
$414$	−9.64017	−0.473788
$415$	6.11997	0.300417
$416$	25.0956	1.23041
$417$	−16.5351	−0.809725
$418$	32.5947	1.59426
$419$	16.6871	0.815217	0.407609	−	0.913157i	$-0.366363\pi$
$419$	16.6871	0.815217	0.407609	+	0.913157i	$0.366363\pi$
$420$	−8.03231	−0.391936
$421$	−5.99803	−0.292326	−0.146163	−	0.989261i	$-0.546692\pi$
$421$	−5.99803	−0.292326	−0.146163	+	0.989261i	$0.546692\pi$
$422$	−3.64914	−0.177637
$423$	−1.65367	−0.0804044
$424$	7.17597	0.348496
$425$	2.68932	0.130451
$426$	−48.0226	−2.32670
$427$	11.5827	0.560526
$428$	−3.23726	−0.156479
$429$	−52.6846	−2.54364
$430$	−5.32794	−0.256936
$431$	3.74992	0.180627	0.0903136	−	0.995913i	$-0.471213\pi$
$431$	3.74992	0.180627	0.0903136	+	0.995913i	$0.471213\pi$
$432$	−1.48398	−0.0713980
$433$	11.9819	0.575812	0.287906	−	0.957659i	$-0.407041\pi$
$433$	11.9819	0.575812	0.287906	+	0.957659i	$0.407041\pi$
$434$	−20.7539	−0.996218
$435$	−17.4933	−0.838738
$436$	17.8392	0.854342
$437$	6.09384	0.291508
$438$	−11.1430	−0.532434
$439$	−3.46305	−0.165282	−0.0826411	−	0.996579i	$-0.526336\pi$
$439$	−3.46305	−0.165282	−0.0826411	+	0.996579i	$0.526336\pi$
$440$	−13.4718	−0.642242
$441$	2.39080	0.113848
$442$	−36.0938	−1.71681
$443$	33.9775	1.61432	0.807159	−	0.590334i	$-0.201004\pi$
$443$	33.9775	1.61432	0.807159	+	0.590334i	$0.201004\pi$
$444$	13.3404	0.633108
$445$	0.379613	0.0179954
$446$	19.3576	0.916609
$447$	−43.9142	−2.07707
$448$	−12.3068	−0.581440
$449$	−36.9931	−1.74581	−0.872907	−	0.487887i	$-0.837768\pi$
$449$	−36.9931	−1.74581	−0.872907	+	0.487887i	$0.837768\pi$
$450$	−5.58624	−0.263338
$451$	−9.33802	−0.439710
$452$	−30.1425	−1.41778
$453$	38.4917	1.80850
$454$	−40.4020	−1.89616
$455$	−5.74399	−0.269282
$456$	−27.9598	−1.30934
$457$	10.7313	0.501988	0.250994	−	0.967989i	$-0.419243\pi$
$457$	10.7313	0.501988	0.250994	+	0.967989i	$0.419243\pi$
$458$	2.33656	0.109180
$459$	−3.80391	−0.177551
$460$	−5.97006	−0.278356
$461$	22.4400	1.04514	0.522568	−	0.852598i	$-0.324974\pi$
$461$	22.4400	1.04514	0.522568	+	0.852598i	$0.324974\pi$
$462$	21.4312	0.997070
$463$	8.43762	0.392129	0.196065	−	0.980591i	$-0.437184\pi$
$463$	8.43762	0.392129	0.196065	+	0.980591i	$0.437184\pi$
$464$	7.90468	0.366966
$465$	−20.6229	−0.956363
$466$	−66.2395	−3.06849
$467$	−23.8396	−1.10316	−0.551582	−	0.834121i	$-0.685976\pi$
$467$	−23.8396	−1.10316	−0.551582	+	0.834121i	$0.685976\pi$
$468$	47.5084	2.19608
$469$	−6.99263	−0.322890
$470$	−1.61616	−0.0745478
$471$	−5.02585	−0.231579
$472$	22.7480	1.04706
$473$	9.00796	0.414186
$474$	51.4251	2.36203
$475$	3.53123	0.162024
$476$	9.30372	0.426435
$477$	−5.03086	−0.230347
$478$	12.9781	0.593606
$479$	16.6445	0.760505	0.380252	−	0.924883i	$-0.375837\pi$
$479$	16.6445	0.760505	0.380252	+	0.924883i	$0.375837\pi$
$480$	−10.1440	−0.463009
$481$	9.53987	0.434980
$482$	−65.6930	−2.99224
$483$	4.00674	0.182313
$484$	15.9339	0.724269
$485$	1.02753	0.0466578
$486$	46.8120	2.12344
$487$	14.6874	0.665548	0.332774	−	0.943007i	$-0.392015\pi$
$487$	14.6874	0.665548	0.332774	+	0.943007i	$0.392015\pi$
$488$	−39.4995	−1.78806
$489$	−34.5402	−1.56196
$490$	2.33656	0.105555
$491$	2.07755	0.0937587	0.0468793	−	0.998901i	$-0.485072\pi$
$491$	2.07755	0.0937587	0.0468793	+	0.998901i	$0.485072\pi$
$492$	18.9868	0.855990
$493$	20.2622	0.912565
$494$	−47.3932	−2.13232
$495$	9.44466	0.424506
$496$	9.31886	0.418429
$497$	8.85202	0.397067
$498$	33.2011	1.48778
$499$	−26.6951	−1.19503	−0.597517	−	0.801856i	$-0.703846\pi$
$499$	−26.6951	−1.19503	−0.597517	+	0.801856i	$0.703846\pi$
$500$	−3.45950	−0.154714
$501$	34.1674	1.52649
$502$	50.8426	2.26922
$503$	−26.5462	−1.18364	−0.591818	−	0.806072i	$-0.701589\pi$
$503$	−26.5462	−1.18364	−0.591818	+	0.806072i	$0.701589\pi$
$504$	−8.15313	−0.363169
$505$	6.11944	0.272311
$506$	15.9289	0.708125
$507$	46.4208	2.06162
$508$	51.2920	2.27572
$509$	13.1359	0.582240	0.291120	−	0.956687i	$-0.405972\pi$
$509$	13.1359	0.582240	0.291120	+	0.956687i	$0.405972\pi$
$510$	14.5897	0.646042
$511$	2.05400	0.0908635
$512$	11.7395	0.518816
$513$	−4.99475	−0.220524
$514$	6.44377	0.284222
$515$	5.99921	0.264357
$516$	−18.3157	−0.806303
$517$	2.73244	0.120173
$518$	−3.88066	−0.170506
$519$	−31.0072	−1.36107
$520$	19.5882	0.859000
$521$	15.6698	0.686507	0.343254	−	0.939243i	$-0.388471\pi$
$521$	15.6698	0.686507	0.343254	+	0.939243i	$0.388471\pi$
$522$	−42.0885	−1.84216
$523$	−21.5672	−0.943067	−0.471533	−	0.881848i	$-0.656299\pi$
$523$	−21.5672	−0.943067	−0.471533	+	0.881848i	$0.656299\pi$
$524$	−15.1729	−0.662831
$525$	2.32181	0.101332
$526$	−15.3418	−0.668933
$527$	23.8872	1.04054
$528$	−9.62300	−0.418787
$529$	−20.0220	−0.870520
$530$	−4.91672	−0.213569
$531$	−15.9479	−0.692080
$532$	12.2163	0.529644
$533$	13.5777	0.588113
$534$	2.05942	0.0891196
$535$	0.935760	0.0404564
$536$	23.8464	1.03001
$537$	−57.9058	−2.49882
$538$	−8.02205	−0.345855
$539$	−3.95042	−0.170157
$540$	4.89329	0.210574
$541$	−14.8600	−0.638882	−0.319441	−	0.947606i	$-0.603495\pi$
$541$	−14.8600	−0.638882	−0.319441	+	0.947606i	$0.603495\pi$
$542$	4.20001	0.180406
$543$	46.7794	2.00750
$544$	11.7497	0.503764
$545$	−5.15657	−0.220883
$546$	−31.1614	−1.33358
$547$	−40.0339	−1.71172	−0.855862	−	0.517204i	$-0.826973\pi$
$547$	−40.0339	−1.71172	−0.855862	+	0.517204i	$0.826973\pi$
$548$	−13.1474	−0.561627
$549$	27.6919	1.18186
$550$	9.23039	0.393585
$551$	26.6054	1.13343
$552$	−13.6639	−0.581572
$553$	−9.47921	−0.403097
$554$	−37.3285	−1.58594
$555$	−3.85616	−0.163685
$556$	−24.6373	−1.04485
$557$	−40.7820	−1.72799	−0.863995	−	0.503500i	$-0.832045\pi$
$557$	−40.7820	−1.72799	−0.863995	+	0.503500i	$0.832045\pi$
$558$	−49.6183	−2.10051
$559$	−13.0977	−0.553975
$560$	−1.04916	−0.0443349
$561$	−24.6668	−1.04143
$562$	−58.2121	−2.45553
$563$	−17.7629	−0.748619	−0.374310	−	0.927304i	$-0.622120\pi$
$563$	−17.7629	−0.748619	−0.374310	+	0.927304i	$0.622120\pi$
$564$	−5.55581	−0.233942
$565$	8.71295	0.366556
$566$	−22.4514	−0.943704
$567$	−10.4565	−0.439131
$568$	−30.1873	−1.26663
$569$	−0.116315	−0.00487619	−0.00243809	−	0.999997i	$-0.500776\pi$
$569$	−0.116315	−0.00487619	−0.00243809	+	0.999997i	$0.500776\pi$
$570$	19.1571	0.802402
$571$	−34.9276	−1.46168	−0.730838	−	0.682551i	$-0.760871\pi$
$571$	−34.9276	−1.46168	−0.730838	+	0.682551i	$0.760871\pi$
$572$	−78.5002	−3.28226
$573$	8.11865	0.339162
$574$	−5.52316	−0.230532
$575$	1.72570	0.0719666
$576$	−29.4230	−1.22596
$577$	−29.0453	−1.20917	−0.604586	−	0.796540i	$-0.706661\pi$
$577$	−29.0453	−1.20917	−0.604586	+	0.796540i	$0.706661\pi$
$578$	22.8224	0.949288
$579$	−2.31362	−0.0961509
$580$	−26.0650	−1.08229
$581$	−6.11997	−0.253899
$582$	5.57440	0.231066
$583$	8.31271	0.344277
$584$	−7.00457	−0.289851
$585$	−13.7327	−0.567778
$586$	−66.8094	−2.75987
$587$	−10.9104	−0.450320	−0.225160	−	0.974322i	$-0.572291\pi$
$587$	−10.9104	−0.450320	−0.225160	+	0.974322i	$0.572291\pi$
$588$	8.03231	0.331247
$589$	31.3653	1.29238
$590$	−15.5861	−0.641669
$591$	25.3483	1.04269
$592$	1.74248	0.0716157
$593$	14.1037	0.579170	0.289585	−	0.957152i	$-0.406483\pi$
$593$	14.1037	0.579170	0.289585	+	0.957152i	$0.406483\pi$
$594$	−13.0559	−0.535691
$595$	−2.68932	−0.110251
$596$	−65.4324	−2.68021
$597$	61.8803	2.53259
$598$	−23.1609	−0.947119
$599$	−20.0018	−0.817250	−0.408625	−	0.912702i	$-0.633992\pi$
$599$	−20.0018	−0.817250	−0.408625	+	0.912702i	$0.633992\pi$
$600$	−7.91787	−0.323246
$601$	26.6238	1.08601	0.543005	−	0.839730i	$-0.317287\pi$
$601$	26.6238	1.08601	0.543005	+	0.839730i	$0.317287\pi$
$602$	5.32794	0.217151
$603$	−16.7180	−0.680808
$604$	57.3527	2.33365
$605$	−4.60584	−0.187254
$606$	33.1982	1.34858
$607$	−44.9271	−1.82353	−0.911767	−	0.410707i	$-0.865282\pi$
$607$	−44.9271	−1.82353	−0.911767	+	0.410707i	$0.865282\pi$
$608$	15.4280	0.625688
$609$	17.4933	0.708863
$610$	27.0636	1.09577
$611$	−3.97302	−0.160731
$612$	22.2433	0.899133
$613$	−34.3065	−1.38562	−0.692812	−	0.721118i	$-0.743629\pi$
$613$	−34.3065	−1.38562	−0.692812	+	0.721118i	$0.743629\pi$
$614$	−81.2215	−3.27783
$615$	−5.48830	−0.221310
$616$	13.4718	0.542794
$617$	9.66127	0.388948	0.194474	−	0.980908i	$-0.437700\pi$
$617$	9.66127	0.388948	0.194474	+	0.980908i	$0.437700\pi$
$618$	32.5460	1.30919
$619$	30.3006	1.21788	0.608942	−	0.793215i	$-0.291594\pi$
$619$	30.3006	1.21788	0.608942	+	0.793215i	$0.291594\pi$
$620$	−30.7282	−1.23407
$621$	−2.44091	−0.0979505
$622$	3.16456	0.126887
$623$	−0.379613	−0.0152089
$624$	13.9920	0.560129
$625$	1.00000	0.0400000
$626$	31.2364	1.24846
$627$	−32.3889	−1.29349
$628$	−7.48853	−0.298825
$629$	4.46655	0.178093
$630$	5.58624	0.222561
$631$	−12.7675	−0.508267	−0.254133	−	0.967169i	$-0.581790\pi$
$631$	−12.7675	−0.508267	−0.254133	+	0.967169i	$0.581790\pi$
$632$	32.3261	1.28586
$633$	3.62611	0.144125
$634$	−27.5819	−1.09542
$635$	−14.8264	−0.588368
$636$	−16.9021	−0.670210
$637$	5.74399	0.227585
$638$	69.5447	2.75330
$639$	21.1634	0.837211
$640$	−20.0174	−0.791259
$641$	13.2673	0.524027	0.262014	−	0.965064i	$-0.415613\pi$
$641$	13.2673	0.524027	0.262014	+	0.965064i	$0.415613\pi$
$642$	5.07654	0.200355
$643$	−37.2830	−1.47030	−0.735149	−	0.677905i	$-0.762888\pi$
$643$	−37.2830	−1.47030	−0.735149	+	0.677905i	$0.762888\pi$
$644$	5.97006	0.235253
$645$	5.29431	0.208463
$646$	−22.1894	−0.873031
$647$	−17.7739	−0.698763	−0.349382	−	0.936981i	$-0.613608\pi$
$647$	−17.7739	−0.698763	−0.349382	+	0.936981i	$0.613608\pi$
$648$	35.6588	1.40081
$649$	26.3514	1.03438
$650$	−13.4212	−0.526421
$651$	20.6229	0.808274
$652$	−51.4650	−2.01552
$653$	−8.10627	−0.317223	−0.158611	−	0.987341i	$-0.550702\pi$
$653$	−8.10627	−0.317223	−0.158611	+	0.987341i	$0.550702\pi$
$654$	−27.9746	−1.09389
$655$	4.38586	0.171370
$656$	2.48000	0.0968277
$657$	4.91069	0.191584
$658$	1.61616	0.0630044
$659$	1.37718	0.0536472	0.0268236	−	0.999640i	$-0.491461\pi$
$659$	1.37718	0.0536472	0.0268236	+	0.999640i	$0.491461\pi$
$660$	31.7310	1.23513
$661$	−1.06918	−0.0415861	−0.0207931	−	0.999784i	$-0.506619\pi$
$661$	−1.06918	−0.0415861	−0.0207931	+	0.999784i	$0.506619\pi$
$662$	33.3833	1.29748
$663$	35.8660	1.39292
$664$	20.8704	0.809928
$665$	−3.53123	−0.136935
$666$	−9.27787	−0.359510
$667$	13.0020	0.503438
$668$	50.9096	1.96975
$669$	−19.2354	−0.743684
$670$	−16.3387	−0.631218
$671$	−45.7565	−1.76641
$672$	10.1440	0.391314
$673$	−0.575373	−0.0221790	−0.0110895	−	0.999939i	$-0.503530\pi$
$673$	−0.575373	−0.0221790	−0.0110895	+	0.999939i	$0.503530\pi$
$674$	0.142238	0.00547880
$675$	−1.41445	−0.0544422
$676$	69.1672	2.66028
$677$	−3.12281	−0.120019	−0.0600097	−	0.998198i	$-0.519113\pi$
$677$	−3.12281	−0.120019	−0.0600097	+	0.998198i	$0.519113\pi$
$678$	47.2681	1.81532
$679$	−1.02753	−0.0394330
$680$	9.17117	0.351698
$681$	40.1470	1.53843
$682$	81.9866	3.13943
$683$	31.9723	1.22339	0.611694	−	0.791095i	$-0.290489\pi$
$683$	31.9723	1.22339	0.611694	+	0.791095i	$0.290489\pi$
$684$	29.2067	1.11675
$685$	3.80036	0.145204
$686$	−2.33656	−0.0892102
$687$	−2.32181	−0.0885825
$688$	−2.39234	−0.0912071
$689$	−12.0868	−0.460472
$690$	9.36199	0.356405
$691$	−10.2920	−0.391526	−0.195763	−	0.980651i	$-0.562718\pi$
$691$	−10.2920	−0.391526	−0.195763	+	0.980651i	$0.562718\pi$
$692$	−46.2009	−1.75629
$693$	−9.44466	−0.358773
$694$	14.8896	0.565203
$695$	7.12163	0.270139
$696$	−59.6558	−2.26125
$697$	6.35703	0.240790
$698$	−36.9252	−1.39764
$699$	65.8214	2.48959
$700$	3.45950	0.130757
$701$	−9.80028	−0.370151	−0.185076	−	0.982724i	$-0.559253\pi$
$701$	−9.80028	−0.370151	−0.185076	+	0.982724i	$0.559253\pi$
$702$	18.9836	0.716488
$703$	5.86483	0.221196
$704$	48.6169	1.83232
$705$	1.60596	0.0604838
$706$	−60.6043	−2.28087
$707$	−6.11944	−0.230145
$708$	−53.5798	−2.01365
$709$	49.0942	1.84377	0.921885	−	0.387463i	$-0.126648\pi$
$709$	49.0942	1.84377	0.921885	+	0.387463i	$0.126648\pi$
$710$	20.6833	0.776229
$711$	−22.6629	−0.849925
$712$	1.29456	0.0485157
$713$	15.3281	0.574041
$714$	−14.5897	−0.546005
$715$	22.6912	0.848602
$716$	−86.2799	−3.22443
$717$	−12.8962	−0.481618
$718$	33.9390	1.26659
$719$	9.09340	0.339127	0.169563	−	0.985519i	$-0.445764\pi$
$719$	9.09340	0.339127	0.169563	+	0.985519i	$0.445764\pi$
$720$	−2.50832	−0.0934796
$721$	−5.99921	−0.223422
$722$	15.2586	0.567868
$723$	65.2784	2.42773
$724$	69.7015	2.59044
$725$	7.53432	0.279818
$726$	−24.9869	−0.927350
$727$	−25.6715	−0.952104	−0.476052	−	0.879417i	$-0.657933\pi$
$727$	−25.6715	−0.952104	−0.476052	+	0.879417i	$0.657933\pi$
$728$	−19.5882	−0.725988
$729$	−15.1471	−0.561003
$730$	4.79928	0.177630
$731$	−6.13233	−0.226813
$732$	93.0358	3.43870
$733$	−23.6426	−0.873261	−0.436630	−	0.899641i	$-0.643828\pi$
$733$	−23.6426	−0.873261	−0.436630	+	0.899641i	$0.643828\pi$
$734$	−63.7706	−2.35382
$735$	−2.32181	−0.0856412
$736$	7.53960	0.277913
$737$	27.6238	1.01754
$738$	−13.2048	−0.486074
$739$	−11.0883	−0.407890	−0.203945	−	0.978982i	$-0.565376\pi$
$739$	−11.0883	−0.407890	−0.203945	+	0.978982i	$0.565376\pi$
$740$	−5.74570	−0.211216
$741$	47.0941	1.73004
$742$	4.91672	0.180499
$743$	−1.83209	−0.0672130	−0.0336065	−	0.999435i	$-0.510699\pi$
$743$	−1.83209	−0.0672130	−0.0336065	+	0.999435i	$0.510699\pi$
$744$	−70.3284	−2.57837
$745$	18.9138	0.692948
$746$	26.8218	0.982016
$747$	−14.6316	−0.535342
$748$	−36.7536	−1.34385
$749$	−0.935760	−0.0341919
$750$	5.42504	0.198095
$751$	18.7240	0.683250	0.341625	−	0.939836i	$-0.389023\pi$
$751$	18.7240	0.683250	0.341625	+	0.939836i	$0.389023\pi$
$752$	−0.725683	−0.0264629
$753$	−50.5217	−1.84111
$754$	−101.119	−3.68255
$755$	−16.5783	−0.603346
$756$	−4.89329	−0.177967
$757$	40.8579	1.48501	0.742503	−	0.669843i	$-0.233639\pi$
$757$	40.8579	1.48501	0.742503	+	0.669843i	$0.233639\pi$
$758$	39.9744	1.45194
$759$	−15.8283	−0.574532
$760$	12.0423	0.436819
$761$	30.4192	1.10269	0.551347	−	0.834276i	$-0.314114\pi$
$761$	30.4192	1.10269	0.551347	+	0.834276i	$0.314114\pi$
$762$	−80.4339	−2.91381
$763$	5.15657	0.186681
$764$	12.0968	0.437648
$765$	−6.42963	−0.232464
$766$	−55.3855	−2.00116
$767$	−38.3155	−1.38349
$768$	−51.4476	−1.85645
$769$	−39.4157	−1.42136	−0.710682	−	0.703513i	$-0.751614\pi$
$769$	−39.4157	−1.42136	−0.710682	+	0.703513i	$0.751614\pi$
$770$	−9.23039	−0.332640
$771$	−6.40309	−0.230602
$772$	−3.44731	−0.124071
$773$	54.4242	1.95750	0.978751	−	0.205054i	$-0.0657371\pi$
$773$	54.4242	1.95750	0.978751	+	0.205054i	$0.0657371\pi$
$774$	12.7380	0.457859
$775$	8.88224	0.319060
$776$	3.50410	0.125790
$777$	3.85616	0.138339
$778$	−5.58255	−0.200144
$779$	8.34714	0.299067
$780$	−46.1375	−1.65199
$781$	−34.9692	−1.25130
$782$	−10.8439	−0.387776
$783$	−10.6569	−0.380847
$784$	1.04916	0.0374699
$785$	2.16463	0.0772588
$786$	23.7935	0.848685
$787$	45.2113	1.61161	0.805805	−	0.592181i	$-0.201733\pi$
$787$	45.2113	1.61161	0.805805	+	0.592181i	$0.201733\pi$
$788$	37.7691	1.34547
$789$	15.2449	0.542734
$790$	−22.1487	−0.788016
$791$	−8.71295	−0.309797
$792$	32.2083	1.14447
$793$	66.5308	2.36258
$794$	−76.9578	−2.73113
$795$	4.88569	0.173278
$796$	92.2018	3.26801
$797$	−28.3201	−1.00315	−0.501575	−	0.865114i	$-0.667246\pi$
$797$	−28.3201	−1.00315	−0.501575	+	0.865114i	$0.667246\pi$
$798$	−19.1571	−0.678153
$799$	−1.86016	−0.0658077
$800$	4.36901	0.154468
$801$	−0.907578	−0.0320677
$802$	36.9969	1.30641
$803$	−8.11416	−0.286342
$804$	−56.1669	−1.98086
$805$	−1.72570	−0.0608229
$806$	−119.210	−4.19899
$807$	7.97141	0.280607
$808$	20.8686	0.734154
$809$	14.3508	0.504549	0.252274	−	0.967656i	$-0.418821\pi$
$809$	14.3508	0.504549	0.252274	+	0.967656i	$0.418821\pi$
$810$	−24.4322	−0.858459
$811$	−22.0283	−0.773520	−0.386760	−	0.922180i	$-0.626406\pi$
$811$	−22.0283	−0.773520	−0.386760	+	0.922180i	$0.626406\pi$
$812$	26.0650	0.914703
$813$	−4.17350	−0.146371
$814$	15.3302	0.537325
$815$	14.8764	0.521098
$816$	6.55103	0.229332
$817$	−8.05210	−0.281707
$818$	−32.9084	−1.15061
$819$	13.7327	0.479860
$820$	−8.17758	−0.285574
$821$	−46.8830	−1.63623	−0.818114	−	0.575056i	$-0.804980\pi$
$821$	−46.8830	−1.63623	−0.818114	+	0.575056i	$0.804980\pi$
$822$	20.6171	0.719104
$823$	15.0297	0.523901	0.261951	−	0.965081i	$-0.415634\pi$
$823$	15.0297	0.523901	0.261951	+	0.965081i	$0.415634\pi$
$824$	20.4586	0.712708
$825$	−9.17213	−0.319332
$826$	15.5861	0.542310
$827$	−45.1716	−1.57077	−0.785385	−	0.619008i	$-0.787535\pi$
$827$	−45.1716	−1.57077	−0.785385	+	0.619008i	$0.787535\pi$
$828$	14.2732	0.496028
$829$	−23.8365	−0.827877	−0.413938	−	0.910305i	$-0.635847\pi$
$829$	−23.8365	−0.827877	−0.413938	+	0.910305i	$0.635847\pi$
$830$	−14.2997	−0.496348
$831$	37.0929	1.28674
$832$	−70.6899	−2.45073
$833$	2.68932	0.0931795
$834$	38.6351	1.33782
$835$	−14.7159	−0.509263
$836$	−48.2596	−1.66909
$837$	−12.5635	−0.434258
$838$	−38.9903	−1.34690
$839$	11.9306	0.411891	0.205945	−	0.978564i	$-0.433973\pi$
$839$	11.9306	0.411891	0.205945	+	0.978564i	$0.433973\pi$
$840$	7.91787	0.273192
$841$	27.7660	0.957448
$842$	14.0147	0.482980
$843$	57.8446	1.99227
$844$	5.40291	0.185976
$845$	−19.9934	−0.687793
$846$	3.86391	0.132844
$847$	4.60584	0.158258
$848$	−2.20770	−0.0758126
$849$	22.3097	0.765667
$850$	−6.28376	−0.215531
$851$	2.86612	0.0982492
$852$	71.1022	2.43592
$853$	52.3194	1.79138	0.895692	−	0.444675i	$-0.146681\pi$
$853$	52.3194	1.79138	0.895692	+	0.444675i	$0.146681\pi$
$854$	−27.0636	−0.926099
$855$	−8.44247	−0.288726
$856$	3.19114	0.109071
$857$	43.7159	1.49331	0.746654	−	0.665213i	$-0.231659\pi$
$857$	43.7159	1.49331	0.746654	+	0.665213i	$0.231659\pi$
$858$	123.101	4.20258
$859$	57.5829	1.96470	0.982351	−	0.187047i	$-0.0598916\pi$
$859$	57.5829	1.96470	0.982351	+	0.187047i	$0.0598916\pi$
$860$	7.88854	0.268997
$861$	5.48830	0.187041
$862$	−8.76190	−0.298432
$863$	−45.9061	−1.56266	−0.781331	−	0.624117i	$-0.785459\pi$
$863$	−45.9061	−1.56266	−0.781331	+	0.624117i	$0.785459\pi$
$864$	−6.17975	−0.210239
$865$	13.3548	0.454076
$866$	−27.9963	−0.951354
$867$	−22.6784	−0.770198
$868$	30.7282	1.04298
$869$	37.4469	1.27030
$870$	40.8740	1.38576
$871$	−40.1656	−1.36096
$872$	−17.5850	−0.595504
$873$	−2.45662	−0.0831439
$874$	−14.2386	−0.481628
$875$	−1.00000	−0.0338062
$876$	16.4983	0.557427
$877$	−15.0708	−0.508903	−0.254452	−	0.967086i	$-0.581895\pi$
$877$	−15.0708	−0.508903	−0.254452	+	0.967086i	$0.581895\pi$
$878$	8.09161	0.273079
$879$	66.3877	2.23920
$880$	4.14461	0.139715
$881$	−5.26540	−0.177396	−0.0886979	−	0.996059i	$-0.528271\pi$
$881$	−5.26540	−0.177396	−0.0886979	+	0.996059i	$0.528271\pi$
$882$	−5.58624	−0.188098
$883$	−8.19734	−0.275862	−0.137931	−	0.990442i	$-0.544045\pi$
$883$	−8.19734	−0.275862	−0.137931	+	0.990442i	$0.544045\pi$
$884$	53.4405	1.79740
$885$	15.4877	0.520614
$886$	−79.3903	−2.66717
$887$	8.62747	0.289682	0.144841	−	0.989455i	$-0.453733\pi$
$887$	8.62747	0.289682	0.144841	+	0.989455i	$0.453733\pi$
$888$	−13.1503	−0.441297
$889$	14.8264	0.497262
$890$	−0.886988	−0.0297319
$891$	41.3075	1.38385
$892$	−28.6608	−0.959635
$893$	−2.44249	−0.0817349
$894$	102.608	3.43173
$895$	24.9400	0.833651
$896$	20.0174	0.668736
$897$	23.0147	0.768438
$898$	86.4366	2.88443
$899$	66.9217	2.23196
$900$	8.27097	0.275699
$901$	−5.65903	−0.188530
$902$	21.8188	0.726487
$903$	−5.29431	−0.176184
$904$	29.7130	0.988240
$905$	−20.1478	−0.669737
$906$	−89.9380	−2.98799
$907$	31.9416	1.06060	0.530301	−	0.847809i	$-0.322079\pi$
$907$	31.9416	1.06060	0.530301	+	0.847809i	$0.322079\pi$
$908$	59.8191	1.98517
$909$	−14.6303	−0.485258
$910$	13.4212	0.444907
$911$	30.2954	1.00373	0.501867	−	0.864945i	$-0.332647\pi$
$911$	30.2954	1.00373	0.501867	+	0.864945i	$0.332647\pi$
$912$	8.60187	0.284836
$913$	24.1764	0.800124
$914$	−25.0743	−0.829382
$915$	−26.8928	−0.889049
$916$	−3.45950	−0.114305
$917$	−4.38586	−0.144834
$918$	8.88806	0.293350
$919$	−40.5331	−1.33706	−0.668531	−	0.743684i	$-0.733077\pi$
$919$	−40.5331	−1.33706	−0.668531	+	0.743684i	$0.733077\pi$
$920$	5.88500	0.194023
$921$	80.7088	2.65945
$922$	−52.4324	−1.72677
$923$	50.8459	1.67361
$924$	−31.7310	−1.04387
$925$	1.66084	0.0546082
$926$	−19.7150	−0.647875
$927$	−14.3429	−0.471083
$928$	32.9176	1.08057
$929$	18.2696	0.599407	0.299704	−	0.954032i	$-0.403112\pi$
$929$	18.2696	0.599407	0.299704	+	0.954032i	$0.403112\pi$
$930$	48.1866	1.58010
$931$	3.53123	0.115731
$932$	98.0741	3.21252
$933$	−3.14458	−0.102949
$934$	55.7025	1.82264
$935$	10.6240	0.347441
$936$	−46.8315	−1.53074
$937$	16.6377	0.543528	0.271764	−	0.962364i	$-0.412393\pi$
$937$	16.6377	0.543528	0.271764	+	0.962364i	$0.412393\pi$
$938$	16.3387	0.533477
$939$	−31.0392	−1.01293
$940$	2.39288	0.0780471
$941$	−49.6366	−1.61811	−0.809053	−	0.587736i	$-0.800019\pi$
$941$	−49.6366	−1.61811	−0.809053	+	0.587736i	$0.800019\pi$
$942$	11.7432	0.382614
$943$	4.07921	0.132837
$944$	−6.99843	−0.227780
$945$	1.41445	0.0460121
$946$	−21.0476	−0.684317
$947$	−27.3923	−0.890131	−0.445066	−	0.895498i	$-0.646820\pi$
$947$	−27.3923	−0.890131	−0.445066	+	0.895498i	$0.646820\pi$
$948$	−76.1399	−2.47291
$949$	11.7981	0.382984
$950$	−8.25093	−0.267696
$951$	27.4078	0.888758
$952$	−9.17117	−0.297239
$953$	−50.8645	−1.64766	−0.823831	−	0.566836i	$-0.808167\pi$
$953$	−50.8645	−1.64766	−0.823831	+	0.566836i	$0.808167\pi$
$954$	11.7549	0.380579
$955$	−3.49669	−0.113150
$956$	−19.2154	−0.621471
$957$	−69.1058	−2.23387
$958$	−38.8907	−1.25650
$959$	−3.80036	−0.122720
$960$	28.5740	0.922221
$961$	47.8943	1.54498
$962$	−22.2905	−0.718673
$963$	−2.23721	−0.0720932
$964$	97.2650	3.13269
$965$	0.996474	0.0320776
$966$	−9.36199	−0.301217
$967$	11.5289	0.370746	0.185373	−	0.982668i	$-0.440651\pi$
$967$	11.5289	0.370746	0.185373	+	0.982668i	$0.440651\pi$
$968$	−15.7069	−0.504839
$969$	22.0494	0.708327
$970$	−2.40088	−0.0770878
$971$	−38.3089	−1.22939	−0.614696	−	0.788764i	$-0.710721\pi$
$971$	−38.3089	−1.22939	−0.614696	+	0.788764i	$0.710721\pi$
$972$	−69.3098	−2.22311
$973$	−7.12163	−0.228309
$974$	−34.3179	−1.09962
$975$	13.3364	0.427108
$976$	12.1521	0.388978
$977$	18.1408	0.580377	0.290189	−	0.956969i	$-0.406282\pi$
$977$	18.1408	0.580377	0.290189	+	0.956969i	$0.406282\pi$
$978$	80.7051	2.58067
$979$	1.49963	0.0479284
$980$	−3.45950	−0.110510
$981$	12.3283	0.393613
$982$	−4.85432	−0.154908
$983$	55.4978	1.77010	0.885052	−	0.465492i	$-0.154123\pi$
$983$	55.4978	1.77010	0.885052	+	0.465492i	$0.154123\pi$
$984$	−18.7163	−0.596653
$985$	−10.9175	−0.347860
$986$	−47.3439	−1.50774
$987$	−1.60596	−0.0511181
$988$	70.1703	2.23242
$989$	−3.93503	−0.125127
$990$	−22.0680	−0.701367
$991$	−13.6401	−0.433292	−0.216646	−	0.976250i	$-0.569512\pi$
$991$	−13.6401	−0.433292	−0.216646	+	0.976250i	$0.569512\pi$
$992$	38.8066	1.23211
$993$	−33.1726	−1.05270
$994$	−20.6833	−0.656033
$995$	−26.6517	−0.844917
$996$	−49.1574	−1.55761
$997$	37.6315	1.19180	0.595901	−	0.803058i	$-0.296795\pi$
$997$	37.6315	1.19180	0.595901	+	0.803058i	$0.296795\pi$
$998$	62.3746	1.97443
$999$	−2.34918	−0.0743248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.8	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.8	✓	68	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33656 q^{2} +2.32181 q^{3} +3.45950 q^{4} -1.00000 q^{5} -5.42504 q^{6} +1.00000 q^{7} -3.41021 q^{8} +2.39080 q^{9} +O(q^{10})\)	\(q-2.33656 q^{2} +2.32181 q^{3} +3.45950 q^{4} -1.00000 q^{5} -5.42504 q^{6} +1.00000 q^{7} -3.41021 q^{8} +2.39080 q^{9} +2.33656 q^{10} -3.95042 q^{11} +8.03231 q^{12} +5.74399 q^{13} -2.33656 q^{14} -2.32181 q^{15} +1.04916 q^{16} +2.68932 q^{17} -5.58624 q^{18} +3.53123 q^{19} -3.45950 q^{20} +2.32181 q^{21} +9.23039 q^{22} +1.72570 q^{23} -7.91787 q^{24} +1.00000 q^{25} -13.4212 q^{26} -1.41445 q^{27} +3.45950 q^{28} +7.53432 q^{29} +5.42504 q^{30} +8.88224 q^{31} +4.36901 q^{32} -9.17213 q^{33} -6.28376 q^{34} -1.00000 q^{35} +8.27097 q^{36} +1.66084 q^{37} -8.25093 q^{38} +13.3364 q^{39} +3.41021 q^{40} +2.36380 q^{41} -5.42504 q^{42} -2.28025 q^{43} -13.6665 q^{44} -2.39080 q^{45} -4.03220 q^{46} -0.691683 q^{47} +2.43594 q^{48} +1.00000 q^{49} -2.33656 q^{50} +6.24409 q^{51} +19.8713 q^{52} -2.10426 q^{53} +3.30494 q^{54} +3.95042 q^{55} -3.41021 q^{56} +8.19885 q^{57} -17.6044 q^{58} -6.67054 q^{59} -8.03231 q^{60} +11.5827 q^{61} -20.7539 q^{62} +2.39080 q^{63} -12.3068 q^{64} -5.74399 q^{65} +21.4312 q^{66} -6.99263 q^{67} +9.30372 q^{68} +4.00674 q^{69} +2.33656 q^{70} +8.85202 q^{71} -8.15313 q^{72} +2.05400 q^{73} -3.88066 q^{74} +2.32181 q^{75} +12.2163 q^{76} -3.95042 q^{77} -31.1614 q^{78} -9.47921 q^{79} -1.04916 q^{80} -10.4565 q^{81} -5.52316 q^{82} -6.11997 q^{83} +8.03231 q^{84} -2.68932 q^{85} +5.32794 q^{86} +17.4933 q^{87} +13.4718 q^{88} -0.379613 q^{89} +5.58624 q^{90} +5.74399 q^{91} +5.97006 q^{92} +20.6229 q^{93} +1.61616 q^{94} -3.53123 q^{95} +10.1440 q^{96} -1.02753 q^{97} -2.33656 q^{98} -9.44466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

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