LMFDB - Embedded newform 8015.2.a.n.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.92788 q^{2} -3.19402 q^{3} +1.71671 q^{4} -1.00000 q^{5} +6.15768 q^{6} +1.00000 q^{7} +0.546142 q^{8} +7.20176 q^{9} +O(q^{10})$	\(q-1.92788 q^{2} -3.19402 q^{3} +1.71671 q^{4} -1.00000 q^{5} +6.15768 q^{6} +1.00000 q^{7} +0.546142 q^{8} +7.20176 q^{9} +1.92788 q^{10} +1.50297 q^{11} -5.48322 q^{12} -0.695699 q^{13} -1.92788 q^{14} +3.19402 q^{15} -4.48632 q^{16} +0.954365 q^{17} -13.8841 q^{18} -5.42948 q^{19} -1.71671 q^{20} -3.19402 q^{21} -2.89754 q^{22} +3.74154 q^{23} -1.74439 q^{24} +1.00000 q^{25} +1.34122 q^{26} -13.4205 q^{27} +1.71671 q^{28} +0.797519 q^{29} -6.15768 q^{30} -9.59018 q^{31} +7.55680 q^{32} -4.80052 q^{33} -1.83990 q^{34} -1.00000 q^{35} +12.3634 q^{36} +8.49337 q^{37} +10.4674 q^{38} +2.22208 q^{39} -0.546142 q^{40} -4.48220 q^{41} +6.15768 q^{42} -8.01544 q^{43} +2.58017 q^{44} -7.20176 q^{45} -7.21323 q^{46} +9.05728 q^{47} +14.3294 q^{48} +1.00000 q^{49} -1.92788 q^{50} -3.04826 q^{51} -1.19432 q^{52} +1.35676 q^{53} +25.8731 q^{54} -1.50297 q^{55} +0.546142 q^{56} +17.3419 q^{57} -1.53752 q^{58} -12.2259 q^{59} +5.48322 q^{60} +1.96345 q^{61} +18.4887 q^{62} +7.20176 q^{63} -5.59594 q^{64} +0.695699 q^{65} +9.25481 q^{66} -3.52411 q^{67} +1.63837 q^{68} -11.9505 q^{69} +1.92788 q^{70} +10.1268 q^{71} +3.93318 q^{72} +9.87727 q^{73} -16.3742 q^{74} -3.19402 q^{75} -9.32086 q^{76} +1.50297 q^{77} -4.28389 q^{78} -9.06539 q^{79} +4.48632 q^{80} +21.2601 q^{81} +8.64113 q^{82} -8.01838 q^{83} -5.48322 q^{84} -0.954365 q^{85} +15.4528 q^{86} -2.54729 q^{87} +0.820835 q^{88} +10.3751 q^{89} +13.8841 q^{90} -0.695699 q^{91} +6.42315 q^{92} +30.6312 q^{93} -17.4613 q^{94} +5.42948 q^{95} -24.1366 q^{96} +3.94827 q^{97} -1.92788 q^{98} +10.8240 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.92788	−1.36322	−0.681608	−	0.731718i	$-0.738719\pi$
$2$	−1.92788	−1.36322	−0.681608	+	0.731718i	$0.738719\pi$
$3$	−3.19402	−1.84407	−0.922034	−	0.387109i	$-0.873474\pi$
$3$	−3.19402	−1.84407	−0.922034	+	0.387109i	$0.873474\pi$
$4$	1.71671	0.858357
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.15768	2.51386
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.546142	0.193090
$9$	7.20176	2.40059
$10$	1.92788	0.609649
$11$	1.50297	0.453162	0.226581	−	0.973992i	$-0.427245\pi$
$11$	1.50297	0.453162	0.226581	+	0.973992i	$0.427245\pi$
$12$	−5.48322	−1.58287
$13$	−0.695699	−0.192952	−0.0964761	−	0.995335i	$-0.530757\pi$
$13$	−0.695699	−0.192952	−0.0964761	+	0.995335i	$0.530757\pi$
$14$	−1.92788	−0.515247
$15$	3.19402	0.824692
$16$	−4.48632	−1.12158
$17$	0.954365	0.231468	0.115734	−	0.993280i	$-0.463078\pi$
$17$	0.954365	0.231468	0.115734	+	0.993280i	$0.463078\pi$
$18$	−13.8841	−3.27252
$19$	−5.42948	−1.24561	−0.622804	−	0.782378i	$-0.714007\pi$
$19$	−5.42948	−1.24561	−0.622804	+	0.782378i	$0.714007\pi$
$20$	−1.71671	−0.383869
$21$	−3.19402	−0.696992
$22$	−2.89754	−0.617758
$23$	3.74154	0.780164	0.390082	−	0.920780i	$-0.372447\pi$
$23$	3.74154	0.780164	0.390082	+	0.920780i	$0.372447\pi$
$24$	−1.74439	−0.356072
$25$	1.00000	0.200000
$26$	1.34122	0.263036
$27$	−13.4205	−2.58278
$28$	1.71671	0.324428
$29$	0.797519	0.148096	0.0740478	−	0.997255i	$-0.476408\pi$
$29$	0.797519	0.148096	0.0740478	+	0.997255i	$0.476408\pi$
$30$	−6.15768	−1.12423
$31$	−9.59018	−1.72245	−0.861224	−	0.508226i	$-0.830301\pi$
$31$	−9.59018	−1.72245	−0.861224	+	0.508226i	$0.830301\pi$
$32$	7.55680	1.33587
$33$	−4.80052	−0.835662
$34$	−1.83990	−0.315540
$35$	−1.00000	−0.169031
$36$	12.3634	2.06056
$37$	8.49337	1.39630	0.698151	−	0.715951i	$-0.254007\pi$
$37$	8.49337	1.39630	0.698151	+	0.715951i	$0.254007\pi$
$38$	10.4674	1.69803
$39$	2.22208	0.355817
$40$	−0.546142	−0.0863526
$41$	−4.48220	−0.700001	−0.350001	−	0.936749i	$-0.613819\pi$
$41$	−4.48220	−0.700001	−0.350001	+	0.936749i	$0.613819\pi$
$42$	6.15768	0.950151
$43$	−8.01544	−1.22234	−0.611171	−	0.791498i	$-0.709301\pi$
$43$	−8.01544	−1.22234	−0.611171	+	0.791498i	$0.709301\pi$
$44$	2.58017	0.388975
$45$	−7.20176	−1.07358
$46$	−7.21323	−1.06353
$47$	9.05728	1.32114	0.660570	−	0.750765i	$-0.270315\pi$
$47$	9.05728	1.32114	0.660570	+	0.750765i	$0.270315\pi$
$48$	14.3294	2.06827
$49$	1.00000	0.142857
$50$	−1.92788	−0.272643
$51$	−3.04826	−0.426842
$52$	−1.19432	−0.165622
$53$	1.35676	0.186366	0.0931830	−	0.995649i	$-0.470296\pi$
$53$	1.35676	0.186366	0.0931830	+	0.995649i	$0.470296\pi$
$54$	25.8731	3.52088
$55$	−1.50297	−0.202660
$56$	0.546142	0.0729813
$57$	17.3419	2.29699
$58$	−1.53752	−0.201886
$59$	−12.2259	−1.59168	−0.795840	−	0.605507i	$-0.792970\pi$
$59$	−12.2259	−1.59168	−0.795840	+	0.605507i	$0.792970\pi$
$60$	5.48322	0.707880
$61$	1.96345	0.251394	0.125697	−	0.992069i	$-0.459883\pi$
$61$	1.96345	0.251394	0.125697	+	0.992069i	$0.459883\pi$
$62$	18.4887	2.34807
$63$	7.20176	0.907337
$64$	−5.59594	−0.699492
$65$	0.695699	0.0862909
$66$	9.25481	1.13919
$67$	−3.52411	−0.430538	−0.215269	−	0.976555i	$-0.569063\pi$
$67$	−3.52411	−0.430538	−0.215269	+	0.976555i	$0.569063\pi$
$68$	1.63837	0.198682
$69$	−11.9505	−1.43868
$70$	1.92788	0.230425
$71$	10.1268	1.20183	0.600917	−	0.799312i	$-0.294802\pi$
$71$	10.1268	1.20183	0.600917	+	0.799312i	$0.294802\pi$
$72$	3.93318	0.463530
$73$	9.87727	1.15605	0.578023	−	0.816020i	$-0.303824\pi$
$73$	9.87727	1.15605	0.578023	+	0.816020i	$0.303824\pi$
$74$	−16.3742	−1.90346
$75$	−3.19402	−0.368814
$76$	−9.32086	−1.06918
$77$	1.50297	0.171279
$78$	−4.28389	−0.485055
$79$	−9.06539	−1.01994	−0.509968	−	0.860193i	$-0.670343\pi$
$79$	−9.06539	−1.01994	−0.509968	+	0.860193i	$0.670343\pi$
$80$	4.48632	0.501586
$81$	21.2601	2.36223
$82$	8.64113	0.954253
$83$	−8.01838	−0.880132	−0.440066	−	0.897965i	$-0.645045\pi$
$83$	−8.01838	−0.880132	−0.440066	+	0.897965i	$0.645045\pi$
$84$	−5.48322	−0.598268
$85$	−0.954365	−0.103515
$86$	15.4528	1.66632
$87$	−2.54729	−0.273098
$88$	0.820835	0.0875013
$89$	10.3751	1.09975	0.549877	−	0.835245i	$-0.314674\pi$
$89$	10.3751	1.09975	0.549877	+	0.835245i	$0.314674\pi$
$90$	13.8841	1.46351
$91$	−0.695699	−0.0729291
$92$	6.42315	0.669659
$93$	30.6312	3.17631
$94$	−17.4613	−1.80100
$95$	5.42948	0.557053
$96$	−24.1366	−2.46343
$97$	3.94827	0.400886	0.200443	−	0.979705i	$-0.435762\pi$
$97$	3.94827	0.400886	0.200443	+	0.979705i	$0.435762\pi$
$98$	−1.92788	−0.194745
$99$	10.8240	1.08786
$100$	1.71671	0.171671
$101$	12.0347	1.19750	0.598750	−	0.800936i	$-0.295664\pi$
$101$	12.0347	1.19750	0.598750	+	0.800936i	$0.295664\pi$
$102$	5.87668	0.581878
$103$	13.1835	1.29900	0.649502	−	0.760360i	$-0.274977\pi$
$103$	13.1835	1.29900	0.649502	+	0.760360i	$0.274977\pi$
$104$	−0.379950	−0.0372572
$105$	3.19402	0.311704
$106$	−2.61568	−0.254057
$107$	14.3960	1.39171	0.695857	−	0.718180i	$-0.255025\pi$
$107$	14.3960	1.39171	0.695857	+	0.718180i	$0.255025\pi$
$108$	−23.0392	−2.21695
$109$	12.3286	1.18087	0.590434	−	0.807086i	$-0.298957\pi$
$109$	12.3286	1.18087	0.590434	+	0.807086i	$0.298957\pi$
$110$	2.89754	0.276270
$111$	−27.1280	−2.57487
$112$	−4.48632	−0.423918
$113$	−9.53128	−0.896628	−0.448314	−	0.893876i	$-0.647975\pi$
$113$	−9.53128	−0.896628	−0.448314	+	0.893876i	$0.647975\pi$
$114$	−33.4330	−3.13129
$115$	−3.74154	−0.348900
$116$	1.36911	0.127119
$117$	−5.01026	−0.463199
$118$	23.5701	2.16980
$119$	0.954365	0.0874865
$120$	1.74439	0.159240
$121$	−8.74108	−0.794644
$122$	−3.78530	−0.342705
$123$	14.3162	1.29085
$124$	−16.4636	−1.47847
$125$	−1.00000	−0.0894427
$126$	−13.8841	−1.23690
$127$	18.8790	1.67524	0.837619	−	0.546255i	$-0.183947\pi$
$127$	18.8790	1.67524	0.837619	+	0.546255i	$0.183947\pi$
$128$	−4.32531	−0.382307
$129$	25.6015	2.25408
$130$	−1.34122	−0.117633
$131$	−8.31891	−0.726827	−0.363413	−	0.931628i	$-0.618389\pi$
$131$	−8.31891	−0.726827	−0.363413	+	0.931628i	$0.618389\pi$
$132$	−8.24111	−0.717297
$133$	−5.42948	−0.470796
$134$	6.79405	0.586916
$135$	13.4205	1.15505
$136$	0.521219	0.0446941
$137$	−14.1369	−1.20780	−0.603900	−	0.797060i	$-0.706387\pi$
$137$	−14.1369	−1.20780	−0.603900	+	0.797060i	$0.706387\pi$
$138$	23.0392	1.96123
$139$	3.26630	0.277044	0.138522	−	0.990359i	$-0.455765\pi$
$139$	3.26630	0.277044	0.138522	+	0.990359i	$0.455765\pi$
$140$	−1.71671	−0.145089
$141$	−28.9291	−2.43627
$142$	−19.5233	−1.63836
$143$	−1.04561	−0.0874387
$144$	−32.3094	−2.69245
$145$	−0.797519	−0.0662304
$146$	−19.0422	−1.57594
$147$	−3.19402	−0.263438
$148$	14.5807	1.19852
$149$	−19.6857	−1.61272	−0.806358	−	0.591428i	$-0.798564\pi$
$149$	−19.6857	−1.61272	−0.806358	+	0.591428i	$0.798564\pi$
$150$	6.15768	0.502773
$151$	6.02935	0.490662	0.245331	−	0.969439i	$-0.421103\pi$
$151$	6.02935	0.490662	0.245331	+	0.969439i	$0.421103\pi$
$152$	−2.96527	−0.240515
$153$	6.87311	0.555658
$154$	−2.89754	−0.233491
$155$	9.59018	0.770302
$156$	3.81467	0.305418
$157$	−12.6899	−1.01277	−0.506384	−	0.862308i	$-0.669018\pi$
$157$	−12.6899	−1.01277	−0.506384	+	0.862308i	$0.669018\pi$
$158$	17.4770	1.39039
$159$	−4.33353	−0.343672
$160$	−7.55680	−0.597417
$161$	3.74154	0.294874
$162$	−40.9869	−3.22023
$163$	9.98618	0.782178	0.391089	−	0.920353i	$-0.372099\pi$
$163$	9.98618	0.782178	0.391089	+	0.920353i	$0.372099\pi$
$164$	−7.69465	−0.600851
$165$	4.80052	0.373720
$166$	15.4585	1.19981
$167$	−17.6627	−1.36678	−0.683389	−	0.730054i	$-0.739495\pi$
$167$	−17.6627	−1.36678	−0.683389	+	0.730054i	$0.739495\pi$
$168$	−1.74439	−0.134582
$169$	−12.5160	−0.962769
$170$	1.83990	0.141114
$171$	−39.1018	−2.99019
$172$	−13.7602	−1.04921
$173$	−15.5210	−1.18004	−0.590019	−	0.807389i	$-0.700880\pi$
$173$	−15.5210	−1.18004	−0.590019	+	0.807389i	$0.700880\pi$
$174$	4.91087	0.372292
$175$	1.00000	0.0755929
$176$	−6.74281	−0.508258
$177$	39.0499	2.93517
$178$	−20.0019	−1.49920
$179$	6.40375	0.478639	0.239319	−	0.970941i	$-0.423076\pi$
$179$	6.40375	0.478639	0.239319	+	0.970941i	$0.423076\pi$
$180$	−12.3634	−0.921511
$181$	10.0083	0.743909	0.371954	−	0.928251i	$-0.378688\pi$
$181$	10.0083	0.743909	0.371954	+	0.928251i	$0.378688\pi$
$182$	1.34122	0.0994181
$183$	−6.27131	−0.463588
$184$	2.04341	0.150642
$185$	−8.49337	−0.624445
$186$	−59.0533	−4.33000
$187$	1.43438	0.104892
$188$	15.5487	1.13401
$189$	−13.4205	−0.976199
$190$	−10.4674	−0.759383
$191$	−3.07859	−0.222759	−0.111379	−	0.993778i	$-0.535527\pi$
$191$	−3.07859	−0.222759	−0.111379	+	0.993778i	$0.535527\pi$
$192$	17.8735	1.28991
$193$	24.4676	1.76121	0.880606	−	0.473848i	$-0.157136\pi$
$193$	24.4676	1.76121	0.880606	+	0.473848i	$0.157136\pi$
$194$	−7.61178	−0.546494
$195$	−2.22208	−0.159126
$196$	1.71671	0.122622
$197$	−7.64493	−0.544679	−0.272339	−	0.962201i	$-0.587797\pi$
$197$	−7.64493	−0.544679	−0.272339	+	0.962201i	$0.587797\pi$
$198$	−20.8674	−1.48298
$199$	−8.62032	−0.611079	−0.305539	−	0.952179i	$-0.598837\pi$
$199$	−8.62032	−0.611079	−0.305539	+	0.952179i	$0.598837\pi$
$200$	0.546142	0.0386181
$201$	11.2561	0.793942
$202$	−23.2015	−1.63245
$203$	0.797519	0.0559749
$204$	−5.23299	−0.366383
$205$	4.48220	0.313050
$206$	−25.4161	−1.77082
$207$	26.9457	1.87285
$208$	3.12113	0.216411
$209$	−8.16034	−0.564463
$210$	−6.15768	−0.424920
$211$	−20.1516	−1.38729	−0.693645	−	0.720317i	$-0.743996\pi$
$211$	−20.1516	−1.38729	−0.693645	+	0.720317i	$0.743996\pi$
$212$	2.32918	0.159968
$213$	−32.3453	−2.21626
$214$	−27.7537	−1.89721
$215$	8.01544	0.546648
$216$	−7.32950	−0.498710
$217$	−9.59018	−0.651024
$218$	−23.7681	−1.60978
$219$	−31.5482	−2.13183
$220$	−2.58017	−0.173955
$221$	−0.663951	−0.0446622
$222$	52.2994	3.51011
$223$	−5.37482	−0.359924	−0.179962	−	0.983674i	$-0.557598\pi$
$223$	−5.37482	−0.359924	−0.179962	+	0.983674i	$0.557598\pi$
$224$	7.55680	0.504910
$225$	7.20176	0.480118
$226$	18.3752	1.22230
$227$	−17.4938	−1.16110	−0.580551	−	0.814224i	$-0.697163\pi$
$227$	−17.4938	−1.16110	−0.580551	+	0.814224i	$0.697163\pi$
$228$	29.7710	1.97163
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	7.21323	0.475626
$231$	−4.80052	−0.315851
$232$	0.435559	0.0285958
$233$	14.4176	0.944531	0.472266	−	0.881456i	$-0.343436\pi$
$233$	14.4176	0.944531	0.472266	+	0.881456i	$0.343436\pi$
$234$	9.65917	0.631440
$235$	−9.05728	−0.590832
$236$	−20.9884	−1.36623
$237$	28.9550	1.88083
$238$	−1.83990	−0.119263
$239$	8.14960	0.527154	0.263577	−	0.964638i	$-0.415098\pi$
$239$	8.14960	0.527154	0.263577	+	0.964638i	$0.415098\pi$
$240$	−14.3294	−0.924959
$241$	−18.3431	−1.18158	−0.590792	−	0.806824i	$-0.701184\pi$
$241$	−18.3431	−1.18158	−0.590792	+	0.806824i	$0.701184\pi$
$242$	16.8517	1.08327
$243$	−27.6436	−1.77334
$244$	3.37069	0.215786
$245$	−1.00000	−0.0638877
$246$	−27.5999	−1.75971
$247$	3.77728	0.240343
$248$	−5.23760	−0.332588
$249$	25.6109	1.62302
$250$	1.92788	0.121930
$251$	−6.74821	−0.425943	−0.212972	−	0.977058i	$-0.568314\pi$
$251$	−6.74821	−0.425943	−0.212972	+	0.977058i	$0.568314\pi$
$252$	12.3634	0.778819
$253$	5.62342	0.353541
$254$	−36.3964	−2.28371
$255$	3.04826	0.190890
$256$	19.5305	1.22066
$257$	28.4128	1.77234	0.886170	−	0.463360i	$-0.153356\pi$
$257$	28.4128	1.77234	0.886170	+	0.463360i	$0.153356\pi$
$258$	−49.3565	−3.07280
$259$	8.49337	0.527752
$260$	1.19432	0.0740683
$261$	5.74354	0.355516
$262$	16.0378	0.990822
$263$	−28.9363	−1.78429	−0.892144	−	0.451751i	$-0.850800\pi$
$263$	−28.9363	−1.78429	−0.892144	+	0.451751i	$0.850800\pi$
$264$	−2.62176	−0.161358
$265$	−1.35676	−0.0833454
$266$	10.4674	0.641796
$267$	−33.1382	−2.02802
$268$	−6.04988	−0.369555
$269$	15.7138	0.958084	0.479042	−	0.877792i	$-0.340984\pi$
$269$	15.7138	0.958084	0.479042	+	0.877792i	$0.340984\pi$
$270$	−25.8731	−1.57459
$271$	18.5489	1.12676	0.563382	−	0.826197i	$-0.309500\pi$
$271$	18.5489	1.12676	0.563382	+	0.826197i	$0.309500\pi$
$272$	−4.28159	−0.259609
$273$	2.22208	0.134486
$274$	27.2543	1.64649
$275$	1.50297	0.0906325
$276$	−20.5157	−1.23490
$277$	31.2604	1.87826	0.939129	−	0.343566i	$-0.111635\pi$
$277$	31.2604	1.87826	0.939129	+	0.343566i	$0.111635\pi$
$278$	−6.29702	−0.377670
$279$	−69.0662	−4.13489
$280$	−0.546142	−0.0326382
$281$	3.04431	0.181608	0.0908042	−	0.995869i	$-0.471056\pi$
$281$	3.04431	0.181608	0.0908042	+	0.995869i	$0.471056\pi$
$282$	55.7718	3.32116
$283$	3.50467	0.208331	0.104165	−	0.994560i	$-0.466783\pi$
$283$	3.50467	0.208331	0.104165	+	0.994560i	$0.466783\pi$
$284$	17.3849	1.03160
$285$	−17.3419	−1.02724
$286$	2.01582	0.119198
$287$	−4.48220	−0.264576
$288$	54.4223	3.20686
$289$	−16.0892	−0.946423
$290$	1.53752	0.0902863
$291$	−12.6108	−0.739261
$292$	16.9564	0.992300
$293$	−24.1849	−1.41289	−0.706447	−	0.707766i	$-0.749703\pi$
$293$	−24.1849	−1.41289	−0.706447	+	0.707766i	$0.749703\pi$
$294$	6.15768	0.359123
$295$	12.2259	0.711821
$296$	4.63858	0.269612
$297$	−20.1706	−1.17042
$298$	37.9516	2.19848
$299$	−2.60298	−0.150534
$300$	−5.48322	−0.316574
$301$	−8.01544	−0.462002
$302$	−11.6239	−0.668878
$303$	−38.4392	−2.20827
$304$	24.3584	1.39705
$305$	−1.96345	−0.112427
$306$	−13.2505	−0.757482
$307$	−6.54758	−0.373690	−0.186845	−	0.982389i	$-0.559826\pi$
$307$	−6.54758	−0.373690	−0.186845	+	0.982389i	$0.559826\pi$
$308$	2.58017	0.147019
$309$	−42.1082	−2.39545
$310$	−18.4887	−1.05009
$311$	−25.0748	−1.42186	−0.710931	−	0.703262i	$-0.751726\pi$
$311$	−25.0748	−1.42186	−0.710931	+	0.703262i	$0.751726\pi$
$312$	1.21357	0.0687048
$313$	−17.0385	−0.963072	−0.481536	−	0.876426i	$-0.659921\pi$
$313$	−17.0385	−0.963072	−0.481536	+	0.876426i	$0.659921\pi$
$314$	24.4647	1.38062
$315$	−7.20176	−0.405773
$316$	−15.5627	−0.875469
$317$	17.0302	0.956509	0.478255	−	0.878221i	$-0.341270\pi$
$317$	17.0302	0.956509	0.478255	+	0.878221i	$0.341270\pi$
$318$	8.35452	0.468498
$319$	1.19865	0.0671114
$320$	5.59594	0.312823
$321$	−45.9811	−2.56642
$322$	−7.21323	−0.401977
$323$	−5.18171	−0.288318
$324$	36.4975	2.02764
$325$	−0.695699	−0.0385904
$326$	−19.2521	−1.06628
$327$	−39.3778	−2.17760
$328$	−2.44791	−0.135163
$329$	9.05728	0.499344
$330$	−9.25481	−0.509460
$331$	30.9188	1.69945	0.849725	−	0.527226i	$-0.176768\pi$
$331$	30.9188	1.69945	0.849725	+	0.527226i	$0.176768\pi$
$332$	−13.7653	−0.755467
$333$	61.1672	3.35194
$334$	34.0515	1.86321
$335$	3.52411	0.192543
$336$	14.3294	0.781733
$337$	−3.39706	−0.185050	−0.0925248	−	0.995710i	$-0.529494\pi$
$337$	−3.39706	−0.185050	−0.0925248	+	0.995710i	$0.529494\pi$
$338$	24.1293	1.31246
$339$	30.4431	1.65344
$340$	−1.63837	−0.0888532
$341$	−14.4138	−0.780548
$342$	75.3835	4.07628
$343$	1.00000	0.0539949
$344$	−4.37757	−0.236023
$345$	11.9505	0.643396
$346$	29.9226	1.60865
$347$	−25.0526	−1.34489	−0.672446	−	0.740146i	$-0.734756\pi$
$347$	−25.0526	−1.34489	−0.672446	+	0.740146i	$0.734756\pi$
$348$	−4.37297	−0.234416
$349$	−13.6330	−0.729759	−0.364879	−	0.931055i	$-0.618890\pi$
$349$	−13.6330	−0.729759	−0.364879	+	0.931055i	$0.618890\pi$
$350$	−1.92788	−0.103049
$351$	9.33664	0.498353
$352$	11.3576	0.605364
$353$	−28.6992	−1.52751	−0.763753	−	0.645509i	$-0.776645\pi$
$353$	−28.6992	−1.52751	−0.763753	+	0.645509i	$0.776645\pi$
$354$	−75.2834	−4.00127
$355$	−10.1268	−0.537476
$356$	17.8110	0.943982
$357$	−3.04826	−0.161331
$358$	−12.3457	−0.652488
$359$	18.9786	1.00165	0.500827	−	0.865547i	$-0.333029\pi$
$359$	18.9786	1.00165	0.500827	+	0.865547i	$0.333029\pi$
$360$	−3.93318	−0.207297
$361$	10.4792	0.551539
$362$	−19.2947	−1.01411
$363$	27.9192	1.46538
$364$	−1.19432	−0.0625992
$365$	−9.87727	−0.517000
$366$	12.0903	0.631971
$367$	3.65777	0.190934	0.0954670	−	0.995433i	$-0.469566\pi$
$367$	3.65777	0.190934	0.0954670	+	0.995433i	$0.469566\pi$
$368$	−16.7857	−0.875017
$369$	−32.2797	−1.68041
$370$	16.3742	0.851253
$371$	1.35676	0.0704397
$372$	52.5850	2.72641
$373$	25.6015	1.32560	0.662798	−	0.748798i	$-0.269369\pi$
$373$	25.6015	1.32560	0.662798	+	0.748798i	$0.269369\pi$
$374$	−2.76531	−0.142991
$375$	3.19402	0.164938
$376$	4.94656	0.255099
$377$	−0.554833	−0.0285754
$378$	25.8731	1.33077
$379$	−13.7972	−0.708717	−0.354358	−	0.935110i	$-0.615301\pi$
$379$	−13.7972	−0.708717	−0.354358	+	0.935110i	$0.615301\pi$
$380$	9.32086	0.478150
$381$	−60.2998	−3.08925
$382$	5.93514	0.303668
$383$	29.3670	1.50058	0.750291	−	0.661107i	$-0.229913\pi$
$383$	29.3670	1.50058	0.750291	+	0.661107i	$0.229913\pi$
$384$	13.8151	0.705000
$385$	−1.50297	−0.0765984
$386$	−47.1705	−2.40091
$387$	−57.7253	−2.93434
$388$	6.77805	0.344103
$389$	−11.6261	−0.589466	−0.294733	−	0.955580i	$-0.595231\pi$
$389$	−11.6261	−0.589466	−0.294733	+	0.955580i	$0.595231\pi$
$390$	4.28389	0.216923
$391$	3.57079	0.180583
$392$	0.546142	0.0275843
$393$	26.5708	1.34032
$394$	14.7385	0.742514
$395$	9.06539	0.456129
$396$	18.5818	0.933769
$397$	26.9806	1.35412	0.677058	−	0.735930i	$-0.263255\pi$
$397$	26.9806	1.35412	0.677058	+	0.735930i	$0.263255\pi$
$398$	16.6189	0.833032
$399$	17.3419	0.868179
$400$	−4.48632	−0.224316
$401$	13.1323	0.655794	0.327897	−	0.944714i	$-0.393660\pi$
$401$	13.1323	0.655794	0.327897	+	0.944714i	$0.393660\pi$
$402$	−21.7003	−1.08231
$403$	6.67188	0.332350
$404$	20.6602	1.02788
$405$	−21.2601	−1.05642
$406$	−1.53752	−0.0763058
$407$	12.7653	0.632751
$408$	−1.66478	−0.0824190
$409$	37.6076	1.85957	0.929787	−	0.368097i	$-0.119990\pi$
$409$	37.6076	1.85957	0.929787	+	0.368097i	$0.119990\pi$
$410$	−8.64113	−0.426755
$411$	45.1536	2.22726
$412$	22.6322	1.11501
$413$	−12.2259	−0.601599
$414$	−51.9480	−2.55310
$415$	8.01838	0.393607
$416$	−5.25726	−0.257758
$417$	−10.4326	−0.510888
$418$	15.7321	0.769484
$419$	25.9338	1.26695	0.633475	−	0.773763i	$-0.281628\pi$
$419$	25.9338	1.26695	0.633475	+	0.773763i	$0.281628\pi$
$420$	5.48322	0.267554
$421$	−27.3300	−1.33198	−0.665992	−	0.745959i	$-0.731992\pi$
$421$	−27.3300	−1.33198	−0.665992	+	0.745959i	$0.731992\pi$
$422$	38.8497	1.89118
$423$	65.2284	3.17151
$424$	0.740986	0.0359855
$425$	0.954365	0.0462935
$426$	62.3578	3.02124
$427$	1.96345	0.0950181
$428$	24.7138	1.19459
$429$	3.33971	0.161243
$430$	−15.4528	−0.745199
$431$	−18.2147	−0.877369	−0.438685	−	0.898641i	$-0.644556\pi$
$431$	−18.2147	−0.877369	−0.438685	+	0.898641i	$0.644556\pi$
$432$	60.2087	2.89679
$433$	10.4677	0.503044	0.251522	−	0.967852i	$-0.419069\pi$
$433$	10.4677	0.503044	0.251522	+	0.967852i	$0.419069\pi$
$434$	18.4887	0.887486
$435$	2.54729	0.122133
$436$	21.1647	1.01361
$437$	−20.3146	−0.971779
$438$	60.8210	2.90614
$439$	17.9222	0.855381	0.427691	−	0.903925i	$-0.359327\pi$
$439$	17.9222	0.855381	0.427691	+	0.903925i	$0.359327\pi$
$440$	−0.820835	−0.0391318
$441$	7.20176	0.342941
$442$	1.28002	0.0608842
$443$	−34.1613	−1.62305	−0.811526	−	0.584316i	$-0.801363\pi$
$443$	−34.1613	−1.62305	−0.811526	+	0.584316i	$0.801363\pi$
$444$	−46.5710	−2.21016
$445$	−10.3751	−0.491825
$446$	10.3620	0.490654
$447$	62.8765	2.97396
$448$	−5.59594	−0.264383
$449$	21.0348	0.992692	0.496346	−	0.868125i	$-0.334675\pi$
$449$	21.0348	0.992692	0.496346	+	0.868125i	$0.334675\pi$
$450$	−13.8841	−0.654504
$451$	−6.73661	−0.317214
$452$	−16.3625	−0.769627
$453$	−19.2579	−0.904814
$454$	33.7258	1.58283
$455$	0.695699	0.0326149
$456$	9.47112	0.443526
$457$	4.83968	0.226391	0.113195	−	0.993573i	$-0.463891\pi$
$457$	4.83968	0.226391	0.113195	+	0.993573i	$0.463891\pi$
$458$	1.92788	0.0900838
$459$	−12.8081	−0.597830
$460$	−6.42315	−0.299481
$461$	3.16749	0.147525	0.0737624	−	0.997276i	$-0.476499\pi$
$461$	3.16749	0.147525	0.0737624	+	0.997276i	$0.476499\pi$
$462$	9.25481	0.430573
$463$	−25.8691	−1.20224	−0.601119	−	0.799159i	$-0.705278\pi$
$463$	−25.8691	−1.20224	−0.601119	+	0.799159i	$0.705278\pi$
$464$	−3.57793	−0.166101
$465$	−30.6312	−1.42049
$466$	−27.7955	−1.28760
$467$	−20.2023	−0.934849	−0.467424	−	0.884033i	$-0.654818\pi$
$467$	−20.2023	−0.934849	−0.467424	+	0.884033i	$0.654818\pi$
$468$	−8.60118	−0.397590
$469$	−3.52411	−0.162728
$470$	17.4613	0.805431
$471$	40.5319	1.86761
$472$	−6.67709	−0.307338
$473$	−12.0470	−0.553920
$474$	−55.8218	−2.56398
$475$	−5.42948	−0.249122
$476$	1.63837	0.0750946
$477$	9.77110	0.447388
$478$	−15.7114	−0.718624
$479$	32.9384	1.50499	0.752497	−	0.658596i	$-0.228849\pi$
$479$	32.9384	1.50499	0.752497	+	0.658596i	$0.228849\pi$
$480$	24.1366	1.10168
$481$	−5.90883	−0.269419
$482$	35.3633	1.61075
$483$	−11.9505	−0.543769
$484$	−15.0059	−0.682088
$485$	−3.94827	−0.179282
$486$	53.2935	2.41744
$487$	−19.2824	−0.873767	−0.436884	−	0.899518i	$-0.643918\pi$
$487$	−19.2824	−0.873767	−0.436884	+	0.899518i	$0.643918\pi$
$488$	1.07232	0.0485418
$489$	−31.8960	−1.44239
$490$	1.92788	0.0870926
$491$	−5.79073	−0.261332	−0.130666	−	0.991426i	$-0.541712\pi$
$491$	−5.79073	−0.261332	−0.130666	+	0.991426i	$0.541712\pi$
$492$	24.5769	1.10801
$493$	0.761124	0.0342793
$494$	−7.28214	−0.327639
$495$	−10.8240	−0.486504
$496$	43.0246	1.93186
$497$	10.1268	0.454250
$498$	−49.3746	−2.21253
$499$	20.6672	0.925189	0.462595	−	0.886570i	$-0.346919\pi$
$499$	20.6672	0.925189	0.462595	+	0.886570i	$0.346919\pi$
$500$	−1.71671	−0.0767738
$501$	56.4149	2.52043
$502$	13.0097	0.580652
$503$	41.4060	1.84620	0.923102	−	0.384556i	$-0.125646\pi$
$503$	41.4060	1.84620	0.923102	+	0.384556i	$0.125646\pi$
$504$	3.93318	0.175198
$505$	−12.0347	−0.535539
$506$	−10.8413	−0.481953
$507$	39.9764	1.77541
$508$	32.4098	1.43795
$509$	4.34245	0.192476	0.0962378	−	0.995358i	$-0.469319\pi$
$509$	4.34245	0.192476	0.0962378	+	0.995358i	$0.469319\pi$
$510$	−5.87668	−0.260224
$511$	9.87727	0.436944
$512$	−29.0019	−1.28171
$513$	72.8664	3.21713
$514$	−54.7764	−2.41608
$515$	−13.1835	−0.580932
$516$	43.9504	1.93481
$517$	13.6128	0.598691
$518$	−16.3742	−0.719440
$519$	49.5743	2.17607
$520$	0.379950	0.0166619
$521$	−19.7431	−0.864960	−0.432480	−	0.901644i	$-0.642361\pi$
$521$	−19.7431	−0.864960	−0.432480	+	0.901644i	$0.642361\pi$
$522$	−11.0729	−0.484646
$523$	−27.7857	−1.21498	−0.607492	−	0.794326i	$-0.707824\pi$
$523$	−27.7857	−1.21498	−0.607492	+	0.794326i	$0.707824\pi$
$524$	−14.2812	−0.623877
$525$	−3.19402	−0.139398
$526$	55.7856	2.43237
$527$	−9.15253	−0.398691
$528$	21.5367	0.937263
$529$	−9.00090	−0.391343
$530$	2.61568	0.113618
$531$	−88.0482	−3.82097
$532$	−9.32086	−0.404111
$533$	3.11826	0.135067
$534$	63.8864	2.76463
$535$	−14.3960	−0.622394
$536$	−1.92466	−0.0831327
$537$	−20.4537	−0.882643
$538$	−30.2942	−1.30608
$539$	1.50297	0.0647375
$540$	23.0392	0.991448
$541$	−16.9915	−0.730521	−0.365260	−	0.930905i	$-0.619020\pi$
$541$	−16.9915	−0.730521	−0.365260	+	0.930905i	$0.619020\pi$
$542$	−35.7600	−1.53602
$543$	−31.9666	−1.37182
$544$	7.21194	0.309210
$545$	−12.3286	−0.528100
$546$	−4.28389	−0.183334
$547$	16.3489	0.699030	0.349515	−	0.936931i	$-0.386346\pi$
$547$	16.3489	0.699030	0.349515	+	0.936931i	$0.386346\pi$
$548$	−24.2691	−1.03672
$549$	14.1403	0.603494
$550$	−2.89754	−0.123552
$551$	−4.33011	−0.184469
$552$	−6.52669	−0.277794
$553$	−9.06539	−0.385500
$554$	−60.2663	−2.56047
$555$	27.1280	1.15152
$556$	5.60730	0.237802
$557$	−35.1263	−1.48835	−0.744174	−	0.667986i	$-0.767156\pi$
$557$	−35.1263	−1.48835	−0.744174	+	0.667986i	$0.767156\pi$
$558$	133.151	5.63674
$559$	5.57633	0.235854
$560$	4.48632	0.189582
$561$	−4.58144	−0.193429
$562$	−5.86906	−0.247571
$563$	7.95621	0.335314	0.167657	−	0.985845i	$-0.446380\pi$
$563$	7.95621	0.335314	0.167657	+	0.985845i	$0.446380\pi$
$564$	−49.6630	−2.09119
$565$	9.53128	0.400984
$566$	−6.75657	−0.284000
$567$	21.2601	0.892840
$568$	5.53068	0.232062
$569$	12.9496	0.542875	0.271437	−	0.962456i	$-0.412501\pi$
$569$	12.9496	0.542875	0.271437	+	0.962456i	$0.412501\pi$
$570$	33.4330	1.40035
$571$	−26.8685	−1.12441	−0.562205	−	0.826998i	$-0.690047\pi$
$571$	−26.8685	−1.12441	−0.562205	+	0.826998i	$0.690047\pi$
$572$	−1.79502	−0.0750536
$573$	9.83306	0.410782
$574$	8.64113	0.360674
$575$	3.74154	0.156033
$576$	−40.3006	−1.67919
$577$	−34.2530	−1.42597	−0.712985	−	0.701179i	$-0.752657\pi$
$577$	−34.2530	−1.42597	−0.712985	+	0.701179i	$0.752657\pi$
$578$	31.0180	1.29018
$579$	−78.1498	−3.24780
$580$	−1.36911	−0.0568493
$581$	−8.01838	−0.332659
$582$	24.3122	1.00777
$583$	2.03918	0.0844541
$584$	5.39439	0.223221
$585$	5.01026	0.207149
$586$	46.6255	1.92608
$587$	33.9867	1.40278	0.701391	−	0.712777i	$-0.252563\pi$
$587$	33.9867	1.40278	0.701391	+	0.712777i	$0.252563\pi$
$588$	−5.48322	−0.226124
$589$	52.0697	2.14549
$590$	−23.5701	−0.970366
$591$	24.4181	1.00442
$592$	−38.1040	−1.56606
$593$	−48.2224	−1.98026	−0.990129	−	0.140161i	$-0.955238\pi$
$593$	−48.2224	−1.98026	−0.990129	+	0.140161i	$0.955238\pi$
$594$	38.8865	1.59553
$595$	−0.954365	−0.0391252
$596$	−33.7947	−1.38429
$597$	27.5335	1.12687
$598$	5.01824	0.205211
$599$	16.3944	0.669858	0.334929	−	0.942243i	$-0.391288\pi$
$599$	16.3944	0.669858	0.334929	+	0.942243i	$0.391288\pi$
$600$	−1.74439	−0.0712143
$601$	12.9817	0.529536	0.264768	−	0.964312i	$-0.414705\pi$
$601$	12.9817	0.529536	0.264768	+	0.964312i	$0.414705\pi$
$602$	15.4528	0.629809
$603$	−25.3798	−1.03354
$604$	10.3507	0.421163
$605$	8.74108	0.355376
$606$	74.1061	3.01035
$607$	43.7463	1.77561	0.887803	−	0.460223i	$-0.152231\pi$
$607$	43.7463	1.77561	0.887803	+	0.460223i	$0.152231\pi$
$608$	−41.0295	−1.66397
$609$	−2.54729	−0.103221
$610$	3.78530	0.153262
$611$	−6.30114	−0.254917
$612$	11.7992	0.476953
$613$	21.5030	0.868499	0.434249	−	0.900793i	$-0.357014\pi$
$613$	21.5030	0.868499	0.434249	+	0.900793i	$0.357014\pi$
$614$	12.6229	0.509420
$615$	−14.3162	−0.577286
$616$	0.820835	0.0330724
$617$	12.9878	0.522870	0.261435	−	0.965221i	$-0.415804\pi$
$617$	12.9878	0.522870	0.261435	+	0.965221i	$0.415804\pi$
$618$	81.1795	3.26552
$619$	33.2894	1.33801	0.669007	−	0.743256i	$-0.266720\pi$
$619$	33.2894	1.33801	0.669007	+	0.743256i	$0.266720\pi$
$620$	16.4636	0.661194
$621$	−50.2133	−2.01499
$622$	48.3412	1.93830
$623$	10.3751	0.415668
$624$	−9.96895	−0.399077
$625$	1.00000	0.0400000
$626$	32.8481	1.31288
$627$	26.0643	1.04091
$628$	−21.7850	−0.869316
$629$	8.10577	0.323198
$630$	13.8841	0.553157
$631$	−16.5418	−0.658519	−0.329259	−	0.944240i	$-0.606799\pi$
$631$	−16.5418	−0.658519	−0.329259	+	0.944240i	$0.606799\pi$
$632$	−4.95099	−0.196940
$633$	64.3645	2.55826
$634$	−32.8321	−1.30393
$635$	−18.8790	−0.749189
$636$	−7.43943	−0.294993
$637$	−0.695699	−0.0275646
$638$	−2.31085	−0.0914873
$639$	72.9310	2.88511
$640$	4.32531	0.170973
$641$	26.9566	1.06472	0.532361	−	0.846517i	$-0.321305\pi$
$641$	26.9566	1.06472	0.532361	+	0.846517i	$0.321305\pi$
$642$	88.6460	3.49858
$643$	−13.2851	−0.523915	−0.261958	−	0.965079i	$-0.584368\pi$
$643$	−13.2851	−0.523915	−0.261958	+	0.965079i	$0.584368\pi$
$644$	6.42315	0.253107
$645$	−25.6015	−1.00806
$646$	9.98970	0.393039
$647$	30.4437	1.19686	0.598432	−	0.801174i	$-0.295791\pi$
$647$	30.4437	1.19686	0.598432	+	0.801174i	$0.295791\pi$
$648$	11.6110	0.456124
$649$	−18.3752	−0.721290
$650$	1.34122	0.0526071
$651$	30.6312	1.20053
$652$	17.1434	0.671387
$653$	6.51066	0.254782	0.127391	−	0.991853i	$-0.459340\pi$
$653$	6.51066	0.254782	0.127391	+	0.991853i	$0.459340\pi$
$654$	75.9157	2.96854
$655$	8.31891	0.325047
$656$	20.1086	0.785108
$657$	71.1337	2.77519
$658$	−17.4613	−0.680713
$659$	−38.1035	−1.48430	−0.742150	−	0.670234i	$-0.766194\pi$
$659$	−38.1035	−1.48430	−0.742150	+	0.670234i	$0.766194\pi$
$660$	8.24111	0.320785
$661$	34.1411	1.32794	0.663968	−	0.747761i	$-0.268871\pi$
$661$	34.1411	1.32794	0.663968	+	0.747761i	$0.268871\pi$
$662$	−59.6077	−2.31672
$663$	2.12067	0.0823601
$664$	−4.37917	−0.169945
$665$	5.42948	0.210546
$666$	−117.923	−4.56942
$667$	2.98395	0.115539
$668$	−30.3217	−1.17318
$669$	17.1673	0.663725
$670$	−6.79405	−0.262477
$671$	2.95101	0.113922
$672$	−24.1366	−0.931088
$673$	22.1381	0.853360	0.426680	−	0.904403i	$-0.359683\pi$
$673$	22.1381	0.853360	0.426680	+	0.904403i	$0.359683\pi$
$674$	6.54911	0.252262
$675$	−13.4205	−0.516556
$676$	−21.4864	−0.826400
$677$	7.23858	0.278201	0.139101	−	0.990278i	$-0.455579\pi$
$677$	7.23858	0.278201	0.139101	+	0.990278i	$0.455579\pi$
$678$	−58.6906	−2.25400
$679$	3.94827	0.151521
$680$	−0.521219	−0.0199878
$681$	55.8754	2.14115
$682$	27.7880	1.06406
$683$	−14.0654	−0.538196	−0.269098	−	0.963113i	$-0.586726\pi$
$683$	−14.0654	−0.538196	−0.269098	+	0.963113i	$0.586726\pi$
$684$	−67.1266	−2.56665
$685$	14.1369	0.540144
$686$	−1.92788	−0.0736067
$687$	3.19402	0.121859
$688$	35.9598	1.37096
$689$	−0.943900	−0.0359597
$690$	−23.0392	−0.877087
$691$	−31.3232	−1.19159	−0.595795	−	0.803137i	$-0.703163\pi$
$691$	−31.3232	−1.19159	−0.595795	+	0.803137i	$0.703163\pi$
$692$	−26.6451	−1.01289
$693$	10.8240	0.411171
$694$	48.2983	1.83338
$695$	−3.26630	−0.123898
$696$	−1.39118	−0.0527326
$697$	−4.27765	−0.162028
$698$	26.2828	0.994818
$699$	−46.0502	−1.74178
$700$	1.71671	0.0648857
$701$	−50.8158	−1.91929	−0.959643	−	0.281223i	$-0.909260\pi$
$701$	−50.8158	−1.91929	−0.959643	+	0.281223i	$0.909260\pi$
$702$	−17.9999	−0.679363
$703$	−46.1146	−1.73924
$704$	−8.41053	−0.316984
$705$	28.9291	1.08953
$706$	55.3286	2.08232
$707$	12.0347	0.452613
$708$	67.0374	2.51942
$709$	37.7117	1.41629	0.708146	−	0.706066i	$-0.249532\pi$
$709$	37.7117	1.41629	0.708146	+	0.706066i	$0.249532\pi$
$710$	19.5233	0.732696
$711$	−65.2868	−2.44845
$712$	5.66626	0.212352
$713$	−35.8820	−1.34379
$714$	5.87668	0.219929
$715$	1.04561	0.0391038
$716$	10.9934	0.410843
$717$	−26.0300	−0.972108
$718$	−36.5885	−1.36547
$719$	3.38264	0.126151	0.0630755	−	0.998009i	$-0.479909\pi$
$719$	3.38264	0.126151	0.0630755	+	0.998009i	$0.479909\pi$
$720$	32.3094	1.20410
$721$	13.1835	0.490977
$722$	−20.2027	−0.751867
$723$	58.5882	2.17892
$724$	17.1813	0.638539
$725$	0.797519	0.0296191
$726$	−53.8248	−1.99763
$727$	15.4559	0.573228	0.286614	−	0.958046i	$-0.407470\pi$
$727$	15.4559	0.573228	0.286614	+	0.958046i	$0.407470\pi$
$728$	−0.379950	−0.0140819
$729$	24.5140	0.907927
$730$	19.0422	0.704782
$731$	−7.64965	−0.282933
$732$	−10.7660	−0.397924
$733$	3.00812	0.111107	0.0555537	−	0.998456i	$-0.482308\pi$
$733$	3.00812	0.111107	0.0555537	+	0.998456i	$0.482308\pi$
$734$	−7.05174	−0.260284
$735$	3.19402	0.117813
$736$	28.2740	1.04219
$737$	−5.29663	−0.195104
$738$	62.2313	2.29077
$739$	−21.7324	−0.799440	−0.399720	−	0.916637i	$-0.630893\pi$
$739$	−21.7324	−0.799440	−0.399720	+	0.916637i	$0.630893\pi$
$740$	−14.5807	−0.535996
$741$	−12.0647	−0.443209
$742$	−2.61568	−0.0960245
$743$	31.1068	1.14120	0.570599	−	0.821229i	$-0.306711\pi$
$743$	31.1068	1.14120	0.570599	+	0.821229i	$0.306711\pi$
$744$	16.7290	0.613315
$745$	19.6857	0.721228
$746$	−49.3566	−1.80707
$747$	−57.7465	−2.11283
$748$	2.46242	0.0900351
$749$	14.3960	0.526019
$750$	−6.15768	−0.224847
$751$	−4.39197	−0.160265	−0.0801326	−	0.996784i	$-0.525534\pi$
$751$	−4.39197	−0.160265	−0.0801326	+	0.996784i	$0.525534\pi$
$752$	−40.6339	−1.48176
$753$	21.5539	0.785468
$754$	1.06965	0.0389544
$755$	−6.02935	−0.219431
$756$	−23.0392	−0.837927
$757$	−20.3419	−0.739341	−0.369670	−	0.929163i	$-0.620529\pi$
$757$	−20.3419	−0.739341	−0.369670	+	0.929163i	$0.620529\pi$
$758$	26.5994	0.966133
$759$	−17.9613	−0.651954
$760$	2.96527	0.107561
$761$	−43.2746	−1.56870	−0.784351	−	0.620317i	$-0.787004\pi$
$761$	−43.2746	−1.56870	−0.784351	+	0.620317i	$0.787004\pi$
$762$	116.251	4.21132
$763$	12.3286	0.446326
$764$	−5.28505	−0.191206
$765$	−6.87311	−0.248498
$766$	−56.6160	−2.04562
$767$	8.50557	0.307118
$768$	−62.3809	−2.25098
$769$	−16.9699	−0.611952	−0.305976	−	0.952039i	$-0.598983\pi$
$769$	−16.9699	−0.611952	−0.305976	+	0.952039i	$0.598983\pi$
$770$	2.89754	0.104420
$771$	−90.7510	−3.26832
$772$	42.0038	1.51175
$773$	23.9365	0.860938	0.430469	−	0.902605i	$-0.358348\pi$
$773$	23.9365	0.860938	0.430469	+	0.902605i	$0.358348\pi$
$774$	111.287	4.00014
$775$	−9.59018	−0.344489
$776$	2.15631	0.0774072
$777$	−27.1280	−0.973211
$778$	22.4137	0.803569
$779$	24.3360	0.871927
$780$	−3.81467	−0.136587
$781$	15.2203	0.544626
$782$	−6.88405	−0.246173
$783$	−10.7031	−0.382498
$784$	−4.48632	−0.160226
$785$	12.6899	0.452924
$786$	−51.2252	−1.82714
$787$	−54.0753	−1.92758	−0.963788	−	0.266670i	$-0.914077\pi$
$787$	−54.0753	−1.92758	−0.963788	+	0.266670i	$0.914077\pi$
$788$	−13.1242	−0.467529
$789$	92.4231	3.29035
$790$	−17.4770	−0.621803
$791$	−9.53128	−0.338893
$792$	5.91146	0.210054
$793$	−1.36597	−0.0485071
$794$	−52.0152	−1.84595
$795$	4.33353	0.153695
$796$	−14.7986	−0.524523
$797$	4.70674	0.166721	0.0833606	−	0.996519i	$-0.473435\pi$
$797$	4.70674	0.166721	0.0833606	+	0.996519i	$0.473435\pi$
$798$	−33.4330	−1.18352
$799$	8.64395	0.305801
$800$	7.55680	0.267173
$801$	74.7188	2.64006
$802$	−25.3174	−0.893988
$803$	14.8452	0.523877
$804$	19.3234	0.681485
$805$	−3.74154	−0.131872
$806$	−12.8626	−0.453065
$807$	−50.1900	−1.76677
$808$	6.57267	0.231226
$809$	−23.8995	−0.840260	−0.420130	−	0.907464i	$-0.638016\pi$
$809$	−23.8995	−0.840260	−0.420130	+	0.907464i	$0.638016\pi$
$810$	40.9869	1.44013
$811$	13.0590	0.458563	0.229282	−	0.973360i	$-0.426362\pi$
$811$	13.0590	0.458563	0.229282	+	0.973360i	$0.426362\pi$
$812$	1.36911	0.0480464
$813$	−59.2455	−2.07783
$814$	−24.6099	−0.862576
$815$	−9.98618	−0.349800
$816$	13.6755	0.478738
$817$	43.5197	1.52256
$818$	−72.5028	−2.53500
$819$	−5.01026	−0.175073
$820$	7.69465	0.268709
$821$	3.46809	0.121037	0.0605187	−	0.998167i	$-0.480725\pi$
$821$	3.46809	0.121037	0.0605187	+	0.998167i	$0.480725\pi$
$822$	−87.0507	−3.03624
$823$	−26.9591	−0.939735	−0.469868	−	0.882737i	$-0.655698\pi$
$823$	−26.9591	−0.939735	−0.469868	+	0.882737i	$0.655698\pi$
$824$	7.20003	0.250825
$825$	−4.80052	−0.167132
$826$	23.5701	0.820109
$827$	9.79205	0.340503	0.170251	−	0.985401i	$-0.445542\pi$
$827$	9.79205	0.340503	0.170251	+	0.985401i	$0.445542\pi$
$828$	46.2580	1.60758
$829$	26.6034	0.923974	0.461987	−	0.886887i	$-0.347137\pi$
$829$	26.6034	0.923974	0.461987	+	0.886887i	$0.347137\pi$
$830$	−15.4585	−0.536571
$831$	−99.8464	−3.46363
$832$	3.89309	0.134969
$833$	0.954365	0.0330668
$834$	20.1128	0.696450
$835$	17.6627	0.611242
$836$	−14.0090	−0.484510
$837$	128.705	4.44870
$838$	−49.9973	−1.72713
$839$	−39.9893	−1.38058	−0.690292	−	0.723530i	$-0.742518\pi$
$839$	−39.9893	−1.38058	−0.690292	+	0.723530i	$0.742518\pi$
$840$	1.74439	0.0601871
$841$	−28.3640	−0.978068
$842$	52.6890	1.81578
$843$	−9.72359	−0.334898
$844$	−34.5945	−1.19079
$845$	12.5160	0.430564
$846$	−125.752	−4.32345
$847$	−8.74108	−0.300347
$848$	−6.08688	−0.209024
$849$	−11.1940	−0.384176
$850$	−1.83990	−0.0631080
$851$	31.7783	1.08934
$852$	−55.5276	−1.90234
$853$	−0.872323	−0.0298678	−0.0149339	−	0.999888i	$-0.504754\pi$
$853$	−0.872323	−0.0298678	−0.0149339	+	0.999888i	$0.504754\pi$
$854$	−3.78530	−0.129530
$855$	39.1018	1.33725
$856$	7.86226	0.268727
$857$	15.6420	0.534321	0.267161	−	0.963652i	$-0.413915\pi$
$857$	15.6420	0.534321	0.267161	+	0.963652i	$0.413915\pi$
$858$	−6.43856	−0.219809
$859$	40.5370	1.38311	0.691553	−	0.722326i	$-0.256927\pi$
$859$	40.5370	1.38311	0.691553	+	0.722326i	$0.256927\pi$
$860$	13.7602	0.469219
$861$	14.3162	0.487896
$862$	35.1156	1.19604
$863$	34.5260	1.17528	0.587639	−	0.809123i	$-0.300058\pi$
$863$	34.5260	1.17528	0.587639	+	0.809123i	$0.300058\pi$
$864$	−101.416	−3.45025
$865$	15.5210	0.527729
$866$	−20.1804	−0.685758
$867$	51.3892	1.74527
$868$	−16.4636	−0.558811
$869$	−13.6250	−0.462197
$870$	−4.91087	−0.166494
$871$	2.45172	0.0830733
$872$	6.73317	0.228014
$873$	28.4345	0.962362
$874$	39.1641	1.32474
$875$	−1.00000	−0.0338062
$876$	−54.1592	−1.82987
$877$	52.2007	1.76269	0.881346	−	0.472471i	$-0.156638\pi$
$877$	52.2007	1.76269	0.881346	+	0.472471i	$0.156638\pi$
$878$	−34.5519	−1.16607
$879$	77.2469	2.60547
$880$	6.74281	0.227300
$881$	0.306165	0.0103150	0.00515748	−	0.999987i	$-0.498358\pi$
$881$	0.306165	0.0103150	0.00515748	+	0.999987i	$0.498358\pi$
$882$	−13.8841	−0.467503
$883$	29.5420	0.994168	0.497084	−	0.867703i	$-0.334404\pi$
$883$	29.5420	0.994168	0.497084	+	0.867703i	$0.334404\pi$
$884$	−1.13981	−0.0383361
$885$	−39.0499	−1.31265
$886$	65.8588	2.21257
$887$	−18.3484	−0.616078	−0.308039	−	0.951374i	$-0.599673\pi$
$887$	−18.3484	−0.616078	−0.308039	+	0.951374i	$0.599673\pi$
$888$	−14.8157	−0.497183
$889$	18.8790	0.633180
$890$	20.0019	0.670464
$891$	31.9533	1.07048
$892$	−9.22702	−0.308943
$893$	−49.1763	−1.64562
$894$	−121.218	−4.05414
$895$	−6.40375	−0.214054
$896$	−4.32531	−0.144498
$897$	8.31398	0.277596
$898$	−40.5525	−1.35325
$899$	−7.64835	−0.255087
$900$	12.3634	0.412112
$901$	1.29485	0.0431377
$902$	12.9874	0.432432
$903$	25.6015	0.851963
$904$	−5.20543	−0.173130
$905$	−10.0083	−0.332686
$906$	37.1268	1.23346
$907$	−30.0498	−0.997787	−0.498894	−	0.866663i	$-0.666260\pi$
$907$	−30.0498	−0.997787	−0.498894	+	0.866663i	$0.666260\pi$
$908$	−30.0318	−0.996640
$909$	86.6713	2.87471
$910$	−1.34122	−0.0444611
$911$	−60.0369	−1.98911	−0.994555	−	0.104214i	$-0.966767\pi$
$911$	−60.0369	−1.98911	−0.994555	+	0.104214i	$0.966767\pi$
$912$	−77.8012	−2.57625
$913$	−12.0514	−0.398843
$914$	−9.33031	−0.308619
$915$	6.27131	0.207323
$916$	−1.71671	−0.0567218
$917$	−8.31891	−0.274715
$918$	24.6924	0.814970
$919$	−1.94212	−0.0640647	−0.0320323	−	0.999487i	$-0.510198\pi$
$919$	−1.94212	−0.0640647	−0.0320323	+	0.999487i	$0.510198\pi$
$920$	−2.04341	−0.0673692
$921$	20.9131	0.689110
$922$	−6.10654	−0.201108
$923$	−7.04523	−0.231896
$924$	−8.24111	−0.271113
$925$	8.49337	0.279260
$926$	49.8724	1.63891
$927$	94.9441	3.11837
$928$	6.02669	0.197836
$929$	−1.80724	−0.0592935	−0.0296467	−	0.999560i	$-0.509438\pi$
$929$	−1.80724	−0.0592935	−0.0296467	+	0.999560i	$0.509438\pi$
$930$	59.0533	1.93643
$931$	−5.42948	−0.177944
$932$	24.7510	0.810745
$933$	80.0894	2.62201
$934$	38.9475	1.27440
$935$	−1.43438	−0.0469093
$936$	−2.73631	−0.0894392
$937$	10.5549	0.344814	0.172407	−	0.985026i	$-0.444846\pi$
$937$	10.5549	0.344814	0.172407	+	0.985026i	$0.444846\pi$
$938$	6.79405	0.221834
$939$	54.4213	1.77597
$940$	−15.5487	−0.507144
$941$	−40.6315	−1.32455	−0.662275	−	0.749261i	$-0.730409\pi$
$941$	−40.6315	−1.32455	−0.662275	+	0.749261i	$0.730409\pi$
$942$	−78.1406	−2.54596
$943$	−16.7703	−0.546116
$944$	54.8494	1.78520
$945$	13.4205	0.436569
$946$	23.2251	0.755112
$947$	−0.966367	−0.0314027	−0.0157014	−	0.999877i	$-0.504998\pi$
$947$	−0.966367	−0.0314027	−0.0157014	+	0.999877i	$0.504998\pi$
$948$	49.7075	1.61442
$949$	−6.87161	−0.223062
$950$	10.4674	0.339606
$951$	−54.3947	−1.76387
$952$	0.521219	0.0168928
$953$	−3.22330	−0.104413	−0.0522064	−	0.998636i	$-0.516625\pi$
$953$	−3.22330	−0.104413	−0.0522064	+	0.998636i	$0.516625\pi$
$954$	−18.8375	−0.609886
$955$	3.07859	0.0996207
$956$	13.9905	0.452486
$957$	−3.82850	−0.123758
$958$	−63.5012	−2.05163
$959$	−14.1369	−0.456505
$960$	−17.8735	−0.576866
$961$	60.9716	1.96682
$962$	11.3915	0.367277
$963$	103.677	3.34093
$964$	−31.4899	−1.01422
$965$	−24.4676	−0.787638
$966$	23.0392	0.741274
$967$	1.32595	0.0426398	0.0213199	−	0.999773i	$-0.493213\pi$
$967$	1.32595	0.0426398	0.0213199	+	0.999773i	$0.493213\pi$
$968$	−4.77387	−0.153438
$969$	16.5505	0.531678
$970$	7.61178	0.244400
$971$	26.9742	0.865643	0.432822	−	0.901480i	$-0.357518\pi$
$971$	26.9742	0.865643	0.432822	+	0.901480i	$0.357518\pi$
$972$	−47.4562	−1.52216
$973$	3.26630	0.104713
$974$	37.1740	1.19113
$975$	2.22208	0.0711634
$976$	−8.80868	−0.281959
$977$	13.6571	0.436930	0.218465	−	0.975845i	$-0.429895\pi$
$977$	13.6571	0.436930	0.218465	+	0.975845i	$0.429895\pi$
$978$	61.4917	1.96629
$979$	15.5934	0.498368
$980$	−1.71671	−0.0548384
$981$	88.7878	2.83478
$982$	11.1638	0.356252
$983$	9.59656	0.306083	0.153041	−	0.988220i	$-0.451093\pi$
$983$	9.59656	0.306083	0.153041	+	0.988220i	$0.451093\pi$
$984$	7.81869	0.249251
$985$	7.64493	0.243588
$986$	−1.46736	−0.0467301
$987$	−28.9291	−0.920824
$988$	6.48452	0.206300
$989$	−29.9901	−0.953628
$990$	20.8674	0.663210
$991$	−10.6116	−0.337088	−0.168544	−	0.985694i	$-0.553907\pi$
$991$	−10.6116	−0.337088	−0.168544	+	0.985694i	$0.553907\pi$
$992$	−72.4710	−2.30096
$993$	−98.7552	−3.13390
$994$	−19.5233	−0.619241
$995$	8.62032	0.273283
$996$	43.9665	1.39313
$997$	9.47721	0.300146	0.150073	−	0.988675i	$-0.452049\pi$
$997$	9.47721	0.300146	0.150073	+	0.988675i	$0.452049\pi$
$998$	−39.8438	−1.26123
$999$	−113.985	−3.60634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.13	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.92788 q^{2} -3.19402 q^{3} +1.71671 q^{4} -1.00000 q^{5} +6.15768 q^{6} +1.00000 q^{7} +0.546142 q^{8} +7.20176 q^{9} +O(q^{10})\)	\(q-1.92788 q^{2} -3.19402 q^{3} +1.71671 q^{4} -1.00000 q^{5} +6.15768 q^{6} +1.00000 q^{7} +0.546142 q^{8} +7.20176 q^{9} +1.92788 q^{10} +1.50297 q^{11} -5.48322 q^{12} -0.695699 q^{13} -1.92788 q^{14} +3.19402 q^{15} -4.48632 q^{16} +0.954365 q^{17} -13.8841 q^{18} -5.42948 q^{19} -1.71671 q^{20} -3.19402 q^{21} -2.89754 q^{22} +3.74154 q^{23} -1.74439 q^{24} +1.00000 q^{25} +1.34122 q^{26} -13.4205 q^{27} +1.71671 q^{28} +0.797519 q^{29} -6.15768 q^{30} -9.59018 q^{31} +7.55680 q^{32} -4.80052 q^{33} -1.83990 q^{34} -1.00000 q^{35} +12.3634 q^{36} +8.49337 q^{37} +10.4674 q^{38} +2.22208 q^{39} -0.546142 q^{40} -4.48220 q^{41} +6.15768 q^{42} -8.01544 q^{43} +2.58017 q^{44} -7.20176 q^{45} -7.21323 q^{46} +9.05728 q^{47} +14.3294 q^{48} +1.00000 q^{49} -1.92788 q^{50} -3.04826 q^{51} -1.19432 q^{52} +1.35676 q^{53} +25.8731 q^{54} -1.50297 q^{55} +0.546142 q^{56} +17.3419 q^{57} -1.53752 q^{58} -12.2259 q^{59} +5.48322 q^{60} +1.96345 q^{61} +18.4887 q^{62} +7.20176 q^{63} -5.59594 q^{64} +0.695699 q^{65} +9.25481 q^{66} -3.52411 q^{67} +1.63837 q^{68} -11.9505 q^{69} +1.92788 q^{70} +10.1268 q^{71} +3.93318 q^{72} +9.87727 q^{73} -16.3742 q^{74} -3.19402 q^{75} -9.32086 q^{76} +1.50297 q^{77} -4.28389 q^{78} -9.06539 q^{79} +4.48632 q^{80} +21.2601 q^{81} +8.64113 q^{82} -8.01838 q^{83} -5.48322 q^{84} -0.954365 q^{85} +15.4528 q^{86} -2.54729 q^{87} +0.820835 q^{88} +10.3751 q^{89} +13.8841 q^{90} -0.695699 q^{91} +6.42315 q^{92} +30.6312 q^{93} -17.4613 q^{94} +5.42948 q^{95} -24.1366 q^{96} +3.94827 q^{97} -1.92788 q^{98} +10.8240 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 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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