LMFDB - Embedded newform 8007.2.a.j.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.155256 q^{2} -1.00000 q^{3} -1.97590 q^{4} +3.70882 q^{5} -0.155256 q^{6} -1.29990 q^{7} -0.617281 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.155256 q^{2} -1.00000 q^{3} -1.97590 q^{4} +3.70882 q^{5} -0.155256 q^{6} -1.29990 q^{7} -0.617281 q^{8} +1.00000 q^{9} +0.575816 q^{10} +3.80325 q^{11} +1.97590 q^{12} +3.05302 q^{13} -0.201816 q^{14} -3.70882 q^{15} +3.85595 q^{16} +1.00000 q^{17} +0.155256 q^{18} +5.56516 q^{19} -7.32824 q^{20} +1.29990 q^{21} +0.590477 q^{22} +0.778480 q^{23} +0.617281 q^{24} +8.75533 q^{25} +0.473999 q^{26} -1.00000 q^{27} +2.56846 q^{28} -0.455768 q^{29} -0.575816 q^{30} +5.94445 q^{31} +1.83322 q^{32} -3.80325 q^{33} +0.155256 q^{34} -4.82108 q^{35} -1.97590 q^{36} +11.4902 q^{37} +0.864023 q^{38} -3.05302 q^{39} -2.28938 q^{40} +7.33432 q^{41} +0.201816 q^{42} +0.414049 q^{43} -7.51483 q^{44} +3.70882 q^{45} +0.120863 q^{46} -10.8019 q^{47} -3.85595 q^{48} -5.31027 q^{49} +1.35932 q^{50} -1.00000 q^{51} -6.03244 q^{52} +0.171533 q^{53} -0.155256 q^{54} +14.1056 q^{55} +0.802401 q^{56} -5.56516 q^{57} -0.0707606 q^{58} -5.06219 q^{59} +7.32824 q^{60} +7.57758 q^{61} +0.922911 q^{62} -1.29990 q^{63} -7.42729 q^{64} +11.3231 q^{65} -0.590477 q^{66} -3.33818 q^{67} -1.97590 q^{68} -0.778480 q^{69} -0.748501 q^{70} +2.79902 q^{71} -0.617281 q^{72} +9.64299 q^{73} +1.78392 q^{74} -8.75533 q^{75} -10.9962 q^{76} -4.94383 q^{77} -0.473999 q^{78} -2.17205 q^{79} +14.3010 q^{80} +1.00000 q^{81} +1.13870 q^{82} -10.4145 q^{83} -2.56846 q^{84} +3.70882 q^{85} +0.0642835 q^{86} +0.455768 q^{87} -2.34767 q^{88} -4.51339 q^{89} +0.575816 q^{90} -3.96861 q^{91} -1.53819 q^{92} -5.94445 q^{93} -1.67705 q^{94} +20.6402 q^{95} -1.83322 q^{96} -17.5238 q^{97} -0.824450 q^{98} +3.80325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	0.155256	0.109782	0.0548912	−	0.998492i	$-0.482519\pi$
$2$	0.155256	0.109782	0.0548912	+	0.998492i	$0.482519\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97590	−0.987948
$5$	3.70882	1.65863	0.829317	−	0.558778i	$-0.188730\pi$
$5$	3.70882	1.65863	0.829317	+	0.558778i	$0.188730\pi$
$6$	−0.155256	−0.0633829
$7$	−1.29990	−0.491315	−0.245657	−	0.969357i	$-0.579004\pi$
$7$	−1.29990	−0.491315	−0.245657	+	0.969357i	$0.579004\pi$
$8$	−0.617281	−0.218242
$9$	1.00000	0.333333
$10$	0.575816	0.182089
$11$	3.80325	1.14672	0.573362	−	0.819302i	$-0.305639\pi$
$11$	3.80325	1.14672	0.573362	+	0.819302i	$0.305639\pi$
$12$	1.97590	0.570392
$13$	3.05302	0.846754	0.423377	−	0.905953i	$-0.360844\pi$
$13$	3.05302	0.846754	0.423377	+	0.905953i	$0.360844\pi$
$14$	−0.201816	−0.0539377
$15$	−3.70882	−0.957613
$16$	3.85595	0.963989
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.155256	0.0365941
$19$	5.56516	1.27673	0.638367	−	0.769732i	$-0.279610\pi$
$19$	5.56516	1.27673	0.638367	+	0.769732i	$0.279610\pi$
$20$	−7.32824	−1.63864
$21$	1.29990	0.283661
$22$	0.590477	0.125890
$23$	0.778480	0.162324	0.0811621	−	0.996701i	$-0.474137\pi$
$23$	0.778480	0.162324	0.0811621	+	0.996701i	$0.474137\pi$
$24$	0.617281	0.126002
$25$	8.75533	1.75107
$26$	0.473999	0.0929588
$27$	−1.00000	−0.192450
$28$	2.56846	0.485393
$29$	−0.455768	−0.0846339	−0.0423170	−	0.999104i	$-0.513474\pi$
$29$	−0.455768	−0.0846339	−0.0423170	+	0.999104i	$0.513474\pi$
$30$	−0.575816	−0.105129
$31$	5.94445	1.06766	0.533828	−	0.845593i	$-0.320753\pi$
$31$	5.94445	1.06766	0.533828	+	0.845593i	$0.320753\pi$
$32$	1.83322	0.324071
$33$	−3.80325	−0.662061
$34$	0.155256	0.0266261
$35$	−4.82108	−0.814911
$36$	−1.97590	−0.329316
$37$	11.4902	1.88898	0.944489	−	0.328542i	$-0.106557\pi$
$37$	11.4902	1.88898	0.944489	+	0.328542i	$0.106557\pi$
$38$	0.864023	0.140163
$39$	−3.05302	−0.488874
$40$	−2.28938	−0.361983
$41$	7.33432	1.14543	0.572714	−	0.819755i	$-0.305890\pi$
$41$	7.33432	1.14543	0.572714	+	0.819755i	$0.305890\pi$
$42$	0.201816	0.0311410
$43$	0.414049	0.0631419	0.0315710	−	0.999502i	$-0.489949\pi$
$43$	0.414049	0.0631419	0.0315710	+	0.999502i	$0.489949\pi$
$44$	−7.51483	−1.13290
$45$	3.70882	0.552878
$46$	0.120863	0.0178203
$47$	−10.8019	−1.57561	−0.787806	−	0.615923i	$-0.788783\pi$
$47$	−10.8019	−1.57561	−0.787806	+	0.615923i	$0.788783\pi$
$48$	−3.85595	−0.556559
$49$	−5.31027	−0.758610
$50$	1.35932	0.192236
$51$	−1.00000	−0.140028
$52$	−6.03244	−0.836549
$53$	0.171533	0.0235618	0.0117809	−	0.999931i	$-0.496250\pi$
$53$	0.171533	0.0235618	0.0117809	+	0.999931i	$0.496250\pi$
$54$	−0.155256	−0.0211276
$55$	14.1056	1.90199
$56$	0.802401	0.107225
$57$	−5.56516	−0.737123
$58$	−0.0707606	−0.00929132
$59$	−5.06219	−0.659041	−0.329520	−	0.944148i	$-0.606887\pi$
$59$	−5.06219	−0.659041	−0.329520	+	0.944148i	$0.606887\pi$
$60$	7.32824	0.946071
$61$	7.57758	0.970210	0.485105	−	0.874456i	$-0.338781\pi$
$61$	7.57758	0.970210	0.485105	+	0.874456i	$0.338781\pi$
$62$	0.922911	0.117210
$63$	−1.29990	−0.163772
$64$	−7.42729	−0.928411
$65$	11.3231	1.40446
$66$	−0.590477	−0.0726827
$67$	−3.33818	−0.407824	−0.203912	−	0.978989i	$-0.565366\pi$
$67$	−3.33818	−0.407824	−0.203912	+	0.978989i	$0.565366\pi$
$68$	−1.97590	−0.239613
$69$	−0.778480	−0.0937179
$70$	−0.748501	−0.0894629
$71$	2.79902	0.332183	0.166091	−	0.986110i	$-0.446885\pi$
$71$	2.79902	0.332183	0.166091	+	0.986110i	$0.446885\pi$
$72$	−0.617281	−0.0727472
$73$	9.64299	1.12863	0.564314	−	0.825561i	$-0.309141\pi$
$73$	9.64299	1.12863	0.564314	+	0.825561i	$0.309141\pi$
$74$	1.78392	0.207377
$75$	−8.75533	−1.01098
$76$	−10.9962	−1.26135
$77$	−4.94383	−0.563402
$78$	−0.473999	−0.0536698
$79$	−2.17205	−0.244375	−0.122187	−	0.992507i	$-0.538991\pi$
$79$	−2.17205	−0.244375	−0.122187	+	0.992507i	$0.538991\pi$
$80$	14.3010	1.59890
$81$	1.00000	0.111111
$82$	1.13870	0.125748
$83$	−10.4145	−1.14314	−0.571570	−	0.820553i	$-0.693665\pi$
$83$	−10.4145	−1.14314	−0.571570	+	0.820553i	$0.693665\pi$
$84$	−2.56846	−0.280242
$85$	3.70882	0.402278
$86$	0.0642835	0.00693187
$87$	0.455768	0.0488634
$88$	−2.34767	−0.250263
$89$	−4.51339	−0.478419	−0.239209	−	0.970968i	$-0.576888\pi$
$89$	−4.51339	−0.478419	−0.239209	+	0.970968i	$0.576888\pi$
$90$	0.575816	0.0606963
$91$	−3.96861	−0.416023
$92$	−1.53819	−0.160368
$93$	−5.94445	−0.616411
$94$	−1.67705	−0.172975
$95$	20.6402	2.11764
$96$	−1.83322	−0.187102
$97$	−17.5238	−1.77927	−0.889635	−	0.456672i	$-0.849041\pi$
$97$	−17.5238	−1.77927	−0.889635	+	0.456672i	$0.849041\pi$
$98$	−0.824450	−0.0832820
$99$	3.80325	0.382241
$100$	−17.2996	−1.72996
$101$	−14.9832	−1.49088	−0.745440	−	0.666573i	$-0.767760\pi$
$101$	−14.9832	−1.49088	−0.745440	+	0.666573i	$0.767760\pi$
$102$	−0.155256	−0.0153726
$103$	13.6762	1.34755	0.673777	−	0.738934i	$-0.264671\pi$
$103$	13.6762	1.34755	0.673777	+	0.738934i	$0.264671\pi$
$104$	−1.88457	−0.184797
$105$	4.82108	0.470489
$106$	0.0266314	0.00258667
$107$	14.4764	1.39948	0.699742	−	0.714396i	$-0.253298\pi$
$107$	14.4764	1.39948	0.699742	+	0.714396i	$0.253298\pi$
$108$	1.97590	0.190131
$109$	13.2387	1.26804	0.634020	−	0.773317i	$-0.281404\pi$
$109$	13.2387	1.26804	0.634020	+	0.773317i	$0.281404\pi$
$110$	2.18997	0.208806
$111$	−11.4902	−1.09060
$112$	−5.01234	−0.473622
$113$	0.526233	0.0495039	0.0247519	−	0.999694i	$-0.492120\pi$
$113$	0.526233	0.0495039	0.0247519	+	0.999694i	$0.492120\pi$
$114$	−0.864023	−0.0809232
$115$	2.88724	0.269237
$116$	0.900549	0.0836139
$117$	3.05302	0.282251
$118$	−0.785934	−0.0723511
$119$	−1.29990	−0.119161
$120$	2.28938	0.208991
$121$	3.46472	0.314974
$122$	1.17646	0.106512
$123$	−7.33432	−0.661314
$124$	−11.7456	−1.05479
$125$	13.9279	1.24574
$126$	−0.201816	−0.0179792
$127$	−9.27851	−0.823334	−0.411667	−	0.911334i	$-0.635053\pi$
$127$	−9.27851	−0.823334	−0.411667	+	0.911334i	$0.635053\pi$
$128$	−4.81957	−0.425994
$129$	−0.414049	−0.0364550
$130$	1.75797	0.154185
$131$	5.40972	0.472650	0.236325	−	0.971674i	$-0.424057\pi$
$131$	5.40972	0.472650	0.236325	+	0.971674i	$0.424057\pi$
$132$	7.51483	0.654082
$133$	−7.23413	−0.627279
$134$	−0.518272	−0.0447719
$135$	−3.70882	−0.319204
$136$	−0.617281	−0.0529314
$137$	4.08578	0.349072	0.174536	−	0.984651i	$-0.444157\pi$
$137$	4.08578	0.349072	0.174536	+	0.984651i	$0.444157\pi$
$138$	−0.120863	−0.0102886
$139$	−22.6926	−1.92476	−0.962380	−	0.271707i	$-0.912412\pi$
$139$	−22.6926	−1.92476	−0.962380	+	0.271707i	$0.912412\pi$
$140$	9.52595	0.805090
$141$	10.8019	0.909680
$142$	0.434564	0.0364678
$143$	11.6114	0.970993
$144$	3.85595	0.321330
$145$	−1.69036	−0.140377
$146$	1.49713	0.123903
$147$	5.31027	0.437984
$148$	−22.7035	−1.86621
$149$	−7.37705	−0.604351	−0.302176	−	0.953252i	$-0.597713\pi$
$149$	−7.37705	−0.604351	−0.302176	+	0.953252i	$0.597713\pi$
$150$	−1.35932	−0.110988
$151$	13.5865	1.10566	0.552828	−	0.833295i	$-0.313549\pi$
$151$	13.5865	1.10566	0.552828	+	0.833295i	$0.313549\pi$
$152$	−3.43527	−0.278637
$153$	1.00000	0.0808452
$154$	−0.767559	−0.0618516
$155$	22.0469	1.77085
$156$	6.03244	0.482982
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−0.337224	−0.0268281
$159$	−0.171533	−0.0136034
$160$	6.79908	0.537515
$161$	−1.01194	−0.0797523
$162$	0.155256	0.0121980
$163$	12.4097	0.972002	0.486001	−	0.873958i	$-0.338455\pi$
$163$	12.4097	0.972002	0.486001	+	0.873958i	$0.338455\pi$
$164$	−14.4919	−1.13162
$165$	−14.1056	−1.09812
$166$	−1.61691	−0.125497
$167$	−21.5819	−1.67006	−0.835030	−	0.550204i	$-0.814550\pi$
$167$	−21.5819	−1.67006	−0.835030	+	0.550204i	$0.814550\pi$
$168$	−0.802401	−0.0619066
$169$	−3.67909	−0.283007
$170$	0.575816	0.0441630
$171$	5.56516	0.425578
$172$	−0.818118	−0.0623809
$173$	12.7193	0.967033	0.483517	−	0.875335i	$-0.339359\pi$
$173$	12.7193	0.967033	0.483517	+	0.875335i	$0.339359\pi$
$174$	0.0707606	0.00536435
$175$	−11.3810	−0.860325
$176$	14.6652	1.10543
$177$	5.06219	0.380497
$178$	−0.700730	−0.0525219
$179$	0.553339	0.0413585	0.0206793	−	0.999786i	$-0.493417\pi$
$179$	0.553339	0.0413585	0.0206793	+	0.999786i	$0.493417\pi$
$180$	−7.32824	−0.546215
$181$	−23.9147	−1.77757	−0.888783	−	0.458328i	$-0.848449\pi$
$181$	−23.9147	−1.77757	−0.888783	+	0.458328i	$0.848449\pi$
$182$	−0.616149	−0.0456720
$183$	−7.57758	−0.560151
$184$	−0.480541	−0.0354259
$185$	42.6151	3.13312
$186$	−0.922911	−0.0676711
$187$	3.80325	0.278121
$188$	21.3433	1.55662
$189$	1.29990	0.0945536
$190$	3.20450	0.232479
$191$	−22.9607	−1.66137	−0.830687	−	0.556739i	$-0.812052\pi$
$191$	−22.9607	−1.66137	−0.830687	+	0.556739i	$0.812052\pi$
$192$	7.42729	0.536019
$193$	12.8669	0.926177	0.463089	−	0.886312i	$-0.346741\pi$
$193$	12.8669	0.926177	0.463089	+	0.886312i	$0.346741\pi$
$194$	−2.72067	−0.195333
$195$	−11.3231	−0.810863
$196$	10.4925	0.749467
$197$	12.3254	0.878152	0.439076	−	0.898450i	$-0.355306\pi$
$197$	12.3254	0.878152	0.439076	+	0.898450i	$0.355306\pi$
$198$	0.590477	0.0419634
$199$	−5.77538	−0.409406	−0.204703	−	0.978824i	$-0.565623\pi$
$199$	−5.77538	−0.409406	−0.204703	+	0.978824i	$0.565623\pi$
$200$	−5.40450	−0.382156
$201$	3.33818	0.235457
$202$	−2.32622	−0.163672
$203$	0.592451	0.0415819
$204$	1.97590	0.138340
$205$	27.2017	1.89985
$206$	2.12331	0.147938
$207$	0.778480	0.0541081
$208$	11.7723	0.816262
$209$	21.1657	1.46406
$210$	0.748501	0.0516515
$211$	−5.50464	−0.378955	−0.189478	−	0.981885i	$-0.560679\pi$
$211$	−5.50464	−0.378955	−0.189478	+	0.981885i	$0.560679\pi$
$212$	−0.338931	−0.0232779
$213$	−2.79902	−0.191786
$214$	2.24754	0.153639
$215$	1.53563	0.104729
$216$	0.617281	0.0420006
$217$	−7.72718	−0.524555
$218$	2.05539	0.139208
$219$	−9.64299	−0.651613
$220$	−27.8711	−1.87907
$221$	3.05302	0.205368
$222$	−1.78392	−0.119729
$223$	−5.89795	−0.394956	−0.197478	−	0.980307i	$-0.563275\pi$
$223$	−5.89795	−0.394956	−0.197478	+	0.980307i	$0.563275\pi$
$224$	−2.38300	−0.159221
$225$	8.75533	0.583689
$226$	0.0817007	0.00543465
$227$	−6.34324	−0.421015	−0.210508	−	0.977592i	$-0.567512\pi$
$227$	−6.34324	−0.421015	−0.210508	+	0.977592i	$0.567512\pi$
$228$	10.9962	0.728239
$229$	−0.402959	−0.0266283	−0.0133142	−	0.999911i	$-0.504238\pi$
$229$	−0.402959	−0.0266283	−0.0133142	+	0.999911i	$0.504238\pi$
$230$	0.448261	0.0295574
$231$	4.94383	0.325280
$232$	0.281337	0.0184707
$233$	11.6527	0.763391	0.381696	−	0.924288i	$-0.375340\pi$
$233$	11.6527	0.763391	0.381696	+	0.924288i	$0.375340\pi$
$234$	0.473999	0.0309863
$235$	−40.0621	−2.61336
$236$	10.0024	0.651098
$237$	2.17205	0.141090
$238$	−0.201816	−0.0130818
$239$	−10.6423	−0.688393	−0.344196	−	0.938898i	$-0.611849\pi$
$239$	−10.6423	−0.688393	−0.344196	+	0.938898i	$0.611849\pi$
$240$	−14.3010	−0.923128
$241$	−9.48537	−0.611006	−0.305503	−	0.952191i	$-0.598825\pi$
$241$	−9.48537	−0.611006	−0.305503	+	0.952191i	$0.598825\pi$
$242$	0.537918	0.0345786
$243$	−1.00000	−0.0641500
$244$	−14.9725	−0.958517
$245$	−19.6948	−1.25826
$246$	−1.13870	−0.0726006
$247$	16.9905	1.08108
$248$	−3.66940	−0.233007
$249$	10.4145	0.659992
$250$	2.16238	0.136761
$251$	7.56217	0.477320	0.238660	−	0.971103i	$-0.423292\pi$
$251$	7.56217	0.477320	0.238660	+	0.971103i	$0.423292\pi$
$252$	2.56846	0.161798
$253$	2.96075	0.186141
$254$	−1.44054	−0.0903876
$255$	−3.70882	−0.232255
$256$	14.1063	0.881645
$257$	−14.3244	−0.893533	−0.446767	−	0.894651i	$-0.647425\pi$
$257$	−14.3244	−0.893533	−0.446767	+	0.894651i	$0.647425\pi$
$258$	−0.0642835	−0.00400212
$259$	−14.9361	−0.928083
$260$	−22.3732	−1.38753
$261$	−0.455768	−0.0282113
$262$	0.839891	0.0518886
$263$	19.2080	1.18441	0.592207	−	0.805786i	$-0.298257\pi$
$263$	19.2080	1.18441	0.592207	+	0.805786i	$0.298257\pi$
$264$	2.34767	0.144489
$265$	0.636184	0.0390805
$266$	−1.12314	−0.0688642
$267$	4.51339	0.276215
$268$	6.59590	0.402909
$269$	19.6982	1.20102	0.600510	−	0.799617i	$-0.294964\pi$
$269$	19.6982	1.20102	0.600510	+	0.799617i	$0.294964\pi$
$270$	−0.575816	−0.0350430
$271$	1.99651	0.121280	0.0606398	−	0.998160i	$-0.480686\pi$
$271$	1.99651	0.121280	0.0606398	+	0.998160i	$0.480686\pi$
$272$	3.85595	0.233802
$273$	3.96861	0.240191
$274$	0.634341	0.0383219
$275$	33.2987	2.00799
$276$	1.53819	0.0925884
$277$	4.42201	0.265693	0.132846	−	0.991137i	$-0.457588\pi$
$277$	4.42201	0.265693	0.132846	+	0.991137i	$0.457588\pi$
$278$	−3.52316	−0.211305
$279$	5.94445	0.355885
$280$	2.97596	0.177848
$281$	−22.5138	−1.34306	−0.671532	−	0.740976i	$-0.734363\pi$
$281$	−22.5138	−1.34306	−0.671532	+	0.740976i	$0.734363\pi$
$282$	1.67705	0.0998669
$283$	−32.2921	−1.91956	−0.959782	−	0.280747i	$-0.909418\pi$
$283$	−32.2921	−1.91956	−0.959782	+	0.280747i	$0.909418\pi$
$284$	−5.53057	−0.328179
$285$	−20.6402	−1.22262
$286$	1.80274	0.106598
$287$	−9.53386	−0.562766
$288$	1.83322	0.108024
$289$	1.00000	0.0588235
$290$	−0.262438	−0.0154109
$291$	17.5238	1.02726
$292$	−19.0535	−1.11502
$293$	9.34148	0.545735	0.272868	−	0.962052i	$-0.412028\pi$
$293$	9.34148	0.545735	0.272868	+	0.962052i	$0.412028\pi$
$294$	0.824450	0.0480829
$295$	−18.7747	−1.09311
$296$	−7.09269	−0.412254
$297$	−3.80325	−0.220687
$298$	−1.14533	−0.0663471
$299$	2.37671	0.137449
$300$	17.2996	0.998794
$301$	−0.538221	−0.0310226
$302$	2.10939	0.121382
$303$	14.9832	0.860760
$304$	21.4590	1.23076
$305$	28.1039	1.60922
$306$	0.155256	0.00887538
$307$	−4.23640	−0.241784	−0.120892	−	0.992666i	$-0.538575\pi$
$307$	−4.23640	−0.241784	−0.120892	+	0.992666i	$0.538575\pi$
$308$	9.76850	0.556612
$309$	−13.6762	−0.778011
$310$	3.42291	0.194408
$311$	18.9858	1.07659	0.538294	−	0.842757i	$-0.319069\pi$
$311$	18.9858	1.07659	0.538294	+	0.842757i	$0.319069\pi$
$312$	1.88457	0.106693
$313$	13.7011	0.774433	0.387217	−	0.921989i	$-0.373437\pi$
$313$	13.7011	0.774433	0.387217	+	0.921989i	$0.373437\pi$
$314$	−0.155256	−0.00876159
$315$	−4.82108	−0.271637
$316$	4.29175	0.241430
$317$	13.9398	0.782937	0.391469	−	0.920191i	$-0.371967\pi$
$317$	13.9398	0.782937	0.391469	+	0.920191i	$0.371967\pi$
$318$	−0.0266314	−0.00149342
$319$	−1.73340	−0.0970517
$320$	−27.5465	−1.53989
$321$	−14.4764	−0.807993
$322$	−0.157110	−0.00875540
$323$	5.56516	0.309654
$324$	−1.97590	−0.109772
$325$	26.7302	1.48272
$326$	1.92668	0.106709
$327$	−13.2387	−0.732103
$328$	−4.52734	−0.249980
$329$	14.0413	0.774122
$330$	−2.18997	−0.120554
$331$	−4.77922	−0.262690	−0.131345	−	0.991337i	$-0.541930\pi$
$331$	−4.77922	−0.262690	−0.131345	+	0.991337i	$0.541930\pi$
$332$	20.5780	1.12936
$333$	11.4902	0.629660
$334$	−3.35072	−0.183343
$335$	−12.3807	−0.676431
$336$	5.01234	0.273446
$337$	17.6179	0.959709	0.479854	−	0.877348i	$-0.340689\pi$
$337$	17.6179	0.959709	0.479854	+	0.877348i	$0.340689\pi$
$338$	−0.571200	−0.0310692
$339$	−0.526233	−0.0285811
$340$	−7.32824	−0.397430
$341$	22.6083	1.22431
$342$	0.864023	0.0467210
$343$	16.0021	0.864031
$344$	−0.255585	−0.0137802
$345$	−2.88724	−0.155444
$346$	1.97475	0.106163
$347$	−25.8145	−1.38580	−0.692898	−	0.721036i	$-0.743666\pi$
$347$	−25.8145	−1.38580	−0.692898	+	0.721036i	$0.743666\pi$
$348$	−0.900549	−0.0482745
$349$	9.91434	0.530703	0.265351	−	0.964152i	$-0.414512\pi$
$349$	9.91434	0.530703	0.265351	+	0.964152i	$0.414512\pi$
$350$	−1.76697	−0.0944486
$351$	−3.05302	−0.162958
$352$	6.97220	0.371619
$353$	−28.2675	−1.50453	−0.752263	−	0.658863i	$-0.771038\pi$
$353$	−28.2675	−1.50453	−0.752263	+	0.658863i	$0.771038\pi$
$354$	0.785934	0.0417719
$355$	10.3811	0.550969
$356$	8.91799	0.472653
$357$	1.29990	0.0687978
$358$	0.0859091	0.00454044
$359$	−6.70303	−0.353772	−0.176886	−	0.984231i	$-0.556602\pi$
$359$	−6.70303	−0.353772	−0.176886	+	0.984231i	$0.556602\pi$
$360$	−2.28938	−0.120661
$361$	11.9710	0.630052
$362$	−3.71290	−0.195146
$363$	−3.46472	−0.181851
$364$	7.84155	0.411009
$365$	35.7641	1.87198
$366$	−1.17646	−0.0614947
$367$	19.8792	1.03768	0.518842	−	0.854870i	$-0.326363\pi$
$367$	19.8792	1.03768	0.518842	+	0.854870i	$0.326363\pi$
$368$	3.00178	0.156479
$369$	7.33432	0.381810
$370$	6.61624	0.343962
$371$	−0.222975	−0.0115763
$372$	11.7456	0.608982
$373$	11.3521	0.587788	0.293894	−	0.955838i	$-0.405049\pi$
$373$	11.3521	0.587788	0.293894	+	0.955838i	$0.405049\pi$
$374$	0.590477	0.0305328
$375$	−13.9279	−0.719231
$376$	6.66778	0.343864
$377$	−1.39147	−0.0716642
$378$	0.201816	0.0103803
$379$	−35.9307	−1.84563	−0.922817	−	0.385238i	$-0.874119\pi$
$379$	−35.9307	−1.84563	−0.922817	+	0.385238i	$0.874119\pi$
$380$	−40.7828	−2.09211
$381$	9.27851	0.475352
$382$	−3.56478	−0.182390
$383$	26.1200	1.33467	0.667334	−	0.744758i	$-0.267435\pi$
$383$	26.1200	1.33467	0.667334	+	0.744758i	$0.267435\pi$
$384$	4.81957	0.245948
$385$	−18.3358	−0.934478
$386$	1.99765	0.101678
$387$	0.414049	0.0210473
$388$	34.6252	1.75783
$389$	−11.6813	−0.592266	−0.296133	−	0.955147i	$-0.595697\pi$
$389$	−11.6813	−0.592266	−0.296133	+	0.955147i	$0.595697\pi$
$390$	−1.75797	−0.0890185
$391$	0.778480	0.0393694
$392$	3.27793	0.165560
$393$	−5.40972	−0.272885
$394$	1.91360	0.0964056
$395$	−8.05575	−0.405329
$396$	−7.51483	−0.377634
$397$	33.7901	1.69587	0.847937	−	0.530097i	$-0.177844\pi$
$397$	33.7901	1.69587	0.847937	+	0.530097i	$0.177844\pi$
$398$	−0.896661	−0.0449455
$399$	7.23413	0.362160
$400$	33.7602	1.68801
$401$	16.2156	0.809767	0.404883	−	0.914368i	$-0.367312\pi$
$401$	16.2156	0.809767	0.404883	+	0.914368i	$0.367312\pi$
$402$	0.518272	0.0258491
$403$	18.1485	0.904042
$404$	29.6051	1.47291
$405$	3.70882	0.184293
$406$	0.0919814	0.00456496
$407$	43.7001	2.16614
$408$	0.617281	0.0305600
$409$	−15.9568	−0.789014	−0.394507	−	0.918893i	$-0.629085\pi$
$409$	−15.9568	−0.789014	−0.394507	+	0.918893i	$0.629085\pi$
$410$	4.22322	0.208570
$411$	−4.08578	−0.201537
$412$	−27.0227	−1.33131
$413$	6.58032	0.323796
$414$	0.120863	0.00594012
$415$	−38.6255	−1.89605
$416$	5.59685	0.274408
$417$	22.6926	1.11126
$418$	3.28610	0.160728
$419$	15.9688	0.780126	0.390063	−	0.920788i	$-0.372453\pi$
$419$	15.9688	0.780126	0.390063	+	0.920788i	$0.372453\pi$
$420$	−9.52595	−0.464819
$421$	19.8657	0.968197	0.484098	−	0.875014i	$-0.339148\pi$
$421$	19.8657	0.968197	0.484098	+	0.875014i	$0.339148\pi$
$422$	−0.854627	−0.0416026
$423$	−10.8019	−0.525204
$424$	−0.105884	−0.00514217
$425$	8.75533	0.424696
$426$	−0.434564	−0.0210547
$427$	−9.85007	−0.476678
$428$	−28.6038	−1.38262
$429$	−11.6114	−0.560603
$430$	0.238416	0.0114974
$431$	9.72186	0.468286	0.234143	−	0.972202i	$-0.424772\pi$
$431$	9.72186	0.468286	0.234143	+	0.972202i	$0.424772\pi$
$432$	−3.85595	−0.185520
$433$	13.6125	0.654176	0.327088	−	0.944994i	$-0.393933\pi$
$433$	13.6125	0.654176	0.327088	+	0.944994i	$0.393933\pi$
$434$	−1.19969	−0.0575869
$435$	1.69036	0.0810465
$436$	−26.1583	−1.25276
$437$	4.33236	0.207245
$438$	−1.49713	−0.0715357
$439$	19.6195	0.936387	0.468194	−	0.883626i	$-0.344905\pi$
$439$	19.6195	0.936387	0.468194	+	0.883626i	$0.344905\pi$
$440$	−8.70710	−0.415095
$441$	−5.31027	−0.252870
$442$	0.473999	0.0225458
$443$	37.7156	1.79192	0.895961	−	0.444132i	$-0.146488\pi$
$443$	37.7156	1.79192	0.895961	+	0.444132i	$0.146488\pi$
$444$	22.7035	1.07746
$445$	−16.7393	−0.793521
$446$	−0.915690	−0.0433592
$447$	7.37705	0.348922
$448$	9.65471	0.456142
$449$	−11.4577	−0.540723	−0.270361	−	0.962759i	$-0.587143\pi$
$449$	−11.4577	−0.540723	−0.270361	+	0.962759i	$0.587143\pi$
$450$	1.35932	0.0640788
$451$	27.8943	1.31349
$452$	−1.03978	−0.0489072
$453$	−13.5865	−0.638351
$454$	−0.984824	−0.0462201
$455$	−14.7188	−0.690030
$456$	3.43527	0.160871
$457$	22.1355	1.03545	0.517727	−	0.855546i	$-0.326778\pi$
$457$	22.1355	1.03545	0.517727	+	0.855546i	$0.326778\pi$
$458$	−0.0625618	−0.00292332
$459$	−1.00000	−0.0466760
$460$	−5.70488	−0.265992
$461$	−32.5091	−1.51410	−0.757049	−	0.653358i	$-0.773360\pi$
$461$	−32.5091	−1.51410	−0.757049	+	0.653358i	$0.773360\pi$
$462$	0.767559	0.0357101
$463$	−31.7137	−1.47386	−0.736931	−	0.675968i	$-0.763726\pi$
$463$	−31.7137	−1.47386	−0.736931	+	0.675968i	$0.763726\pi$
$464$	−1.75742	−0.0815862
$465$	−22.0469	−1.02240
$466$	1.80914	0.0838070
$467$	6.03317	0.279182	0.139591	−	0.990209i	$-0.455421\pi$
$467$	6.03317	0.279182	0.139591	+	0.990209i	$0.455421\pi$
$468$	−6.03244	−0.278850
$469$	4.33929	0.200370
$470$	−6.21988	−0.286901
$471$	1.00000	0.0460776
$472$	3.12479	0.143830
$473$	1.57473	0.0724063
$474$	0.337224	0.0154892
$475$	48.7248	2.23565
$476$	2.56846	0.117725
$477$	0.171533	0.00785394
$478$	−1.65228	−0.0755734
$479$	−12.8313	−0.586279	−0.293140	−	0.956070i	$-0.594700\pi$
$479$	−12.8313	−0.586279	−0.293140	+	0.956070i	$0.594700\pi$
$480$	−6.79908	−0.310334
$481$	35.0798	1.59950
$482$	−1.47266	−0.0670777
$483$	1.01194	0.0460450
$484$	−6.84592	−0.311178
$485$	−64.9925	−2.95116
$486$	−0.155256	−0.00704255
$487$	−7.25498	−0.328755	−0.164377	−	0.986398i	$-0.552561\pi$
$487$	−7.25498	−0.328755	−0.164377	+	0.986398i	$0.552561\pi$
$488$	−4.67749	−0.211740
$489$	−12.4097	−0.561186
$490$	−3.05774	−0.138134
$491$	−24.6057	−1.11044	−0.555221	−	0.831703i	$-0.687366\pi$
$491$	−24.6057	−1.11044	−0.555221	+	0.831703i	$0.687366\pi$
$492$	14.4919	0.653343
$493$	−0.455768	−0.0205267
$494$	2.63788	0.118684
$495$	14.1056	0.633998
$496$	22.9215	1.02921
$497$	−3.63844	−0.163206
$498$	1.61691	0.0724556
$499$	0.837982	0.0375132	0.0187566	−	0.999824i	$-0.494029\pi$
$499$	0.837982	0.0375132	0.0187566	+	0.999824i	$0.494029\pi$
$500$	−27.5200	−1.23073
$501$	21.5819	0.964210
$502$	1.17407	0.0524013
$503$	−17.2839	−0.770652	−0.385326	−	0.922780i	$-0.625911\pi$
$503$	−17.2839	−0.770652	−0.385326	+	0.922780i	$0.625911\pi$
$504$	0.802401	0.0357418
$505$	−55.5698	−2.47282
$506$	0.459674	0.0204350
$507$	3.67909	0.163394
$508$	18.3334	0.813411
$509$	25.5901	1.13426	0.567131	−	0.823628i	$-0.308053\pi$
$509$	25.5901	1.13426	0.567131	+	0.823628i	$0.308053\pi$
$510$	−0.575816	−0.0254975
$511$	−12.5349	−0.554511
$512$	11.8292	0.522783
$513$	−5.56516	−0.245708
$514$	−2.22395	−0.0980942
$515$	50.7225	2.23510
$516$	0.818118	0.0360156
$517$	−41.0822	−1.80679
$518$	−2.31891	−0.101887
$519$	−12.7193	−0.558317
$520$	−6.98952	−0.306511
$521$	−9.43208	−0.413227	−0.206613	−	0.978423i	$-0.566244\pi$
$521$	−9.43208	−0.413227	−0.206613	+	0.978423i	$0.566244\pi$
$522$	−0.0707606	−0.00309711
$523$	−2.59041	−0.113271	−0.0566355	−	0.998395i	$-0.518037\pi$
$523$	−2.59041	−0.113271	−0.0566355	+	0.998395i	$0.518037\pi$
$524$	−10.6891	−0.466953
$525$	11.3810	0.496709
$526$	2.98215	0.130028
$527$	5.94445	0.258944
$528$	−14.6652	−0.638219
$529$	−22.3940	−0.973651
$530$	0.0987712	0.00429035
$531$	−5.06219	−0.219680
$532$	14.2939	0.619719
$533$	22.3918	0.969897
$534$	0.700730	0.0303236
$535$	53.6902	2.32123
$536$	2.06060	0.0890042
$537$	−0.553339	−0.0238784
$538$	3.05826	0.131851
$539$	−20.1963	−0.869916
$540$	7.32824	0.315357
$541$	17.4478	0.750141	0.375070	−	0.926996i	$-0.377619\pi$
$541$	17.4478	0.750141	0.375070	+	0.926996i	$0.377619\pi$
$542$	0.309970	0.0133144
$543$	23.9147	1.02628
$544$	1.83322	0.0785987
$545$	49.1000	2.10321
$546$	0.616149	0.0263687
$547$	27.2466	1.16498	0.582490	−	0.812838i	$-0.302078\pi$
$547$	27.2466	1.16498	0.582490	+	0.812838i	$0.302078\pi$
$548$	−8.07308	−0.344865
$549$	7.57758	0.323403
$550$	5.16982	0.220442
$551$	−2.53642	−0.108055
$552$	0.480541	0.0204532
$553$	2.82344	0.120065
$554$	0.686543	0.0291684
$555$	−42.6151	−1.80891
$556$	44.8382	1.90156
$557$	0.567913	0.0240633	0.0120316	−	0.999928i	$-0.496170\pi$
$557$	0.567913	0.0240633	0.0120316	+	0.999928i	$0.496170\pi$
$558$	0.922911	0.0390699
$559$	1.26410	0.0534657
$560$	−18.5899	−0.785565
$561$	−3.80325	−0.160573
$562$	−3.49540	−0.147445
$563$	−0.518584	−0.0218557	−0.0109279	−	0.999940i	$-0.503479\pi$
$563$	−0.518584	−0.0218557	−0.0109279	+	0.999940i	$0.503479\pi$
$564$	−21.3433	−0.898717
$565$	1.95170	0.0821088
$566$	−5.01353	−0.210734
$567$	−1.29990	−0.0545905
$568$	−1.72778	−0.0724961
$569$	24.5987	1.03123	0.515616	−	0.856820i	$-0.327563\pi$
$569$	24.5987	1.03123	0.515616	+	0.856820i	$0.327563\pi$
$570$	−3.20450	−0.134222
$571$	19.0977	0.799216	0.399608	−	0.916686i	$-0.369146\pi$
$571$	19.0977	0.799216	0.399608	+	0.916686i	$0.369146\pi$
$572$	−22.9429	−0.959291
$573$	22.9607	0.959195
$574$	−1.48019	−0.0617818
$575$	6.81585	0.284241
$576$	−7.42729	−0.309470
$577$	−46.0475	−1.91698	−0.958492	−	0.285121i	$-0.907966\pi$
$577$	−46.0475	−1.91698	−0.958492	+	0.285121i	$0.907966\pi$
$578$	0.155256	0.00645779
$579$	−12.8669	−0.534729
$580$	3.33997	0.138685
$581$	13.5378	0.561642
$582$	2.72067	0.112775
$583$	0.652382	0.0270189
$584$	−5.95244	−0.246314
$585$	11.3231	0.468152
$586$	1.45032	0.0599121
$587$	−20.2697	−0.836622	−0.418311	−	0.908304i	$-0.637378\pi$
$587$	−20.2697	−0.836622	−0.418311	+	0.908304i	$0.637378\pi$
$588$	−10.4925	−0.432705
$589$	33.0818	1.36311
$590$	−2.91489	−0.120004
$591$	−12.3254	−0.507001
$592$	44.3057	1.82095
$593$	−3.52399	−0.144713	−0.0723564	−	0.997379i	$-0.523052\pi$
$593$	−3.52399	−0.144713	−0.0723564	+	0.997379i	$0.523052\pi$
$594$	−0.590477	−0.0242276
$595$	−4.82108	−0.197645
$596$	14.5763	0.597067
$597$	5.77538	0.236370
$598$	0.368998	0.0150895
$599$	10.1849	0.416144	0.208072	−	0.978114i	$-0.433281\pi$
$599$	10.1849	0.416144	0.208072	+	0.978114i	$0.433281\pi$
$600$	5.40450	0.220638
$601$	−25.5506	−1.04223	−0.521116	−	0.853486i	$-0.674484\pi$
$601$	−25.5506	−1.04223	−0.521116	+	0.853486i	$0.674484\pi$
$602$	−0.0835620	−0.00340573
$603$	−3.33818	−0.135941
$604$	−26.8456	−1.09233
$605$	12.8500	0.522427
$606$	2.32622	0.0944963
$607$	−7.04308	−0.285870	−0.142935	−	0.989732i	$-0.545654\pi$
$607$	−7.04308	−0.285870	−0.142935	+	0.989732i	$0.545654\pi$
$608$	10.2022	0.413752
$609$	−0.592451	−0.0240073
$610$	4.36329	0.176664
$611$	−32.9782	−1.33416
$612$	−1.97590	−0.0798708
$613$	27.2093	1.09897	0.549486	−	0.835503i	$-0.314824\pi$
$613$	27.2093	1.09897	0.549486	+	0.835503i	$0.314824\pi$
$614$	−0.657725	−0.0265436
$615$	−27.2017	−1.09688
$616$	3.05173	0.122958
$617$	−9.41966	−0.379221	−0.189611	−	0.981859i	$-0.560723\pi$
$617$	−9.41966	−0.379221	−0.189611	+	0.981859i	$0.560723\pi$
$618$	−2.12331	−0.0854119
$619$	12.1872	0.489846	0.244923	−	0.969543i	$-0.421237\pi$
$619$	12.1872	0.489846	0.244923	+	0.969543i	$0.421237\pi$
$620$	−43.5624	−1.74951
$621$	−0.778480	−0.0312393
$622$	2.94766	0.118191
$623$	5.86694	0.235054
$624$	−11.7723	−0.471269
$625$	7.87920	0.315168
$626$	2.12718	0.0850191
$627$	−21.1657	−0.845276
$628$	1.97590	0.0788468
$629$	11.4902	0.458145
$630$	−0.748501	−0.0298210
$631$	14.8795	0.592345	0.296172	−	0.955135i	$-0.404290\pi$
$631$	14.8795	0.592345	0.296172	+	0.955135i	$0.404290\pi$
$632$	1.34077	0.0533328
$633$	5.50464	0.218790
$634$	2.16424	0.0859528
$635$	−34.4123	−1.36561
$636$	0.338931	0.0134395
$637$	−16.2123	−0.642356
$638$	−0.269120	−0.0106546
$639$	2.79902	0.110728
$640$	−17.8749	−0.706568
$641$	−19.6636	−0.776667	−0.388334	−	0.921519i	$-0.626949\pi$
$641$	−19.6636	−0.776667	−0.388334	+	0.921519i	$0.626949\pi$
$642$	−2.24754	−0.0887034
$643$	21.6370	0.853282	0.426641	−	0.904421i	$-0.359697\pi$
$643$	21.6370	0.853282	0.426641	+	0.904421i	$0.359697\pi$
$644$	1.99949	0.0787911
$645$	−1.53563	−0.0604655
$646$	0.864023	0.0339945
$647$	−14.9892	−0.589285	−0.294643	−	0.955608i	$-0.595201\pi$
$647$	−14.9892	−0.589285	−0.294643	+	0.955608i	$0.595201\pi$
$648$	−0.617281	−0.0242491
$649$	−19.2528	−0.755737
$650$	4.15002	0.162777
$651$	7.72718	0.302852
$652$	−24.5203	−0.960287
$653$	13.8183	0.540751	0.270376	−	0.962755i	$-0.412852\pi$
$653$	13.8183	0.540751	0.270376	+	0.962755i	$0.412852\pi$
$654$	−2.05539	−0.0803720
$655$	20.0637	0.783953
$656$	28.2808	1.10418
$657$	9.64299	0.376209
$658$	2.17999	0.0849849
$659$	6.95477	0.270919	0.135460	−	0.990783i	$-0.456749\pi$
$659$	6.95477	0.270919	0.135460	+	0.990783i	$0.456749\pi$
$660$	27.8711	1.08488
$661$	−42.4624	−1.65160	−0.825799	−	0.563965i	$-0.809275\pi$
$661$	−42.4624	−1.65160	−0.825799	+	0.563965i	$0.809275\pi$
$662$	−0.742002	−0.0288387
$663$	−3.05302	−0.118569
$664$	6.42867	0.249481
$665$	−26.8301	−1.04043
$666$	1.78392	0.0691256
$667$	−0.354806	−0.0137381
$668$	42.6437	1.64993
$669$	5.89795	0.228028
$670$	−1.92218	−0.0742602
$671$	28.8194	1.11256
$672$	2.38300	0.0919261
$673$	35.9809	1.38696	0.693480	−	0.720476i	$-0.256077\pi$
$673$	35.9809	1.38696	0.693480	+	0.720476i	$0.256077\pi$
$674$	2.73528	0.105359
$675$	−8.75533	−0.336993
$676$	7.26950	0.279596
$677$	−8.58003	−0.329757	−0.164879	−	0.986314i	$-0.552723\pi$
$677$	−8.58003	−0.329757	−0.164879	+	0.986314i	$0.552723\pi$
$678$	−0.0817007	−0.00313770
$679$	22.7791	0.874182
$680$	−2.28938	−0.0877938
$681$	6.34324	0.243073
$682$	3.51006	0.134407
$683$	−41.9732	−1.60606	−0.803029	−	0.595940i	$-0.796780\pi$
$683$	−41.9732	−1.60606	−0.803029	+	0.595940i	$0.796780\pi$
$684$	−10.9962	−0.420449
$685$	15.1534	0.578982
$686$	2.48442	0.0948554
$687$	0.402959	0.0153739
$688$	1.59656	0.0608681
$689$	0.523692	0.0199511
$690$	−0.448261	−0.0170650
$691$	22.3517	0.850299	0.425150	−	0.905123i	$-0.360222\pi$
$691$	22.3517	0.850299	0.425150	+	0.905123i	$0.360222\pi$
$692$	−25.1321	−0.955378
$693$	−4.94383	−0.187801
$694$	−4.00785	−0.152136
$695$	−84.1627	−3.19247
$696$	−0.281337	−0.0106640
$697$	7.33432	0.277807
$698$	1.53926	0.0582618
$699$	−11.6527	−0.440744
$700$	22.4877	0.849956
$701$	−11.0778	−0.418401	−0.209201	−	0.977873i	$-0.567086\pi$
$701$	−11.0778	−0.418401	−0.209201	+	0.977873i	$0.567086\pi$
$702$	−0.473999	−0.0178899
$703$	63.9448	2.41172
$704$	−28.2479	−1.06463
$705$	40.0621	1.50883
$706$	−4.38869	−0.165171
$707$	19.4765	0.732491
$708$	−10.0024	−0.375911
$709$	12.6027	0.473305	0.236653	−	0.971594i	$-0.423950\pi$
$709$	12.6027	0.473305	0.236653	+	0.971594i	$0.423950\pi$
$710$	1.61172	0.0604867
$711$	−2.17205	−0.0814583
$712$	2.78603	0.104411
$713$	4.62764	0.173306
$714$	0.201816	0.00755279
$715$	43.0645	1.61052
$716$	−1.09334	−0.0408601
$717$	10.6423	0.397444
$718$	−1.04068	−0.0388380
$719$	−1.21862	−0.0454470	−0.0227235	−	0.999742i	$-0.507234\pi$
$719$	−1.21862	−0.0454470	−0.0227235	+	0.999742i	$0.507234\pi$
$720$	14.3010	0.532968
$721$	−17.7776	−0.662074
$722$	1.85857	0.0691686
$723$	9.48537	0.352765
$724$	47.2530	1.75614
$725$	−3.99040	−0.148200
$726$	−0.537918	−0.0199640
$727$	−1.22016	−0.0452533	−0.0226266	−	0.999744i	$-0.507203\pi$
$727$	−1.22016	−0.0452533	−0.0226266	+	0.999744i	$0.507203\pi$
$728$	2.44974	0.0907936
$729$	1.00000	0.0370370
$730$	5.55259	0.205510
$731$	0.414049	0.0153142
$732$	14.9725	0.553400
$733$	−29.4592	−1.08810	−0.544050	−	0.839053i	$-0.683110\pi$
$733$	−29.4592	−1.08810	−0.544050	+	0.839053i	$0.683110\pi$
$734$	3.08636	0.113920
$735$	19.6948	0.726454
$736$	1.42713	0.0526045
$737$	−12.6959	−0.467661
$738$	1.13870	0.0419160
$739$	4.34308	0.159763	0.0798813	−	0.996804i	$-0.474546\pi$
$739$	4.34308	0.159763	0.0798813	+	0.996804i	$0.474546\pi$
$740$	−84.2030	−3.09536
$741$	−16.9905	−0.624162
$742$	−0.0346181	−0.00127087
$743$	−14.4216	−0.529076	−0.264538	−	0.964375i	$-0.585220\pi$
$743$	−14.4216	−0.529076	−0.264538	+	0.964375i	$0.585220\pi$
$744$	3.66940	0.134527
$745$	−27.3601	−1.00240
$746$	1.76248	0.0645288
$747$	−10.4145	−0.381047
$748$	−7.51483	−0.274769
$749$	−18.8178	−0.687587
$750$	−2.16238	−0.0789589
$751$	−15.6152	−0.569807	−0.284904	−	0.958556i	$-0.591962\pi$
$751$	−15.6152	−0.569807	−0.284904	+	0.958556i	$0.591962\pi$
$752$	−41.6515	−1.51887
$753$	−7.56217	−0.275581
$754$	−0.216033	−0.00786747
$755$	50.3900	1.83388
$756$	−2.56846	−0.0934140
$757$	45.7645	1.66334	0.831670	−	0.555271i	$-0.187385\pi$
$757$	45.7645	1.66334	0.831670	+	0.555271i	$0.187385\pi$
$758$	−5.57844	−0.202618
$759$	−2.96075	−0.107469
$760$	−12.7408	−0.462157
$761$	−26.2818	−0.952714	−0.476357	−	0.879252i	$-0.658043\pi$
$761$	−26.2818	−0.952714	−0.476357	+	0.879252i	$0.658043\pi$
$762$	1.44054	0.0521853
$763$	−17.2090	−0.623006
$764$	45.3679	1.64135
$765$	3.70882	0.134093
$766$	4.05528	0.146523
$767$	−15.4549	−0.558046
$768$	−14.1063	−0.509018
$769$	−4.40852	−0.158975	−0.0794877	−	0.996836i	$-0.525328\pi$
$769$	−4.40852	−0.158975	−0.0794877	+	0.996836i	$0.525328\pi$
$770$	−2.84674	−0.102589
$771$	14.3244	0.515882
$772$	−25.4236	−0.915015
$773$	25.9414	0.933047	0.466524	−	0.884509i	$-0.345506\pi$
$773$	25.9414	0.933047	0.466524	+	0.884509i	$0.345506\pi$
$774$	0.0642835	0.00231062
$775$	52.0457	1.86954
$776$	10.8171	0.388311
$777$	14.9361	0.535829
$778$	−1.81359	−0.0650204
$779$	40.8167	1.46241
$780$	22.3732	0.801090
$781$	10.6454	0.380921
$782$	0.120863	0.00432207
$783$	0.455768	0.0162878
$784$	−20.4762	−0.731291
$785$	−3.70882	−0.132373
$786$	−0.839891	−0.0299579
$787$	3.98250	0.141961	0.0709804	−	0.997478i	$-0.477387\pi$
$787$	3.98250	0.141961	0.0709804	+	0.997478i	$0.477387\pi$
$788$	−24.3538	−0.867568
$789$	−19.2080	−0.683821
$790$	−1.25070	−0.0444980
$791$	−0.684049	−0.0243220
$792$	−2.34767	−0.0834210
$793$	23.1345	0.821529
$794$	5.24610	0.186177
$795$	−0.636184	−0.0225631
$796$	11.4115	0.404471
$797$	−44.9181	−1.59108	−0.795540	−	0.605901i	$-0.792813\pi$
$797$	−44.9181	−1.59108	−0.795540	+	0.605901i	$0.792813\pi$
$798$	1.12314	0.0397587
$799$	−10.8019	−0.382142
$800$	16.0505	0.567470
$801$	−4.51339	−0.159473
$802$	2.51756	0.0888982
$803$	36.6747	1.29422
$804$	−6.59590	−0.232619
$805$	−3.75311	−0.132280
$806$	2.81766	0.0992479
$807$	−19.6982	−0.693409
$808$	9.24881	0.325372
$809$	−12.2766	−0.431623	−0.215812	−	0.976435i	$-0.569240\pi$
$809$	−12.2766	−0.431623	−0.215812	+	0.976435i	$0.569240\pi$
$810$	0.575816	0.0202321
$811$	−29.1369	−1.02314	−0.511568	−	0.859243i	$-0.670935\pi$
$811$	−29.1369	−1.02314	−0.511568	+	0.859243i	$0.670935\pi$
$812$	−1.17062	−0.0410808
$813$	−1.99651	−0.0700208
$814$	6.78470	0.237804
$815$	46.0253	1.61220
$816$	−3.85595	−0.134985
$817$	2.30425	0.0806155
$818$	−2.47739	−0.0866198
$819$	−3.96861	−0.138674
$820$	−53.7477	−1.87695
$821$	19.9280	0.695494	0.347747	−	0.937588i	$-0.386947\pi$
$821$	19.9280	0.695494	0.347747	+	0.937588i	$0.386947\pi$
$822$	−0.634341	−0.0221252
$823$	−27.6992	−0.965534	−0.482767	−	0.875749i	$-0.660368\pi$
$823$	−27.6992	−0.965534	−0.482767	+	0.875749i	$0.660368\pi$
$824$	−8.44205	−0.294093
$825$	−33.2987	−1.15931
$826$	1.02163	0.0355471
$827$	44.5997	1.55088	0.775441	−	0.631420i	$-0.217528\pi$
$827$	44.5997	1.55088	0.775441	+	0.631420i	$0.217528\pi$
$828$	−1.53819	−0.0534560
$829$	15.9571	0.554213	0.277106	−	0.960839i	$-0.410625\pi$
$829$	15.9571	0.554213	0.277106	+	0.960839i	$0.410625\pi$
$830$	−5.99683	−0.208153
$831$	−4.42201	−0.153398
$832$	−22.6756	−0.786137
$833$	−5.31027	−0.183990
$834$	3.52316	0.121997
$835$	−80.0435	−2.77002
$836$	−41.8212	−1.44642
$837$	−5.94445	−0.205470
$838$	2.47925	0.0856442
$839$	−29.3516	−1.01333	−0.506664	−	0.862143i	$-0.669122\pi$
$839$	−29.3516	−1.01333	−0.506664	+	0.862143i	$0.669122\pi$
$840$	−2.97596	−0.102680
$841$	−28.7923	−0.992837
$842$	3.08427	0.106291
$843$	22.5138	0.775418
$844$	10.8766	0.374388
$845$	−13.6451	−0.469405
$846$	−1.67705	−0.0576582
$847$	−4.50378	−0.154752
$848$	0.661422	0.0227133
$849$	32.2921	1.10826
$850$	1.35932	0.0466242
$851$	8.94489	0.306627
$852$	5.53057	0.189474
$853$	13.9614	0.478030	0.239015	−	0.971016i	$-0.423176\pi$
$853$	13.9614	0.478030	0.239015	+	0.971016i	$0.423176\pi$
$854$	−1.52928	−0.0523309
$855$	20.6402	0.705879
$856$	−8.93599	−0.305426
$857$	56.9348	1.94485	0.972427	−	0.233206i	$-0.0749215\pi$
$857$	56.9348	1.94485	0.972427	+	0.233206i	$0.0749215\pi$
$858$	−1.80274	−0.0615444
$859$	−30.8842	−1.05376	−0.526878	−	0.849941i	$-0.676638\pi$
$859$	−30.8842	−1.05376	−0.526878	+	0.849941i	$0.676638\pi$
$860$	−3.03425	−0.103467
$861$	9.53386	0.324913
$862$	1.50938	0.0514095
$863$	−23.4243	−0.797372	−0.398686	−	0.917088i	$-0.630534\pi$
$863$	−23.4243	−0.797372	−0.398686	+	0.917088i	$0.630534\pi$
$864$	−1.83322	−0.0623674
$865$	47.1737	1.60395
$866$	2.11342	0.0718171
$867$	−1.00000	−0.0339618
$868$	15.2681	0.518233
$869$	−8.26086	−0.280230
$870$	0.262438	0.00889749
$871$	−10.1915	−0.345327
$872$	−8.17201	−0.276739
$873$	−17.5238	−0.593090
$874$	0.672624	0.0227519
$875$	−18.1048	−0.612053
$876$	19.0535	0.643760
$877$	44.0288	1.48675	0.743373	−	0.668877i	$-0.233225\pi$
$877$	44.0288	1.48675	0.743373	+	0.668877i	$0.233225\pi$
$878$	3.04604	0.102799
$879$	−9.34148	−0.315080
$880$	54.3904	1.83350
$881$	−2.84893	−0.0959828	−0.0479914	−	0.998848i	$-0.515282\pi$
$881$	−2.84893	−0.0959828	−0.0479914	+	0.998848i	$0.515282\pi$
$882$	−0.824450	−0.0277607
$883$	51.8972	1.74648	0.873240	−	0.487290i	$-0.162015\pi$
$883$	51.8972	1.74648	0.873240	+	0.487290i	$0.162015\pi$
$884$	−6.03244	−0.202893
$885$	18.7747	0.631106
$886$	5.85557	0.196722
$887$	37.9686	1.27486	0.637431	−	0.770507i	$-0.279997\pi$
$887$	37.9686	1.27486	0.637431	+	0.770507i	$0.279997\pi$
$888$	7.09269	0.238015
$889$	12.0611	0.404516
$890$	−2.59888	−0.0871147
$891$	3.80325	0.127414
$892$	11.6537	0.390196
$893$	−60.1140	−2.01164
$894$	1.14533	0.0383055
$895$	2.05224	0.0685987
$896$	6.26495	0.209297
$897$	−2.37671	−0.0793561
$898$	−1.77888	−0.0593618
$899$	−2.70929	−0.0903599
$900$	−17.2996	−0.576654
$901$	0.171533	0.00571458
$902$	4.33075	0.144198
$903$	0.538221	0.0179109
$904$	−0.324834	−0.0108038
$905$	−88.6953	−2.94833
$906$	−2.10939	−0.0700797
$907$	−31.5350	−1.04710	−0.523551	−	0.851994i	$-0.675393\pi$
$907$	−31.5350	−1.04710	−0.523551	+	0.851994i	$0.675393\pi$
$908$	12.5336	0.415941
$909$	−14.9832	−0.496960
$910$	−2.28518	−0.0757531
$911$	−24.4739	−0.810856	−0.405428	−	0.914127i	$-0.632878\pi$
$911$	−24.4739	−0.810856	−0.405428	+	0.914127i	$0.632878\pi$
$912$	−21.4590	−0.710578
$913$	−39.6090	−1.31087
$914$	3.43666	0.113675
$915$	−28.1039	−0.929085
$916$	0.796206	0.0263074
$917$	−7.03208	−0.232220
$918$	−0.155256	−0.00512420
$919$	13.6784	0.451208	0.225604	−	0.974219i	$-0.427564\pi$
$919$	13.6784	0.451208	0.225604	+	0.974219i	$0.427564\pi$
$920$	−1.78224	−0.0587586
$921$	4.23640	0.139594
$922$	−5.04722	−0.166221
$923$	8.54545	0.281277
$924$	−9.76850	−0.321360
$925$	100.601	3.30773
$926$	−4.92374	−0.161804
$927$	13.6762	0.449185
$928$	−0.835523	−0.0274274
$929$	25.9162	0.850283	0.425142	−	0.905127i	$-0.360224\pi$
$929$	25.9162	0.850283	0.425142	+	0.905127i	$0.360224\pi$
$930$	−3.42291	−0.112242
$931$	−29.5525	−0.968544
$932$	−23.0244	−0.754191
$933$	−18.9858	−0.621569
$934$	0.936685	0.0306493
$935$	14.1056	0.461301
$936$	−1.88457	−0.0615991
$937$	50.9691	1.66509	0.832544	−	0.553959i	$-0.186884\pi$
$937$	50.9691	1.66509	0.832544	+	0.553959i	$0.186884\pi$
$938$	0.673700	0.0219971
$939$	−13.7011	−0.447119
$940$	79.1586	2.58187
$941$	6.23267	0.203179	0.101590	−	0.994826i	$-0.467607\pi$
$941$	6.23267	0.203179	0.101590	+	0.994826i	$0.467607\pi$
$942$	0.155256	0.00505851
$943$	5.70962	0.185931
$944$	−19.5196	−0.635308
$945$	4.82108	0.156830
$946$	0.244486	0.00794894
$947$	17.3628	0.564216	0.282108	−	0.959383i	$-0.408966\pi$
$947$	17.3628	0.564216	0.282108	+	0.959383i	$0.408966\pi$
$948$	−4.29175	−0.139389
$949$	29.4402	0.955670
$950$	7.56481	0.245435
$951$	−13.9398	−0.452029
$952$	0.802401	0.0260060
$953$	7.46156	0.241704	0.120852	−	0.992671i	$-0.461437\pi$
$953$	7.46156	0.241704	0.120852	+	0.992671i	$0.461437\pi$
$954$	0.0266314	0.000862225 0
$955$	−85.1569	−2.75561
$956$	21.0281	0.680096
$957$	1.73340	0.0560328
$958$	−1.99214	−0.0643632
$959$	−5.31109	−0.171504
$960$	27.5465	0.889059
$961$	4.33654	0.139888
$962$	5.44634	0.175597
$963$	14.4764	0.466495
$964$	18.7421	0.603642
$965$	47.7209	1.53619
$966$	0.157110	0.00505493
$967$	−3.32954	−0.107071	−0.0535353	−	0.998566i	$-0.517049\pi$
$967$	−3.32954	−0.107071	−0.0535353	+	0.998566i	$0.517049\pi$
$968$	−2.13870	−0.0687405
$969$	−5.56516	−0.178779
$970$	−10.0905	−0.323985
$971$	26.1802	0.840161	0.420081	−	0.907487i	$-0.362002\pi$
$971$	26.1802	0.840161	0.420081	+	0.907487i	$0.362002\pi$
$972$	1.97590	0.0633769
$973$	29.4980	0.945663
$974$	−1.12638	−0.0360915
$975$	−26.7302	−0.856051
$976$	29.2188	0.935271
$977$	55.8330	1.78626	0.893128	−	0.449802i	$-0.148505\pi$
$977$	55.8330	1.78626	0.893128	+	0.449802i	$0.148505\pi$
$978$	−1.92668	−0.0616083
$979$	−17.1656	−0.548614
$980$	38.9149	1.24309
$981$	13.2387	0.422680
$982$	−3.82018	−0.121907
$983$	−31.9165	−1.01798	−0.508989	−	0.860773i	$-0.669981\pi$
$983$	−31.9165	−1.01798	−0.508989	+	0.860773i	$0.669981\pi$
$984$	4.52734	0.144326
$985$	45.7128	1.45653
$986$	−0.0707606	−0.00225348
$987$	−14.0413	−0.446939
$988$	−33.5715	−1.06805
$989$	0.322329	0.0102495
$990$	2.18997	0.0696018
$991$	11.1296	0.353544	0.176772	−	0.984252i	$-0.443435\pi$
$991$	11.1296	0.353544	0.176772	+	0.984252i	$0.443435\pi$
$992$	10.8975	0.345996
$993$	4.77922	0.151664
$994$	−0.564888	−0.0179172
$995$	−21.4198	−0.679054
$996$	−20.5780	−0.652038
$997$	36.9168	1.16917	0.584583	−	0.811334i	$-0.301258\pi$
$997$	36.9168	1.16917	0.584583	+	0.811334i	$0.301258\pi$
$998$	0.130102	0.00411829
$999$	−11.4902	−0.363534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.34	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.34	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+0.155256 q^{2} -1.00000 q^{3} -1.97590 q^{4} +3.70882 q^{5} -0.155256 q^{6} -1.29990 q^{7} -0.617281 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.155256 q^{2} -1.00000 q^{3} -1.97590 q^{4} +3.70882 q^{5} -0.155256 q^{6} -1.29990 q^{7} -0.617281 q^{8} +1.00000 q^{9} +0.575816 q^{10} +3.80325 q^{11} +1.97590 q^{12} +3.05302 q^{13} -0.201816 q^{14} -3.70882 q^{15} +3.85595 q^{16} +1.00000 q^{17} +0.155256 q^{18} +5.56516 q^{19} -7.32824 q^{20} +1.29990 q^{21} +0.590477 q^{22} +0.778480 q^{23} +0.617281 q^{24} +8.75533 q^{25} +0.473999 q^{26} -1.00000 q^{27} +2.56846 q^{28} -0.455768 q^{29} -0.575816 q^{30} +5.94445 q^{31} +1.83322 q^{32} -3.80325 q^{33} +0.155256 q^{34} -4.82108 q^{35} -1.97590 q^{36} +11.4902 q^{37} +0.864023 q^{38} -3.05302 q^{39} -2.28938 q^{40} +7.33432 q^{41} +0.201816 q^{42} +0.414049 q^{43} -7.51483 q^{44} +3.70882 q^{45} +0.120863 q^{46} -10.8019 q^{47} -3.85595 q^{48} -5.31027 q^{49} +1.35932 q^{50} -1.00000 q^{51} -6.03244 q^{52} +0.171533 q^{53} -0.155256 q^{54} +14.1056 q^{55} +0.802401 q^{56} -5.56516 q^{57} -0.0707606 q^{58} -5.06219 q^{59} +7.32824 q^{60} +7.57758 q^{61} +0.922911 q^{62} -1.29990 q^{63} -7.42729 q^{64} +11.3231 q^{65} -0.590477 q^{66} -3.33818 q^{67} -1.97590 q^{68} -0.778480 q^{69} -0.748501 q^{70} +2.79902 q^{71} -0.617281 q^{72} +9.64299 q^{73} +1.78392 q^{74} -8.75533 q^{75} -10.9962 q^{76} -4.94383 q^{77} -0.473999 q^{78} -2.17205 q^{79} +14.3010 q^{80} +1.00000 q^{81} +1.13870 q^{82} -10.4145 q^{83} -2.56846 q^{84} +3.70882 q^{85} +0.0642835 q^{86} +0.455768 q^{87} -2.34767 q^{88} -4.51339 q^{89} +0.575816 q^{90} -3.96861 q^{91} -1.53819 q^{92} -5.94445 q^{93} -1.67705 q^{94} +20.6402 q^{95} -1.83322 q^{96} -17.5238 q^{97} -0.824450 q^{98} +3.80325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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