LMFDB - Embedded newform 8007.2.a.h.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.47538 q^{2} +1.00000 q^{3} +4.12750 q^{4} +2.16981 q^{5} -2.47538 q^{6} +1.33731 q^{7} -5.26636 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.47538 q^{2} +1.00000 q^{3} +4.12750 q^{4} +2.16981 q^{5} -2.47538 q^{6} +1.33731 q^{7} -5.26636 q^{8} +1.00000 q^{9} -5.37109 q^{10} +2.17120 q^{11} +4.12750 q^{12} +4.24454 q^{13} -3.31036 q^{14} +2.16981 q^{15} +4.78123 q^{16} -1.00000 q^{17} -2.47538 q^{18} +3.41119 q^{19} +8.95586 q^{20} +1.33731 q^{21} -5.37454 q^{22} +7.91081 q^{23} -5.26636 q^{24} -0.291944 q^{25} -10.5068 q^{26} +1.00000 q^{27} +5.51975 q^{28} +7.63238 q^{29} -5.37109 q^{30} +1.81838 q^{31} -1.30264 q^{32} +2.17120 q^{33} +2.47538 q^{34} +2.90171 q^{35} +4.12750 q^{36} +0.367828 q^{37} -8.44399 q^{38} +4.24454 q^{39} -11.4270 q^{40} +7.79243 q^{41} -3.31036 q^{42} +5.87306 q^{43} +8.96162 q^{44} +2.16981 q^{45} -19.5822 q^{46} -7.16761 q^{47} +4.78123 q^{48} -5.21159 q^{49} +0.722671 q^{50} -1.00000 q^{51} +17.5193 q^{52} +12.1578 q^{53} -2.47538 q^{54} +4.71108 q^{55} -7.04277 q^{56} +3.41119 q^{57} -18.8930 q^{58} +2.91257 q^{59} +8.95586 q^{60} -2.42278 q^{61} -4.50118 q^{62} +1.33731 q^{63} -6.33793 q^{64} +9.20983 q^{65} -5.37454 q^{66} -11.9448 q^{67} -4.12750 q^{68} +7.91081 q^{69} -7.18283 q^{70} +2.07758 q^{71} -5.26636 q^{72} +0.912685 q^{73} -0.910514 q^{74} -0.291944 q^{75} +14.0797 q^{76} +2.90357 q^{77} -10.5068 q^{78} -0.818017 q^{79} +10.3743 q^{80} +1.00000 q^{81} -19.2892 q^{82} -10.9253 q^{83} +5.51975 q^{84} -2.16981 q^{85} -14.5380 q^{86} +7.63238 q^{87} -11.4343 q^{88} +4.54937 q^{89} -5.37109 q^{90} +5.67628 q^{91} +32.6518 q^{92} +1.81838 q^{93} +17.7426 q^{94} +7.40162 q^{95} -1.30264 q^{96} +11.7351 q^{97} +12.9007 q^{98} +2.17120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.47538	−1.75036	−0.875178	−	0.483801i	$-0.839256\pi$
$2$	−2.47538	−1.75036	−0.875178	+	0.483801i	$0.839256\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.12750	2.06375
$5$	2.16981	0.970367	0.485183	−	0.874412i	$-0.338753\pi$
$5$	2.16981	0.970367	0.485183	+	0.874412i	$0.338753\pi$
$6$	−2.47538	−1.01057
$7$	1.33731	0.505457	0.252728	−	0.967537i	$-0.418672\pi$
$7$	1.33731	0.505457	0.252728	+	0.967537i	$0.418672\pi$
$8$	−5.26636	−1.86194
$9$	1.00000	0.333333
$10$	−5.37109	−1.69849
$11$	2.17120	0.654641	0.327321	−	0.944913i	$-0.393854\pi$
$11$	2.17120	0.654641	0.327321	+	0.944913i	$0.393854\pi$
$12$	4.12750	1.19151
$13$	4.24454	1.17722	0.588612	−	0.808415i	$-0.299674\pi$
$13$	4.24454	1.17722	0.588612	+	0.808415i	$0.299674\pi$
$14$	−3.31036	−0.884730
$15$	2.16981	0.560241
$16$	4.78123	1.19531
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.47538	−0.583452
$19$	3.41119	0.782581	0.391290	−	0.920267i	$-0.372029\pi$
$19$	3.41119	0.782581	0.391290	+	0.920267i	$0.372029\pi$
$20$	8.95586	2.00259
$21$	1.33731	0.291826
$22$	−5.37454	−1.14586
$23$	7.91081	1.64952	0.824759	−	0.565485i	$-0.191311\pi$
$23$	7.91081	1.64952	0.824759	+	0.565485i	$0.191311\pi$
$24$	−5.26636	−1.07499
$25$	−0.291944	−0.0583887
$26$	−10.5068	−2.06056
$27$	1.00000	0.192450
$28$	5.51975	1.04314
$29$	7.63238	1.41730	0.708649	−	0.705561i	$-0.249305\pi$
$29$	7.63238	1.41730	0.708649	+	0.705561i	$0.249305\pi$
$30$	−5.37109	−0.980622
$31$	1.81838	0.326591	0.163295	−	0.986577i	$-0.447788\pi$
$31$	1.81838	0.326591	0.163295	+	0.986577i	$0.447788\pi$
$32$	−1.30264	−0.230277
$33$	2.17120	0.377957
$34$	2.47538	0.424524
$35$	2.90171	0.490478
$36$	4.12750	0.687916
$37$	0.367828	0.0604706	0.0302353	−	0.999543i	$-0.490374\pi$
$37$	0.367828	0.0604706	0.0302353	+	0.999543i	$0.490374\pi$
$38$	−8.44399	−1.36980
$39$	4.24454	0.679671
$40$	−11.4270	−1.80676
$41$	7.79243	1.21697	0.608487	−	0.793564i	$-0.291777\pi$
$41$	7.79243	1.21697	0.608487	+	0.793564i	$0.291777\pi$
$42$	−3.31036	−0.510799
$43$	5.87306	0.895633	0.447816	−	0.894126i	$-0.352202\pi$
$43$	5.87306	0.895633	0.447816	+	0.894126i	$0.352202\pi$
$44$	8.96162	1.35101
$45$	2.16981	0.323456
$46$	−19.5822	−2.88724
$47$	−7.16761	−1.04550	−0.522752	−	0.852485i	$-0.675095\pi$
$47$	−7.16761	−1.04550	−0.522752	+	0.852485i	$0.675095\pi$
$48$	4.78123	0.690111
$49$	−5.21159	−0.744513
$50$	0.722671	0.102201
$51$	−1.00000	−0.140028
$52$	17.5193	2.42949
$53$	12.1578	1.67000	0.835000	−	0.550250i	$-0.185467\pi$
$53$	12.1578	1.67000	0.835000	+	0.550250i	$0.185467\pi$
$54$	−2.47538	−0.336856
$55$	4.71108	0.635242
$56$	−7.04277	−0.941130
$57$	3.41119	0.451823
$58$	−18.8930	−2.48078
$59$	2.91257	0.379185	0.189592	−	0.981863i	$-0.439283\pi$
$59$	2.91257	0.379185	0.189592	+	0.981863i	$0.439283\pi$
$60$	8.95586	1.15620
$61$	−2.42278	−0.310205	−0.155102	−	0.987898i	$-0.549571\pi$
$61$	−2.42278	−0.310205	−0.155102	+	0.987898i	$0.549571\pi$
$62$	−4.50118	−0.571650
$63$	1.33731	0.168486
$64$	−6.33793	−0.792242
$65$	9.20983	1.14234
$66$	−5.37454	−0.661560
$67$	−11.9448	−1.45929	−0.729643	−	0.683828i	$-0.760314\pi$
$67$	−11.9448	−1.45929	−0.729643	+	0.683828i	$0.760314\pi$
$68$	−4.12750	−0.500532
$69$	7.91081	0.952349
$70$	−7.18283	−0.858512
$71$	2.07758	0.246564	0.123282	−	0.992372i	$-0.460658\pi$
$71$	2.07758	0.246564	0.123282	+	0.992372i	$0.460658\pi$
$72$	−5.26636	−0.620646
$73$	0.912685	0.106822	0.0534109	−	0.998573i	$-0.482991\pi$
$73$	0.912685	0.106822	0.0534109	+	0.998573i	$0.482991\pi$
$74$	−0.910514	−0.105845
$75$	−0.291944	−0.0337107
$76$	14.0797	1.61505
$77$	2.90357	0.330893
$78$	−10.5068	−1.18967
$79$	−0.818017	−0.0920341	−0.0460170	−	0.998941i	$-0.514653\pi$
$79$	−0.818017	−0.0920341	−0.0460170	+	0.998941i	$0.514653\pi$
$80$	10.3743	1.15989
$81$	1.00000	0.111111
$82$	−19.2892	−2.13014
$83$	−10.9253	−1.19920	−0.599602	−	0.800298i	$-0.704674\pi$
$83$	−10.9253	−1.19920	−0.599602	+	0.800298i	$0.704674\pi$
$84$	5.51975	0.602255
$85$	−2.16981	−0.235348
$86$	−14.5380	−1.56768
$87$	7.63238	0.818277
$88$	−11.4343	−1.21890
$89$	4.54937	0.482233	0.241116	−	0.970496i	$-0.422486\pi$
$89$	4.54937	0.482233	0.241116	+	0.970496i	$0.422486\pi$
$90$	−5.37109	−0.566162
$91$	5.67628	0.595036
$92$	32.6518	3.40419
$93$	1.81838	0.188557
$94$	17.7426	1.83000
$95$	7.40162	0.759390
$96$	−1.30264	−0.132950
$97$	11.7351	1.19152	0.595759	−	0.803164i	$-0.296852\pi$
$97$	11.7351	1.19152	0.595759	+	0.803164i	$0.296852\pi$
$98$	12.9007	1.30316
$99$	2.17120	0.218214
$100$	−1.20500	−0.120500
$101$	−8.26125	−0.822025	−0.411013	−	0.911630i	$-0.634825\pi$
$101$	−8.26125	−0.822025	−0.411013	+	0.911630i	$0.634825\pi$
$102$	2.47538	0.245099
$103$	2.37067	0.233589	0.116794	−	0.993156i	$-0.462738\pi$
$103$	2.37067	0.233589	0.116794	+	0.993156i	$0.462738\pi$
$104$	−22.3533	−2.19192
$105$	2.90171	0.283178
$106$	−30.0951	−2.92310
$107$	4.15024	0.401219	0.200609	−	0.979671i	$-0.435708\pi$
$107$	4.15024	0.401219	0.200609	+	0.979671i	$0.435708\pi$
$108$	4.12750	0.397168
$109$	−11.5594	−1.10719	−0.553595	−	0.832786i	$-0.686744\pi$
$109$	−11.5594	−1.10719	−0.553595	+	0.832786i	$0.686744\pi$
$110$	−11.6617	−1.11190
$111$	0.367828	0.0349127
$112$	6.39400	0.604177
$113$	−17.8708	−1.68114	−0.840570	−	0.541703i	$-0.817780\pi$
$113$	−17.8708	−1.68114	−0.840570	+	0.541703i	$0.817780\pi$
$114$	−8.44399	−0.790852
$115$	17.1649	1.60064
$116$	31.5026	2.92495
$117$	4.24454	0.392408
$118$	−7.20972	−0.663709
$119$	−1.33731	−0.122591
$120$	−11.4270	−1.04313
$121$	−6.28589	−0.571445
$122$	5.99729	0.542969
$123$	7.79243	0.702620
$124$	7.50536	0.674001
$125$	−11.4825	−1.02703
$126$	−3.31036	−0.294910
$127$	−9.28832	−0.824205	−0.412102	−	0.911138i	$-0.635205\pi$
$127$	−9.28832	−0.824205	−0.412102	+	0.911138i	$0.635205\pi$
$128$	18.2941	1.61698
$129$	5.87306	0.517094
$130$	−22.7978	−1.99950
$131$	−0.102550	−0.00895983	−0.00447992	−	0.999990i	$-0.501426\pi$
$131$	−0.102550	−0.00895983	−0.00447992	+	0.999990i	$0.501426\pi$
$132$	8.96162	0.780009
$133$	4.56183	0.395561
$134$	29.5678	2.55427
$135$	2.16981	0.186747
$136$	5.26636	0.451586
$137$	−17.6123	−1.50472	−0.752362	−	0.658750i	$-0.771086\pi$
$137$	−17.6123	−1.50472	−0.752362	+	0.658750i	$0.771086\pi$
$138$	−19.5822	−1.66695
$139$	−16.7812	−1.42336	−0.711679	−	0.702504i	$-0.752065\pi$
$139$	−16.7812	−1.42336	−0.711679	+	0.702504i	$0.752065\pi$
$140$	11.9768	1.01222
$141$	−7.16761	−0.603622
$142$	−5.14280	−0.431575
$143$	9.21575	0.770660
$144$	4.78123	0.398436
$145$	16.5608	1.37530
$146$	−2.25924	−0.186976
$147$	−5.21159	−0.429845
$148$	1.51821	0.124796
$149$	18.4951	1.51517	0.757587	−	0.652734i	$-0.226378\pi$
$149$	18.4951	1.51517	0.757587	+	0.652734i	$0.226378\pi$
$150$	0.722671	0.0590058
$151$	−17.3286	−1.41018	−0.705090	−	0.709118i	$-0.749093\pi$
$151$	−17.3286	−1.41018	−0.705090	+	0.709118i	$0.749093\pi$
$152$	−17.9646	−1.45712
$153$	−1.00000	−0.0808452
$154$	−7.18744	−0.579181
$155$	3.94553	0.316913
$156$	17.5193	1.40267
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	2.02490	0.161092
$159$	12.1578	0.964175
$160$	−2.82648	−0.223453
$161$	10.5792	0.833760
$162$	−2.47538	−0.194484
$163$	5.35862	0.419719	0.209860	−	0.977732i	$-0.432699\pi$
$163$	5.35862	0.419719	0.209860	+	0.977732i	$0.432699\pi$
$164$	32.1632	2.51153
$165$	4.71108	0.366757
$166$	27.0442	2.09903
$167$	−9.37612	−0.725546	−0.362773	−	0.931878i	$-0.618170\pi$
$167$	−9.37612	−0.725546	−0.362773	+	0.931878i	$0.618170\pi$
$168$	−7.04277	−0.543361
$169$	5.01615	0.385858
$170$	5.37109	0.411944
$171$	3.41119	0.260860
$172$	24.2410	1.84836
$173$	19.2058	1.46019	0.730096	−	0.683344i	$-0.239475\pi$
$173$	19.2058	1.46019	0.730096	+	0.683344i	$0.239475\pi$
$174$	−18.8930	−1.43228
$175$	−0.390420	−0.0295130
$176$	10.3810	0.782498
$177$	2.91257	0.218922
$178$	−11.2614	−0.844079
$179$	10.8677	0.812289	0.406144	−	0.913809i	$-0.366873\pi$
$179$	10.8677	0.812289	0.406144	+	0.913809i	$0.366873\pi$
$180$	8.95586	0.667531
$181$	−5.95805	−0.442858	−0.221429	−	0.975176i	$-0.571072\pi$
$181$	−5.95805	−0.442858	−0.221429	+	0.975176i	$0.571072\pi$
$182$	−14.0509	−1.04153
$183$	−2.42278	−0.179097
$184$	−41.6611	−3.07130
$185$	0.798116	0.0586787
$186$	−4.50118	−0.330042
$187$	−2.17120	−0.158774
$188$	−29.5843	−2.15766
$189$	1.33731	0.0972752
$190$	−18.3218	−1.32920
$191$	−26.1657	−1.89328	−0.946641	−	0.322289i	$-0.895548\pi$
$191$	−26.1657	−1.89328	−0.946641	+	0.322289i	$0.895548\pi$
$192$	−6.33793	−0.457401
$193$	−19.7340	−1.42048	−0.710241	−	0.703959i	$-0.751414\pi$
$193$	−19.7340	−1.42048	−0.710241	+	0.703959i	$0.751414\pi$
$194$	−29.0488	−2.08558
$195$	9.20983	0.659530
$196$	−21.5108	−1.53649
$197$	12.4286	0.885501	0.442751	−	0.896645i	$-0.354003\pi$
$197$	12.4286	0.885501	0.442751	+	0.896645i	$0.354003\pi$
$198$	−5.37454	−0.381952
$199$	−7.40536	−0.524952	−0.262476	−	0.964939i	$-0.584539\pi$
$199$	−7.40536	−0.524952	−0.262476	+	0.964939i	$0.584539\pi$
$200$	1.53748	0.108716
$201$	−11.9448	−0.842520
$202$	20.4497	1.43884
$203$	10.2069	0.716383
$204$	−4.12750	−0.288983
$205$	16.9081	1.18091
$206$	−5.86830	−0.408864
$207$	7.91081	0.549839
$208$	20.2941	1.40715
$209$	7.40638	0.512310
$210$	−7.18283	−0.495662
$211$	25.9263	1.78484	0.892419	−	0.451207i	$-0.149006\pi$
$211$	25.9263	1.78484	0.892419	+	0.451207i	$0.149006\pi$
$212$	50.1812	3.44646
$213$	2.07758	0.142354
$214$	−10.2734	−0.702276
$215$	12.7434	0.869092
$216$	−5.26636	−0.358330
$217$	2.43174	0.165078
$218$	28.6139	1.93798
$219$	0.912685	0.0616736
$220$	19.4450	1.31098
$221$	−4.24454	−0.285519
$222$	−0.910514	−0.0611097
$223$	17.9129	1.19954	0.599768	−	0.800174i	$-0.295259\pi$
$223$	17.9129	1.19954	0.599768	+	0.800174i	$0.295259\pi$
$224$	−1.74204	−0.116395
$225$	−0.291944	−0.0194629
$226$	44.2369	2.94260
$227$	−3.26881	−0.216959	−0.108479	−	0.994099i	$-0.534598\pi$
$227$	−3.26881	−0.216959	−0.108479	+	0.994099i	$0.534598\pi$
$228$	14.0797	0.932450
$229$	5.89201	0.389355	0.194677	−	0.980867i	$-0.437634\pi$
$229$	5.89201	0.389355	0.194677	+	0.980867i	$0.437634\pi$
$230$	−42.4896	−2.80168
$231$	2.90357	0.191041
$232$	−40.1949	−2.63892
$233$	17.4540	1.14345	0.571723	−	0.820446i	$-0.306275\pi$
$233$	17.4540	1.14345	0.571723	+	0.820446i	$0.306275\pi$
$234$	−10.5068	−0.686854
$235$	−15.5523	−1.01452
$236$	12.0216	0.782542
$237$	−0.818017	−0.0531359
$238$	3.31036	0.214578
$239$	−12.9861	−0.840004	−0.420002	−	0.907523i	$-0.637971\pi$
$239$	−12.9861	−0.840004	−0.420002	+	0.907523i	$0.637971\pi$
$240$	10.3743	0.669661
$241$	−27.7778	−1.78933	−0.894664	−	0.446741i	$-0.852585\pi$
$241$	−27.7778	−1.78933	−0.894664	+	0.446741i	$0.852585\pi$
$242$	15.5600	1.00023
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	−11.3081	−0.722451
$246$	−19.2892	−1.22984
$247$	14.4790	0.921274
$248$	−9.57624	−0.608092
$249$	−10.9253	−0.692361
$250$	28.4235	1.79766
$251$	−5.77826	−0.364721	−0.182360	−	0.983232i	$-0.558374\pi$
$251$	−5.77826	−0.364721	−0.182360	+	0.983232i	$0.558374\pi$
$252$	5.51975	0.347712
$253$	17.1759	1.07984
$254$	22.9921	1.44265
$255$	−2.16981	−0.135878
$256$	−32.6089	−2.03805
$257$	20.7387	1.29364	0.646822	−	0.762641i	$-0.276098\pi$
$257$	20.7387	1.29364	0.646822	+	0.762641i	$0.276098\pi$
$258$	−14.5380	−0.905099
$259$	0.491902	0.0305653
$260$	38.0136	2.35750
$261$	7.63238	0.472433
$262$	0.253850	0.0156829
$263$	−16.4037	−1.01150	−0.505748	−	0.862681i	$-0.668783\pi$
$263$	−16.4037	−1.01150	−0.505748	+	0.862681i	$0.668783\pi$
$264$	−11.4343	−0.703733
$265$	26.3800	1.62051
$266$	−11.2923	−0.692373
$267$	4.54937	0.278417
$268$	−49.3020	−3.01160
$269$	14.4681	0.882138	0.441069	−	0.897473i	$-0.354599\pi$
$269$	14.4681	0.882138	0.441069	+	0.897473i	$0.354599\pi$
$270$	−5.37109	−0.326874
$271$	28.9833	1.76061	0.880306	−	0.474407i	$-0.157337\pi$
$271$	28.9833	1.76061	0.880306	+	0.474407i	$0.157337\pi$
$272$	−4.78123	−0.289905
$273$	5.67628	0.343544
$274$	43.5972	2.63380
$275$	−0.633868	−0.0382237
$276$	32.6518	1.96541
$277$	−0.848847	−0.0510023	−0.0255011	−	0.999675i	$-0.508118\pi$
$277$	−0.848847	−0.0510023	−0.0255011	+	0.999675i	$0.508118\pi$
$278$	41.5397	2.49139
$279$	1.81838	0.108864
$280$	−15.2814	−0.913241
$281$	−8.81983	−0.526147	−0.263073	−	0.964776i	$-0.584736\pi$
$281$	−8.81983	−0.526147	−0.263073	+	0.964776i	$0.584736\pi$
$282$	17.7426	1.05655
$283$	−12.3468	−0.733938	−0.366969	−	0.930233i	$-0.619605\pi$
$283$	−12.3468	−0.733938	−0.366969	+	0.930233i	$0.619605\pi$
$284$	8.57522	0.508846
$285$	7.40162	0.438434
$286$	−22.8125	−1.34893
$287$	10.4209	0.615128
$288$	−1.30264	−0.0767589
$289$	1.00000	0.0588235
$290$	−40.9942	−2.40726
$291$	11.7351	0.687923
$292$	3.76710	0.220453
$293$	−31.1177	−1.81791	−0.908956	−	0.416891i	$-0.863120\pi$
$293$	−31.1177	−1.81791	−0.908956	+	0.416891i	$0.863120\pi$
$294$	12.9007	0.752382
$295$	6.31972	0.367948
$296$	−1.93712	−0.112593
$297$	2.17120	0.125986
$298$	−45.7823	−2.65210
$299$	33.5778	1.94185
$300$	−1.20500	−0.0695705
$301$	7.85412	0.452704
$302$	42.8948	2.46832
$303$	−8.26125	−0.474596
$304$	16.3097	0.935425
$305$	−5.25695	−0.301012
$306$	2.47538	0.141508
$307$	−3.74595	−0.213793	−0.106896	−	0.994270i	$-0.534091\pi$
$307$	−3.74595	−0.213793	−0.106896	+	0.994270i	$0.534091\pi$
$308$	11.9845	0.682880
$309$	2.37067	0.134863
$310$	−9.76668	−0.554710
$311$	−2.48339	−0.140820	−0.0704102	−	0.997518i	$-0.522431\pi$
$311$	−2.48339	−0.140820	−0.0704102	+	0.997518i	$0.522431\pi$
$312$	−22.3533	−1.26551
$313$	0.762401	0.0430935	0.0215467	−	0.999768i	$-0.493141\pi$
$313$	0.762401	0.0430935	0.0215467	+	0.999768i	$0.493141\pi$
$314$	2.47538	0.139694
$315$	2.90171	0.163493
$316$	−3.37636	−0.189935
$317$	−1.08864	−0.0611439	−0.0305719	−	0.999533i	$-0.509733\pi$
$317$	−1.08864	−0.0611439	−0.0305719	+	0.999533i	$0.509733\pi$
$318$	−30.0951	−1.68765
$319$	16.5714	0.927822
$320$	−13.7521	−0.768765
$321$	4.15024	0.231644
$322$	−26.1876	−1.45938
$323$	−3.41119	−0.189804
$324$	4.12750	0.229305
$325$	−1.23917	−0.0687366
$326$	−13.2646	−0.734659
$327$	−11.5594	−0.639236
$328$	−41.0377	−2.26593
$329$	−9.58535	−0.528457
$330$	−11.6617	−0.641956
$331$	−4.16032	−0.228672	−0.114336	−	0.993442i	$-0.536474\pi$
$331$	−4.16032	−0.228672	−0.114336	+	0.993442i	$0.536474\pi$
$332$	−45.0940	−2.47485
$333$	0.367828	0.0201569
$334$	23.2094	1.26996
$335$	−25.9178	−1.41604
$336$	6.39400	0.348822
$337$	−33.1849	−1.80770	−0.903849	−	0.427851i	$-0.859271\pi$
$337$	−33.1849	−1.80770	−0.903849	+	0.427851i	$0.859271\pi$
$338$	−12.4169	−0.675388
$339$	−17.8708	−0.970607
$340$	−8.95586	−0.485700
$341$	3.94807	0.213800
$342$	−8.44399	−0.456599
$343$	−16.3307	−0.881776
$344$	−30.9296	−1.66761
$345$	17.1649	0.924128
$346$	−47.5417	−2.55586
$347$	−8.43834	−0.452994	−0.226497	−	0.974012i	$-0.572727\pi$
$347$	−8.43834	−0.452994	−0.226497	+	0.974012i	$0.572727\pi$
$348$	31.5026	1.68872
$349$	4.49441	0.240580	0.120290	−	0.992739i	$-0.461618\pi$
$349$	4.49441	0.240580	0.120290	+	0.992739i	$0.461618\pi$
$350$	0.966437	0.0516582
$351$	4.24454	0.226557
$352$	−2.82829	−0.150749
$353$	0.620871	0.0330456	0.0165228	−	0.999863i	$-0.494740\pi$
$353$	0.620871	0.0330456	0.0165228	+	0.999863i	$0.494740\pi$
$354$	−7.20972	−0.383192
$355$	4.50795	0.239257
$356$	18.7775	0.995207
$357$	−1.33731	−0.0707781
$358$	−26.9016	−1.42180
$359$	25.8901	1.36642	0.683212	−	0.730220i	$-0.260582\pi$
$359$	25.8901	1.36642	0.683212	+	0.730220i	$0.260582\pi$
$360$	−11.4270	−0.602254
$361$	−7.36377	−0.387567
$362$	14.7484	0.775160
$363$	−6.28589	−0.329924
$364$	23.4288	1.22800
$365$	1.98035	0.103656
$366$	5.99729	0.313483
$367$	1.27630	0.0666224	0.0333112	−	0.999445i	$-0.489395\pi$
$367$	1.27630	0.0666224	0.0333112	+	0.999445i	$0.489395\pi$
$368$	37.8234	1.97168
$369$	7.79243	0.405658
$370$	−1.97564	−0.102709
$371$	16.2588	0.844113
$372$	7.50536	0.389135
$373$	−36.8856	−1.90986	−0.954932	−	0.296825i	$-0.904072\pi$
$373$	−36.8856	−1.90986	−0.954932	+	0.296825i	$0.904072\pi$
$374$	5.37454	0.277911
$375$	−11.4825	−0.592953
$376$	37.7472	1.94666
$377$	32.3960	1.66848
$378$	−3.31036	−0.170266
$379$	−26.2660	−1.34919	−0.674596	−	0.738187i	$-0.735682\pi$
$379$	−26.2660	−1.34919	−0.674596	+	0.738187i	$0.735682\pi$
$380$	30.5502	1.56719
$381$	−9.28832	−0.475855
$382$	64.7700	3.31392
$383$	22.0677	1.12761	0.563803	−	0.825909i	$-0.309338\pi$
$383$	22.0677	1.12761	0.563803	+	0.825909i	$0.309338\pi$
$384$	18.2941	0.933565
$385$	6.30019	0.321087
$386$	48.8490	2.48635
$387$	5.87306	0.298544
$388$	48.4365	2.45899
$389$	11.6799	0.592195	0.296098	−	0.955158i	$-0.404315\pi$
$389$	11.6799	0.592195	0.296098	+	0.955158i	$0.404315\pi$
$390$	−22.7978	−1.15441
$391$	−7.91081	−0.400067
$392$	27.4461	1.38624
$393$	−0.102550	−0.00517296
$394$	−30.7655	−1.54994
$395$	−1.77494	−0.0893068
$396$	8.96162	0.450338
$397$	−18.9138	−0.949255	−0.474628	−	0.880187i	$-0.657417\pi$
$397$	−18.9138	−0.949255	−0.474628	+	0.880187i	$0.657417\pi$
$398$	18.3311	0.918853
$399$	4.56183	0.228377
$400$	−1.39585	−0.0697925
$401$	−30.7789	−1.53702	−0.768512	−	0.639836i	$-0.779002\pi$
$401$	−30.7789	−1.53702	−0.768512	+	0.639836i	$0.779002\pi$
$402$	29.5678	1.47471
$403$	7.71819	0.384471
$404$	−34.0983	−1.69645
$405$	2.16981	0.107819
$406$	−25.2659	−1.25393
$407$	0.798629	0.0395866
$408$	5.26636	0.260724
$409$	−5.90067	−0.291769	−0.145885	−	0.989302i	$-0.546603\pi$
$409$	−5.90067	−0.291769	−0.145885	+	0.989302i	$0.546603\pi$
$410$	−41.8539	−2.06701
$411$	−17.6123	−0.868753
$412$	9.78493	0.482069
$413$	3.89502	0.191662
$414$	−19.5822	−0.962414
$415$	−23.7057	−1.16367
$416$	−5.52912	−0.271087
$417$	−16.7812	−0.821777
$418$	−18.3336	−0.896725
$419$	−37.1739	−1.81606	−0.908032	−	0.418900i	$-0.862416\pi$
$419$	−37.1739	−1.81606	−0.908032	+	0.418900i	$0.862416\pi$
$420$	11.9768	0.584408
$421$	−31.6358	−1.54184	−0.770918	−	0.636935i	$-0.780202\pi$
$421$	−31.6358	−1.54184	−0.770918	+	0.636935i	$0.780202\pi$
$422$	−64.1773	−3.12410
$423$	−7.16761	−0.348501
$424$	−64.0272	−3.10944
$425$	0.291944	0.0141613
$426$	−5.14280	−0.249170
$427$	−3.24001	−0.156795
$428$	17.1301	0.828014
$429$	9.21575	0.444941
$430$	−31.5447	−1.52122
$431$	14.6966	0.707909	0.353955	−	0.935263i	$-0.384837\pi$
$431$	14.6966	0.707909	0.353955	+	0.935263i	$0.384837\pi$
$432$	4.78123	0.230037
$433$	37.8571	1.81929	0.909647	−	0.415382i	$-0.136352\pi$
$433$	37.8571	1.81929	0.909647	+	0.415382i	$0.136352\pi$
$434$	−6.01949	−0.288945
$435$	16.5608	0.794029
$436$	−47.7114	−2.28496
$437$	26.9853	1.29088
$438$	−2.25924	−0.107951
$439$	19.7316	0.941736	0.470868	−	0.882204i	$-0.343941\pi$
$439$	19.7316	0.941736	0.470868	+	0.882204i	$0.343941\pi$
$440$	−24.8102	−1.18278
$441$	−5.21159	−0.248171
$442$	10.5068	0.499760
$443$	11.5274	0.547686	0.273843	−	0.961774i	$-0.411705\pi$
$443$	11.5274	0.547686	0.273843	+	0.961774i	$0.411705\pi$
$444$	1.51821	0.0720511
$445$	9.87126	0.467943
$446$	−44.3412	−2.09962
$447$	18.4951	0.874786
$448$	−8.47580	−0.400444
$449$	−33.3241	−1.57266	−0.786332	−	0.617804i	$-0.788022\pi$
$449$	−33.3241	−1.57266	−0.786332	+	0.617804i	$0.788022\pi$
$450$	0.722671	0.0340670
$451$	16.9189	0.796681
$452$	−73.7615	−3.46945
$453$	−17.3286	−0.814167
$454$	8.09155	0.379755
$455$	12.3164	0.577403
$456$	−17.9646	−0.841267
$457$	−38.6907	−1.80987	−0.904937	−	0.425546i	$-0.860082\pi$
$457$	−38.6907	−1.80987	−0.904937	+	0.425546i	$0.860082\pi$
$458$	−14.5849	−0.681510
$459$	−1.00000	−0.0466760
$460$	70.8481	3.30331
$461$	−7.06483	−0.329042	−0.164521	−	0.986374i	$-0.552608\pi$
$461$	−7.06483	−0.329042	−0.164521	+	0.986374i	$0.552608\pi$
$462$	−7.18744	−0.334390
$463$	22.3103	1.03685	0.518423	−	0.855124i	$-0.326519\pi$
$463$	22.3103	1.03685	0.518423	+	0.855124i	$0.326519\pi$
$464$	36.4922	1.69411
$465$	3.94553	0.182970
$466$	−43.2051	−2.00144
$467$	16.6746	0.771609	0.385805	−	0.922581i	$-0.373924\pi$
$467$	16.6746	0.771609	0.385805	+	0.922581i	$0.373924\pi$
$468$	17.5193	0.809832
$469$	−15.9739	−0.737607
$470$	38.4979	1.77578
$471$	−1.00000	−0.0460776
$472$	−15.3387	−0.706019
$473$	12.7516	0.586318
$474$	2.02490	0.0930068
$475$	−0.995875	−0.0456939
$476$	−5.51975	−0.252998
$477$	12.1578	0.556667
$478$	32.1456	1.47031
$479$	−12.1918	−0.557057	−0.278528	−	0.960428i	$-0.589847\pi$
$479$	−12.1918	−0.557057	−0.278528	+	0.960428i	$0.589847\pi$
$480$	−2.82648	−0.129011
$481$	1.56126	0.0711875
$482$	68.7606	3.13196
$483$	10.5792	0.481371
$484$	−25.9450	−1.17932
$485$	25.4628	1.15621
$486$	−2.47538	−0.112285
$487$	−20.3584	−0.922526	−0.461263	−	0.887264i	$-0.652603\pi$
$487$	−20.3584	−0.922526	−0.461263	+	0.887264i	$0.652603\pi$
$488$	12.7592	0.577582
$489$	5.35862	0.242325
$490$	27.9919	1.26455
$491$	−9.83486	−0.443841	−0.221920	−	0.975065i	$-0.571233\pi$
$491$	−9.83486	−0.443841	−0.221920	+	0.975065i	$0.571233\pi$
$492$	32.1632	1.45003
$493$	−7.63238	−0.343745
$494$	−35.8409	−1.61256
$495$	4.71108	0.211747
$496$	8.69410	0.390376
$497$	2.77838	0.124627
$498$	27.0442	1.21188
$499$	−27.1026	−1.21328	−0.606639	−	0.794978i	$-0.707482\pi$
$499$	−27.1026	−1.21328	−0.606639	+	0.794978i	$0.707482\pi$
$500$	−47.3939	−2.11952
$501$	−9.37612	−0.418894
$502$	14.3034	0.638391
$503$	−12.4005	−0.552913	−0.276456	−	0.961026i	$-0.589160\pi$
$503$	−12.4005	−0.552913	−0.276456	+	0.961026i	$0.589160\pi$
$504$	−7.04277	−0.313710
$505$	−17.9253	−0.797666
$506$	−42.5169	−1.89011
$507$	5.01615	0.222775
$508$	−38.3375	−1.70095
$509$	−3.61330	−0.160157	−0.0800784	−	0.996789i	$-0.525517\pi$
$509$	−3.61330	−0.160157	−0.0800784	+	0.996789i	$0.525517\pi$
$510$	5.37109	0.237836
$511$	1.22055	0.0539938
$512$	44.1311	1.95034
$513$	3.41119	0.150608
$514$	−51.3361	−2.26434
$515$	5.14389	0.226667
$516$	24.2410	1.06715
$517$	−15.5623	−0.684430
$518$	−1.21764	−0.0535001
$519$	19.2058	0.843043
$520$	−48.5023	−2.12697
$521$	11.2236	0.491716	0.245858	−	0.969306i	$-0.420930\pi$
$521$	11.2236	0.491716	0.245858	+	0.969306i	$0.420930\pi$
$522$	−18.8930	−0.826926
$523$	−5.27592	−0.230700	−0.115350	−	0.993325i	$-0.536799\pi$
$523$	−5.27592	−0.230700	−0.115350	+	0.993325i	$0.536799\pi$
$524$	−0.423275	−0.0184908
$525$	−0.390420	−0.0170393
$526$	40.6054	1.77048
$527$	−1.81838	−0.0792099
$528$	10.3810	0.451775
$529$	39.5808	1.72091
$530$	−65.3006	−2.83647
$531$	2.91257	0.126395
$532$	18.8289	0.816338
$533$	33.0753	1.43265
$534$	−11.2614	−0.487329
$535$	9.00521	0.389329
$536$	62.9055	2.71710
$537$	10.8677	0.468975
$538$	−35.8141	−1.54406
$539$	−11.3154	−0.487389
$540$	8.95586	0.385399
$541$	42.4690	1.82588	0.912942	−	0.408089i	$-0.133805\pi$
$541$	42.4690	1.82588	0.912942	+	0.408089i	$0.133805\pi$
$542$	−71.7447	−3.08170
$543$	−5.95805	−0.255684
$544$	1.30264	0.0558503
$545$	−25.0816	−1.07438
$546$	−14.0509	−0.601325
$547$	−27.6473	−1.18211	−0.591057	−	0.806630i	$-0.701289\pi$
$547$	−27.6473	−1.18211	−0.591057	+	0.806630i	$0.701289\pi$
$548$	−72.6949	−3.10537
$549$	−2.42278	−0.103402
$550$	1.56906	0.0669050
$551$	26.0355	1.10915
$552$	−41.6611	−1.77322
$553$	−1.09394	−0.0465193
$554$	2.10122	0.0892721
$555$	0.798116	0.0338781
$556$	−69.2641	−2.93745
$557$	20.7000	0.877087	0.438543	−	0.898710i	$-0.355495\pi$
$557$	20.7000	0.877087	0.438543	+	0.898710i	$0.355495\pi$
$558$	−4.50118	−0.190550
$559$	24.9284	1.05436
$560$	13.8737	0.586273
$561$	−2.17120	−0.0916681
$562$	21.8324	0.920944
$563$	9.55921	0.402873	0.201436	−	0.979502i	$-0.435439\pi$
$563$	9.55921	0.402873	0.201436	+	0.979502i	$0.435439\pi$
$564$	−29.5843	−1.24572
$565$	−38.7761	−1.63132
$566$	30.5629	1.28465
$567$	1.33731	0.0561619
$568$	−10.9413	−0.459087
$569$	−22.8295	−0.957061	−0.478530	−	0.878071i	$-0.658830\pi$
$569$	−22.8295	−0.957061	−0.478530	+	0.878071i	$0.658830\pi$
$570$	−18.3218	−0.767416
$571$	−1.93883	−0.0811376	−0.0405688	−	0.999177i	$-0.512917\pi$
$571$	−1.93883	−0.0811376	−0.0405688	+	0.999177i	$0.512917\pi$
$572$	38.0380	1.59045
$573$	−26.1657	−1.09309
$574$	−25.7957	−1.07669
$575$	−2.30951	−0.0963132
$576$	−6.33793	−0.264081
$577$	−17.4161	−0.725041	−0.362520	−	0.931976i	$-0.618084\pi$
$577$	−17.4161	−0.725041	−0.362520	+	0.931976i	$0.618084\pi$
$578$	−2.47538	−0.102962
$579$	−19.7340	−0.820115
$580$	68.3546	2.83827
$581$	−14.6105	−0.606146
$582$	−29.0488	−1.20411
$583$	26.3970	1.09325
$584$	−4.80653	−0.198895
$585$	9.20983	0.380780
$586$	77.0279	3.18200
$587$	18.0550	0.745211	0.372606	−	0.927990i	$-0.378464\pi$
$587$	18.0550	0.745211	0.372606	+	0.927990i	$0.378464\pi$
$588$	−21.5108	−0.887092
$589$	6.20284	0.255584
$590$	−15.6437	−0.644041
$591$	12.4286	0.511244
$592$	1.75867	0.0722810
$593$	−23.3352	−0.958262	−0.479131	−	0.877743i	$-0.659048\pi$
$593$	−23.3352	−0.958262	−0.479131	+	0.877743i	$0.659048\pi$
$594$	−5.37454	−0.220520
$595$	−2.90171	−0.118958
$596$	76.3383	3.12694
$597$	−7.40536	−0.303081
$598$	−83.1176	−3.39893
$599$	30.8181	1.25919	0.629597	−	0.776922i	$-0.283220\pi$
$599$	30.8181	1.25919	0.629597	+	0.776922i	$0.283220\pi$
$600$	1.53748	0.0627673
$601$	−44.9216	−1.83239	−0.916195	−	0.400732i	$-0.868756\pi$
$601$	−44.9216	−1.83239	−0.916195	+	0.400732i	$0.868756\pi$
$602$	−19.4419	−0.792393
$603$	−11.9448	−0.486429
$604$	−71.5236	−2.91025
$605$	−13.6392	−0.554511
$606$	20.4497	0.830713
$607$	−32.2604	−1.30941	−0.654705	−	0.755884i	$-0.727207\pi$
$607$	−32.2604	−1.30941	−0.654705	+	0.755884i	$0.727207\pi$
$608$	−4.44356	−0.180210
$609$	10.2069	0.413604
$610$	13.0129	0.526879
$611$	−30.4233	−1.23079
$612$	−4.12750	−0.166844
$613$	12.8951	0.520828	0.260414	−	0.965497i	$-0.416141\pi$
$613$	12.8951	0.520828	0.260414	+	0.965497i	$0.416141\pi$
$614$	9.27265	0.374214
$615$	16.9081	0.681799
$616$	−15.2913	−0.616102
$617$	3.74277	0.150678	0.0753391	−	0.997158i	$-0.475996\pi$
$617$	3.74277	0.150678	0.0753391	+	0.997158i	$0.475996\pi$
$618$	−5.86830	−0.236058
$619$	−5.98128	−0.240408	−0.120204	−	0.992749i	$-0.538355\pi$
$619$	−5.98128	−0.240408	−0.120204	+	0.992749i	$0.538355\pi$
$620$	16.2852	0.654028
$621$	7.91081	0.317450
$622$	6.14734	0.246486
$623$	6.08394	0.243748
$624$	20.2941	0.812416
$625$	−23.4551	−0.938202
$626$	−1.88723	−0.0754289
$627$	7.40638	0.295782
$628$	−4.12750	−0.164705
$629$	−0.367828	−0.0146663
$630$	−7.18283	−0.286171
$631$	8.53005	0.339576	0.169788	−	0.985481i	$-0.445692\pi$
$631$	8.53005	0.339576	0.169788	+	0.985481i	$0.445692\pi$
$632$	4.30797	0.171362
$633$	25.9263	1.03048
$634$	2.69478	0.107024
$635$	−20.1538	−0.799781
$636$	50.1812	1.98981
$637$	−22.1208	−0.876459
$638$	−41.0205	−1.62402
$639$	2.07758	0.0821879
$640$	39.6946	1.56907
$641$	28.7629	1.13606	0.568032	−	0.823006i	$-0.307705\pi$
$641$	28.7629	1.13606	0.568032	+	0.823006i	$0.307705\pi$
$642$	−10.2734	−0.405459
$643$	7.57520	0.298737	0.149368	−	0.988782i	$-0.452276\pi$
$643$	7.57520	0.298737	0.149368	+	0.988782i	$0.452276\pi$
$644$	43.6657	1.72067
$645$	12.7434	0.501771
$646$	8.44399	0.332224
$647$	36.3836	1.43039	0.715194	−	0.698926i	$-0.246338\pi$
$647$	36.3836	1.43039	0.715194	+	0.698926i	$0.246338\pi$
$648$	−5.26636	−0.206882
$649$	6.32378	0.248230
$650$	3.06741	0.120314
$651$	2.43174	0.0953076
$652$	22.1177	0.866195
$653$	−21.0281	−0.822893	−0.411446	−	0.911434i	$-0.634976\pi$
$653$	−21.0281	−0.822893	−0.411446	+	0.911434i	$0.634976\pi$
$654$	28.6139	1.11889
$655$	−0.222514	−0.00869432
$656$	37.2574	1.45466
$657$	0.912685	0.0356072
$658$	23.7274	0.924989
$659$	−40.3676	−1.57250	−0.786250	−	0.617909i	$-0.787980\pi$
$659$	−40.3676	−1.57250	−0.786250	+	0.617909i	$0.787980\pi$
$660$	19.4450	0.756894
$661$	45.3130	1.76247	0.881236	−	0.472676i	$-0.156712\pi$
$661$	45.3130	1.76247	0.881236	+	0.472676i	$0.156712\pi$
$662$	10.2984	0.400258
$663$	−4.24454	−0.164844
$664$	57.5364	2.23284
$665$	9.89829	0.383839
$666$	−0.910514	−0.0352817
$667$	60.3783	2.33786
$668$	−38.6999	−1.49734
$669$	17.9129	0.692553
$670$	64.1565	2.47858
$671$	−5.26033	−0.203073
$672$	−1.74204	−0.0672006
$673$	−10.9368	−0.421583	−0.210791	−	0.977531i	$-0.567604\pi$
$673$	−10.9368	−0.421583	−0.210791	+	0.977531i	$0.567604\pi$
$674$	82.1452	3.16412
$675$	−0.291944	−0.0112369
$676$	20.7041	0.796313
$677$	−0.0838001	−0.00322070	−0.00161035	−	0.999999i	$-0.500513\pi$
$677$	−0.0838001	−0.00322070	−0.00161035	+	0.999999i	$0.500513\pi$
$678$	44.2369	1.69891
$679$	15.6935	0.602260
$680$	11.4270	0.438204
$681$	−3.26881	−0.125261
$682$	−9.77296	−0.374226
$683$	18.5555	0.710006	0.355003	−	0.934865i	$-0.384480\pi$
$683$	18.5555	0.710006	0.355003	+	0.934865i	$0.384480\pi$
$684$	14.0797	0.538350
$685$	−38.2154	−1.46013
$686$	40.4247	1.54342
$687$	5.89201	0.224794
$688$	28.0804	1.07056
$689$	51.6043	1.96597
$690$	−42.4896	−1.61755
$691$	0.606310	0.0230651	0.0115326	−	0.999933i	$-0.496329\pi$
$691$	0.606310	0.0230651	0.0115326	+	0.999933i	$0.496329\pi$
$692$	79.2720	3.01347
$693$	2.90357	0.110298
$694$	20.8881	0.792901
$695$	−36.4118	−1.38118
$696$	−40.1949	−1.52358
$697$	−7.79243	−0.295159
$698$	−11.1254	−0.421101
$699$	17.4540	0.660169
$700$	−1.61146	−0.0609073
$701$	−17.8987	−0.676025	−0.338013	−	0.941142i	$-0.609755\pi$
$701$	−17.8987	−0.676025	−0.338013	+	0.941142i	$0.609755\pi$
$702$	−10.5068	−0.396555
$703$	1.25473	0.0473231
$704$	−13.7609	−0.518634
$705$	−15.5523	−0.585735
$706$	−1.53689	−0.0578416
$707$	−11.0479	−0.415498
$708$	12.0216	0.451801
$709$	26.5552	0.997301	0.498650	−	0.866803i	$-0.333829\pi$
$709$	26.5552	0.997301	0.498650	+	0.866803i	$0.333829\pi$
$710$	−11.1589	−0.418786
$711$	−0.818017	−0.0306780
$712$	−23.9586	−0.897888
$713$	14.3849	0.538717
$714$	3.31036	0.123887
$715$	19.9964	0.747822
$716$	44.8563	1.67636
$717$	−12.9861	−0.484976
$718$	−64.0877	−2.39173
$719$	−22.9332	−0.855264	−0.427632	−	0.903953i	$-0.640652\pi$
$719$	−22.9332	−0.855264	−0.427632	+	0.903953i	$0.640652\pi$
$720$	10.3743	0.386629
$721$	3.17033	0.118069
$722$	18.2281	0.678380
$723$	−27.7778	−1.03307
$724$	−24.5918	−0.913948
$725$	−2.22823	−0.0827542
$726$	15.5600	0.577484
$727$	5.26510	0.195272	0.0976358	−	0.995222i	$-0.468872\pi$
$727$	5.26510	0.195272	0.0976358	+	0.995222i	$0.468872\pi$
$728$	−29.8933	−1.10792
$729$	1.00000	0.0370370
$730$	−4.90211	−0.181435
$731$	−5.87306	−0.217223
$732$	−10.0000	−0.369611
$733$	29.7397	1.09846	0.549231	−	0.835670i	$-0.314921\pi$
$733$	29.7397	1.09846	0.549231	+	0.835670i	$0.314921\pi$
$734$	−3.15933	−0.116613
$735$	−11.3081	−0.417107
$736$	−10.3049	−0.379845
$737$	−25.9345	−0.955309
$738$	−19.2892	−0.710046
$739$	41.5929	1.53002	0.765009	−	0.644019i	$-0.222734\pi$
$739$	41.5929	1.53002	0.765009	+	0.644019i	$0.222734\pi$
$740$	3.29422	0.121098
$741$	14.4790	0.531898
$742$	−40.2466	−1.47750
$743$	31.6042	1.15945	0.579724	−	0.814813i	$-0.303161\pi$
$743$	31.6042	1.15945	0.579724	+	0.814813i	$0.303161\pi$
$744$	−9.57624	−0.351082
$745$	40.1307	1.47027
$746$	91.3058	3.34294
$747$	−10.9253	−0.399735
$748$	−8.96162	−0.327669
$749$	5.55017	0.202799
$750$	28.4235	1.03788
$751$	−10.8567	−0.396167	−0.198083	−	0.980185i	$-0.563472\pi$
$751$	−10.8567	−0.396167	−0.198083	+	0.980185i	$0.563472\pi$
$752$	−34.2700	−1.24970
$753$	−5.77826	−0.210572
$754$	−80.1923	−2.92043
$755$	−37.5996	−1.36839
$756$	5.51975	0.200752
$757$	9.33730	0.339370	0.169685	−	0.985498i	$-0.445725\pi$
$757$	9.33730	0.339370	0.169685	+	0.985498i	$0.445725\pi$
$758$	65.0182	2.36157
$759$	17.1759	0.623447
$760$	−38.9796	−1.41394
$761$	−46.9362	−1.70144	−0.850718	−	0.525623i	$-0.823832\pi$
$761$	−46.9362	−1.70144	−0.850718	+	0.525623i	$0.823832\pi$
$762$	22.9921	0.832916
$763$	−15.4585	−0.559636
$764$	−107.999	−3.90726
$765$	−2.16981	−0.0784495
$766$	−54.6259	−1.97371
$767$	12.3625	0.446386
$768$	−32.6089	−1.17667
$769$	0.948912	0.0342186	0.0171093	−	0.999854i	$-0.494554\pi$
$769$	0.948912	0.0342186	0.0171093	+	0.999854i	$0.494554\pi$
$770$	−15.5954	−0.562017
$771$	20.7387	0.746886
$772$	−81.4518	−2.93152
$773$	27.8259	1.00083	0.500415	−	0.865786i	$-0.333181\pi$
$773$	27.8259	1.00083	0.500415	+	0.865786i	$0.333181\pi$
$774$	−14.5380	−0.522559
$775$	−0.530864	−0.0190692
$776$	−61.8011	−2.21853
$777$	0.491902	0.0176469
$778$	−28.9122	−1.03655
$779$	26.5815	0.952380
$780$	38.0136	1.36110
$781$	4.51085	0.161411
$782$	19.5822	0.700259
$783$	7.63238	0.272759
$784$	−24.9178	−0.889923
$785$	−2.16981	−0.0774437
$786$	0.253850	0.00905453
$787$	37.6340	1.34151	0.670753	−	0.741681i	$-0.265971\pi$
$787$	37.6340	1.34151	0.670753	+	0.741681i	$0.265971\pi$
$788$	51.2990	1.82745
$789$	−16.4037	−0.583987
$790$	4.39364	0.156319
$791$	−23.8988	−0.849744
$792$	−11.4343	−0.406301
$793$	−10.2836	−0.365181
$794$	46.8187	1.66154
$795$	26.3800	0.935603
$796$	−30.5656	−1.08337
$797$	2.23575	0.0791945	0.0395973	−	0.999216i	$-0.487393\pi$
$797$	2.23575	0.0791945	0.0395973	+	0.999216i	$0.487393\pi$
$798$	−11.2923	−0.399742
$799$	7.16761	0.253572
$800$	0.380298	0.0134456
$801$	4.54937	0.160744
$802$	76.1893	2.69034
$803$	1.98162	0.0699299
$804$	−49.3020	−1.73875
$805$	22.9549	0.809053
$806$	−19.1054	−0.672961
$807$	14.4681	0.509303
$808$	43.5067	1.53056
$809$	7.72027	0.271430	0.135715	−	0.990748i	$-0.456667\pi$
$809$	7.72027	0.271430	0.135715	+	0.990748i	$0.456667\pi$
$810$	−5.37109	−0.188721
$811$	2.19627	0.0771215	0.0385608	−	0.999256i	$-0.487723\pi$
$811$	2.19627	0.0771215	0.0385608	+	0.999256i	$0.487723\pi$
$812$	42.1289	1.47843
$813$	28.9833	1.01649
$814$	−1.97691	−0.0692906
$815$	11.6272	0.407282
$816$	−4.78123	−0.167377
$817$	20.0341	0.700905
$818$	14.6064	0.510701
$819$	5.67628	0.198345
$820$	69.7880	2.43710
$821$	32.1507	1.12207	0.561033	−	0.827793i	$-0.310404\pi$
$821$	32.1507	1.12207	0.561033	+	0.827793i	$0.310404\pi$
$822$	43.5972	1.52063
$823$	31.0542	1.08248	0.541240	−	0.840868i	$-0.317955\pi$
$823$	31.0542	1.08248	0.541240	+	0.840868i	$0.317955\pi$
$824$	−12.4848	−0.434928
$825$	−0.633868	−0.0220684
$826$	−9.64165	−0.335476
$827$	56.7543	1.97354	0.986770	−	0.162125i	$-0.0518349\pi$
$827$	56.7543	1.97354	0.986770	+	0.162125i	$0.0518349\pi$
$828$	32.6518	1.13473
$829$	37.3798	1.29825	0.649127	−	0.760680i	$-0.275135\pi$
$829$	37.3798	1.29825	0.649127	+	0.760680i	$0.275135\pi$
$830$	58.6806	2.03683
$831$	−0.848847	−0.0294462
$832$	−26.9016	−0.932646
$833$	5.21159	0.180571
$834$	41.5397	1.43840
$835$	−20.3444	−0.704045
$836$	30.5698	1.05728
$837$	1.81838	0.0628524
$838$	92.0195	3.17876
$839$	−14.3296	−0.494712	−0.247356	−	0.968925i	$-0.579562\pi$
$839$	−14.3296	−0.494712	−0.247356	+	0.968925i	$0.579562\pi$
$840$	−15.2814	−0.527260
$841$	29.2533	1.00873
$842$	78.3106	2.69876
$843$	−8.81983	−0.303771
$844$	107.011	3.68346
$845$	10.8841	0.374423
$846$	17.7426	0.610002
$847$	−8.40621	−0.288841
$848$	58.1292	1.99616
$849$	−12.3468	−0.423739
$850$	−0.722671	−0.0247874
$851$	2.90982	0.0997473
$852$	8.57522	0.293782
$853$	−6.36156	−0.217816	−0.108908	−	0.994052i	$-0.534735\pi$
$853$	−6.36156	−0.217816	−0.108908	+	0.994052i	$0.534735\pi$
$854$	8.02025	0.274447
$855$	7.40162	0.253130
$856$	−21.8566	−0.747044
$857$	−34.8293	−1.18975	−0.594873	−	0.803820i	$-0.702798\pi$
$857$	−34.8293	−1.18975	−0.594873	+	0.803820i	$0.702798\pi$
$858$	−22.8125	−0.778805
$859$	−36.0495	−1.22999	−0.614997	−	0.788530i	$-0.710843\pi$
$859$	−36.0495	−1.22999	−0.614997	+	0.788530i	$0.710843\pi$
$860$	52.5983	1.79359
$861$	10.4209	0.355144
$862$	−36.3796	−1.23909
$863$	−9.98388	−0.339855	−0.169928	−	0.985457i	$-0.554353\pi$
$863$	−9.98388	−0.339855	−0.169928	+	0.985457i	$0.554353\pi$
$864$	−1.30264	−0.0443168
$865$	41.6729	1.41692
$866$	−93.7105	−3.18441
$867$	1.00000	0.0339618
$868$	10.0370	0.340678
$869$	−1.77608	−0.0602493
$870$	−40.9942	−1.38983
$871$	−50.7001	−1.71791
$872$	60.8759	2.06152
$873$	11.7351	0.397172
$874$	−66.7987	−2.25950
$875$	−15.3557	−0.519117
$876$	3.76710	0.127279
$877$	2.78775	0.0941357	0.0470679	−	0.998892i	$-0.485012\pi$
$877$	2.78775	0.0941357	0.0470679	+	0.998892i	$0.485012\pi$
$878$	−48.8431	−1.64837
$879$	−31.1177	−1.04957
$880$	22.5248	0.759310
$881$	17.4100	0.586559	0.293280	−	0.956027i	$-0.405253\pi$
$881$	17.4100	0.586559	0.293280	+	0.956027i	$0.405253\pi$
$882$	12.9007	0.434388
$883$	51.2871	1.72595	0.862974	−	0.505248i	$-0.168599\pi$
$883$	51.2871	1.72595	0.862974	+	0.505248i	$0.168599\pi$
$884$	−17.5193	−0.589239
$885$	6.31972	0.212435
$886$	−28.5348	−0.958645
$887$	−38.5570	−1.29462	−0.647308	−	0.762228i	$-0.724105\pi$
$887$	−38.5570	−1.29462	−0.647308	+	0.762228i	$0.724105\pi$
$888$	−1.93712	−0.0650053
$889$	−12.4214	−0.416600
$890$	−24.4351	−0.819066
$891$	2.17120	0.0727379
$892$	73.9354	2.47554
$893$	−24.4501	−0.818192
$894$	−45.7823	−1.53119
$895$	23.5808	0.788218
$896$	24.4649	0.817315
$897$	33.5778	1.12113
$898$	82.4899	2.75272
$899$	13.8786	0.462876
$900$	−1.20500	−0.0401665
$901$	−12.1578	−0.405035
$902$	−41.8807	−1.39448
$903$	7.85412	0.261369
$904$	94.1138	3.13018
$905$	−12.9278	−0.429735
$906$	42.8948	1.42508
$907$	39.1700	1.30062	0.650309	−	0.759670i	$-0.274640\pi$
$907$	39.1700	1.30062	0.650309	+	0.759670i	$0.274640\pi$
$908$	−13.4920	−0.447748
$909$	−8.26125	−0.274008
$910$	−30.4878	−1.01066
$911$	−12.6338	−0.418575	−0.209288	−	0.977854i	$-0.567115\pi$
$911$	−12.6338	−0.418575	−0.209288	+	0.977854i	$0.567115\pi$
$912$	16.3097	0.540068
$913$	−23.7209	−0.785048
$914$	95.7740	3.16792
$915$	−5.25695	−0.173790
$916$	24.3192	0.803530
$917$	−0.137141	−0.00452881
$918$	2.47538	0.0816996
$919$	−35.0664	−1.15673	−0.578367	−	0.815777i	$-0.696310\pi$
$919$	−35.0664	−1.15673	−0.578367	+	0.815777i	$0.696310\pi$
$920$	−90.3965	−2.98029
$921$	−3.74595	−0.123433
$922$	17.4881	0.575941
$923$	8.81839	0.290261
$924$	11.9845	0.394261
$925$	−0.107385	−0.00353080
$926$	−55.2263	−1.81485
$927$	2.37067	0.0778630
$928$	−9.94226	−0.326371
$929$	41.3087	1.35529	0.677647	−	0.735387i	$-0.263000\pi$
$929$	41.3087	1.35529	0.677647	+	0.735387i	$0.263000\pi$
$930$	−9.76668	−0.320262
$931$	−17.7777	−0.582642
$932$	72.0411	2.35979
$933$	−2.48339	−0.0813026
$934$	−41.2760	−1.35059
$935$	−4.71108	−0.154069
$936$	−22.3533	−0.730640
$937$	7.59825	0.248224	0.124112	−	0.992268i	$-0.460392\pi$
$937$	7.59825	0.248224	0.124112	+	0.992268i	$0.460392\pi$
$938$	39.5415	1.29107
$939$	0.762401	0.0248800
$940$	−64.1922	−2.09372
$941$	−7.88120	−0.256920	−0.128460	−	0.991715i	$-0.541003\pi$
$941$	−7.88120	−0.256920	−0.128460	+	0.991715i	$0.541003\pi$
$942$	2.47538	0.0806522
$943$	61.6444	2.00742
$944$	13.9257	0.453243
$945$	2.90171	0.0943926
$946$	−31.5650	−1.02627
$947$	−34.2561	−1.11317	−0.556587	−	0.830789i	$-0.687889\pi$
$947$	−34.2561	−1.11317	−0.556587	+	0.830789i	$0.687889\pi$
$948$	−3.37636	−0.109659
$949$	3.87393	0.125753
$950$	2.46517	0.0799806
$951$	−1.08864	−0.0353014
$952$	7.04277	0.228257
$953$	55.5377	1.79904	0.899522	−	0.436876i	$-0.143915\pi$
$953$	55.5377	1.79904	0.899522	+	0.436876i	$0.143915\pi$
$954$	−30.0951	−0.974365
$955$	−56.7745	−1.83718
$956$	−53.6003	−1.73356
$957$	16.5714	0.535678
$958$	30.1793	0.975048
$959$	−23.5532	−0.760573
$960$	−13.7521	−0.443847
$961$	−27.6935	−0.893338
$962$	−3.86472	−0.124603
$963$	4.15024	0.133740
$964$	−114.653	−3.69272
$965$	−42.8189	−1.37839
$966$	−26.1876	−0.842572
$967$	−43.2898	−1.39211	−0.696054	−	0.717990i	$-0.745062\pi$
$967$	−43.2898	−1.39211	−0.696054	+	0.717990i	$0.745062\pi$
$968$	33.1038	1.06399
$969$	−3.41119	−0.109583
$970$	−63.0302	−2.02378
$971$	−4.10786	−0.131828	−0.0659138	−	0.997825i	$-0.520996\pi$
$971$	−4.10786	−0.131828	−0.0659138	+	0.997825i	$0.520996\pi$
$972$	4.12750	0.132389
$973$	−22.4417	−0.719446
$974$	50.3947	1.61475
$975$	−1.23917	−0.0396851
$976$	−11.5839	−0.370790
$977$	3.99533	0.127822	0.0639109	−	0.997956i	$-0.479643\pi$
$977$	3.99533	0.127822	0.0639109	+	0.997956i	$0.479643\pi$
$978$	−13.2646	−0.424155
$979$	9.87760	0.315689
$980$	−46.6743	−1.49096
$981$	−11.5594	−0.369063
$982$	24.3450	0.776880
$983$	28.4759	0.908241	0.454121	−	0.890940i	$-0.349954\pi$
$983$	28.4759	0.908241	0.454121	+	0.890940i	$0.349954\pi$
$984$	−41.0377	−1.30824
$985$	26.9676	0.859261
$986$	18.8930	0.601677
$987$	−9.58535	−0.305105
$988$	59.7618	1.90128
$989$	46.4606	1.47736
$990$	−11.6617	−0.370633
$991$	12.7247	0.404214	0.202107	−	0.979363i	$-0.435221\pi$
$991$	12.7247	0.404214	0.202107	+	0.979363i	$0.435221\pi$
$992$	−2.36870	−0.0752062
$993$	−4.16032	−0.132024
$994$	−6.87754	−0.218142
$995$	−16.0682	−0.509396
$996$	−45.0940	−1.42886
$997$	40.8691	1.29434	0.647168	−	0.762347i	$-0.275953\pi$
$997$	40.8691	1.29434	0.647168	+	0.762347i	$0.275953\pi$
$998$	67.0891	2.12367
$999$	0.367828	0.0116376

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.47538 q^{2} +1.00000 q^{3} +4.12750 q^{4} +2.16981 q^{5} -2.47538 q^{6} +1.33731 q^{7} -5.26636 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.47538 q^{2} +1.00000 q^{3} +4.12750 q^{4} +2.16981 q^{5} -2.47538 q^{6} +1.33731 q^{7} -5.26636 q^{8} +1.00000 q^{9} -5.37109 q^{10} +2.17120 q^{11} +4.12750 q^{12} +4.24454 q^{13} -3.31036 q^{14} +2.16981 q^{15} +4.78123 q^{16} -1.00000 q^{17} -2.47538 q^{18} +3.41119 q^{19} +8.95586 q^{20} +1.33731 q^{21} -5.37454 q^{22} +7.91081 q^{23} -5.26636 q^{24} -0.291944 q^{25} -10.5068 q^{26} +1.00000 q^{27} +5.51975 q^{28} +7.63238 q^{29} -5.37109 q^{30} +1.81838 q^{31} -1.30264 q^{32} +2.17120 q^{33} +2.47538 q^{34} +2.90171 q^{35} +4.12750 q^{36} +0.367828 q^{37} -8.44399 q^{38} +4.24454 q^{39} -11.4270 q^{40} +7.79243 q^{41} -3.31036 q^{42} +5.87306 q^{43} +8.96162 q^{44} +2.16981 q^{45} -19.5822 q^{46} -7.16761 q^{47} +4.78123 q^{48} -5.21159 q^{49} +0.722671 q^{50} -1.00000 q^{51} +17.5193 q^{52} +12.1578 q^{53} -2.47538 q^{54} +4.71108 q^{55} -7.04277 q^{56} +3.41119 q^{57} -18.8930 q^{58} +2.91257 q^{59} +8.95586 q^{60} -2.42278 q^{61} -4.50118 q^{62} +1.33731 q^{63} -6.33793 q^{64} +9.20983 q^{65} -5.37454 q^{66} -11.9448 q^{67} -4.12750 q^{68} +7.91081 q^{69} -7.18283 q^{70} +2.07758 q^{71} -5.26636 q^{72} +0.912685 q^{73} -0.910514 q^{74} -0.291944 q^{75} +14.0797 q^{76} +2.90357 q^{77} -10.5068 q^{78} -0.818017 q^{79} +10.3743 q^{80} +1.00000 q^{81} -19.2892 q^{82} -10.9253 q^{83} +5.51975 q^{84} -2.16981 q^{85} -14.5380 q^{86} +7.63238 q^{87} -11.4343 q^{88} +4.54937 q^{89} -5.37109 q^{90} +5.67628 q^{91} +32.6518 q^{92} +1.81838 q^{93} +17.7426 q^{94} +7.40162 q^{95} -1.30264 q^{96} +11.7351 q^{97} +12.9007 q^{98} +2.17120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 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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