LMFDB - Embedded newform 8041.2.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38029 q^{2} +3.05182 q^{3} +3.66578 q^{4} +3.97493 q^{5} -7.26423 q^{6} -3.90026 q^{7} -3.96504 q^{8} +6.31363 q^{9} +O(q^{10})$	\(q-2.38029 q^{2} +3.05182 q^{3} +3.66578 q^{4} +3.97493 q^{5} -7.26423 q^{6} -3.90026 q^{7} -3.96504 q^{8} +6.31363 q^{9} -9.46150 q^{10} -1.00000 q^{11} +11.1873 q^{12} -2.36196 q^{13} +9.28375 q^{14} +12.1308 q^{15} +2.10639 q^{16} -1.00000 q^{17} -15.0283 q^{18} -1.59876 q^{19} +14.5712 q^{20} -11.9029 q^{21} +2.38029 q^{22} -7.86563 q^{23} -12.1006 q^{24} +10.8001 q^{25} +5.62215 q^{26} +10.1126 q^{27} -14.2975 q^{28} +0.964418 q^{29} -28.8748 q^{30} -9.21807 q^{31} +2.91626 q^{32} -3.05182 q^{33} +2.38029 q^{34} -15.5033 q^{35} +23.1444 q^{36} -1.49961 q^{37} +3.80552 q^{38} -7.20829 q^{39} -15.7608 q^{40} +3.86568 q^{41} +28.3324 q^{42} -1.00000 q^{43} -3.66578 q^{44} +25.0963 q^{45} +18.7225 q^{46} -2.85316 q^{47} +6.42834 q^{48} +8.21201 q^{49} -25.7074 q^{50} -3.05182 q^{51} -8.65843 q^{52} -1.34902 q^{53} -24.0710 q^{54} -3.97493 q^{55} +15.4647 q^{56} -4.87915 q^{57} -2.29559 q^{58} +2.01671 q^{59} +44.4689 q^{60} -12.8259 q^{61} +21.9417 q^{62} -24.6248 q^{63} -11.1543 q^{64} -9.38863 q^{65} +7.26423 q^{66} -11.7066 q^{67} -3.66578 q^{68} -24.0045 q^{69} +36.9023 q^{70} -14.7818 q^{71} -25.0338 q^{72} -12.9346 q^{73} +3.56951 q^{74} +32.9600 q^{75} -5.86072 q^{76} +3.90026 q^{77} +17.1578 q^{78} -4.39387 q^{79} +8.37277 q^{80} +11.9210 q^{81} -9.20144 q^{82} +8.69222 q^{83} -43.6334 q^{84} -3.97493 q^{85} +2.38029 q^{86} +2.94323 q^{87} +3.96504 q^{88} +1.42217 q^{89} -59.7364 q^{90} +9.21225 q^{91} -28.8337 q^{92} -28.1319 q^{93} +6.79135 q^{94} -6.35498 q^{95} +8.89992 q^{96} +11.4040 q^{97} -19.5470 q^{98} -6.31363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−2.38029	−1.68312	−0.841560	−	0.540164i	$-0.818362\pi$
$2$	−2.38029	−1.68312	−0.841560	+	0.540164i	$0.818362\pi$
$3$	3.05182	1.76197	0.880986	−	0.473143i	$-0.156881\pi$
$3$	3.05182	1.76197	0.880986	+	0.473143i	$0.156881\pi$
$4$	3.66578	1.83289
$5$	3.97493	1.77764	0.888822	−	0.458252i	$-0.151524\pi$
$5$	3.97493	1.77764	0.888822	+	0.458252i	$0.151524\pi$
$6$	−7.26423	−2.96561
$7$	−3.90026	−1.47416	−0.737079	−	0.675806i	$-0.763796\pi$
$7$	−3.90026	−1.47416	−0.737079	+	0.675806i	$0.763796\pi$
$8$	−3.96504	−1.40185
$9$	6.31363	2.10454
$10$	−9.46150	−2.99199
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	11.1873	3.22950
$13$	−2.36196	−0.655090	−0.327545	−	0.944836i	$-0.606221\pi$
$13$	−2.36196	−0.655090	−0.327545	+	0.944836i	$0.606221\pi$
$14$	9.28375	2.48119
$15$	12.1308	3.13216
$16$	2.10639	0.526598
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−15.0283	−3.54220
$19$	−1.59876	−0.366782	−0.183391	−	0.983040i	$-0.558707\pi$
$19$	−1.59876	−0.366782	−0.183391	+	0.983040i	$0.558707\pi$
$20$	14.5712	3.25823
$21$	−11.9029	−2.59743
$22$	2.38029	0.507480
$23$	−7.86563	−1.64010	−0.820049	−	0.572293i	$-0.806054\pi$
$23$	−7.86563	−1.64010	−0.820049	+	0.572293i	$0.806054\pi$
$24$	−12.1006	−2.47003
$25$	10.8001	2.16002
$26$	5.62215	1.10259
$27$	10.1126	1.94617
$28$	−14.2975	−2.70197
$29$	0.964418	0.179088	0.0895440	−	0.995983i	$-0.471459\pi$
$29$	0.964418	0.179088	0.0895440	+	0.995983i	$0.471459\pi$
$30$	−28.8748	−5.27180
$31$	−9.21807	−1.65561	−0.827807	−	0.561013i	$-0.810412\pi$
$31$	−9.21807	−1.65561	−0.827807	+	0.561013i	$0.810412\pi$
$32$	2.91626	0.515527
$33$	−3.05182	−0.531254
$34$	2.38029	0.408216
$35$	−15.5033	−2.62053
$36$	23.1444	3.85740
$37$	−1.49961	−0.246535	−0.123267	−	0.992373i	$-0.539337\pi$
$37$	−1.49961	−0.246535	−0.123267	+	0.992373i	$0.539337\pi$
$38$	3.80552	0.617337
$39$	−7.20829	−1.15425
$40$	−15.7608	−2.49200
$41$	3.86568	0.603718	0.301859	−	0.953353i	$-0.402393\pi$
$41$	3.86568	0.603718	0.301859	+	0.953353i	$0.402393\pi$
$42$	28.3324	4.37178
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−3.66578	−0.552637
$45$	25.0963	3.74113
$46$	18.7225	2.76048
$47$	−2.85316	−0.416176	−0.208088	−	0.978110i	$-0.566724\pi$
$47$	−2.85316	−0.416176	−0.208088	+	0.978110i	$0.566724\pi$
$48$	6.42834	0.927851
$49$	8.21201	1.17314
$50$	−25.7074	−3.63557
$51$	−3.05182	−0.427341
$52$	−8.65843	−1.20071
$53$	−1.34902	−0.185302	−0.0926511	−	0.995699i	$-0.529534\pi$
$53$	−1.34902	−0.185302	−0.0926511	+	0.995699i	$0.529534\pi$
$54$	−24.0710	−3.27564
$55$	−3.97493	−0.535980
$56$	15.4647	2.06656
$57$	−4.87915	−0.646259
$58$	−2.29559	−0.301426
$59$	2.01671	0.262553	0.131276	−	0.991346i	$-0.458092\pi$
$59$	2.01671	0.262553	0.131276	+	0.991346i	$0.458092\pi$
$60$	44.4689	5.74090
$61$	−12.8259	−1.64219	−0.821095	−	0.570791i	$-0.806637\pi$
$61$	−12.8259	−1.64219	−0.821095	+	0.570791i	$0.806637\pi$
$62$	21.9417	2.78660
$63$	−24.6248	−3.10243
$64$	−11.1543	−1.39429
$65$	−9.38863	−1.16452
$66$	7.26423	0.894164
$67$	−11.7066	−1.43018	−0.715092	−	0.699031i	$-0.753615\pi$
$67$	−11.7066	−1.43018	−0.715092	+	0.699031i	$0.753615\pi$
$68$	−3.66578	−0.444541
$69$	−24.0045	−2.88981
$70$	36.9023	4.41066
$71$	−14.7818	−1.75427	−0.877136	−	0.480242i	$-0.840549\pi$
$71$	−14.7818	−1.75427	−0.877136	+	0.480242i	$0.840549\pi$
$72$	−25.0338	−2.95026
$73$	−12.9346	−1.51388	−0.756941	−	0.653484i	$-0.773307\pi$
$73$	−12.9346	−1.51388	−0.756941	+	0.653484i	$0.773307\pi$
$74$	3.56951	0.414948
$75$	32.9600	3.80589
$76$	−5.86072	−0.672271
$77$	3.90026	0.444476
$78$	17.1578	1.94274
$79$	−4.39387	−0.494349	−0.247175	−	0.968971i	$-0.579502\pi$
$79$	−4.39387	−0.494349	−0.247175	+	0.968971i	$0.579502\pi$
$80$	8.37277	0.936104
$81$	11.9210	1.32456
$82$	−9.20144	−1.01613
$83$	8.69222	0.954095	0.477048	−	0.878877i	$-0.341707\pi$
$83$	8.69222	0.954095	0.477048	+	0.878877i	$0.341707\pi$
$84$	−43.6334	−4.76080
$85$	−3.97493	−0.431142
$86$	2.38029	0.256673
$87$	2.94323	0.315548
$88$	3.96504	0.422675
$89$	1.42217	0.150749	0.0753747	−	0.997155i	$-0.475985\pi$
$89$	1.42217	0.150749	0.0753747	+	0.997155i	$0.475985\pi$
$90$	−59.7364	−6.29677
$91$	9.21225	0.965706
$92$	−28.8337	−3.00612
$93$	−28.1319	−2.91714
$94$	6.79135	0.700474
$95$	−6.35498	−0.652007
$96$	8.89992	0.908344
$97$	11.4040	1.15790	0.578949	−	0.815364i	$-0.303463\pi$
$97$	11.4040	1.15790	0.578949	+	0.815364i	$0.303463\pi$
$98$	−19.5470	−1.97454
$99$	−6.31363	−0.634544
$100$	39.5908	3.95908
$101$	5.68020	0.565201	0.282600	−	0.959238i	$-0.408803\pi$
$101$	5.68020	0.565201	0.282600	+	0.959238i	$0.408803\pi$
$102$	7.26423	0.719266
$103$	4.40880	0.434412	0.217206	−	0.976126i	$-0.430306\pi$
$103$	4.40880	0.434412	0.217206	+	0.976126i	$0.430306\pi$
$104$	9.36528	0.918341
$105$	−47.3132	−4.61730
$106$	3.21106	0.311886
$107$	14.6001	1.41144	0.705721	−	0.708490i	$-0.250623\pi$
$107$	14.6001	1.41144	0.705721	+	0.708490i	$0.250623\pi$
$108$	37.0706	3.56712
$109$	−4.62433	−0.442930	−0.221465	−	0.975168i	$-0.571084\pi$
$109$	−4.62433	−0.442930	−0.221465	+	0.975168i	$0.571084\pi$
$110$	9.46150	0.902118
$111$	−4.57656	−0.434387
$112$	−8.21547	−0.776289
$113$	−11.6118	−1.09235	−0.546175	−	0.837671i	$-0.683917\pi$
$113$	−11.6118	−1.09235	−0.546175	+	0.837671i	$0.683917\pi$
$114$	11.6138	1.08773
$115$	−31.2654	−2.91551
$116$	3.53535	0.328249
$117$	−14.9125	−1.37866
$118$	−4.80035	−0.441908
$119$	3.90026	0.357536
$120$	−48.0991	−4.39083
$121$	1.00000	0.0909091
$122$	30.5294	2.76400
$123$	11.7974	1.06373
$124$	−33.7914	−3.03456
$125$	23.0550	2.06210
$126$	58.6141	5.22176
$127$	6.65479	0.590517	0.295259	−	0.955417i	$-0.404594\pi$
$127$	6.65479	0.590517	0.295259	+	0.955417i	$0.404594\pi$
$128$	20.7180	1.83123
$129$	−3.05182	−0.268698
$130$	22.3477	1.96002
$131$	14.5751	1.27343	0.636714	−	0.771100i	$-0.280293\pi$
$131$	14.5751	1.27343	0.636714	+	0.771100i	$0.280293\pi$
$132$	−11.1873	−0.973731
$133$	6.23559	0.540694
$134$	27.8650	2.40717
$135$	40.1970	3.45960
$136$	3.96504	0.340000
$137$	15.3841	1.31435	0.657176	−	0.753737i	$-0.271751\pi$
$137$	15.3841	1.31435	0.657176	+	0.753737i	$0.271751\pi$
$138$	57.1377	4.86389
$139$	6.88297	0.583806	0.291903	−	0.956448i	$-0.405712\pi$
$139$	6.88297	0.583806	0.291903	+	0.956448i	$0.405712\pi$
$140$	−56.8316	−4.80315
$141$	−8.70735	−0.733291
$142$	35.1849	2.95265
$143$	2.36196	0.197517
$144$	13.2990	1.10825
$145$	3.83350	0.318355
$146$	30.7881	2.54804
$147$	25.0616	2.06705
$148$	−5.49725	−0.451872
$149$	−11.4889	−0.941210	−0.470605	−	0.882344i	$-0.655964\pi$
$149$	−11.4889	−0.941210	−0.470605	+	0.882344i	$0.655964\pi$
$150$	−78.4543	−6.40577
$151$	−21.3416	−1.73676	−0.868379	−	0.495901i	$-0.834838\pi$
$151$	−21.3416	−1.73676	−0.868379	+	0.495901i	$0.834838\pi$
$152$	6.33917	0.514175
$153$	−6.31363	−0.510427
$154$	−9.28375	−0.748106
$155$	−36.6412	−2.94309
$156$	−26.4240	−2.11561
$157$	20.3915	1.62742	0.813711	−	0.581269i	$-0.197444\pi$
$157$	20.3915	1.62742	0.813711	+	0.581269i	$0.197444\pi$
$158$	10.4587	0.832049
$159$	−4.11697	−0.326497
$160$	11.5920	0.916424
$161$	30.6780	2.41776
$162$	−28.3755	−2.22939
$163$	−12.5323	−0.981602	−0.490801	−	0.871272i	$-0.663296\pi$
$163$	−12.5323	−0.981602	−0.490801	+	0.871272i	$0.663296\pi$
$164$	14.1707	1.10655
$165$	−12.1308	−0.944381
$166$	−20.6900	−1.60586
$167$	−3.54501	−0.274321	−0.137161	−	0.990549i	$-0.543798\pi$
$167$	−3.54501	−0.274321	−0.137161	+	0.990549i	$0.543798\pi$
$168$	47.1955	3.64121
$169$	−7.42115	−0.570857
$170$	9.46150	0.725664
$171$	−10.0940	−0.771908
$172$	−3.66578	−0.279513
$173$	13.1932	1.00306	0.501531	−	0.865140i	$-0.332770\pi$
$173$	13.1932	1.00306	0.501531	+	0.865140i	$0.332770\pi$
$174$	−7.00575	−0.531105
$175$	−42.1232	−3.18421
$176$	−2.10639	−0.158775
$177$	6.15463	0.462611
$178$	−3.38517	−0.253729
$179$	1.48020	0.110635	0.0553176	−	0.998469i	$-0.482383\pi$
$179$	1.48020	0.110635	0.0553176	+	0.998469i	$0.482383\pi$
$180$	91.9974	6.85708
$181$	−25.6135	−1.90384	−0.951919	−	0.306350i	$-0.900892\pi$
$181$	−25.6135	−1.90384	−0.951919	+	0.306350i	$0.900892\pi$
$182$	−21.9278	−1.62540
$183$	−39.1424	−2.89349
$184$	31.1876	2.29918
$185$	−5.96086	−0.438251
$186$	66.9621	4.90990
$187$	1.00000	0.0731272
$188$	−10.4591	−0.762806
$189$	−39.4418	−2.86897
$190$	15.1267	1.09741
$191$	12.1222	0.877133	0.438566	−	0.898699i	$-0.355486\pi$
$191$	12.1222	0.877133	0.438566	+	0.898699i	$0.355486\pi$
$192$	−34.0411	−2.45670
$193$	−9.89823	−0.712490	−0.356245	−	0.934393i	$-0.615943\pi$
$193$	−9.89823	−0.712490	−0.356245	+	0.934393i	$0.615943\pi$
$194$	−27.1448	−1.94888
$195$	−28.6525	−2.05184
$196$	30.1034	2.15025
$197$	2.71823	0.193666	0.0968329	−	0.995301i	$-0.469129\pi$
$197$	2.71823	0.193666	0.0968329	+	0.995301i	$0.469129\pi$
$198$	15.0283	1.06801
$199$	−14.7913	−1.04852	−0.524262	−	0.851557i	$-0.675659\pi$
$199$	−14.7913	−1.04852	−0.524262	+	0.851557i	$0.675659\pi$
$200$	−42.8229	−3.02803
$201$	−35.7263	−2.51994
$202$	−13.5205	−0.951300
$203$	−3.76148	−0.264004
$204$	−11.1873	−0.783269
$205$	15.3658	1.07320
$206$	−10.4942	−0.731168
$207$	−49.6607	−3.45166
$208$	−4.97521	−0.344969
$209$	1.59876	0.110589
$210$	112.619	7.77147
$211$	−19.8747	−1.36823	−0.684115	−	0.729374i	$-0.739811\pi$
$211$	−19.8747	−1.36823	−0.684115	+	0.729374i	$0.739811\pi$
$212$	−4.94522	−0.339639
$213$	−45.1113	−3.09098
$214$	−34.7524	−2.37562
$215$	−3.97493	−0.271088
$216$	−40.0970	−2.72825
$217$	35.9528	2.44064
$218$	11.0072	0.745504
$219$	−39.4741	−2.66742
$220$	−14.5712	−0.982393
$221$	2.36196	0.158883
$222$	10.8935	0.731126
$223$	14.0860	0.943267	0.471633	−	0.881795i	$-0.343665\pi$
$223$	14.0860	0.943267	0.471633	+	0.881795i	$0.343665\pi$
$224$	−11.3742	−0.759969
$225$	68.1878	4.54585
$226$	27.6395	1.83856
$227$	−22.6709	−1.50472	−0.752361	−	0.658751i	$-0.771085\pi$
$227$	−22.6709	−1.50472	−0.752361	+	0.658751i	$0.771085\pi$
$228$	−17.8859	−1.18452
$229$	−3.14716	−0.207970	−0.103985	−	0.994579i	$-0.533159\pi$
$229$	−3.14716	−0.207970	−0.103985	+	0.994579i	$0.533159\pi$
$230$	74.4206	4.90715
$231$	11.9029	0.783153
$232$	−3.82396	−0.251055
$233$	4.30236	0.281857	0.140928	−	0.990020i	$-0.454991\pi$
$233$	4.30236	0.281857	0.140928	+	0.990020i	$0.454991\pi$
$234$	35.4962	2.32046
$235$	−11.3411	−0.739813
$236$	7.39281	0.481231
$237$	−13.4093	−0.871029
$238$	−9.28375	−0.601776
$239$	−0.153053	−0.00990016	−0.00495008	−	0.999988i	$-0.501576\pi$
$239$	−0.153053	−0.00990016	−0.00495008	+	0.999988i	$0.501576\pi$
$240$	25.5522	1.64939
$241$	23.4689	1.51176	0.755882	−	0.654708i	$-0.227208\pi$
$241$	23.4689	1.51176	0.755882	+	0.654708i	$0.227208\pi$
$242$	−2.38029	−0.153011
$243$	6.04303	0.387660
$244$	−47.0170	−3.00996
$245$	32.6422	2.08543
$246$	−28.0812	−1.79039
$247$	3.77622	0.240275
$248$	36.5501	2.32093
$249$	26.5271	1.68109
$250$	−54.8776	−3.47076
$251$	15.2463	0.962337	0.481168	−	0.876628i	$-0.340213\pi$
$251$	15.2463	0.962337	0.481168	+	0.876628i	$0.340213\pi$
$252$	−90.2691	−5.68642
$253$	7.86563	0.494508
$254$	−15.8403	−0.993911
$255$	−12.1308	−0.759660
$256$	−27.0063	−1.68789
$257$	20.3984	1.27242	0.636208	−	0.771518i	$-0.280502\pi$
$257$	20.3984	1.27242	0.636208	+	0.771518i	$0.280502\pi$
$258$	7.26423	0.452251
$259$	5.84888	0.363432
$260$	−34.4167	−2.13443
$261$	6.08898	0.376898
$262$	−34.6929	−2.14333
$263$	−2.05878	−0.126950	−0.0634750	−	0.997983i	$-0.520218\pi$
$263$	−2.05878	−0.126950	−0.0634750	+	0.997983i	$0.520218\pi$
$264$	12.1006	0.744741
$265$	−5.36227	−0.329402
$266$	−14.8425	−0.910053
$267$	4.34020	0.265616
$268$	−42.9137	−2.62137
$269$	4.84407	0.295348	0.147674	−	0.989036i	$-0.452821\pi$
$269$	4.84407	0.295348	0.147674	+	0.989036i	$0.452821\pi$
$270$	−95.6804	−5.82293
$271$	12.1618	0.738778	0.369389	−	0.929275i	$-0.379567\pi$
$271$	12.1618	0.738778	0.369389	+	0.929275i	$0.379567\pi$
$272$	−2.10639	−0.127719
$273$	28.1142	1.70155
$274$	−36.6186	−2.21221
$275$	−10.8001	−0.651270
$276$	−87.9954	−5.29670
$277$	5.80183	0.348598	0.174299	−	0.984693i	$-0.444234\pi$
$277$	5.80183	0.348598	0.174299	+	0.984693i	$0.444234\pi$
$278$	−16.3835	−0.982615
$279$	−58.1995	−3.48431
$280$	61.4711	3.67360
$281$	−15.6759	−0.935143	−0.467571	−	0.883955i	$-0.654871\pi$
$281$	−15.6759	−0.935143	−0.467571	+	0.883955i	$0.654871\pi$
$282$	20.7260	1.23422
$283$	−7.14727	−0.424861	−0.212431	−	0.977176i	$-0.568138\pi$
$283$	−7.14727	−0.424861	−0.212431	+	0.977176i	$0.568138\pi$
$284$	−54.1867	−3.21539
$285$	−19.3943	−1.14882
$286$	−5.62215	−0.332445
$287$	−15.0771	−0.889976
$288$	18.4122	1.08495
$289$	1.00000	0.0588235
$290$	−9.12484	−0.535829
$291$	34.8029	2.04018
$292$	−47.4155	−2.77478
$293$	−11.1213	−0.649712	−0.324856	−	0.945763i	$-0.605316\pi$
$293$	−11.1213	−0.649712	−0.324856	+	0.945763i	$0.605316\pi$
$294$	−59.6539	−3.47909
$295$	8.01627	0.466725
$296$	5.94603	0.345606
$297$	−10.1126	−0.586793
$298$	27.3470	1.58417
$299$	18.5783	1.07441
$300$	120.824	6.97578
$301$	3.90026	0.224807
$302$	50.7993	2.92317
$303$	17.3350	0.995867
$304$	−3.36762	−0.193147
$305$	−50.9822	−2.91923
$306$	15.0283	0.859109
$307$	14.0856	0.803909	0.401954	−	0.915660i	$-0.368331\pi$
$307$	14.0856	0.803909	0.401954	+	0.915660i	$0.368331\pi$
$308$	14.2975	0.814675
$309$	13.4549	0.765422
$310$	87.2167	4.95358
$311$	−25.5009	−1.44602	−0.723012	−	0.690836i	$-0.757243\pi$
$311$	−25.5009	−1.44602	−0.723012	+	0.690836i	$0.757243\pi$
$312$	28.5812	1.61809
$313$	4.50851	0.254836	0.127418	−	0.991849i	$-0.459331\pi$
$313$	4.50851	0.254836	0.127418	+	0.991849i	$0.459331\pi$
$314$	−48.5378	−2.73915
$315$	−97.8819	−5.51502
$316$	−16.1070	−0.906088
$317$	14.2330	0.799403	0.399702	−	0.916645i	$-0.369114\pi$
$317$	14.2330	0.799403	0.399702	+	0.916645i	$0.369114\pi$
$318$	9.79959	0.549534
$319$	−0.964418	−0.0539970
$320$	−44.3377	−2.47856
$321$	44.5568	2.48692
$322$	−73.0225	−4.06939
$323$	1.59876	0.0889576
$324$	43.6999	2.42777
$325$	−25.5094	−1.41501
$326$	29.8304	1.65215
$327$	−14.1126	−0.780430
$328$	−15.3276	−0.846325
$329$	11.1281	0.613510
$330$	28.8748	1.58951
$331$	9.36883	0.514958	0.257479	−	0.966284i	$-0.417108\pi$
$331$	9.36883	0.514958	0.257479	+	0.966284i	$0.417108\pi$
$332$	31.8638	1.74875
$333$	−9.46800	−0.518843
$334$	8.43816	0.461716
$335$	−46.5328	−2.54236
$336$	−25.0722	−1.36780
$337$	0.168606	0.00918457	0.00459229	−	0.999989i	$-0.498538\pi$
$337$	0.168606	0.00918457	0.00459229	+	0.999989i	$0.498538\pi$
$338$	17.6645	0.960821
$339$	−35.4373	−1.92469
$340$	−14.5712	−0.790236
$341$	9.21807	0.499186
$342$	24.0267	1.29921
$343$	−4.72715	−0.255242
$344$	3.96504	0.213781
$345$	−95.4164	−5.13705
$346$	−31.4037	−1.68827
$347$	−1.46974	−0.0788999	−0.0394500	−	0.999222i	$-0.512561\pi$
$347$	−1.46974	−0.0788999	−0.0394500	+	0.999222i	$0.512561\pi$
$348$	10.7893	0.578365
$349$	3.46448	0.185449	0.0927246	−	0.995692i	$-0.470442\pi$
$349$	3.46448	0.185449	0.0927246	+	0.995692i	$0.470442\pi$
$350$	100.265	5.35941
$351$	−23.8856	−1.27492
$352$	−2.91626	−0.155437
$353$	−20.1359	−1.07173	−0.535863	−	0.844305i	$-0.680014\pi$
$353$	−20.1359	−1.07173	−0.535863	+	0.844305i	$0.680014\pi$
$354$	−14.6498	−0.778629
$355$	−58.7565	−3.11847
$356$	5.21335	0.276307
$357$	11.9029	0.629968
$358$	−3.52330	−0.186212
$359$	−20.8177	−1.09871	−0.549357	−	0.835588i	$-0.685127\pi$
$359$	−20.8177	−1.09871	−0.549357	+	0.835588i	$0.685127\pi$
$360$	−99.5078	−5.24452
$361$	−16.4440	−0.865471
$362$	60.9676	3.20439
$363$	3.05182	0.160179
$364$	33.7701	1.77003
$365$	−51.4142	−2.69114
$366$	93.1704	4.87009
$367$	−7.37707	−0.385080	−0.192540	−	0.981289i	$-0.561672\pi$
$367$	−7.37707	−0.385080	−0.192540	+	0.981289i	$0.561672\pi$
$368$	−16.5681	−0.863672
$369$	24.4065	1.27055
$370$	14.1886	0.737629
$371$	5.26153	0.273165
$372$	−103.125	−5.34681
$373$	14.1880	0.734626	0.367313	−	0.930097i	$-0.380278\pi$
$373$	14.1880	0.734626	0.367313	+	0.930097i	$0.380278\pi$
$374$	−2.38029	−0.123082
$375$	70.3598	3.63336
$376$	11.3129	0.583419
$377$	−2.27792	−0.117319
$378$	93.8829	4.82882
$379$	7.83499	0.402457	0.201228	−	0.979544i	$-0.435507\pi$
$379$	7.83499	0.402457	0.201228	+	0.979544i	$0.435507\pi$
$380$	−23.2960	−1.19506
$381$	20.3093	1.04047
$382$	−28.8544	−1.47632
$383$	2.35115	0.120138	0.0600690	−	0.998194i	$-0.480868\pi$
$383$	2.35115	0.120138	0.0600690	+	0.998194i	$0.480868\pi$
$384$	63.2278	3.22658
$385$	15.5033	0.790120
$386$	23.5607	1.19921
$387$	−6.31363	−0.320940
$388$	41.8045	2.12230
$389$	−32.0897	−1.62701	−0.813506	−	0.581557i	$-0.802444\pi$
$389$	−32.0897	−1.62701	−0.813506	+	0.581557i	$0.802444\pi$
$390$	68.2012	3.45350
$391$	7.86563	0.397782
$392$	−32.5610	−1.64458
$393$	44.4805	2.24374
$394$	−6.47018	−0.325963
$395$	−17.4653	−0.878777
$396$	−23.1444	−1.16305
$397$	−31.7177	−1.59187	−0.795933	−	0.605385i	$-0.793019\pi$
$397$	−31.7177	−1.59187	−0.795933	+	0.605385i	$0.793019\pi$
$398$	35.2075	1.76479
$399$	19.0299	0.952688
$400$	22.7492	1.13746
$401$	−5.42740	−0.271031	−0.135516	−	0.990775i	$-0.543269\pi$
$401$	−5.42740	−0.271031	−0.135516	+	0.990775i	$0.543269\pi$
$402$	85.0391	4.24136
$403$	21.7727	1.08458
$404$	20.8224	1.03595
$405$	47.3853	2.35459
$406$	8.95341	0.444350
$407$	1.49961	0.0743331
$408$	12.1006	0.599070
$409$	15.6985	0.776240	0.388120	−	0.921609i	$-0.373125\pi$
$409$	15.6985	0.776240	0.388120	+	0.921609i	$0.373125\pi$
$410$	−36.5751	−1.80632
$411$	46.9496	2.31585
$412$	16.1617	0.796230
$413$	−7.86567	−0.387045
$414$	118.207	5.80955
$415$	34.5510	1.69604
$416$	−6.88810	−0.337717
$417$	21.0056	1.02865
$418$	−3.80552	−0.186134
$419$	15.9083	0.777169	0.388584	−	0.921413i	$-0.372964\pi$
$419$	15.9083	0.777169	0.388584	+	0.921413i	$0.372964\pi$
$420$	−173.440	−8.46300
$421$	−1.80478	−0.0879595	−0.0439797	−	0.999032i	$-0.514004\pi$
$421$	−1.80478	−0.0879595	−0.0439797	+	0.999032i	$0.514004\pi$
$422$	47.3075	2.30290
$423$	−18.0138	−0.875861
$424$	5.34893	0.259767
$425$	−10.8001	−0.523882
$426$	107.378	5.20248
$427$	50.0244	2.42085
$428$	53.5206	2.58702
$429$	7.20829	0.348019
$430$	9.46150	0.456274
$431$	−32.0777	−1.54513	−0.772564	−	0.634936i	$-0.781026\pi$
$431$	−32.0777	−1.54513	−0.772564	+	0.634936i	$0.781026\pi$
$432$	21.3011	1.02485
$433$	9.38697	0.451109	0.225555	−	0.974231i	$-0.427581\pi$
$433$	9.38697	0.451109	0.225555	+	0.974231i	$0.427581\pi$
$434$	−85.5782	−4.10789
$435$	11.6992	0.560932
$436$	−16.9518	−0.811842
$437$	12.5753	0.601558
$438$	93.9599	4.48958
$439$	−32.6210	−1.55692	−0.778458	−	0.627697i	$-0.783998\pi$
$439$	−32.6210	−1.55692	−0.778458	+	0.627697i	$0.783998\pi$
$440$	15.7608	0.751366
$441$	51.8476	2.46893
$442$	−5.62215	−0.267418
$443$	12.7123	0.603980	0.301990	−	0.953311i	$-0.402349\pi$
$443$	12.7123	0.603980	0.301990	+	0.953311i	$0.402349\pi$
$444$	−16.7767	−0.796185
$445$	5.65302	0.267979
$446$	−33.5287	−1.58763
$447$	−35.0622	−1.65838
$448$	43.5048	2.05541
$449$	20.3201	0.958964	0.479482	−	0.877552i	$-0.340825\pi$
$449$	20.3201	0.958964	0.479482	+	0.877552i	$0.340825\pi$
$450$	−162.307	−7.65121
$451$	−3.86568	−0.182028
$452$	−42.5665	−2.00216
$453$	−65.1309	−3.06012
$454$	53.9634	2.53263
$455$	36.6181	1.71668
$456$	19.3460	0.905961
$457$	−4.61745	−0.215995	−0.107998	−	0.994151i	$-0.534444\pi$
$457$	−4.61745	−0.215995	−0.107998	+	0.994151i	$0.534444\pi$
$458$	7.49116	0.350039
$459$	−10.1126	−0.472016
$460$	−114.612	−5.34381
$461$	27.2776	1.27044	0.635222	−	0.772330i	$-0.280909\pi$
$461$	27.2776	1.27044	0.635222	+	0.772330i	$0.280909\pi$
$462$	−28.3324	−1.31814
$463$	4.16878	0.193739	0.0968697	−	0.995297i	$-0.469117\pi$
$463$	4.16878	0.193739	0.0968697	+	0.995297i	$0.469117\pi$
$464$	2.03144	0.0943074
$465$	−111.823	−5.18565
$466$	−10.2409	−0.474399
$467$	−31.7833	−1.47076	−0.735378	−	0.677657i	$-0.762996\pi$
$467$	−31.7833	−1.47076	−0.735378	+	0.677657i	$0.762996\pi$
$468$	−54.6661	−2.52694
$469$	45.6586	2.10832
$470$	26.9952	1.24519
$471$	62.2314	2.86747
$472$	−7.99633	−0.368061
$473$	1.00000	0.0459800
$474$	31.9181	1.46605
$475$	−17.2668	−0.792255
$476$	14.2975	0.655325
$477$	−8.51722	−0.389977
$478$	0.364310	0.0166632
$479$	5.27876	0.241193	0.120596	−	0.992702i	$-0.461519\pi$
$479$	5.27876	0.241193	0.120596	+	0.992702i	$0.461519\pi$
$480$	35.3766	1.61471
$481$	3.54203	0.161503
$482$	−55.8627	−2.54448
$483$	93.6238	4.26003
$484$	3.66578	0.166626
$485$	45.3300	2.05833
$486$	−14.3842	−0.652479
$487$	38.2290	1.73232	0.866161	−	0.499765i	$-0.166580\pi$
$487$	38.2290	1.73232	0.866161	+	0.499765i	$0.166580\pi$
$488$	50.8553	2.30211
$489$	−38.2462	−1.72955
$490$	−77.6979	−3.51003
$491$	−36.5482	−1.64940	−0.824698	−	0.565573i	$-0.808655\pi$
$491$	−36.5482	−1.64940	−0.824698	+	0.565573i	$0.808655\pi$
$492$	43.2466	1.94971
$493$	−0.964418	−0.0434352
$494$	−8.98849	−0.404411
$495$	−25.0963	−1.12799
$496$	−19.4169	−0.871843
$497$	57.6527	2.58608
$498$	−63.1423	−2.82947
$499$	31.4483	1.40782	0.703911	−	0.710289i	$-0.251436\pi$
$499$	31.4483	1.40782	0.703911	+	0.710289i	$0.251436\pi$
$500$	84.5146	3.77961
$501$	−10.8188	−0.483346
$502$	−36.2906	−1.61973
$503$	17.7669	0.792185	0.396093	−	0.918211i	$-0.370366\pi$
$503$	17.7669	0.792185	0.396093	+	0.918211i	$0.370366\pi$
$504$	97.6383	4.34916
$505$	22.5784	1.00473
$506$	−18.7225	−0.832316
$507$	−22.6480	−1.00583
$508$	24.3950	1.08235
$509$	−30.8069	−1.36549	−0.682746	−	0.730656i	$-0.739215\pi$
$509$	−30.8069	−1.36549	−0.682746	+	0.730656i	$0.739215\pi$
$510$	28.8748	1.27860
$511$	50.4483	2.23170
$512$	22.8467	1.00969
$513$	−16.1677	−0.713821
$514$	−48.5540	−2.14163
$515$	17.5247	0.772230
$516$	−11.1873	−0.492494
$517$	2.85316	0.125482
$518$	−13.9220	−0.611699
$519$	40.2634	1.76737
$520$	37.2263	1.63248
$521$	42.6343	1.86784	0.933921	−	0.357479i	$-0.116364\pi$
$521$	42.6343	1.86784	0.933921	+	0.357479i	$0.116364\pi$
$522$	−14.4935	−0.634365
$523$	35.0044	1.53064	0.765318	−	0.643652i	$-0.222582\pi$
$523$	35.0044	1.53064	0.765318	+	0.643652i	$0.222582\pi$
$524$	53.4290	2.33406
$525$	−128.552	−5.61049
$526$	4.90050	0.213672
$527$	9.21807	0.401545
$528$	−6.42834	−0.279758
$529$	38.8682	1.68992
$530$	12.7638	0.554422
$531$	12.7327	0.552554
$532$	22.8583	0.991034
$533$	−9.13058	−0.395489
$534$	−10.3309	−0.447064
$535$	58.0343	2.50904
$536$	46.4170	2.00491
$537$	4.51730	0.194936
$538$	−11.5303	−0.497107
$539$	−8.21201	−0.353716
$540$	147.353	6.34108
$541$	29.1385	1.25276	0.626382	−	0.779516i	$-0.284535\pi$
$541$	29.1385	1.25276	0.626382	+	0.779516i	$0.284535\pi$
$542$	−28.9486	−1.24345
$543$	−78.1679	−3.35451
$544$	−2.91626	−0.125034
$545$	−18.3814	−0.787372
$546$	−66.9199	−2.86391
$547$	−11.9893	−0.512627	−0.256314	−	0.966594i	$-0.582508\pi$
$547$	−11.9893	−0.512627	−0.256314	+	0.966594i	$0.582508\pi$
$548$	56.3948	2.40906
$549$	−80.9781	−3.45606
$550$	25.7074	1.09617
$551$	−1.54188	−0.0656862
$552$	95.1790	4.05109
$553$	17.1372	0.728749
$554$	−13.8100	−0.586732
$555$	−18.1915	−0.772186
$556$	25.2315	1.07005
$557$	−28.2150	−1.19551	−0.597753	−	0.801680i	$-0.703940\pi$
$557$	−28.2150	−1.19551	−0.597753	+	0.801680i	$0.703940\pi$
$558$	138.532	5.86451
$559$	2.36196	0.0999003
$560$	−32.6560	−1.37997
$561$	3.05182	0.128848
$562$	37.3131	1.57396
$563$	34.6634	1.46089	0.730445	−	0.682971i	$-0.239313\pi$
$563$	34.6634	1.46089	0.730445	+	0.682971i	$0.239313\pi$
$564$	−31.9192	−1.34404
$565$	−46.1563	−1.94181
$566$	17.0126	0.715092
$567$	−46.4951	−1.95261
$568$	58.6103	2.45923
$569$	−10.3241	−0.432811	−0.216405	−	0.976304i	$-0.569433\pi$
$569$	−10.3241	−0.432811	−0.216405	+	0.976304i	$0.569433\pi$
$570$	46.1640	1.93360
$571$	−36.3862	−1.52271	−0.761357	−	0.648333i	$-0.775467\pi$
$571$	−36.3862	−1.52271	−0.761357	+	0.648333i	$0.775467\pi$
$572$	8.65843	0.362027
$573$	36.9949	1.54548
$574$	35.8880	1.49794
$575$	−84.9496	−3.54264
$576$	−70.4243	−2.93435
$577$	34.3389	1.42955	0.714774	−	0.699355i	$-0.246529\pi$
$577$	34.3389	1.42955	0.714774	+	0.699355i	$0.246529\pi$
$578$	−2.38029	−0.0990070
$579$	−30.2077	−1.25539
$580$	14.0528	0.583509
$581$	−33.9019	−1.40649
$582$	−82.8410	−3.43387
$583$	1.34902	0.0558707
$584$	51.2863	2.12224
$585$	−59.2763	−2.45078
$586$	26.4719	1.09354
$587$	−24.1098	−0.995119	−0.497560	−	0.867430i	$-0.665770\pi$
$587$	−24.1098	−0.995119	−0.497560	+	0.867430i	$0.665770\pi$
$588$	91.8704	3.78867
$589$	14.7375	0.607249
$590$	−19.0811	−0.785555
$591$	8.29556	0.341234
$592$	−3.15877	−0.129825
$593$	8.82363	0.362343	0.181172	−	0.983452i	$-0.442011\pi$
$593$	8.82363	0.362343	0.181172	+	0.983452i	$0.442011\pi$
$594$	24.0710	0.987643
$595$	15.5033	0.635572
$596$	−42.1159	−1.72513
$597$	−45.1403	−1.84747
$598$	−44.2218	−1.80836
$599$	6.75030	0.275810	0.137905	−	0.990445i	$-0.455963\pi$
$599$	6.75030	0.275810	0.137905	+	0.990445i	$0.455963\pi$
$600$	−130.688	−5.33531
$601$	−8.35200	−0.340685	−0.170342	−	0.985385i	$-0.554487\pi$
$601$	−8.35200	−0.340685	−0.170342	+	0.985385i	$0.554487\pi$
$602$	−9.28375	−0.378377
$603$	−73.9108	−3.00988
$604$	−78.2338	−3.18329
$605$	3.97493	0.161604
$606$	−41.2622	−1.67616
$607$	28.7901	1.16855	0.584277	−	0.811554i	$-0.301378\pi$
$607$	28.7901	1.16855	0.584277	+	0.811554i	$0.301378\pi$
$608$	−4.66242	−0.189086
$609$	−11.4794	−0.465168
$610$	121.352	4.91341
$611$	6.73905	0.272633
$612$	−23.1444	−0.935556
$613$	4.21447	0.170221	0.0851105	−	0.996372i	$-0.472876\pi$
$613$	4.21447	0.170221	0.0851105	+	0.996372i	$0.472876\pi$
$614$	−33.5279	−1.35307
$615$	46.8938	1.89094
$616$	−15.4647	−0.623090
$617$	1.09186	0.0439568	0.0219784	−	0.999758i	$-0.493003\pi$
$617$	1.09186	0.0439568	0.0219784	+	0.999758i	$0.493003\pi$
$618$	−32.0265	−1.28830
$619$	−45.6057	−1.83305	−0.916523	−	0.399982i	$-0.869017\pi$
$619$	−45.6057	−1.83305	−0.916523	+	0.399982i	$0.869017\pi$
$620$	−134.319	−5.39437
$621$	−79.5421	−3.19191
$622$	60.6995	2.43383
$623$	−5.54682	−0.222229
$624$	−15.1835	−0.607826
$625$	37.6416	1.50566
$626$	−10.7316	−0.428919
$627$	4.87915	0.194854
$628$	74.7510	2.98289
$629$	1.49961	0.0597935
$630$	232.987	9.28243
$631$	23.7457	0.945300	0.472650	−	0.881250i	$-0.343297\pi$
$631$	23.7457	0.945300	0.472650	+	0.881250i	$0.343297\pi$
$632$	17.4219	0.693006
$633$	−60.6541	−2.41078
$634$	−33.8786	−1.34549
$635$	26.4524	1.04973
$636$	−15.0919	−0.598434
$637$	−19.3964	−0.768515
$638$	2.29559	0.0908835
$639$	−93.3265	−3.69194
$640$	82.3528	3.25528
$641$	−42.5926	−1.68230	−0.841152	−	0.540798i	$-0.818122\pi$
$641$	−42.5926	−1.68230	−0.841152	+	0.540798i	$0.818122\pi$
$642$	−106.058	−4.18578
$643$	41.9483	1.65428	0.827140	−	0.561995i	$-0.189966\pi$
$643$	41.9483	1.65428	0.827140	+	0.561995i	$0.189966\pi$
$644$	112.459	4.43150
$645$	−12.1308	−0.477650
$646$	−3.80552	−0.149726
$647$	1.43468	0.0564031	0.0282015	−	0.999602i	$-0.491022\pi$
$647$	1.43468	0.0564031	0.0282015	+	0.999602i	$0.491022\pi$
$648$	−47.2674	−1.85684
$649$	−2.01671	−0.0791626
$650$	60.7198	2.38163
$651$	109.722	4.30033
$652$	−45.9405	−1.79917
$653$	19.7425	0.772582	0.386291	−	0.922377i	$-0.373756\pi$
$653$	19.7425	0.772582	0.386291	+	0.922377i	$0.373756\pi$
$654$	33.5921	1.31356
$655$	57.9349	2.26370
$656$	8.14264	0.317917
$657$	−81.6643	−3.18603
$658$	−26.4880	−1.03261
$659$	3.20854	0.124987	0.0624935	−	0.998045i	$-0.480095\pi$
$659$	3.20854	0.124987	0.0624935	+	0.998045i	$0.480095\pi$
$660$	−44.4689	−1.73095
$661$	−22.3124	−0.867852	−0.433926	−	0.900949i	$-0.642872\pi$
$661$	−22.3124	−0.867852	−0.433926	+	0.900949i	$0.642872\pi$
$662$	−22.3005	−0.866735
$663$	7.20829	0.279947
$664$	−34.4650	−1.33750
$665$	24.7861	0.961162
$666$	22.5366	0.873275
$667$	−7.58576	−0.293722
$668$	−12.9952	−0.502801
$669$	42.9879	1.66201
$670$	110.761	4.27909
$671$	12.8259	0.495139
$672$	−34.7120	−1.33904
$673$	12.6503	0.487634	0.243817	−	0.969821i	$-0.421600\pi$
$673$	12.6503	0.487634	0.243817	+	0.969821i	$0.421600\pi$
$674$	−0.401332	−0.0154587
$675$	109.217	4.20377
$676$	−27.2043	−1.04632
$677$	−16.9413	−0.651108	−0.325554	−	0.945524i	$-0.605551\pi$
$677$	−16.9413	−0.651108	−0.325554	+	0.945524i	$0.605551\pi$
$678$	84.3510	3.23948
$679$	−44.4784	−1.70692
$680$	15.7608	0.604399
$681$	−69.1877	−2.65128
$682$	−21.9417	−0.840190
$683$	−43.1401	−1.65071	−0.825356	−	0.564613i	$-0.809025\pi$
$683$	−43.1401	−1.65071	−0.825356	+	0.564613i	$0.809025\pi$
$684$	−37.0024	−1.41482
$685$	61.1508	2.33645
$686$	11.2520	0.429603
$687$	−9.60458	−0.366438
$688$	−2.10639	−0.0803055
$689$	3.18633	0.121390
$690$	227.119	8.64626
$691$	36.3015	1.38098	0.690488	−	0.723344i	$-0.257396\pi$
$691$	36.3015	1.38098	0.690488	+	0.723344i	$0.257396\pi$
$692$	48.3635	1.83850
$693$	24.6248	0.935418
$694$	3.49841	0.132798
$695$	27.3594	1.03780
$696$	−11.6701	−0.442352
$697$	−3.86568	−0.146423
$698$	−8.24646	−0.312133
$699$	13.1300	0.496624
$700$	−154.414	−5.83631
$701$	33.0039	1.24654	0.623270	−	0.782007i	$-0.285804\pi$
$701$	33.0039	1.24654	0.623270	+	0.782007i	$0.285804\pi$
$702$	56.8546	2.14584
$703$	2.39753	0.0904245
$704$	11.1543	0.420395
$705$	−34.6111	−1.30353
$706$	47.9293	1.80384
$707$	−22.1542	−0.833195
$708$	22.5615	0.847915
$709$	22.8500	0.858148	0.429074	−	0.903269i	$-0.358840\pi$
$709$	22.8500	0.858148	0.429074	+	0.903269i	$0.358840\pi$
$710$	139.858	5.24876
$711$	−27.7413	−1.04038
$712$	−5.63896	−0.211329
$713$	72.5060	2.71537
$714$	−28.3324	−1.06031
$715$	9.38863	0.351115
$716$	5.42608	0.202782
$717$	−0.467090	−0.0174438
$718$	49.5521	1.84927
$719$	29.6910	1.10729	0.553643	−	0.832754i	$-0.313237\pi$
$719$	29.6910	1.10729	0.553643	+	0.832754i	$0.313237\pi$
$720$	52.8626	1.97007
$721$	−17.1955	−0.640393
$722$	39.1414	1.45669
$723$	71.6229	2.66368
$724$	−93.8936	−3.48953
$725$	10.4158	0.386833
$726$	−7.26423	−0.269601
$727$	−45.0486	−1.67076	−0.835380	−	0.549673i	$-0.814752\pi$
$727$	−45.0486	−1.67076	−0.835380	+	0.549673i	$0.814752\pi$
$728$	−36.5270	−1.35378
$729$	−17.3208	−0.641512
$730$	122.381	4.52951
$731$	1.00000	0.0369863
$732$	−143.488	−5.30346
$733$	−13.0921	−0.483568	−0.241784	−	0.970330i	$-0.577733\pi$
$733$	−13.0921	−0.483568	−0.241784	+	0.970330i	$0.577733\pi$
$734$	17.5596	0.648135
$735$	99.6182	3.67447
$736$	−22.9383	−0.845515
$737$	11.7066	0.431216
$738$	−58.0945	−2.13849
$739$	53.4062	1.96458	0.982290	−	0.187369i	$-0.0599959\pi$
$739$	53.4062	1.96458	0.982290	+	0.187369i	$0.0599959\pi$
$740$	−21.8512	−0.803267
$741$	11.5243	0.423357
$742$	−12.5240	−0.459769
$743$	10.2612	0.376446	0.188223	−	0.982126i	$-0.439727\pi$
$743$	10.2612	0.376446	0.188223	+	0.982126i	$0.439727\pi$
$744$	111.544	4.08941
$745$	−45.6677	−1.67314
$746$	−33.7715	−1.23646
$747$	54.8795	2.00793
$748$	3.66578	0.134034
$749$	−56.9440	−2.08069
$750$	−167.477	−6.11538
$751$	−40.3234	−1.47142	−0.735710	−	0.677296i	$-0.763152\pi$
$751$	−40.3234	−1.47142	−0.735710	+	0.677296i	$0.763152\pi$
$752$	−6.00988	−0.219158
$753$	46.5290	1.69561
$754$	5.42210	0.197461
$755$	−84.8316	−3.08734
$756$	−144.585	−5.25851
$757$	51.9570	1.88841	0.944204	−	0.329362i	$-0.106834\pi$
$757$	51.9570	1.88841	0.944204	+	0.329362i	$0.106834\pi$
$758$	−18.6496	−0.677382
$759$	24.0045	0.871309
$760$	25.1978	0.914019
$761$	−35.5671	−1.28931	−0.644653	−	0.764475i	$-0.722998\pi$
$761$	−35.5671	−1.28931	−0.644653	+	0.764475i	$0.722998\pi$
$762$	−48.3419	−1.75124
$763$	18.0361	0.652949
$764$	44.4374	1.60769
$765$	−25.0963	−0.907357
$766$	−5.59641	−0.202207
$767$	−4.76338	−0.171996
$768$	−82.4184	−2.97402
$769$	−33.3934	−1.20420	−0.602099	−	0.798421i	$-0.705669\pi$
$769$	−33.3934	−1.20420	−0.602099	+	0.798421i	$0.705669\pi$
$770$	−36.9023	−1.32987
$771$	62.2522	2.24196
$772$	−36.2848	−1.30592
$773$	50.8929	1.83049	0.915246	−	0.402895i	$-0.131996\pi$
$773$	50.8929	1.83049	0.915246	+	0.402895i	$0.131996\pi$
$774$	15.0283	0.540180
$775$	−99.5560	−3.57616
$776$	−45.2172	−1.62320
$777$	17.8497	0.640356
$778$	76.3828	2.73845
$779$	−6.18031	−0.221433
$780$	−105.034	−3.76081
$781$	14.7818	0.528933
$782$	−18.7225	−0.669515
$783$	9.75278	0.348536
$784$	17.2977	0.617776
$785$	81.0550	2.89298
$786$	−105.877	−3.77649
$787$	−45.8519	−1.63444	−0.817222	−	0.576323i	$-0.804487\pi$
$787$	−45.8519	−1.63444	−0.817222	+	0.576323i	$0.804487\pi$
$788$	9.96444	0.354968
$789$	−6.28305	−0.223682
$790$	41.5726	1.47909
$791$	45.2892	1.61030
$792$	25.0338	0.889538
$793$	30.2943	1.07578
$794$	75.4973	2.67930
$795$	−16.3647	−0.580396
$796$	−54.2215	−1.92183
$797$	20.4179	0.723238	0.361619	−	0.932326i	$-0.382224\pi$
$797$	20.4179	0.723238	0.361619	+	0.932326i	$0.382224\pi$
$798$	−45.2968	−1.60349
$799$	2.85316	0.100938
$800$	31.4959	1.11355
$801$	8.97904	0.317259
$802$	12.9188	0.456178
$803$	12.9346	0.456452
$804$	−130.965	−4.61878
$805$	121.943	4.29793
$806$	−51.8254	−1.82547
$807$	14.7833	0.520395
$808$	−22.5222	−0.792329
$809$	41.1287	1.44601	0.723004	−	0.690844i	$-0.242761\pi$
$809$	41.1287	1.44601	0.723004	+	0.690844i	$0.242761\pi$
$810$	−112.791	−3.96306
$811$	−46.5188	−1.63350	−0.816748	−	0.576995i	$-0.804225\pi$
$811$	−46.5188	−1.63350	−0.816748	+	0.576995i	$0.804225\pi$
$812$	−13.7888	−0.483891
$813$	37.1157	1.30170
$814$	−3.56951	−0.125111
$815$	−49.8149	−1.74494
$816$	−6.42834	−0.225037
$817$	1.59876	0.0559337
$818$	−37.3669	−1.30650
$819$	58.1627	2.03237
$820$	56.3277	1.96705
$821$	−5.67947	−0.198215	−0.0991074	−	0.995077i	$-0.531599\pi$
$821$	−5.67947	−0.198215	−0.0991074	+	0.995077i	$0.531599\pi$
$822$	−111.754	−3.89785
$823$	28.7627	1.00261	0.501303	−	0.865272i	$-0.332854\pi$
$823$	28.7627	1.00261	0.501303	+	0.865272i	$0.332854\pi$
$824$	−17.4811	−0.608983
$825$	−32.9600	−1.14752
$826$	18.7226	0.651442
$827$	43.1493	1.50045	0.750225	−	0.661183i	$-0.229945\pi$
$827$	43.1493	1.50045	0.750225	+	0.661183i	$0.229945\pi$
$828$	−182.045	−6.32651
$829$	9.70305	0.337001	0.168500	−	0.985702i	$-0.446108\pi$
$829$	9.70305	0.337001	0.168500	+	0.985702i	$0.446108\pi$
$830$	−82.2414	−2.85464
$831$	17.7062	0.614220
$832$	26.3461	0.913387
$833$	−8.21201	−0.284529
$834$	−49.9995	−1.73134
$835$	−14.0912	−0.487646
$836$	5.86072	0.202697
$837$	−93.2188	−3.22211
$838$	−37.8663	−1.30807
$839$	4.36840	0.150814	0.0754069	−	0.997153i	$-0.475974\pi$
$839$	4.36840	0.150814	0.0754069	+	0.997153i	$0.475974\pi$
$840$	187.599	6.47278
$841$	−28.0699	−0.967928
$842$	4.29589	0.148046
$843$	−47.8399	−1.64769
$844$	−72.8563	−2.50782
$845$	−29.4986	−1.01478
$846$	42.8781	1.47418
$847$	−3.90026	−0.134014
$848$	−2.84157	−0.0975798
$849$	−21.8122	−0.748593
$850$	25.7074	0.881755
$851$	11.7954	0.404341
$852$	−165.368	−5.66542
$853$	−41.9248	−1.43548	−0.717739	−	0.696313i	$-0.754823\pi$
$853$	−41.9248	−1.43548	−0.717739	+	0.696313i	$0.754823\pi$
$854$	−119.073	−4.07458
$855$	−40.1230	−1.37218
$856$	−57.8899	−1.97864
$857$	−39.5453	−1.35084	−0.675421	−	0.737432i	$-0.736038\pi$
$857$	−39.5453	−1.35084	−0.675421	+	0.737432i	$0.736038\pi$
$858$	−17.1578	−0.585758
$859$	−52.1191	−1.77828	−0.889140	−	0.457636i	$-0.848696\pi$
$859$	−52.1191	−1.77828	−0.889140	+	0.457636i	$0.848696\pi$
$860$	−14.5712	−0.496875
$861$	−46.0128	−1.56811
$862$	76.3543	2.60064
$863$	8.91404	0.303438	0.151719	−	0.988424i	$-0.451519\pi$
$863$	8.91404	0.303438	0.151719	+	0.988424i	$0.451519\pi$
$864$	29.4910	1.00331
$865$	52.4422	1.78309
$866$	−22.3437	−0.759271
$867$	3.05182	0.103645
$868$	131.795	4.47342
$869$	4.39387	0.149052
$870$	−27.8474	−0.944115
$871$	27.6504	0.936898
$872$	18.3357	0.620924
$873$	72.0004	2.43684
$874$	−29.9328	−1.01249
$875$	−89.9204	−3.03987
$876$	−144.704	−4.88908
$877$	−8.22514	−0.277743	−0.138872	−	0.990310i	$-0.544348\pi$
$877$	−8.22514	−0.277743	−0.138872	+	0.990310i	$0.544348\pi$
$878$	77.6475	2.62048
$879$	−33.9402	−1.14477
$880$	−8.37277	−0.282246
$881$	16.0690	0.541378	0.270689	−	0.962667i	$-0.412748\pi$
$881$	16.0690	0.541378	0.270689	+	0.962667i	$0.412748\pi$
$882$	−123.412	−4.15551
$883$	7.52160	0.253122	0.126561	−	0.991959i	$-0.459606\pi$
$883$	7.52160	0.253122	0.126561	+	0.991959i	$0.459606\pi$
$884$	8.65843	0.291215
$885$	24.4643	0.822357
$886$	−30.2590	−1.01657
$887$	−25.5521	−0.857954	−0.428977	−	0.903315i	$-0.641126\pi$
$887$	−25.5521	−0.857954	−0.428977	+	0.903315i	$0.641126\pi$
$888$	18.1462	0.608948
$889$	−25.9554	−0.870516
$890$	−13.4558	−0.451040
$891$	−11.9210	−0.399369
$892$	51.6361	1.72890
$893$	4.56153	0.152646
$894$	83.4582	2.79126
$895$	5.88369	0.196670
$896$	−80.8057	−2.69953
$897$	56.6977	1.89308
$898$	−48.3677	−1.61405
$899$	−8.89007	−0.296500
$900$	249.962	8.33205
$901$	1.34902	0.0449424
$902$	9.20144	0.306374
$903$	11.9029	0.396104
$904$	46.0414	1.53132
$905$	−101.812	−3.38435
$906$	155.031	5.15055
$907$	−5.17575	−0.171858	−0.0859290	−	0.996301i	$-0.527386\pi$
$907$	−5.17575	−0.171858	−0.0859290	+	0.996301i	$0.527386\pi$
$908$	−83.1067	−2.75799
$909$	35.8626	1.18949
$910$	−87.1617	−2.88938
$911$	−44.6776	−1.48024	−0.740118	−	0.672477i	$-0.765230\pi$
$911$	−44.6776	−1.48024	−0.740118	+	0.672477i	$0.765230\pi$
$912$	−10.2774	−0.340319
$913$	−8.69222	−0.287670
$914$	10.9909	0.363546
$915$	−155.589	−5.14360
$916$	−11.5368	−0.381187
$917$	−56.8465	−1.87724
$918$	24.0710	0.794460
$919$	23.1495	0.763632	0.381816	−	0.924238i	$-0.375299\pi$
$919$	23.1495	0.763632	0.381816	+	0.924238i	$0.375299\pi$
$920$	123.969	4.08712
$921$	42.9868	1.41646
$922$	−64.9286	−2.13831
$923$	34.9139	1.14921
$924$	43.6334	1.43543
$925$	−16.1960	−0.532520
$926$	−9.92290	−0.326087
$927$	27.8355	0.914239
$928$	2.81250	0.0923247
$929$	−32.7003	−1.07286	−0.536432	−	0.843944i	$-0.680228\pi$
$929$	−32.7003	−1.07286	−0.536432	+	0.843944i	$0.680228\pi$
$930$	266.170	8.72806
$931$	−13.1291	−0.430288
$932$	15.7715	0.516613
$933$	−77.8243	−2.54785
$934$	75.6535	2.47546
$935$	3.97493	0.129994
$936$	59.1289	1.93269
$937$	20.7841	0.678986	0.339493	−	0.940609i	$-0.389744\pi$
$937$	20.7841	0.678986	0.339493	+	0.940609i	$0.389744\pi$
$938$	−108.681	−3.54855
$939$	13.7592	0.449013
$940$	−41.5741	−1.35600
$941$	3.80983	0.124197	0.0620985	−	0.998070i	$-0.480221\pi$
$941$	3.80983	0.124197	0.0620985	+	0.998070i	$0.480221\pi$
$942$	−148.129	−4.82630
$943$	−30.4060	−0.990156
$944$	4.24798	0.138260
$945$	−156.778	−5.10000
$946$	−2.38029	−0.0773899
$947$	−7.08098	−0.230101	−0.115050	−	0.993360i	$-0.536703\pi$
$947$	−7.08098	−0.230101	−0.115050	+	0.993360i	$0.536703\pi$
$948$	−49.1556	−1.59650
$949$	30.5510	0.991728
$950$	41.1000	1.33346
$951$	43.4365	1.40853
$952$	−15.4647	−0.501214
$953$	18.6112	0.602874	0.301437	−	0.953486i	$-0.402534\pi$
$953$	18.6112	0.602874	0.301437	+	0.953486i	$0.402534\pi$
$954$	20.2735	0.656377
$955$	48.1850	1.55923
$956$	−0.561058	−0.0181459
$957$	−2.94323	−0.0951412
$958$	−12.5650	−0.405956
$959$	−60.0020	−1.93756
$960$	−135.311	−4.36714
$961$	53.9728	1.74106
$962$	−8.43105	−0.271828
$963$	92.1794	2.97044
$964$	86.0318	2.77090
$965$	−39.3448	−1.26655
$966$	−222.852	−7.17014
$967$	−5.20828	−0.167487	−0.0837435	−	0.996487i	$-0.526688\pi$
$967$	−5.20828	−0.167487	−0.0837435	+	0.996487i	$0.526688\pi$
$968$	−3.96504	−0.127441
$969$	4.87915	0.156741
$970$	−107.899	−3.46441
$971$	−27.7112	−0.889294	−0.444647	−	0.895706i	$-0.646671\pi$
$971$	−27.7112	−0.889294	−0.444647	+	0.895706i	$0.646671\pi$
$972$	22.1524	0.710539
$973$	−26.8454	−0.860623
$974$	−90.9961	−2.91570
$975$	−77.8502	−2.49320
$976$	−27.0164	−0.864774
$977$	41.0935	1.31470	0.657349	−	0.753586i	$-0.271678\pi$
$977$	41.0935	1.31470	0.657349	+	0.753586i	$0.271678\pi$
$978$	91.0371	2.91105
$979$	−1.42217	−0.0454527
$980$	119.659	3.82237
$981$	−29.1963	−0.932165
$982$	86.9953	2.77613
$983$	−28.8589	−0.920456	−0.460228	−	0.887801i	$-0.652232\pi$
$983$	−28.8589	−0.920456	−0.460228	+	0.887801i	$0.652232\pi$
$984$	−46.7771	−1.49120
$985$	10.8048	0.344269
$986$	2.29559	0.0731066
$987$	33.9609	1.08099
$988$	13.8428	0.440398
$989$	7.86563	0.250113
$990$	59.7364	1.89855
$991$	−21.6667	−0.688266	−0.344133	−	0.938921i	$-0.611827\pi$
$991$	−21.6667	−0.688266	−0.344133	+	0.938921i	$0.611827\pi$
$992$	−26.8823	−0.853514
$993$	28.5920	0.907341
$994$	−137.230	−4.35267
$995$	−58.7942	−1.86390
$996$	97.2426	3.08125
$997$	−26.4028	−0.836185	−0.418092	−	0.908405i	$-0.637301\pi$
$997$	−26.4028	−0.836185	−0.418092	+	0.908405i	$0.637301\pi$
$998$	−74.8562	−2.36953
$999$	−15.1650	−0.479800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.9	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.9	✓	74	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38029 q^{2} +3.05182 q^{3} +3.66578 q^{4} +3.97493 q^{5} -7.26423 q^{6} -3.90026 q^{7} -3.96504 q^{8} +6.31363 q^{9} +O(q^{10})\)	\(q-2.38029 q^{2} +3.05182 q^{3} +3.66578 q^{4} +3.97493 q^{5} -7.26423 q^{6} -3.90026 q^{7} -3.96504 q^{8} +6.31363 q^{9} -9.46150 q^{10} -1.00000 q^{11} +11.1873 q^{12} -2.36196 q^{13} +9.28375 q^{14} +12.1308 q^{15} +2.10639 q^{16} -1.00000 q^{17} -15.0283 q^{18} -1.59876 q^{19} +14.5712 q^{20} -11.9029 q^{21} +2.38029 q^{22} -7.86563 q^{23} -12.1006 q^{24} +10.8001 q^{25} +5.62215 q^{26} +10.1126 q^{27} -14.2975 q^{28} +0.964418 q^{29} -28.8748 q^{30} -9.21807 q^{31} +2.91626 q^{32} -3.05182 q^{33} +2.38029 q^{34} -15.5033 q^{35} +23.1444 q^{36} -1.49961 q^{37} +3.80552 q^{38} -7.20829 q^{39} -15.7608 q^{40} +3.86568 q^{41} +28.3324 q^{42} -1.00000 q^{43} -3.66578 q^{44} +25.0963 q^{45} +18.7225 q^{46} -2.85316 q^{47} +6.42834 q^{48} +8.21201 q^{49} -25.7074 q^{50} -3.05182 q^{51} -8.65843 q^{52} -1.34902 q^{53} -24.0710 q^{54} -3.97493 q^{55} +15.4647 q^{56} -4.87915 q^{57} -2.29559 q^{58} +2.01671 q^{59} +44.4689 q^{60} -12.8259 q^{61} +21.9417 q^{62} -24.6248 q^{63} -11.1543 q^{64} -9.38863 q^{65} +7.26423 q^{66} -11.7066 q^{67} -3.66578 q^{68} -24.0045 q^{69} +36.9023 q^{70} -14.7818 q^{71} -25.0338 q^{72} -12.9346 q^{73} +3.56951 q^{74} +32.9600 q^{75} -5.86072 q^{76} +3.90026 q^{77} +17.1578 q^{78} -4.39387 q^{79} +8.37277 q^{80} +11.9210 q^{81} -9.20144 q^{82} +8.69222 q^{83} -43.6334 q^{84} -3.97493 q^{85} +2.38029 q^{86} +2.94323 q^{87} +3.96504 q^{88} +1.42217 q^{89} -59.7364 q^{90} +9.21225 q^{91} -28.8337 q^{92} -28.1319 q^{93} +6.79135 q^{94} -6.35498 q^{95} +8.89992 q^{96} +11.4040 q^{97} -19.5470 q^{98} -6.31363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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