LMFDB - Embedded newform 8007.2.a.h.1.14

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:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-1.32549 q^{2} +1.00000 q^{3} -0.243069 q^{4} +4.13081 q^{5} -1.32549 q^{6} +1.12393 q^{7} +2.97317 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.32549 q^{2} +1.00000 q^{3} -0.243069 q^{4} +4.13081 q^{5} -1.32549 q^{6} +1.12393 q^{7} +2.97317 q^{8} +1.00000 q^{9} -5.47535 q^{10} +2.39556 q^{11} -0.243069 q^{12} -4.30301 q^{13} -1.48977 q^{14} +4.13081 q^{15} -3.45478 q^{16} -1.00000 q^{17} -1.32549 q^{18} +4.26910 q^{19} -1.00407 q^{20} +1.12393 q^{21} -3.17529 q^{22} +8.47236 q^{23} +2.97317 q^{24} +12.0636 q^{25} +5.70361 q^{26} +1.00000 q^{27} -0.273194 q^{28} -9.45358 q^{29} -5.47535 q^{30} -3.48750 q^{31} -1.36706 q^{32} +2.39556 q^{33} +1.32549 q^{34} +4.64275 q^{35} -0.243069 q^{36} +0.176480 q^{37} -5.65867 q^{38} -4.30301 q^{39} +12.2816 q^{40} +0.619343 q^{41} -1.48977 q^{42} +4.87331 q^{43} -0.582286 q^{44} +4.13081 q^{45} -11.2301 q^{46} -3.95118 q^{47} -3.45478 q^{48} -5.73677 q^{49} -15.9902 q^{50} -1.00000 q^{51} +1.04593 q^{52} +0.557824 q^{53} -1.32549 q^{54} +9.89558 q^{55} +3.34165 q^{56} +4.26910 q^{57} +12.5307 q^{58} +9.64875 q^{59} -1.00407 q^{60} +2.61722 q^{61} +4.62266 q^{62} +1.12393 q^{63} +8.72159 q^{64} -17.7749 q^{65} -3.17529 q^{66} +16.1099 q^{67} +0.243069 q^{68} +8.47236 q^{69} -6.15393 q^{70} +4.84683 q^{71} +2.97317 q^{72} -6.81252 q^{73} -0.233923 q^{74} +12.0636 q^{75} -1.03769 q^{76} +2.69245 q^{77} +5.70361 q^{78} +6.51811 q^{79} -14.2710 q^{80} +1.00000 q^{81} -0.820935 q^{82} -8.43584 q^{83} -0.273194 q^{84} -4.13081 q^{85} -6.45953 q^{86} -9.45358 q^{87} +7.12240 q^{88} -9.84503 q^{89} -5.47535 q^{90} -4.83630 q^{91} -2.05937 q^{92} -3.48750 q^{93} +5.23726 q^{94} +17.6348 q^{95} -1.36706 q^{96} -1.82501 q^{97} +7.60405 q^{98} +2.39556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.32549	−0.937265	−0.468632	−	0.883393i	$-0.655253\pi$
$2$	−1.32549	−0.937265	−0.468632	+	0.883393i	$0.655253\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.243069	−0.121535
$5$	4.13081	1.84735	0.923676	−	0.383174i	$-0.125169\pi$
$5$	4.13081	1.84735	0.923676	+	0.383174i	$0.125169\pi$
$6$	−1.32549	−0.541130
$7$	1.12393	0.424807	0.212403	−	0.977182i	$-0.431871\pi$
$7$	1.12393	0.424807	0.212403	+	0.977182i	$0.431871\pi$
$8$	2.97317	1.05117
$9$	1.00000	0.333333
$10$	−5.47535	−1.73146
$11$	2.39556	0.722287	0.361144	−	0.932510i	$-0.382386\pi$
$11$	2.39556	0.722287	0.361144	+	0.932510i	$0.382386\pi$
$12$	−0.243069	−0.0701680
$13$	−4.30301	−1.19344	−0.596721	−	0.802449i	$-0.703530\pi$
$13$	−4.30301	−1.19344	−0.596721	+	0.802449i	$0.703530\pi$
$14$	−1.48977	−0.398157
$15$	4.13081	1.06657
$16$	−3.45478	−0.863695
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.32549	−0.312422
$19$	4.26910	0.979400	0.489700	−	0.871891i	$-0.337106\pi$
$19$	4.26910	0.979400	0.489700	+	0.871891i	$0.337106\pi$
$20$	−1.00407	−0.224517
$21$	1.12393	0.245262
$22$	−3.17529	−0.676975
$23$	8.47236	1.76661	0.883305	−	0.468799i	$-0.155313\pi$
$23$	8.47236	1.76661	0.883305	+	0.468799i	$0.155313\pi$
$24$	2.97317	0.606896
$25$	12.0636	2.41271
$26$	5.70361	1.11857
$27$	1.00000	0.192450
$28$	−0.273194	−0.0516287
$29$	−9.45358	−1.75549	−0.877743	−	0.479131i	$-0.840952\pi$
$29$	−9.45358	−1.75549	−0.877743	+	0.479131i	$0.840952\pi$
$30$	−5.47535	−0.999658
$31$	−3.48750	−0.626374	−0.313187	−	0.949692i	$-0.601397\pi$
$31$	−3.48750	−0.626374	−0.313187	+	0.949692i	$0.601397\pi$
$32$	−1.36706	−0.241664
$33$	2.39556	0.417013
$34$	1.32549	0.227320
$35$	4.64275	0.784768
$36$	−0.243069	−0.0405115
$37$	0.176480	0.0290132	0.0145066	−	0.999895i	$-0.495382\pi$
$37$	0.176480	0.0290132	0.0145066	+	0.999895i	$0.495382\pi$
$38$	−5.65867	−0.917957
$39$	−4.30301	−0.689034
$40$	12.2816	1.94189
$41$	0.619343	0.0967252	0.0483626	−	0.998830i	$-0.484600\pi$
$41$	0.619343	0.0967252	0.0483626	+	0.998830i	$0.484600\pi$
$42$	−1.48977	−0.229876
$43$	4.87331	0.743172	0.371586	−	0.928398i	$-0.378814\pi$
$43$	4.87331	0.743172	0.371586	+	0.928398i	$0.378814\pi$
$44$	−0.582286	−0.0877829
$45$	4.13081	0.615784
$46$	−11.2301	−1.65578
$47$	−3.95118	−0.576339	−0.288170	−	0.957579i	$-0.593047\pi$
$47$	−3.95118	−0.576339	−0.288170	+	0.957579i	$0.593047\pi$
$48$	−3.45478	−0.498654
$49$	−5.73677	−0.819539
$50$	−15.9902	−2.26135
$51$	−1.00000	−0.140028
$52$	1.04593	0.145044
$53$	0.557824	0.0766230	0.0383115	−	0.999266i	$-0.487802\pi$
$53$	0.557824	0.0766230	0.0383115	+	0.999266i	$0.487802\pi$
$54$	−1.32549	−0.180377
$55$	9.89558	1.33432
$56$	3.34165	0.446546
$57$	4.26910	0.565457
$58$	12.5307	1.64536
$59$	9.64875	1.25616	0.628080	−	0.778149i	$-0.283841\pi$
$59$	9.64875	1.25616	0.628080	+	0.778149i	$0.283841\pi$
$60$	−1.00407	−0.129625
$61$	2.61722	0.335101	0.167550	−	0.985864i	$-0.446414\pi$
$61$	2.61722	0.335101	0.167550	+	0.985864i	$0.446414\pi$
$62$	4.62266	0.587078
$63$	1.12393	0.141602
$64$	8.72159	1.09020
$65$	−17.7749	−2.20471
$66$	−3.17529	−0.390851
$67$	16.1099	1.96814	0.984070	−	0.177782i	$-0.0568922\pi$
$67$	16.1099	1.96814	0.984070	+	0.177782i	$0.0568922\pi$
$68$	0.243069	0.0294765
$69$	8.47236	1.01995
$70$	−6.15393	−0.735535
$71$	4.84683	0.575213	0.287606	−	0.957749i	$-0.407141\pi$
$71$	4.84683	0.575213	0.287606	+	0.957749i	$0.407141\pi$
$72$	2.97317	0.350392
$73$	−6.81252	−0.797345	−0.398672	−	0.917093i	$-0.630529\pi$
$73$	−6.81252	−0.797345	−0.398672	+	0.917093i	$0.630529\pi$
$74$	−0.233923	−0.0271930
$75$	12.0636	1.39298
$76$	−1.03769	−0.119031
$77$	2.69245	0.306833
$78$	5.70361	0.645807
$79$	6.51811	0.733345	0.366672	−	0.930350i	$-0.380497\pi$
$79$	6.51811	0.733345	0.366672	+	0.930350i	$0.380497\pi$
$80$	−14.2710	−1.59555
$81$	1.00000	0.111111
$82$	−0.820935	−0.0906571
$83$	−8.43584	−0.925954	−0.462977	−	0.886370i	$-0.653219\pi$
$83$	−8.43584	−0.925954	−0.462977	+	0.886370i	$0.653219\pi$
$84$	−0.273194	−0.0298079
$85$	−4.13081	−0.448049
$86$	−6.45953	−0.696549
$87$	−9.45358	−1.01353
$88$	7.12240	0.759250
$89$	−9.84503	−1.04357	−0.521786	−	0.853077i	$-0.674734\pi$
$89$	−9.84503	−1.04357	−0.521786	+	0.853077i	$0.674734\pi$
$90$	−5.47535	−0.577153
$91$	−4.83630	−0.506982
$92$	−2.05937	−0.214704
$93$	−3.48750	−0.361637
$94$	5.23726	0.540183
$95$	17.6348	1.80930
$96$	−1.36706	−0.139525
$97$	−1.82501	−0.185302	−0.0926510	−	0.995699i	$-0.529534\pi$
$97$	−1.82501	−0.185302	−0.0926510	+	0.995699i	$0.529534\pi$
$98$	7.60405	0.768125
$99$	2.39556	0.240762
$100$	−2.93228	−0.293228
$101$	−3.04469	−0.302958	−0.151479	−	0.988460i	$-0.548404\pi$
$101$	−3.04469	−0.302958	−0.151479	+	0.988460i	$0.548404\pi$
$102$	1.32549	0.131243
$103$	4.94953	0.487692	0.243846	−	0.969814i	$-0.421591\pi$
$103$	4.94953	0.487692	0.243846	+	0.969814i	$0.421591\pi$
$104$	−12.7936	−1.25452
$105$	4.64275	0.453086
$106$	−0.739392	−0.0718161
$107$	−0.810532	−0.0783571	−0.0391785	−	0.999232i	$-0.512474\pi$
$107$	−0.810532	−0.0783571	−0.0391785	+	0.999232i	$0.512474\pi$
$108$	−0.243069	−0.0233893
$109$	1.63008	0.156134	0.0780668	−	0.996948i	$-0.475125\pi$
$109$	1.63008	0.156134	0.0780668	+	0.996948i	$0.475125\pi$
$110$	−13.1165	−1.25061
$111$	0.176480	0.0167508
$112$	−3.88294	−0.366903
$113$	−9.73032	−0.915352	−0.457676	−	0.889119i	$-0.651318\pi$
$113$	−9.73032	−0.915352	−0.457676	+	0.889119i	$0.651318\pi$
$114$	−5.65867	−0.529983
$115$	34.9977	3.26355
$116$	2.29787	0.213352
$117$	−4.30301	−0.397814
$118$	−12.7893	−1.17735
$119$	−1.12393	−0.103031
$120$	12.2816	1.12115
$121$	−5.26131	−0.478301
$122$	−3.46911	−0.314078
$123$	0.619343	0.0558443
$124$	0.847704	0.0761261
$125$	29.1782	2.60977
$126$	−1.48977	−0.132719
$127$	17.2880	1.53406	0.767030	−	0.641611i	$-0.221734\pi$
$127$	17.2880	1.53406	0.767030	+	0.641611i	$0.221734\pi$
$128$	−8.82628	−0.780140
$129$	4.87331	0.429071
$130$	23.5605	2.06639
$131$	12.4148	1.08469	0.542343	−	0.840157i	$-0.317537\pi$
$131$	12.4148	1.08469	0.542343	+	0.840157i	$0.317537\pi$
$132$	−0.582286	−0.0506815
$133$	4.79819	0.416056
$134$	−21.3536	−1.84467
$135$	4.13081	0.355523
$136$	−2.97317	−0.254947
$137$	12.2033	1.04259	0.521297	−	0.853375i	$-0.325448\pi$
$137$	12.2033	1.04259	0.521297	+	0.853375i	$0.325448\pi$
$138$	−11.2301	−0.955966
$139$	15.5725	1.32084	0.660420	−	0.750896i	$-0.270378\pi$
$139$	15.5725	1.32084	0.660420	+	0.750896i	$0.270378\pi$
$140$	−1.12851	−0.0953764
$141$	−3.95118	−0.332750
$142$	−6.42444	−0.539127
$143$	−10.3081	−0.862007
$144$	−3.45478	−0.287898
$145$	−39.0509	−3.24300
$146$	9.02994	0.747323
$147$	−5.73677	−0.473161
$148$	−0.0428969	−0.00352611
$149$	15.8907	1.30182	0.650909	−	0.759156i	$-0.274388\pi$
$149$	15.8907	1.30182	0.650909	+	0.759156i	$0.274388\pi$
$150$	−15.9902	−1.30559
$151$	10.1894	0.829203	0.414601	−	0.910003i	$-0.363921\pi$
$151$	10.1894	0.829203	0.414601	+	0.910003i	$0.363921\pi$
$152$	12.6928	1.02952
$153$	−1.00000	−0.0808452
$154$	−3.56882	−0.287583
$155$	−14.4062	−1.15713
$156$	1.04593	0.0837414
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−8.63971	−0.687338
$159$	0.557824	0.0442383
$160$	−5.64706	−0.446439
$161$	9.52237	0.750468
$162$	−1.32549	−0.104141
$163$	3.34168	0.261740	0.130870	−	0.991400i	$-0.458223\pi$
$163$	3.34168	0.261740	0.130870	+	0.991400i	$0.458223\pi$
$164$	−0.150543	−0.0117555
$165$	9.89558	0.770370
$166$	11.1816	0.867864
$167$	−11.7448	−0.908843	−0.454422	−	0.890787i	$-0.650154\pi$
$167$	−11.7448	−0.908843	−0.454422	+	0.890787i	$0.650154\pi$
$168$	3.34165	0.257814
$169$	5.51592	0.424302
$170$	5.47535	0.419940
$171$	4.26910	0.326467
$172$	−1.18455	−0.0903211
$173$	1.06551	0.0810095	0.0405047	−	0.999179i	$-0.487103\pi$
$173$	1.06551	0.0810095	0.0405047	+	0.999179i	$0.487103\pi$
$174$	12.5307	0.949947
$175$	13.5586	1.02494
$176$	−8.27612	−0.623836
$177$	9.64875	0.725245
$178$	13.0495	0.978102
$179$	15.7293	1.17567	0.587833	−	0.808982i	$-0.299981\pi$
$179$	15.7293	1.17567	0.587833	+	0.808982i	$0.299981\pi$
$180$	−1.00407	−0.0748391
$181$	10.2979	0.765439	0.382720	−	0.923865i	$-0.374988\pi$
$181$	10.2979	0.765439	0.382720	+	0.923865i	$0.374988\pi$
$182$	6.41048	0.475176
$183$	2.61722	0.193471
$184$	25.1898	1.85702
$185$	0.729006	0.0535976
$186$	4.62266	0.338950
$187$	−2.39556	−0.175180
$188$	0.960411	0.0700451
$189$	1.12393	0.0817541
$190$	−23.3749	−1.69579
$191$	−1.59804	−0.115630	−0.0578151	−	0.998327i	$-0.518413\pi$
$191$	−1.59804	−0.115630	−0.0578151	+	0.998327i	$0.518413\pi$
$192$	8.72159	0.629426
$193$	1.83367	0.131991	0.0659953	−	0.997820i	$-0.478978\pi$
$193$	1.83367	0.131991	0.0659953	+	0.997820i	$0.478978\pi$
$194$	2.41904	0.173677
$195$	−17.7749	−1.27289
$196$	1.39443	0.0996023
$197$	1.55816	0.111014	0.0555071	−	0.998458i	$-0.482322\pi$
$197$	1.55816	0.111014	0.0555071	+	0.998458i	$0.482322\pi$
$198$	−3.17529	−0.225658
$199$	−18.6216	−1.32005	−0.660024	−	0.751244i	$-0.729454\pi$
$199$	−18.6216	−1.32005	−0.660024	+	0.751244i	$0.729454\pi$
$200$	35.8670	2.53618
$201$	16.1099	1.13631
$202$	4.03572	0.283952
$203$	−10.6252	−0.745743
$204$	0.243069	0.0170182
$205$	2.55839	0.178685
$206$	−6.56057	−0.457097
$207$	8.47236	0.588870
$208$	14.8660	1.03077
$209$	10.2269	0.707408
$210$	−6.15393	−0.424662
$211$	22.4954	1.54864	0.774322	−	0.632792i	$-0.218091\pi$
$211$	22.4954	1.54864	0.774322	+	0.632792i	$0.218091\pi$
$212$	−0.135590	−0.00931235
$213$	4.84683	0.332099
$214$	1.07435	0.0734413
$215$	20.1307	1.37290
$216$	2.97317	0.202299
$217$	−3.91972	−0.266088
$218$	−2.16066	−0.146339
$219$	−6.81252	−0.460347
$220$	−2.40531	−0.162166
$221$	4.30301	0.289452
$222$	−0.233923	−0.0156999
$223$	−16.4025	−1.09839	−0.549196	−	0.835694i	$-0.685066\pi$
$223$	−16.4025	−1.09839	−0.549196	+	0.835694i	$0.685066\pi$
$224$	−1.53648	−0.102661
$225$	12.0636	0.804237
$226$	12.8975	0.857927
$227$	11.1153	0.737746	0.368873	−	0.929480i	$-0.379744\pi$
$227$	11.1153	0.737746	0.368873	+	0.929480i	$0.379744\pi$
$228$	−1.03769	−0.0687225
$229$	16.3975	1.08358	0.541790	−	0.840514i	$-0.317747\pi$
$229$	16.3975	1.08358	0.541790	+	0.840514i	$0.317747\pi$
$230$	−46.3892	−3.05881
$231$	2.69245	0.177150
$232$	−28.1071	−1.84532
$233$	−1.83065	−0.119930	−0.0599650	−	0.998200i	$-0.519099\pi$
$233$	−1.83065	−0.119930	−0.0599650	+	0.998200i	$0.519099\pi$
$234$	5.70361	0.372857
$235$	−16.3216	−1.06470
$236$	−2.34531	−0.152667
$237$	6.51811	0.423397
$238$	1.48977	0.0965671
$239$	−1.45542	−0.0941434	−0.0470717	−	0.998892i	$-0.514989\pi$
$239$	−1.45542	−0.0941434	−0.0470717	+	0.998892i	$0.514989\pi$
$240$	−14.2710	−0.921190
$241$	−24.7738	−1.59582	−0.797911	−	0.602775i	$-0.794062\pi$
$241$	−24.7738	−1.59582	−0.797911	+	0.602775i	$0.794062\pi$
$242$	6.97383	0.448295
$243$	1.00000	0.0641500
$244$	−0.636166	−0.0407263
$245$	−23.6975	−1.51398
$246$	−0.820935	−0.0523409
$247$	−18.3700	−1.16886
$248$	−10.3689	−0.658428
$249$	−8.43584	−0.534600
$250$	−38.6754	−2.44605
$251$	0.764272	0.0482404	0.0241202	−	0.999709i	$-0.492322\pi$
$251$	0.764272	0.0482404	0.0241202	+	0.999709i	$0.492322\pi$
$252$	−0.273194	−0.0172096
$253$	20.2960	1.27600
$254$	−22.9151	−1.43782
$255$	−4.13081	−0.258681
$256$	−5.74400	−0.359000
$257$	−22.4408	−1.39982	−0.699909	−	0.714232i	$-0.746776\pi$
$257$	−22.4408	−1.39982	−0.699909	+	0.714232i	$0.746776\pi$
$258$	−6.45953	−0.402153
$259$	0.198352	0.0123250
$260$	4.32053	0.267948
$261$	−9.45358	−0.585162
$262$	−16.4557	−1.01664
$263$	8.19790	0.505504	0.252752	−	0.967531i	$-0.418664\pi$
$263$	8.19790	0.505504	0.252752	+	0.967531i	$0.418664\pi$
$264$	7.12240	0.438353
$265$	2.30426	0.141550
$266$	−6.35996	−0.389954
$267$	−9.84503	−0.602506
$268$	−3.91582	−0.239197
$269$	4.61222	0.281212	0.140606	−	0.990066i	$-0.455095\pi$
$269$	4.61222	0.281212	0.140606	+	0.990066i	$0.455095\pi$
$270$	−5.47535	−0.333219
$271$	−17.7056	−1.07554	−0.537768	−	0.843093i	$-0.680732\pi$
$271$	−17.7056	−1.07554	−0.537768	+	0.843093i	$0.680732\pi$
$272$	3.45478	0.209477
$273$	−4.83630	−0.292706
$274$	−16.1753	−0.977187
$275$	28.8989	1.74267
$276$	−2.05937	−0.123960
$277$	−6.07925	−0.365267	−0.182633	−	0.983181i	$-0.558462\pi$
$277$	−6.07925	−0.365267	−0.182633	+	0.983181i	$0.558462\pi$
$278$	−20.6412	−1.23798
$279$	−3.48750	−0.208791
$280$	13.8037	0.824928
$281$	−19.6731	−1.17360	−0.586800	−	0.809732i	$-0.699613\pi$
$281$	−19.6731	−1.17360	−0.586800	+	0.809732i	$0.699613\pi$
$282$	5.23726	0.311875
$283$	−24.5440	−1.45899	−0.729494	−	0.683987i	$-0.760245\pi$
$283$	−24.5440	−1.45899	−0.729494	+	0.683987i	$0.760245\pi$
$284$	−1.17811	−0.0699082
$285$	17.6348	1.04460
$286$	13.6633	0.807929
$287$	0.696101	0.0410895
$288$	−1.36706	−0.0805547
$289$	1.00000	0.0588235
$290$	51.7617	3.03955
$291$	−1.82501	−0.106984
$292$	1.65591	0.0969050
$293$	−25.8764	−1.51171	−0.755857	−	0.654737i	$-0.772779\pi$
$293$	−25.8764	−1.51171	−0.755857	+	0.654737i	$0.772779\pi$
$294$	7.60405	0.443477
$295$	39.8571	2.32057
$296$	0.524706	0.0304979
$297$	2.39556	0.139004
$298$	−21.0630	−1.22015
$299$	−36.4567	−2.10834
$300$	−2.93228	−0.169295
$301$	5.47727	0.315705
$302$	−13.5060	−0.777183
$303$	−3.04469	−0.174913
$304$	−14.7488	−0.845902
$305$	10.8112	0.619049
$306$	1.32549	0.0757734
$307$	−19.3449	−1.10407	−0.552037	−	0.833820i	$-0.686149\pi$
$307$	−19.3449	−1.10407	−0.552037	+	0.833820i	$0.686149\pi$
$308$	−0.654450	−0.0372908
$309$	4.94953	0.281569
$310$	19.0953	1.08454
$311$	−5.64864	−0.320305	−0.160153	−	0.987092i	$-0.551199\pi$
$311$	−5.64864	−0.320305	−0.160153	+	0.987092i	$0.551199\pi$
$312$	−12.7936	−0.724295
$313$	0.465494	0.0263113	0.0131556	−	0.999913i	$-0.495812\pi$
$313$	0.465494	0.0263113	0.0131556	+	0.999913i	$0.495812\pi$
$314$	1.32549	0.0748019
$315$	4.64275	0.261589
$316$	−1.58435	−0.0891268
$317$	16.6798	0.936831	0.468415	−	0.883508i	$-0.344825\pi$
$317$	16.6798	0.936831	0.468415	+	0.883508i	$0.344825\pi$
$318$	−0.739392	−0.0414630
$319$	−22.6466	−1.26797
$320$	36.0272	2.01398
$321$	−0.810532	−0.0452395
$322$	−12.6218	−0.703387
$323$	−4.26910	−0.237539
$324$	−0.243069	−0.0135038
$325$	−51.9096	−2.87943
$326$	−4.42937	−0.245320
$327$	1.63008	0.0901438
$328$	1.84141	0.101675
$329$	−4.44087	−0.244833
$330$	−13.1165	−0.722040
$331$	−21.0245	−1.15561	−0.577807	−	0.816174i	$-0.696091\pi$
$331$	−21.0245	−1.15561	−0.577807	+	0.816174i	$0.696091\pi$
$332$	2.05049	0.112535
$333$	0.176480	0.00967106
$334$	15.5677	0.851827
$335$	66.5469	3.63585
$336$	−3.88294	−0.211832
$337$	−3.63096	−0.197791	−0.0988956	−	0.995098i	$-0.531531\pi$
$337$	−3.63096	−0.197791	−0.0988956	+	0.995098i	$0.531531\pi$
$338$	−7.31131	−0.397683
$339$	−9.73032	−0.528479
$340$	1.00407	0.0544534
$341$	−8.35450	−0.452422
$342$	−5.65867	−0.305986
$343$	−14.3153	−0.772953
$344$	14.4892	0.781204
$345$	34.9977	1.88421
$346$	−1.41233	−0.0759273
$347$	23.9798	1.28730	0.643652	−	0.765318i	$-0.277418\pi$
$347$	23.9798	1.28730	0.643652	+	0.765318i	$0.277418\pi$
$348$	2.29787	0.123179
$349$	9.65666	0.516909	0.258455	−	0.966023i	$-0.416787\pi$
$349$	9.65666	0.516909	0.258455	+	0.966023i	$0.416787\pi$
$350$	−17.9719	−0.960636
$351$	−4.30301	−0.229678
$352$	−3.27487	−0.174551
$353$	24.4430	1.30097	0.650485	−	0.759519i	$-0.274566\pi$
$353$	24.4430	1.30097	0.650485	+	0.759519i	$0.274566\pi$
$354$	−12.7893	−0.679746
$355$	20.0213	1.06262
$356$	2.39302	0.126830
$357$	−1.12393	−0.0594849
$358$	−20.8491	−1.10191
$359$	−29.1483	−1.53839	−0.769194	−	0.639016i	$-0.779342\pi$
$359$	−29.1483	−1.53839	−0.769194	+	0.639016i	$0.779342\pi$
$360$	12.2816	0.647297
$361$	−0.774746	−0.0407761
$362$	−13.6498	−0.717419
$363$	−5.26131	−0.276147
$364$	1.17556	0.0616158
$365$	−28.1412	−1.47298
$366$	−3.46911	−0.181333
$367$	5.80801	0.303175	0.151588	−	0.988444i	$-0.451561\pi$
$367$	5.80801	0.303175	0.151588	+	0.988444i	$0.451561\pi$
$368$	−29.2701	−1.52581
$369$	0.619343	0.0322417
$370$	−0.966292	−0.0502351
$371$	0.626957	0.0325500
$372$	0.847704	0.0439514
$373$	16.1918	0.838379	0.419190	−	0.907899i	$-0.362314\pi$
$373$	16.1918	0.838379	0.419190	+	0.907899i	$0.362314\pi$
$374$	3.17529	0.164190
$375$	29.1782	1.50675
$376$	−11.7475	−0.605833
$377$	40.6789	2.09507
$378$	−1.48977	−0.0766253
$379$	10.2046	0.524177	0.262089	−	0.965044i	$-0.415589\pi$
$379$	10.2046	0.524177	0.262089	+	0.965044i	$0.415589\pi$
$380$	−4.28649	−0.219892
$381$	17.2880	0.885690
$382$	2.11819	0.108376
$383$	−34.8240	−1.77942	−0.889712	−	0.456523i	$-0.849095\pi$
$383$	−34.8240	−1.77942	−0.889712	+	0.456523i	$0.849095\pi$
$384$	−8.82628	−0.450414
$385$	11.1220	0.566828
$386$	−2.43052	−0.123710
$387$	4.87331	0.247724
$388$	0.443605	0.0225206
$389$	−14.9888	−0.759964	−0.379982	−	0.924994i	$-0.624070\pi$
$389$	−14.9888	−0.759964	−0.379982	+	0.924994i	$0.624070\pi$
$390$	23.5605	1.19303
$391$	−8.47236	−0.428466
$392$	−17.0564	−0.861479
$393$	12.4148	0.626244
$394$	−2.06533	−0.104050
$395$	26.9251	1.35475
$396$	−0.582286	−0.0292610
$397$	27.1407	1.36215	0.681077	−	0.732212i	$-0.261512\pi$
$397$	27.1407	1.36215	0.681077	+	0.732212i	$0.261512\pi$
$398$	24.6828	1.23724
$399$	4.79819	0.240210
$400$	−41.6769	−2.08385
$401$	9.47911	0.473364	0.236682	−	0.971587i	$-0.423940\pi$
$401$	9.47911	0.473364	0.236682	+	0.971587i	$0.423940\pi$
$402$	−21.3536	−1.06502
$403$	15.0068	0.747540
$404$	0.740071	0.0368199
$405$	4.13081	0.205261
$406$	14.0836	0.698958
$407$	0.422769	0.0209559
$408$	−2.97317	−0.147194
$409$	−30.5769	−1.51193	−0.755965	−	0.654612i	$-0.772832\pi$
$409$	−30.5769	−1.51193	−0.755965	+	0.654612i	$0.772832\pi$
$410$	−3.39112	−0.167476
$411$	12.2033	0.601942
$412$	−1.20308	−0.0592714
$413$	10.8446	0.533626
$414$	−11.2301	−0.551927
$415$	−34.8468	−1.71056
$416$	5.88247	0.288412
$417$	15.5725	0.762588
$418$	−13.5557	−0.663029
$419$	28.4379	1.38928	0.694642	−	0.719355i	$-0.255563\pi$
$419$	28.4379	1.38928	0.694642	+	0.719355i	$0.255563\pi$
$420$	−1.12851	−0.0550656
$421$	23.8522	1.16249	0.581243	−	0.813730i	$-0.302566\pi$
$421$	23.8522	1.16249	0.581243	+	0.813730i	$0.302566\pi$
$422$	−29.8174	−1.45149
$423$	−3.95118	−0.192113
$424$	1.65851	0.0805442
$425$	−12.0636	−0.585168
$426$	−6.42444	−0.311265
$427$	2.94158	0.142353
$428$	0.197015	0.00952310
$429$	−10.3081	−0.497680
$430$	−26.6831	−1.28677
$431$	−3.56597	−0.171767	−0.0858833	−	0.996305i	$-0.527371\pi$
$431$	−3.56597	−0.171767	−0.0858833	+	0.996305i	$0.527371\pi$
$432$	−3.45478	−0.166218
$433$	−8.90615	−0.428002	−0.214001	−	0.976833i	$-0.568650\pi$
$433$	−8.90615	−0.428002	−0.214001	+	0.976833i	$0.568650\pi$
$434$	5.19556	0.249395
$435$	−39.0509	−1.87235
$436$	−0.396223	−0.0189756
$437$	36.1694	1.73022
$438$	9.02994	0.431467
$439$	−16.9651	−0.809702	−0.404851	−	0.914383i	$-0.632677\pi$
$439$	−16.9651	−0.809702	−0.404851	+	0.914383i	$0.632677\pi$
$440$	29.4212	1.40260
$441$	−5.73677	−0.273180
$442$	−5.70361	−0.271293
$443$	−20.3160	−0.965244	−0.482622	−	0.875829i	$-0.660315\pi$
$443$	−20.3160	−0.965244	−0.482622	+	0.875829i	$0.660315\pi$
$444$	−0.0428969	−0.00203580
$445$	−40.6679	−1.92784
$446$	21.7414	1.02948
$447$	15.8907	0.751605
$448$	9.80248	0.463124
$449$	3.20098	0.151063	0.0755317	−	0.997143i	$-0.475935\pi$
$449$	3.20098	0.151063	0.0755317	+	0.997143i	$0.475935\pi$
$450$	−15.9902	−0.753783
$451$	1.48367	0.0698634
$452$	2.36514	0.111247
$453$	10.1894	0.478740
$454$	−14.7332	−0.691463
$455$	−19.9778	−0.936574
$456$	12.6928	0.594394
$457$	6.43673	0.301098	0.150549	−	0.988603i	$-0.451896\pi$
$457$	6.43673	0.301098	0.150549	+	0.988603i	$0.451896\pi$
$458$	−21.7348	−1.01560
$459$	−1.00000	−0.0466760
$460$	−8.50686	−0.396634
$461$	35.3495	1.64639	0.823195	−	0.567759i	$-0.192190\pi$
$461$	35.3495	1.64639	0.823195	+	0.567759i	$0.192190\pi$
$462$	−3.56882	−0.166036
$463$	−1.10272	−0.0512477	−0.0256238	−	0.999672i	$-0.508157\pi$
$463$	−1.10272	−0.0512477	−0.0256238	+	0.999672i	$0.508157\pi$
$464$	32.6600	1.51620
$465$	−14.4062	−0.668071
$466$	2.42652	0.112406
$467$	24.5100	1.13419	0.567093	−	0.823654i	$-0.308068\pi$
$467$	24.5100	1.13419	0.567093	+	0.823654i	$0.308068\pi$
$468$	1.04593	0.0483481
$469$	18.1065	0.836079
$470$	21.6341	0.997907
$471$	−1.00000	−0.0460776
$472$	28.6874	1.32044
$473$	11.6743	0.536784
$474$	−8.63971	−0.396835
$475$	51.5006	2.36301
$476$	0.273194	0.0125218
$477$	0.557824	0.0255410
$478$	1.92915	0.0882373
$479$	−25.8787	−1.18243	−0.591215	−	0.806514i	$-0.701352\pi$
$479$	−25.8787	−1.18243	−0.591215	+	0.806514i	$0.701352\pi$
$480$	−5.64706	−0.257752
$481$	−0.759397	−0.0346255
$482$	32.8375	1.49571
$483$	9.52237	0.433283
$484$	1.27886	0.0581301
$485$	−7.53878	−0.342318
$486$	−1.32549	−0.0601256
$487$	−25.1521	−1.13975	−0.569875	−	0.821731i	$-0.693008\pi$
$487$	−25.1521	−1.13975	−0.569875	+	0.821731i	$0.693008\pi$
$488$	7.78145	0.352250
$489$	3.34168	0.151116
$490$	31.4109	1.41900
$491$	−13.4937	−0.608964	−0.304482	−	0.952518i	$-0.598483\pi$
$491$	−13.4937	−0.608964	−0.304482	+	0.952518i	$0.598483\pi$
$492$	−0.150543	−0.00678701
$493$	9.45358	0.425768
$494$	24.3493	1.09553
$495$	9.89558	0.444773
$496$	12.0485	0.540996
$497$	5.44751	0.244354
$498$	11.1816	0.501061
$499$	−31.7885	−1.42305	−0.711525	−	0.702661i	$-0.751995\pi$
$499$	−31.7885	−1.42305	−0.711525	+	0.702661i	$0.751995\pi$
$500$	−7.09231	−0.317178
$501$	−11.7448	−0.524721
$502$	−1.01304	−0.0452141
$503$	−13.8605	−0.618011	−0.309006	−	0.951060i	$-0.599996\pi$
$503$	−13.8605	−0.618011	−0.309006	+	0.951060i	$0.599996\pi$
$504$	3.34165	0.148849
$505$	−12.5770	−0.559670
$506$	−26.9022	−1.19595
$507$	5.51592	0.244971
$508$	−4.20217	−0.186441
$509$	−38.2944	−1.69737	−0.848684	−	0.528900i	$-0.822605\pi$
$509$	−38.2944	−1.69737	−0.848684	+	0.528900i	$0.822605\pi$
$510$	5.47535	0.242453
$511$	−7.65681	−0.338717
$512$	25.2662	1.11662
$513$	4.26910	0.188486
$514$	29.7451	1.31200
$515$	20.4456	0.900939
$516$	−1.18455	−0.0521469
$517$	−9.46528	−0.416283
$518$	−0.262914	−0.0115518
$519$	1.06551	0.0467708
$520$	−52.8479	−2.31753
$521$	7.00046	0.306696	0.153348	−	0.988172i	$-0.450995\pi$
$521$	7.00046	0.306696	0.153348	+	0.988172i	$0.450995\pi$
$522$	12.5307	0.548452
$523$	13.5795	0.593791	0.296896	−	0.954910i	$-0.404049\pi$
$523$	13.5795	0.593791	0.296896	+	0.954910i	$0.404049\pi$
$524$	−3.01765	−0.131827
$525$	13.5586	0.591747
$526$	−10.8662	−0.473791
$527$	3.48750	0.151918
$528$	−8.27612	−0.360172
$529$	48.7809	2.12091
$530$	−3.05428	−0.132670
$531$	9.64875	0.418720
$532$	−1.16629	−0.0505652
$533$	−2.66504	−0.115436
$534$	13.0495	0.564708
$535$	−3.34815	−0.144753
$536$	47.8976	2.06886
$537$	15.7293	0.678771
$538$	−6.11346	−0.263570
$539$	−13.7428	−0.591943
$540$	−1.00407	−0.0432084
$541$	−18.0132	−0.774446	−0.387223	−	0.921986i	$-0.626566\pi$
$541$	−18.0132	−0.774446	−0.387223	+	0.921986i	$0.626566\pi$
$542$	23.4686	1.00806
$543$	10.2979	0.441926
$544$	1.36706	0.0586122
$545$	6.73355	0.288434
$546$	6.41048	0.274343
$547$	−23.5719	−1.00786	−0.503932	−	0.863743i	$-0.668114\pi$
$547$	−23.5719	−1.00786	−0.503932	+	0.863743i	$0.668114\pi$
$548$	−2.96623	−0.126711
$549$	2.61722	0.111700
$550$	−38.3053	−1.63334
$551$	−40.3583	−1.71932
$552$	25.1898	1.07215
$553$	7.32592	0.311530
$554$	8.05800	0.342352
$555$	0.729006	0.0309446
$556$	−3.78519	−0.160528
$557$	−12.3278	−0.522347	−0.261174	−	0.965292i	$-0.584109\pi$
$557$	−12.3278	−0.522347	−0.261174	+	0.965292i	$0.584109\pi$
$558$	4.62266	0.195693
$559$	−20.9699	−0.886932
$560$	−16.0397	−0.677800
$561$	−2.39556	−0.101140
$562$	26.0766	1.09997
$563$	36.5798	1.54166	0.770828	−	0.637043i	$-0.219843\pi$
$563$	36.5798	1.54166	0.770828	+	0.637043i	$0.219843\pi$
$564$	0.960411	0.0404406
$565$	−40.1941	−1.69098
$566$	32.5329	1.36746
$567$	1.12393	0.0472008
$568$	14.4105	0.604649
$569$	31.9737	1.34041	0.670204	−	0.742177i	$-0.266206\pi$
$569$	31.9737	1.34041	0.670204	+	0.742177i	$0.266206\pi$
$570$	−23.3749	−0.979065
$571$	1.42981	0.0598357	0.0299178	−	0.999552i	$-0.490475\pi$
$571$	1.42981	0.0598357	0.0299178	+	0.999552i	$0.490475\pi$
$572$	2.50558	0.104764
$573$	−1.59804	−0.0667591
$574$	−0.922676	−0.0385118
$575$	102.207	4.26232
$576$	8.72159	0.363399
$577$	−40.4030	−1.68200	−0.841000	−	0.541035i	$-0.818033\pi$
$577$	−40.4030	−1.68200	−0.841000	+	0.541035i	$0.818033\pi$
$578$	−1.32549	−0.0551332
$579$	1.83367	0.0762048
$580$	9.49207	0.394137
$581$	−9.48132	−0.393351
$582$	2.41904	0.100273
$583$	1.33630	0.0553438
$584$	−20.2548	−0.838149
$585$	−17.7749	−0.734902
$586$	34.2989	1.41688
$587$	36.5084	1.50686	0.753431	−	0.657527i	$-0.228397\pi$
$587$	36.5084	1.50686	0.753431	+	0.657527i	$0.228397\pi$
$588$	1.39443	0.0575054
$589$	−14.8885	−0.613470
$590$	−52.8303	−2.17499
$591$	1.55816	0.0640941
$592$	−0.609701	−0.0250585
$593$	−43.7114	−1.79501	−0.897506	−	0.441002i	$-0.854623\pi$
$593$	−43.7114	−1.79501	−0.897506	+	0.441002i	$0.854623\pi$
$594$	−3.17529	−0.130284
$595$	−4.64275	−0.190334
$596$	−3.86254	−0.158216
$597$	−18.6216	−0.762131
$598$	48.3231	1.97608
$599$	2.80035	0.114419	0.0572095	−	0.998362i	$-0.481780\pi$
$599$	2.80035	0.114419	0.0572095	+	0.998362i	$0.481780\pi$
$600$	35.8670	1.46426
$601$	−6.18670	−0.252361	−0.126180	−	0.992007i	$-0.540272\pi$
$601$	−6.18670	−0.252361	−0.126180	+	0.992007i	$0.540272\pi$
$602$	−7.26008	−0.295899
$603$	16.1099	0.656047
$604$	−2.47673	−0.100777
$605$	−21.7334	−0.883590
$606$	4.03572	0.163940
$607$	1.38245	0.0561121	0.0280560	−	0.999606i	$-0.491068\pi$
$607$	1.38245	0.0561121	0.0280560	+	0.999606i	$0.491068\pi$
$608$	−5.83612	−0.236686
$609$	−10.6252	−0.430555
$610$	−14.3302	−0.580213
$611$	17.0020	0.687827
$612$	0.243069	0.00982549
$613$	0.640901	0.0258858	0.0129429	−	0.999916i	$-0.495880\pi$
$613$	0.640901	0.0258858	0.0129429	+	0.999916i	$0.495880\pi$
$614$	25.6416	1.03481
$615$	2.55839	0.103164
$616$	8.00510	0.322535
$617$	−15.5763	−0.627077	−0.313538	−	0.949576i	$-0.601514\pi$
$617$	−15.5763	−0.627077	−0.313538	+	0.949576i	$0.601514\pi$
$618$	−6.56057	−0.263905
$619$	22.7161	0.913038	0.456519	−	0.889714i	$-0.349096\pi$
$619$	22.7161	0.913038	0.456519	+	0.889714i	$0.349096\pi$
$620$	3.50170	0.140632
$621$	8.47236	0.339984
$622$	7.48724	0.300211
$623$	−11.0652	−0.443316
$624$	14.8660	0.595115
$625$	60.2115	2.40846
$626$	−0.617009	−0.0246606
$627$	10.2269	0.408422
$628$	0.243069	0.00969952
$629$	−0.176480	−0.00703673
$630$	−6.15393	−0.245178
$631$	2.83402	0.112821	0.0564104	−	0.998408i	$-0.482034\pi$
$631$	2.83402	0.112821	0.0564104	+	0.998408i	$0.482034\pi$
$632$	19.3795	0.770874
$633$	22.4954	0.894110
$634$	−22.1089	−0.878058
$635$	71.4133	2.83395
$636$	−0.135590	−0.00537649
$637$	24.6854	0.978072
$638$	30.0179	1.18842
$639$	4.84683	0.191738
$640$	−36.4596	−1.44119
$641$	13.7958	0.544901	0.272450	−	0.962170i	$-0.412166\pi$
$641$	13.7958	0.544901	0.272450	+	0.962170i	$0.412166\pi$
$642$	1.07435	0.0424014
$643$	21.6439	0.853553	0.426776	−	0.904357i	$-0.359649\pi$
$643$	21.6439	0.853553	0.426776	+	0.904357i	$0.359649\pi$
$644$	−2.31459	−0.0912078
$645$	20.1307	0.792645
$646$	5.65867	0.222637
$647$	44.0807	1.73299	0.866496	−	0.499183i	$-0.166367\pi$
$647$	44.0807	1.73299	0.866496	+	0.499183i	$0.166367\pi$
$648$	2.97317	0.116797
$649$	23.1141	0.907309
$650$	68.8058	2.69879
$651$	−3.91972	−0.153626
$652$	−0.812258	−0.0318105
$653$	39.4127	1.54234	0.771169	−	0.636631i	$-0.219672\pi$
$653$	39.4127	1.54234	0.771169	+	0.636631i	$0.219672\pi$
$654$	−2.16066	−0.0844886
$655$	51.2831	2.00380
$656$	−2.13969	−0.0835410
$657$	−6.81252	−0.265782
$658$	5.88634	0.229473
$659$	−3.07256	−0.119690	−0.0598449	−	0.998208i	$-0.519061\pi$
$659$	−3.07256	−0.119690	−0.0598449	+	0.998208i	$0.519061\pi$
$660$	−2.40531	−0.0936265
$661$	6.03262	0.234642	0.117321	−	0.993094i	$-0.462569\pi$
$661$	6.03262	0.234642	0.117321	+	0.993094i	$0.462569\pi$
$662$	27.8679	1.08312
$663$	4.30301	0.167115
$664$	−25.0812	−0.973339
$665$	19.8204	0.768602
$666$	−0.233923	−0.00906435
$667$	−80.0942	−3.10126
$668$	2.85481	0.110456
$669$	−16.4025	−0.634157
$670$	−88.2075	−3.40775
$671$	6.26970	0.242039
$672$	−1.53648	−0.0592711
$673$	−9.96820	−0.384246	−0.192123	−	0.981371i	$-0.561537\pi$
$673$	−9.96820	−0.384246	−0.192123	+	0.981371i	$0.561537\pi$
$674$	4.81282	0.185383
$675$	12.0636	0.464326
$676$	−1.34075	−0.0515673
$677$	−11.7896	−0.453112	−0.226556	−	0.973998i	$-0.572747\pi$
$677$	−11.7896	−0.453112	−0.226556	+	0.973998i	$0.572747\pi$
$678$	12.8975	0.495324
$679$	−2.05119	−0.0787176
$680$	−12.2816	−0.470978
$681$	11.1153	0.425938
$682$	11.0738	0.424039
$683$	49.1404	1.88030	0.940152	−	0.340754i	$-0.110682\pi$
$683$	49.1404	1.88030	0.940152	+	0.340754i	$0.110682\pi$
$684$	−1.03769	−0.0396770
$685$	50.4093	1.92604
$686$	18.9748	0.724461
$687$	16.3975	0.625605
$688$	−16.8362	−0.641874
$689$	−2.40032	−0.0914451
$690$	−46.3892	−1.76601
$691$	−1.25199	−0.0476281	−0.0238140	−	0.999716i	$-0.507581\pi$
$691$	−1.25199	−0.0476281	−0.0238140	+	0.999716i	$0.507581\pi$
$692$	−0.258993	−0.00984545
$693$	2.69245	0.102278
$694$	−31.7851	−1.20655
$695$	64.3269	2.44006
$696$	−28.1071	−1.06540
$697$	−0.619343	−0.0234593
$698$	−12.7998	−0.484481
$699$	−1.83065	−0.0692416
$700$	−3.29568	−0.124565
$701$	−10.6240	−0.401264	−0.200632	−	0.979667i	$-0.564300\pi$
$701$	−10.6240	−0.401264	−0.200632	+	0.979667i	$0.564300\pi$
$702$	5.70361	0.215269
$703$	0.753413	0.0284155
$704$	20.8930	0.787436
$705$	−16.3216	−0.614706
$706$	−32.3990	−1.21935
$707$	−3.42203	−0.128699
$708$	−2.34531	−0.0881423
$709$	−10.3598	−0.389071	−0.194535	−	0.980895i	$-0.562320\pi$
$709$	−10.3598	−0.389071	−0.194535	+	0.980895i	$0.562320\pi$
$710$	−26.5381	−0.995957
$711$	6.51811	0.244448
$712$	−29.2710	−1.09698
$713$	−29.5474	−1.10656
$714$	1.48977	0.0557531
$715$	−42.5808	−1.59243
$716$	−3.82332	−0.142884
$717$	−1.45542	−0.0543537
$718$	38.6358	1.44188
$719$	−36.3732	−1.35649	−0.678245	−	0.734836i	$-0.737259\pi$
$719$	−36.3732	−1.35649	−0.678245	+	0.734836i	$0.737259\pi$
$720$	−14.2710	−0.531849
$721$	5.56294	0.207175
$722$	1.02692	0.0382180
$723$	−24.7738	−0.921348
$724$	−2.50311	−0.0930273
$725$	−114.044	−4.23548
$726$	6.97383	0.258823
$727$	−44.1941	−1.63907	−0.819535	−	0.573029i	$-0.805768\pi$
$727$	−44.1941	−1.63907	−0.819535	+	0.573029i	$0.805768\pi$
$728$	−14.3791	−0.532927
$729$	1.00000	0.0370370
$730$	37.3009	1.38057
$731$	−4.87331	−0.180246
$732$	−0.636166	−0.0235134
$733$	−42.3336	−1.56363	−0.781814	−	0.623511i	$-0.785706\pi$
$733$	−42.3336	−1.56363	−0.781814	+	0.623511i	$0.785706\pi$
$734$	−7.69847	−0.284156
$735$	−23.6975	−0.874095
$736$	−11.5822	−0.426926
$737$	38.5922	1.42156
$738$	−0.820935	−0.0302190
$739$	0.930052	0.0342125	0.0171063	−	0.999854i	$-0.494555\pi$
$739$	0.930052	0.0342125	0.0171063	+	0.999854i	$0.494555\pi$
$740$	−0.177199	−0.00651396
$741$	−18.3700	−0.674839
$742$	−0.831027	−0.0305080
$743$	12.2935	0.451006	0.225503	−	0.974242i	$-0.427597\pi$
$743$	12.2935	0.451006	0.225503	+	0.974242i	$0.427597\pi$
$744$	−10.3689	−0.380144
$745$	65.6414	2.40492
$746$	−21.4621	−0.785783
$747$	−8.43584	−0.308651
$748$	0.582286	0.0212905
$749$	−0.910984	−0.0332866
$750$	−38.6754	−1.41223
$751$	33.4363	1.22011	0.610054	−	0.792360i	$-0.291148\pi$
$751$	33.4363	1.22011	0.610054	+	0.792360i	$0.291148\pi$
$752$	13.6505	0.497781
$753$	0.764272	0.0278516
$754$	−53.9196	−1.96364
$755$	42.0905	1.53183
$756$	−0.273194	−0.00993595
$757$	−3.01824	−0.109700	−0.0548500	−	0.998495i	$-0.517468\pi$
$757$	−3.01824	−0.109700	−0.0548500	+	0.998495i	$0.517468\pi$
$758$	−13.5262	−0.491293
$759$	20.2960	0.736699
$760$	52.4314	1.90189
$761$	5.86440	0.212584	0.106292	−	0.994335i	$-0.466102\pi$
$761$	5.86440	0.212584	0.106292	+	0.994335i	$0.466102\pi$
$762$	−22.9151	−0.830126
$763$	1.83210	0.0663266
$764$	0.388435	0.0140531
$765$	−4.13081	−0.149350
$766$	46.1590	1.66779
$767$	−41.5187	−1.49915
$768$	−5.74400	−0.207269
$769$	5.82211	0.209950	0.104975	−	0.994475i	$-0.466524\pi$
$769$	5.82211	0.209950	0.104975	+	0.994475i	$0.466524\pi$
$770$	−14.7421	−0.531268
$771$	−22.4408	−0.808186
$772$	−0.445709	−0.0160414
$773$	−14.3329	−0.515518	−0.257759	−	0.966209i	$-0.582984\pi$
$773$	−14.3329	−0.515518	−0.257759	+	0.966209i	$0.582984\pi$
$774$	−6.45953	−0.232183
$775$	−42.0716	−1.51126
$776$	−5.42608	−0.194785
$777$	0.198352	0.00711584
$778$	19.8676	0.712288
$779$	2.64404	0.0947326
$780$	4.32053	0.154700
$781$	11.6109	0.415469
$782$	11.2301	0.401586
$783$	−9.45358	−0.337844
$784$	19.8193	0.707832
$785$	−4.13081	−0.147435
$786$	−16.4557	−0.586956
$787$	19.8671	0.708184	0.354092	−	0.935211i	$-0.384790\pi$
$787$	19.8671	0.708184	0.354092	+	0.935211i	$0.384790\pi$
$788$	−0.378740	−0.0134921
$789$	8.19790	0.291853
$790$	−35.6890	−1.26976
$791$	−10.9362	−0.388848
$792$	7.12240	0.253083
$793$	−11.2619	−0.399923
$794$	−35.9748	−1.27670
$795$	2.30426	0.0817238
$796$	4.52633	0.160432
$797$	27.1993	0.963450	0.481725	−	0.876323i	$-0.340010\pi$
$797$	27.1993	0.963450	0.481725	+	0.876323i	$0.340010\pi$
$798$	−6.35996	−0.225140
$799$	3.95118	0.139783
$800$	−16.4916	−0.583066
$801$	−9.84503	−0.347857
$802$	−12.5645	−0.443667
$803$	−16.3198	−0.575912
$804$	−3.91582	−0.138100
$805$	39.3351	1.38638
$806$	−19.8914	−0.700643
$807$	4.61222	0.162358
$808$	−9.05239	−0.318462
$809$	−1.45687	−0.0512207	−0.0256103	−	0.999672i	$-0.508153\pi$
$809$	−1.45687	−0.0512207	−0.0256103	+	0.999672i	$0.508153\pi$
$810$	−5.47535	−0.192384
$811$	0.914371	0.0321079	0.0160540	−	0.999871i	$-0.494890\pi$
$811$	0.914371	0.0321079	0.0160540	+	0.999871i	$0.494890\pi$
$812$	2.58266	0.0906335
$813$	−17.7056	−0.620961
$814$	−0.560377	−0.0196412
$815$	13.8038	0.483526
$816$	3.45478	0.120941
$817$	20.8047	0.727863
$818$	40.5294	1.41708
$819$	−4.83630	−0.168994
$820$	−0.621865	−0.0217165
$821$	−46.4847	−1.62233	−0.811164	−	0.584818i	$-0.801166\pi$
$821$	−46.4847	−1.62233	−0.811164	+	0.584818i	$0.801166\pi$
$822$	−16.1753	−0.564179
$823$	48.5874	1.69365	0.846825	−	0.531872i	$-0.178511\pi$
$823$	48.5874	1.69365	0.846825	+	0.531872i	$0.178511\pi$
$824$	14.7158	0.512650
$825$	28.8989	1.00613
$826$	−14.3744	−0.500148
$827$	14.7199	0.511863	0.255931	−	0.966695i	$-0.417618\pi$
$827$	14.7199	0.511863	0.255931	+	0.966695i	$0.417618\pi$
$828$	−2.05937	−0.0715681
$829$	42.8250	1.48737	0.743687	−	0.668528i	$-0.233075\pi$
$829$	42.8250	1.48737	0.743687	+	0.668528i	$0.233075\pi$
$830$	46.1892	1.60325
$831$	−6.07925	−0.210887
$832$	−37.5291	−1.30109
$833$	5.73677	0.198767
$834$	−20.6412	−0.714747
$835$	−48.5157	−1.67895
$836$	−2.48584	−0.0859745
$837$	−3.48750	−0.120546
$838$	−37.6943	−1.30213
$839$	31.9505	1.10305	0.551526	−	0.834158i	$-0.314046\pi$
$839$	31.9505	1.10305	0.551526	+	0.834158i	$0.314046\pi$
$840$	13.8037	0.476273
$841$	60.3703	2.08173
$842$	−31.6160	−1.08956
$843$	−19.6731	−0.677579
$844$	−5.46793	−0.188214
$845$	22.7852	0.783834
$846$	5.23726	0.180061
$847$	−5.91336	−0.203186
$848$	−1.92716	−0.0661789
$849$	−24.5440	−0.842348
$850$	15.9902	0.548458
$851$	1.49521	0.0512550
$852$	−1.17811	−0.0403615
$853$	3.79375	0.129896	0.0649478	−	0.997889i	$-0.479312\pi$
$853$	3.79375	0.129896	0.0649478	+	0.997889i	$0.479312\pi$
$854$	−3.89905	−0.133423
$855$	17.6348	0.603099
$856$	−2.40985	−0.0823670
$857$	4.30552	0.147074	0.0735369	−	0.997292i	$-0.476571\pi$
$857$	4.30552	0.147074	0.0735369	+	0.997292i	$0.476571\pi$
$858$	13.6633	0.466458
$859$	−25.3310	−0.864283	−0.432142	−	0.901806i	$-0.642242\pi$
$859$	−25.3310	−0.864283	−0.432142	+	0.901806i	$0.642242\pi$
$860$	−4.89315	−0.166855
$861$	0.696101	0.0237230
$862$	4.72666	0.160991
$863$	7.83443	0.266687	0.133344	−	0.991070i	$-0.457429\pi$
$863$	7.83443	0.266687	0.133344	+	0.991070i	$0.457429\pi$
$864$	−1.36706	−0.0465083
$865$	4.40143	0.149653
$866$	11.8050	0.401151
$867$	1.00000	0.0339618
$868$	0.952763	0.0323389
$869$	15.6145	0.529686
$870$	51.7617	1.75489
$871$	−69.3212	−2.34886
$872$	4.84652	0.164124
$873$	−1.82501	−0.0617673
$874$	−47.9423	−1.62167
$875$	32.7943	1.10865
$876$	1.65591	0.0559481
$877$	−32.6829	−1.10362	−0.551812	−	0.833968i	$-0.686064\pi$
$877$	−32.6829	−1.10362	−0.551812	+	0.833968i	$0.686064\pi$
$878$	22.4872	0.758905
$879$	−25.8764	−0.872788
$880$	−34.1870	−1.15244
$881$	42.8975	1.44525	0.722627	−	0.691239i	$-0.242935\pi$
$881$	42.8975	1.44525	0.722627	+	0.691239i	$0.242935\pi$
$882$	7.60405	0.256042
$883$	−2.66840	−0.0897987	−0.0448993	−	0.998992i	$-0.514297\pi$
$883$	−2.66840	−0.0897987	−0.0448993	+	0.998992i	$0.514297\pi$
$884$	−1.04593	−0.0351784
$885$	39.8571	1.33978
$886$	26.9287	0.904689
$887$	−32.2834	−1.08397	−0.541985	−	0.840388i	$-0.682327\pi$
$887$	−32.2834	−1.08397	−0.541985	+	0.840388i	$0.682327\pi$
$888$	0.524706	0.0176080
$889$	19.4305	0.651679
$890$	53.9050	1.80690
$891$	2.39556	0.0802542
$892$	3.98694	0.133493
$893$	−16.8680	−0.564467
$894$	−21.0630	−0.704453
$895$	64.9749	2.17187
$896$	−9.92015	−0.331409
$897$	−36.4567	−1.21725
$898$	−4.24287	−0.141586
$899$	32.9694	1.09959
$900$	−2.93228	−0.0977426
$901$	−0.557824	−0.0185838
$902$	−1.96660	−0.0654805
$903$	5.47727	0.182272
$904$	−28.9299	−0.962195
$905$	42.5387	1.41404
$906$	−13.5060	−0.448707
$907$	28.4938	0.946120	0.473060	−	0.881030i	$-0.343149\pi$
$907$	28.4938	0.946120	0.473060	+	0.881030i	$0.343149\pi$
$908$	−2.70178	−0.0896616
$909$	−3.04469	−0.100986
$910$	26.4804	0.877818
$911$	21.7455	0.720460	0.360230	−	0.932864i	$-0.382698\pi$
$911$	21.7455	0.720460	0.360230	+	0.932864i	$0.382698\pi$
$912$	−14.7488	−0.488382
$913$	−20.2085	−0.668805
$914$	−8.53184	−0.282208
$915$	10.8112	0.357408
$916$	−3.98574	−0.131692
$917$	13.9534	0.460782
$918$	1.32549	0.0437478
$919$	29.2517	0.964923	0.482462	−	0.875917i	$-0.339743\pi$
$919$	29.2517	0.964923	0.482462	+	0.875917i	$0.339743\pi$
$920$	104.054	3.43056
$921$	−19.3449	−0.637437
$922$	−46.8555	−1.54310
$923$	−20.8560	−0.686483
$924$	−0.654450	−0.0215298
$925$	2.12898	0.0700004
$926$	1.46165	0.0480326
$927$	4.94953	0.162564
$928$	12.9236	0.424238
$929$	−30.3325	−0.995177	−0.497588	−	0.867413i	$-0.665781\pi$
$929$	−30.3325	−0.995177	−0.497588	+	0.867413i	$0.665781\pi$
$930$	19.0953	0.626159
$931$	−24.4909	−0.802656
$932$	0.444975	0.0145756
$933$	−5.64864	−0.184928
$934$	−32.4878	−1.06303
$935$	−9.89558	−0.323620
$936$	−12.7936	−0.418172
$937$	42.6887	1.39458	0.697290	−	0.716789i	$-0.254389\pi$
$937$	42.6887	1.39458	0.697290	+	0.716789i	$0.254389\pi$
$938$	−24.0000	−0.783628
$939$	0.465494	0.0151908
$940$	3.96727	0.129398
$941$	−17.7264	−0.577864	−0.288932	−	0.957350i	$-0.593300\pi$
$941$	−17.7264	−0.577864	−0.288932	+	0.957350i	$0.593300\pi$
$942$	1.32549	0.0431869
$943$	5.24730	0.170876
$944$	−33.3343	−1.08494
$945$	4.64275	0.151029
$946$	−15.4742	−0.503109
$947$	25.7932	0.838168	0.419084	−	0.907948i	$-0.362351\pi$
$947$	25.7932	0.838168	0.419084	+	0.907948i	$0.362351\pi$
$948$	−1.58435	−0.0514574
$949$	29.3143	0.951584
$950$	−68.2636	−2.21476
$951$	16.6798	0.540879
$952$	−3.34165	−0.108303
$953$	−4.56325	−0.147818	−0.0739090	−	0.997265i	$-0.523547\pi$
$953$	−4.56325	−0.147818	−0.0739090	+	0.997265i	$0.523547\pi$
$954$	−0.739392	−0.0239387
$955$	−6.60120	−0.213610
$956$	0.353768	0.0114417
$957$	−22.6466	−0.732060
$958$	34.3021	1.10825
$959$	13.7156	0.442901
$960$	36.0272	1.16277
$961$	−18.8373	−0.607656
$962$	1.00658	0.0324533
$963$	−0.810532	−0.0261190
$964$	6.02175	0.193948
$965$	7.57454	0.243833
$966$	−12.6218	−0.406101
$967$	42.3476	1.36181	0.680904	−	0.732373i	$-0.261587\pi$
$967$	42.3476	1.36181	0.680904	+	0.732373i	$0.261587\pi$
$968$	−15.6428	−0.502778
$969$	−4.26910	−0.137143
$970$	9.99259	0.320843
$971$	34.6533	1.11208	0.556038	−	0.831157i	$-0.312321\pi$
$971$	34.6533	1.11208	0.556038	+	0.831157i	$0.312321\pi$
$972$	−0.243069	−0.00779645
$973$	17.5024	0.561102
$974$	33.3389	1.06825
$975$	−51.9096	−1.66244
$976$	−9.04192	−0.289425
$977$	4.23666	0.135543	0.0677714	−	0.997701i	$-0.478411\pi$
$977$	4.23666	0.135543	0.0677714	+	0.997701i	$0.478411\pi$
$978$	−4.42937	−0.141636
$979$	−23.5843	−0.753758
$980$	5.76013	0.184001
$981$	1.63008	0.0520445
$982$	17.8859	0.570761
$983$	−56.5642	−1.80412	−0.902058	−	0.431614i	$-0.857944\pi$
$983$	−56.5642	−1.80412	−0.902058	+	0.431614i	$0.857944\pi$
$984$	1.84141	0.0587021
$985$	6.43645	0.205082
$986$	−12.5307	−0.399057
$987$	−4.44087	−0.141354
$988$	4.46518	0.142056
$989$	41.2884	1.31290
$990$	−13.1165	−0.416870
$991$	23.3158	0.740652	0.370326	−	0.928902i	$-0.379246\pi$
$991$	23.3158	0.740652	0.370326	+	0.928902i	$0.379246\pi$
$992$	4.76762	0.151372
$993$	−21.0245	−0.667193
$994$	−7.22064	−0.229025
$995$	−76.9221	−2.43860
$996$	2.05049	0.0649723
$997$	9.01794	0.285601	0.142800	−	0.989751i	$-0.454389\pi$
$997$	9.01794	0.285601	0.142800	+	0.989751i	$0.454389\pi$
$998$	42.1355	1.33378
$999$	0.176480	0.00558359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.14	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.14	✓	56	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)

\(f(q)\)	\(=\)	\(q-1.32549 q^{2} +1.00000 q^{3} -0.243069 q^{4} +4.13081 q^{5} -1.32549 q^{6} +1.12393 q^{7} +2.97317 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.32549 q^{2} +1.00000 q^{3} -0.243069 q^{4} +4.13081 q^{5} -1.32549 q^{6} +1.12393 q^{7} +2.97317 q^{8} +1.00000 q^{9} -5.47535 q^{10} +2.39556 q^{11} -0.243069 q^{12} -4.30301 q^{13} -1.48977 q^{14} +4.13081 q^{15} -3.45478 q^{16} -1.00000 q^{17} -1.32549 q^{18} +4.26910 q^{19} -1.00407 q^{20} +1.12393 q^{21} -3.17529 q^{22} +8.47236 q^{23} +2.97317 q^{24} +12.0636 q^{25} +5.70361 q^{26} +1.00000 q^{27} -0.273194 q^{28} -9.45358 q^{29} -5.47535 q^{30} -3.48750 q^{31} -1.36706 q^{32} +2.39556 q^{33} +1.32549 q^{34} +4.64275 q^{35} -0.243069 q^{36} +0.176480 q^{37} -5.65867 q^{38} -4.30301 q^{39} +12.2816 q^{40} +0.619343 q^{41} -1.48977 q^{42} +4.87331 q^{43} -0.582286 q^{44} +4.13081 q^{45} -11.2301 q^{46} -3.95118 q^{47} -3.45478 q^{48} -5.73677 q^{49} -15.9902 q^{50} -1.00000 q^{51} +1.04593 q^{52} +0.557824 q^{53} -1.32549 q^{54} +9.89558 q^{55} +3.34165 q^{56} +4.26910 q^{57} +12.5307 q^{58} +9.64875 q^{59} -1.00407 q^{60} +2.61722 q^{61} +4.62266 q^{62} +1.12393 q^{63} +8.72159 q^{64} -17.7749 q^{65} -3.17529 q^{66} +16.1099 q^{67} +0.243069 q^{68} +8.47236 q^{69} -6.15393 q^{70} +4.84683 q^{71} +2.97317 q^{72} -6.81252 q^{73} -0.233923 q^{74} +12.0636 q^{75} -1.03769 q^{76} +2.69245 q^{77} +5.70361 q^{78} +6.51811 q^{79} -14.2710 q^{80} +1.00000 q^{81} -0.820935 q^{82} -8.43584 q^{83} -0.273194 q^{84} -4.13081 q^{85} -6.45953 q^{86} -9.45358 q^{87} +7.12240 q^{88} -9.84503 q^{89} -5.47535 q^{90} -4.83630 q^{91} -2.05937 q^{92} -3.48750 q^{93} +5.23726 q^{94} +17.6348 q^{95} -1.36706 q^{96} -1.82501 q^{97} +7.60405 q^{98} +2.39556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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