LMFDB - Embedded newform 6001.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05839 q^{2} +1.11600 q^{3} +2.23697 q^{4} +1.51993 q^{5} -2.29716 q^{6} +0.698036 q^{7} -0.487784 q^{8} -1.75454 q^{9} +O(q^{10})$	\(q-2.05839 q^{2} +1.11600 q^{3} +2.23697 q^{4} +1.51993 q^{5} -2.29716 q^{6} +0.698036 q^{7} -0.487784 q^{8} -1.75454 q^{9} -3.12862 q^{10} -1.93696 q^{11} +2.49646 q^{12} -2.36410 q^{13} -1.43683 q^{14} +1.69625 q^{15} -3.46990 q^{16} -1.00000 q^{17} +3.61154 q^{18} +4.76630 q^{19} +3.40005 q^{20} +0.779009 q^{21} +3.98703 q^{22} +1.56468 q^{23} -0.544367 q^{24} -2.68980 q^{25} +4.86625 q^{26} -5.30607 q^{27} +1.56149 q^{28} -7.64102 q^{29} -3.49154 q^{30} -8.37503 q^{31} +8.11797 q^{32} -2.16165 q^{33} +2.05839 q^{34} +1.06097 q^{35} -3.92487 q^{36} +8.95625 q^{37} -9.81092 q^{38} -2.63834 q^{39} -0.741400 q^{40} +10.5910 q^{41} -1.60350 q^{42} +5.85645 q^{43} -4.33293 q^{44} -2.66679 q^{45} -3.22073 q^{46} +0.674352 q^{47} -3.87240 q^{48} -6.51275 q^{49} +5.53666 q^{50} -1.11600 q^{51} -5.28844 q^{52} +3.02487 q^{53} +10.9220 q^{54} -2.94405 q^{55} -0.340491 q^{56} +5.31920 q^{57} +15.7282 q^{58} -2.50316 q^{59} +3.79446 q^{60} -0.950318 q^{61} +17.2391 q^{62} -1.22474 q^{63} -9.77017 q^{64} -3.59328 q^{65} +4.44952 q^{66} +6.59576 q^{67} -2.23697 q^{68} +1.74619 q^{69} -2.18389 q^{70} -9.26260 q^{71} +0.855839 q^{72} +12.9385 q^{73} -18.4355 q^{74} -3.00182 q^{75} +10.6621 q^{76} -1.35207 q^{77} +5.43074 q^{78} -2.67025 q^{79} -5.27401 q^{80} -0.657942 q^{81} -21.8004 q^{82} +5.29091 q^{83} +1.74262 q^{84} -1.51993 q^{85} -12.0549 q^{86} -8.52738 q^{87} +0.944820 q^{88} -1.84505 q^{89} +5.48930 q^{90} -1.65023 q^{91} +3.50016 q^{92} -9.34653 q^{93} -1.38808 q^{94} +7.24447 q^{95} +9.05966 q^{96} -8.40340 q^{97} +13.4058 q^{98} +3.39849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.05839	−1.45550	−0.727751	−	0.685841i	$-0.759434\pi$
$2$	−2.05839	−1.45550	−0.727751	+	0.685841i	$0.759434\pi$
$3$	1.11600	0.644323	0.322161	−	0.946685i	$-0.395591\pi$
$3$	1.11600	0.644323	0.322161	+	0.946685i	$0.395591\pi$
$4$	2.23697	1.11849
$5$	1.51993	0.679735	0.339867	−	0.940473i	$-0.389618\pi$
$5$	1.51993	0.679735	0.339867	+	0.940473i	$0.389618\pi$
$6$	−2.29716	−0.937813
$7$	0.698036	0.263833	0.131916	−	0.991261i	$-0.457887\pi$
$7$	0.698036	0.263833	0.131916	+	0.991261i	$0.457887\pi$
$8$	−0.487784	−0.172458
$9$	−1.75454	−0.584848
$10$	−3.12862	−0.989356
$11$	−1.93696	−0.584016	−0.292008	−	0.956416i	$-0.594323\pi$
$11$	−1.93696	−0.584016	−0.292008	+	0.956416i	$0.594323\pi$
$12$	2.49646	0.720667
$13$	−2.36410	−0.655685	−0.327842	−	0.944732i	$-0.606321\pi$
$13$	−2.36410	−0.655685	−0.327842	+	0.944732i	$0.606321\pi$
$14$	−1.43683	−0.384009
$15$	1.69625	0.437969
$16$	−3.46990	−0.867474
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.61154	0.851248
$19$	4.76630	1.09347	0.546733	−	0.837307i	$-0.315871\pi$
$19$	4.76630	1.09347	0.546733	+	0.837307i	$0.315871\pi$
$20$	3.40005	0.760275
$21$	0.779009	0.169994
$22$	3.98703	0.850037
$23$	1.56468	0.326259	0.163130	−	0.986605i	$-0.447841\pi$
$23$	1.56468	0.326259	0.163130	+	0.986605i	$0.447841\pi$
$24$	−0.544367	−0.111118
$25$	−2.68980	−0.537960
$26$	4.86625	0.954350
$27$	−5.30607	−1.02115
$28$	1.56149	0.295094
$29$	−7.64102	−1.41890	−0.709451	−	0.704754i	$-0.751057\pi$
$29$	−7.64102	−1.41890	−0.709451	+	0.704754i	$0.751057\pi$
$30$	−3.49154	−0.637465
$31$	−8.37503	−1.50420	−0.752100	−	0.659049i	$-0.770959\pi$
$31$	−8.37503	−1.50420	−0.752100	+	0.659049i	$0.770959\pi$
$32$	8.11797	1.43507
$33$	−2.16165	−0.376295
$34$	2.05839	0.353011
$35$	1.06097	0.179337
$36$	−3.92487	−0.654145
$37$	8.95625	1.47240	0.736199	−	0.676765i	$-0.236619\pi$
$37$	8.95625	1.47240	0.736199	+	0.676765i	$0.236619\pi$
$38$	−9.81092	−1.59154
$39$	−2.63834	−0.422473
$40$	−0.741400	−0.117226
$41$	10.5910	1.65404	0.827019	−	0.562174i	$-0.190035\pi$
$41$	10.5910	1.65404	0.827019	+	0.562174i	$0.190035\pi$
$42$	−1.60350	−0.247426
$43$	5.85645	0.893101	0.446550	−	0.894759i	$-0.352652\pi$
$43$	5.85645	0.893101	0.446550	+	0.894759i	$0.352652\pi$
$44$	−4.33293	−0.653214
$45$	−2.66679	−0.397542
$46$	−3.22073	−0.474871
$47$	0.674352	0.0983643	0.0491822	−	0.998790i	$-0.484339\pi$
$47$	0.674352	0.0983643	0.0491822	+	0.998790i	$0.484339\pi$
$48$	−3.87240	−0.558933
$49$	−6.51275	−0.930392
$50$	5.53666	0.783002
$51$	−1.11600	−0.156271
$52$	−5.28844	−0.733375
$53$	3.02487	0.415498	0.207749	−	0.978182i	$-0.433386\pi$
$53$	3.02487	0.415498	0.207749	+	0.978182i	$0.433386\pi$
$54$	10.9220	1.48629
$55$	−2.94405	−0.396976
$56$	−0.340491	−0.0455000
$57$	5.31920	0.704545
$58$	15.7282	2.06522
$59$	−2.50316	−0.325883	−0.162942	−	0.986636i	$-0.552098\pi$
$59$	−2.50316	−0.325883	−0.162942	+	0.986636i	$0.552098\pi$
$60$	3.79446	0.489862
$61$	−0.950318	−0.121676	−0.0608379	−	0.998148i	$-0.519377\pi$
$61$	−0.950318	−0.121676	−0.0608379	+	0.998148i	$0.519377\pi$
$62$	17.2391	2.18937
$63$	−1.22474	−0.154302
$64$	−9.77017	−1.22127
$65$	−3.59328	−0.445692
$66$	4.44952	0.547698
$67$	6.59576	0.805801	0.402900	−	0.915244i	$-0.368002\pi$
$67$	6.59576	0.805801	0.402900	+	0.915244i	$0.368002\pi$
$68$	−2.23697	−0.271273
$69$	1.74619	0.210216
$70$	−2.18389	−0.261025
$71$	−9.26260	−1.09927	−0.549634	−	0.835405i	$-0.685233\pi$
$71$	−9.26260	−1.09927	−0.549634	+	0.835405i	$0.685233\pi$
$72$	0.855839	0.100862
$73$	12.9385	1.51434	0.757168	−	0.653220i	$-0.226582\pi$
$73$	12.9385	1.51434	0.757168	+	0.653220i	$0.226582\pi$
$74$	−18.4355	−2.14308
$75$	−3.00182	−0.346620
$76$	10.6621	1.22303
$77$	−1.35207	−0.154083
$78$	5.43074	0.614910
$79$	−2.67025	−0.300426	−0.150213	−	0.988654i	$-0.547996\pi$
$79$	−2.67025	−0.300426	−0.150213	+	0.988654i	$0.547996\pi$
$80$	−5.27401	−0.589653
$81$	−0.657942	−0.0731047
$82$	−21.8004	−2.40746
$83$	5.29091	0.580753	0.290376	−	0.956913i	$-0.406220\pi$
$83$	5.29091	0.580753	0.290376	+	0.956913i	$0.406220\pi$
$84$	1.74262	0.190136
$85$	−1.51993	−0.164860
$86$	−12.0549	−1.29991
$87$	−8.52738	−0.914231
$88$	0.944820	0.100718
$89$	−1.84505	−0.195575	−0.0977877	−	0.995207i	$-0.531177\pi$
$89$	−1.84505	−0.195575	−0.0977877	+	0.995207i	$0.531177\pi$
$90$	5.48930	0.578623
$91$	−1.65023	−0.172991
$92$	3.50016	0.364917
$93$	−9.34653	−0.969190
$94$	−1.38808	−0.143169
$95$	7.24447	0.743267
$96$	9.05966	0.924647
$97$	−8.40340	−0.853236	−0.426618	−	0.904432i	$-0.640295\pi$
$97$	−8.40340	−0.853236	−0.426618	+	0.904432i	$0.640295\pi$
$98$	13.4058	1.35419
$99$	3.39849	0.341561
$100$	−6.01702	−0.601702
$101$	18.9561	1.88621	0.943104	−	0.332499i	$-0.107892\pi$
$101$	18.9561	1.88621	0.943104	+	0.332499i	$0.107892\pi$
$102$	2.29716	0.227453
$103$	11.3709	1.12041	0.560205	−	0.828354i	$-0.310722\pi$
$103$	11.3709	1.12041	0.560205	+	0.828354i	$0.310722\pi$
$104$	1.15317	0.113078
$105$	1.18404	0.115551
$106$	−6.22637	−0.604758
$107$	14.7157	1.42262	0.711309	−	0.702880i	$-0.248103\pi$
$107$	14.7157	1.42262	0.711309	+	0.702880i	$0.248103\pi$
$108$	−11.8695	−1.14215
$109$	11.3788	1.08989	0.544945	−	0.838472i	$-0.316551\pi$
$109$	11.3788	1.08989	0.544945	+	0.838472i	$0.316551\pi$
$110$	6.06002	0.577800
$111$	9.99518	0.948700
$112$	−2.42211	−0.228868
$113$	−2.04746	−0.192608	−0.0963042	−	0.995352i	$-0.530702\pi$
$113$	−2.04746	−0.192608	−0.0963042	+	0.995352i	$0.530702\pi$
$114$	−10.9490	−1.02547
$115$	2.37822	0.221770
$116$	−17.0928	−1.58702
$117$	4.14793	0.383476
$118$	5.15248	0.474324
$119$	−0.698036	−0.0639889
$120$	−0.827402	−0.0755311
$121$	−7.24818	−0.658925
$122$	1.95613	0.177099
$123$	11.8196	1.06573
$124$	−18.7347	−1.68243
$125$	−11.6880	−1.04541
$126$	2.52099	0.224587
$127$	7.65465	0.679240	0.339620	−	0.940563i	$-0.389701\pi$
$127$	7.65465	0.679240	0.339620	+	0.940563i	$0.389701\pi$
$128$	3.87488	0.342494
$129$	6.53580	0.575445
$130$	7.39638	0.648705
$131$	0.0373663	0.00326471	0.00163235	−	0.999999i	$-0.499480\pi$
$131$	0.0373663	0.00326471	0.00163235	+	0.999999i	$0.499480\pi$
$132$	−4.83555	−0.420881
$133$	3.32705	0.288492
$134$	−13.5767	−1.17285
$135$	−8.06488	−0.694114
$136$	0.487784	0.0418272
$137$	9.19372	0.785472	0.392736	−	0.919651i	$-0.371529\pi$
$137$	9.19372	0.785472	0.392736	+	0.919651i	$0.371529\pi$
$138$	−3.59434	−0.305970
$139$	17.6517	1.49720	0.748598	−	0.663024i	$-0.230727\pi$
$139$	17.6517	1.49720	0.748598	+	0.663024i	$0.230727\pi$
$140$	2.37336	0.200586
$141$	0.752576	0.0633784
$142$	19.0661	1.59999
$143$	4.57918	0.382930
$144$	6.08809	0.507341
$145$	−11.6139	−0.964478
$146$	−26.6325	−2.20412
$147$	−7.26822	−0.599473
$148$	20.0349	1.64686
$149$	15.4002	1.26163	0.630816	−	0.775933i	$-0.282720\pi$
$149$	15.4002	1.26163	0.630816	+	0.775933i	$0.282720\pi$
$150$	6.17892	0.504506
$151$	11.7637	0.957318	0.478659	−	0.878001i	$-0.341123\pi$
$151$	11.7637	0.957318	0.478659	+	0.878001i	$0.341123\pi$
$152$	−2.32493	−0.188577
$153$	1.75454	0.141846
$154$	2.78309	0.224268
$155$	−12.7295	−1.02246
$156$	−5.90190	−0.472530
$157$	12.4406	0.992868	0.496434	−	0.868075i	$-0.334642\pi$
$157$	12.4406	0.992868	0.496434	+	0.868075i	$0.334642\pi$
$158$	5.49641	0.437271
$159$	3.37575	0.267715
$160$	12.3388	0.975466
$161$	1.09221	0.0860780
$162$	1.35430	0.106404
$163$	6.34719	0.497150	0.248575	−	0.968613i	$-0.420038\pi$
$163$	6.34719	0.497150	0.248575	+	0.968613i	$0.420038\pi$
$164$	23.6918	1.85002
$165$	−3.28557	−0.255781
$166$	−10.8908	−0.845287
$167$	11.5678	0.895144	0.447572	−	0.894248i	$-0.352289\pi$
$167$	11.5678	0.895144	0.447572	+	0.894248i	$0.352289\pi$
$168$	−0.379988	−0.0293167
$169$	−7.41101	−0.570078
$170$	3.12862	0.239954
$171$	−8.36269	−0.639511
$172$	13.1007	0.998921
$173$	3.70539	0.281716	0.140858	−	0.990030i	$-0.455014\pi$
$173$	3.70539	0.281716	0.140858	+	0.990030i	$0.455014\pi$
$174$	17.5527	1.33067
$175$	−1.87758	−0.141932
$176$	6.72106	0.506619
$177$	−2.79352	−0.209974
$178$	3.79784	0.284660
$179$	15.1471	1.13215	0.566075	−	0.824354i	$-0.308461\pi$
$179$	15.1471	1.13215	0.566075	+	0.824354i	$0.308461\pi$
$180$	−5.96554	−0.444645
$181$	16.2129	1.20509	0.602546	−	0.798084i	$-0.294153\pi$
$181$	16.2129	1.20509	0.602546	+	0.798084i	$0.294153\pi$
$182$	3.39682	0.251789
$183$	−1.06055	−0.0783985
$184$	−0.763229	−0.0562660
$185$	13.6129	1.00084
$186$	19.2388	1.41066
$187$	1.93696	0.141645
$188$	1.50851	0.110019
$189$	−3.70383	−0.269414
$190$	−14.9119	−1.08183
$191$	−0.120028	−0.00868491	−0.00434245	−	0.999991i	$-0.501382\pi$
$191$	−0.120028	−0.00868491	−0.00434245	+	0.999991i	$0.501382\pi$
$192$	−10.9035	−0.786893
$193$	−12.8266	−0.923279	−0.461640	−	0.887068i	$-0.652739\pi$
$193$	−12.8266	−0.923279	−0.461640	+	0.887068i	$0.652739\pi$
$194$	17.2975	1.24189
$195$	−4.01010	−0.287169
$196$	−14.5688	−1.04063
$197$	8.33265	0.593677	0.296838	−	0.954928i	$-0.404068\pi$
$197$	8.33265	0.593677	0.296838	+	0.954928i	$0.404068\pi$
$198$	−6.99541	−0.497142
$199$	7.70587	0.546255	0.273127	−	0.961978i	$-0.411942\pi$
$199$	7.70587	0.546255	0.273127	+	0.961978i	$0.411942\pi$
$200$	1.31204	0.0927754
$201$	7.36087	0.519196
$202$	−39.0192	−2.74538
$203$	−5.33371	−0.374353
$204$	−2.49646	−0.174787
$205$	16.0976	1.12431
$206$	−23.4058	−1.63076
$207$	−2.74531	−0.190812
$208$	8.20320	0.568789
$209$	−9.23216	−0.638602
$210$	−2.43722	−0.168184
$211$	−18.5351	−1.27601	−0.638005	−	0.770032i	$-0.720240\pi$
$211$	−18.5351	−1.27601	−0.638005	+	0.770032i	$0.720240\pi$
$212$	6.76655	0.464729
$213$	−10.3371	−0.708284
$214$	−30.2906	−2.07062
$215$	8.90142	0.607072
$216$	2.58822	0.176106
$217$	−5.84608	−0.396858
$218$	−23.4220	−1.58634
$219$	14.4394	0.975721
$220$	−6.58577	−0.444013
$221$	2.36410	0.159027
$222$	−20.5740	−1.38084
$223$	−11.9412	−0.799639	−0.399820	−	0.916594i	$-0.630927\pi$
$223$	−11.9412	−0.799639	−0.399820	+	0.916594i	$0.630927\pi$
$224$	5.66664	0.378618
$225$	4.71938	0.314625
$226$	4.21447	0.280342
$227$	−14.0882	−0.935064	−0.467532	−	0.883976i	$-0.654857\pi$
$227$	−14.0882	−0.935064	−0.467532	+	0.883976i	$0.654857\pi$
$228$	11.8989	0.788024
$229$	−21.9411	−1.44991	−0.724954	−	0.688797i	$-0.758139\pi$
$229$	−21.9411	−1.44991	−0.724954	+	0.688797i	$0.758139\pi$
$230$	−4.89530	−0.322787
$231$	−1.50891	−0.0992790
$232$	3.72717	0.244701
$233$	23.4513	1.53635	0.768173	−	0.640242i	$-0.221166\pi$
$233$	23.4513	1.53635	0.768173	+	0.640242i	$0.221166\pi$
$234$	−8.53805	−0.558150
$235$	1.02497	0.0668617
$236$	−5.59950	−0.364496
$237$	−2.97999	−0.193571
$238$	1.43683	0.0931360
$239$	−11.8661	−0.767555	−0.383777	−	0.923426i	$-0.625377\pi$
$239$	−11.8661	−0.767555	−0.383777	+	0.923426i	$0.625377\pi$
$240$	−5.88580	−0.379927
$241$	−28.8137	−1.85605	−0.928026	−	0.372516i	$-0.878495\pi$
$241$	−28.8137	−1.85605	−0.928026	+	0.372516i	$0.878495\pi$
$242$	14.9196	0.959067
$243$	15.1839	0.974051
$244$	−2.12584	−0.136093
$245$	−9.89894	−0.632420
$246$	−24.3293	−1.55118
$247$	−11.2680	−0.716968
$248$	4.08521	0.259411
$249$	5.90465	0.374192
$250$	24.0585	1.52159
$251$	−3.01870	−0.190539	−0.0952694	−	0.995452i	$-0.530371\pi$
$251$	−3.01870	−0.190539	−0.0952694	+	0.995452i	$0.530371\pi$
$252$	−2.73970	−0.172585
$253$	−3.03074	−0.190541
$254$	−15.7563	−0.988636
$255$	−1.69625	−0.106223
$256$	11.5643	0.722770
$257$	18.3149	1.14245	0.571227	−	0.820792i	$-0.306468\pi$
$257$	18.3149	1.14245	0.571227	+	0.820792i	$0.306468\pi$
$258$	−13.4532	−0.837562
$259$	6.25179	0.388467
$260$	−8.03808	−0.498500
$261$	13.4065	0.829842
$262$	−0.0769145	−0.00475179
$263$	6.91483	0.426386	0.213193	−	0.977010i	$-0.431614\pi$
$263$	6.91483	0.426386	0.213193	+	0.977010i	$0.431614\pi$
$264$	1.05442	0.0648950
$265$	4.59760	0.282428
$266$	−6.84838	−0.419901
$267$	−2.05908	−0.126014
$268$	14.7546	0.901278
$269$	31.3016	1.90849	0.954247	−	0.299021i	$-0.0966601\pi$
$269$	31.3016	1.90849	0.954247	+	0.299021i	$0.0966601\pi$
$270$	16.6007	1.01028
$271$	−8.93474	−0.542747	−0.271373	−	0.962474i	$-0.587478\pi$
$271$	−8.93474	−0.542747	−0.271373	+	0.962474i	$0.587478\pi$
$272$	3.46990	0.210393
$273$	−1.84166	−0.111462
$274$	−18.9243	−1.14326
$275$	5.21005	0.314178
$276$	3.90618	0.235124
$277$	−21.8836	−1.31486	−0.657428	−	0.753517i	$-0.728356\pi$
$277$	−21.8836	−1.31486	−0.657428	+	0.753517i	$0.728356\pi$
$278$	−36.3341	−2.17917
$279$	14.6944	0.879728
$280$	−0.517524	−0.0309280
$281$	0.205291	0.0122466	0.00612331	−	0.999981i	$-0.498051\pi$
$281$	0.205291	0.0122466	0.00612331	+	0.999981i	$0.498051\pi$
$282$	−1.54910	−0.0922474
$283$	−25.3023	−1.50406	−0.752032	−	0.659126i	$-0.770926\pi$
$283$	−25.3023	−1.50406	−0.752032	+	0.659126i	$0.770926\pi$
$284$	−20.7202	−1.22952
$285$	8.08482	0.478904
$286$	−9.42575	−0.557356
$287$	7.39291	0.436390
$288$	−14.2433	−0.839297
$289$	1.00000	0.0588235
$290$	23.9058	1.40380
$291$	−9.37819	−0.549759
$292$	28.9431	1.69376
$293$	−0.254813	−0.0148863	−0.00744316	−	0.999972i	$-0.502369\pi$
$293$	−0.254813	−0.0148863	−0.00744316	+	0.999972i	$0.502369\pi$
$294$	14.9608	0.872534
$295$	−3.80463	−0.221514
$296$	−4.36872	−0.253927
$297$	10.2777	0.596370
$298$	−31.6996	−1.83631
$299$	−3.69908	−0.213923
$300$	−6.71499	−0.387690
$301$	4.08802	0.235629
$302$	−24.2143	−1.39338
$303$	21.1551	1.21533
$304$	−16.5386	−0.948553
$305$	−1.44442	−0.0827073
$306$	−3.61154	−0.206458
$307$	11.6750	0.666326	0.333163	−	0.942869i	$-0.391884\pi$
$307$	11.6750	0.666326	0.333163	+	0.942869i	$0.391884\pi$
$308$	−3.02455	−0.172340
$309$	12.6900	0.721906
$310$	26.2023	1.48819
$311$	−6.92561	−0.392715	−0.196358	−	0.980532i	$-0.562911\pi$
$311$	−6.92561	−0.392715	−0.196358	+	0.980532i	$0.562911\pi$
$312$	1.28694	0.0728587
$313$	−5.02480	−0.284019	−0.142009	−	0.989865i	$-0.545356\pi$
$313$	−5.02480	−0.284019	−0.142009	+	0.989865i	$0.545356\pi$
$314$	−25.6076	−1.44512
$315$	−1.86152	−0.104885
$316$	−5.97327	−0.336023
$317$	−12.4001	−0.696459	−0.348229	−	0.937409i	$-0.613217\pi$
$317$	−12.4001	−0.696459	−0.348229	+	0.937409i	$0.613217\pi$
$318$	−6.94862	−0.389659
$319$	14.8004	0.828662
$320$	−14.8500	−0.830141
$321$	16.4227	0.916625
$322$	−2.24819	−0.125287
$323$	−4.76630	−0.265204
$324$	−1.47180	−0.0817667
$325$	6.35897	0.352732
$326$	−13.0650	−0.723604
$327$	12.6987	0.702241
$328$	−5.16613	−0.285252
$329$	0.470722	0.0259517
$330$	6.76298	0.372290
$331$	25.7684	1.41636	0.708179	−	0.706033i	$-0.249517\pi$
$331$	25.7684	1.41636	0.708179	+	0.706033i	$0.249517\pi$
$332$	11.8356	0.649564
$333$	−15.7141	−0.861129
$334$	−23.8111	−1.30288
$335$	10.0251	0.547731
$336$	−2.70308	−0.147465
$337$	12.2271	0.666052	0.333026	−	0.942918i	$-0.391930\pi$
$337$	12.2271	0.666052	0.333026	+	0.942918i	$0.391930\pi$
$338$	15.2548	0.829749
$339$	−2.28496	−0.124102
$340$	−3.40005	−0.184394
$341$	16.2221	0.878477
$342$	17.2137	0.930810
$343$	−9.43239	−0.509301
$344$	−2.85668	−0.154022
$345$	2.65409	0.142891
$346$	−7.62715	−0.410038
$347$	−11.1520	−0.598673	−0.299337	−	0.954148i	$-0.596765\pi$
$347$	−11.1520	−0.598673	−0.299337	+	0.954148i	$0.596765\pi$
$348$	−19.0755	−1.02256
$349$	−8.09508	−0.433320	−0.216660	−	0.976247i	$-0.569516\pi$
$349$	−8.09508	−0.433320	−0.216660	+	0.976247i	$0.569516\pi$
$350$	3.86479	0.206582
$351$	12.5441	0.669555
$352$	−15.7242	−0.838103
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	5.75017	0.305618
$355$	−14.0785	−0.747211
$356$	−4.12734	−0.218748
$357$	−0.779009	−0.0412295
$358$	−31.1787	−1.64785
$359$	−26.8077	−1.41486	−0.707428	−	0.706785i	$-0.750145\pi$
$359$	−26.8077	−1.41486	−0.707428	+	0.706785i	$0.750145\pi$
$360$	1.30082	0.0685592
$361$	3.71766	0.195666
$362$	−33.3724	−1.75401
$363$	−8.08896	−0.424560
$364$	−3.69152	−0.193488
$365$	19.6657	1.02935
$366$	2.18304	0.114109
$367$	−15.3726	−0.802443	−0.401221	−	0.915981i	$-0.631414\pi$
$367$	−15.3726	−0.802443	−0.401221	+	0.915981i	$0.631414\pi$
$368$	−5.42929	−0.283022
$369$	−18.5824	−0.967361
$370$	−28.0207	−1.45673
$371$	2.11147	0.109622
$372$	−20.9079	−1.08403
$373$	22.5929	1.16982	0.584908	−	0.811100i	$-0.301131\pi$
$373$	22.5929	1.16982	0.584908	+	0.811100i	$0.301131\pi$
$374$	−3.98703	−0.206164
$375$	−13.0438	−0.673579
$376$	−0.328938	−0.0169637
$377$	18.0642	0.930353
$378$	7.62393	0.392133
$379$	6.05855	0.311207	0.155603	−	0.987820i	$-0.450268\pi$
$379$	6.05855	0.311207	0.155603	+	0.987820i	$0.450268\pi$
$380$	16.2057	0.831334
$381$	8.54259	0.437650
$382$	0.247064	0.0126409
$383$	−15.8174	−0.808229	−0.404115	−	0.914708i	$-0.632420\pi$
$383$	−15.8174	−0.808229	−0.404115	+	0.914708i	$0.632420\pi$
$384$	4.32437	0.220677
$385$	−2.05506	−0.104735
$386$	26.4022	1.34384
$387$	−10.2754	−0.522328
$388$	−18.7982	−0.954333
$389$	4.78894	0.242809	0.121404	−	0.992603i	$-0.461260\pi$
$389$	4.78894	0.242809	0.121404	+	0.992603i	$0.461260\pi$
$390$	8.25436	0.417976
$391$	−1.56468	−0.0791295
$392$	3.17681	0.160453
$393$	0.0417008	0.00210353
$394$	−17.1519	−0.864098
$395$	−4.05860	−0.204210
$396$	7.60232	0.382031
$397$	22.7799	1.14329	0.571645	−	0.820501i	$-0.306306\pi$
$397$	22.7799	1.14329	0.571645	+	0.820501i	$0.306306\pi$
$398$	−15.8617	−0.795075
$399$	3.71299	0.185882
$400$	9.33333	0.466667
$401$	−15.1135	−0.754730	−0.377365	−	0.926065i	$-0.623170\pi$
$401$	−15.1135	−0.754730	−0.377365	+	0.926065i	$0.623170\pi$
$402$	−15.1516	−0.755691
$403$	19.7994	0.986281
$404$	42.4044	2.10970
$405$	−1.00003	−0.0496918
$406$	10.9789	0.544872
$407$	−17.3479	−0.859905
$408$	0.544367	0.0269502
$409$	−10.7531	−0.531705	−0.265853	−	0.964014i	$-0.585653\pi$
$409$	−10.7531	−0.531705	−0.265853	+	0.964014i	$0.585653\pi$
$410$	−33.1352	−1.63643
$411$	10.2602	0.506098
$412$	25.4365	1.25316
$413$	−1.74730	−0.0859788
$414$	5.65092	0.277727
$415$	8.04183	0.394758
$416$	−19.1917	−0.940952
$417$	19.6993	0.964678
$418$	19.0034	0.929486
$419$	11.7460	0.573828	0.286914	−	0.957956i	$-0.407371\pi$
$419$	11.7460	0.573828	0.286914	+	0.957956i	$0.407371\pi$
$420$	2.64867	0.129242
$421$	27.8289	1.35630	0.678148	−	0.734925i	$-0.262783\pi$
$421$	27.8289	1.35630	0.678148	+	0.734925i	$0.262783\pi$
$422$	38.1525	1.85724
$423$	−1.18318	−0.0575282
$424$	−1.47548	−0.0716558
$425$	2.68980	0.130475
$426$	21.2777	1.03091
$427$	−0.663357	−0.0321021
$428$	32.9186	1.59118
$429$	5.11037	0.246731
$430$	−18.3226	−0.883594
$431$	−33.6303	−1.61992	−0.809958	−	0.586487i	$-0.800510\pi$
$431$	−33.6303	−1.61992	−0.809958	+	0.586487i	$0.800510\pi$
$432$	18.4115	0.885825
$433$	−13.7837	−0.662401	−0.331201	−	0.943560i	$-0.607454\pi$
$433$	−13.7837	−0.662401	−0.331201	+	0.943560i	$0.607454\pi$
$434$	12.0335	0.577627
$435$	−12.9611	−0.621435
$436$	25.4540	1.21903
$437$	7.45776	0.356753
$438$	−29.7218	−1.42016
$439$	−1.06980	−0.0510588	−0.0255294	−	0.999674i	$-0.508127\pi$
$439$	−1.06980	−0.0510588	−0.0255294	+	0.999674i	$0.508127\pi$
$440$	1.43606	0.0684616
$441$	11.4269	0.544138
$442$	−4.86625	−0.231464
$443$	23.8360	1.13248	0.566242	−	0.824239i	$-0.308397\pi$
$443$	23.8360	1.13248	0.566242	+	0.824239i	$0.308397\pi$
$444$	22.3589	1.06111
$445$	−2.80436	−0.132939
$446$	24.5796	1.16388
$447$	17.1866	0.812898
$448$	−6.81993	−0.322212
$449$	−28.0378	−1.32319	−0.661593	−	0.749863i	$-0.730120\pi$
$449$	−28.0378	−1.32319	−0.661593	+	0.749863i	$0.730120\pi$
$450$	−9.71432	−0.457937
$451$	−20.5144	−0.965985
$452$	−4.58011	−0.215430
$453$	13.1283	0.616822
$454$	28.9989	1.36099
$455$	−2.50824	−0.117588
$456$	−2.59462	−0.121504
$457$	22.6160	1.05793	0.528967	−	0.848642i	$-0.322580\pi$
$457$	22.6160	1.05793	0.528967	+	0.848642i	$0.322580\pi$
$458$	45.1633	2.11034
$459$	5.30607	0.247666
$460$	5.32001	0.248047
$461$	8.86856	0.413050	0.206525	−	0.978441i	$-0.433785\pi$
$461$	8.86856	0.413050	0.206525	+	0.978441i	$0.433785\pi$
$462$	3.10593	0.144501
$463$	−14.9198	−0.693383	−0.346691	−	0.937979i	$-0.612695\pi$
$463$	−14.9198	−0.693383	−0.346691	+	0.937979i	$0.612695\pi$
$464$	26.5136	1.23086
$465$	−14.2061	−0.658793
$466$	−48.2720	−2.23616
$467$	21.6220	1.00055	0.500273	−	0.865868i	$-0.333233\pi$
$467$	21.6220	1.00055	0.500273	+	0.865868i	$0.333233\pi$
$468$	9.27880	0.428913
$469$	4.60408	0.212597
$470$	−2.10979	−0.0973173
$471$	13.8837	0.639727
$472$	1.22100	0.0562011
$473$	−11.3437	−0.521585
$474$	6.13399	0.281744
$475$	−12.8204	−0.588241
$476$	−1.56149	−0.0715707
$477$	−5.30727	−0.243003
$478$	24.4251	1.11718
$479$	14.7024	0.671771	0.335886	−	0.941903i	$-0.390964\pi$
$479$	14.7024	0.671771	0.335886	+	0.941903i	$0.390964\pi$
$480$	13.7701	0.628515
$481$	−21.1735	−0.965429
$482$	59.3098	2.70149
$483$	1.21890	0.0554620
$484$	−16.2140	−0.736999
$485$	−12.7726	−0.579974
$486$	−31.2545	−1.41773
$487$	29.7812	1.34951	0.674757	−	0.738040i	$-0.264248\pi$
$487$	29.7812	1.34951	0.674757	+	0.738040i	$0.264248\pi$
$488$	0.463550	0.0209839
$489$	7.08347	0.320325
$490$	20.3759	0.920489
$491$	27.6918	1.24971	0.624857	−	0.780739i	$-0.285157\pi$
$491$	27.6918	1.24971	0.624857	+	0.780739i	$0.285157\pi$
$492$	26.4401	1.19201
$493$	7.64102	0.344134
$494$	23.1940	1.04355
$495$	5.16547	0.232171
$496$	29.0605	1.30485
$497$	−6.46563	−0.290023
$498$	−12.1541	−0.544638
$499$	−31.7615	−1.42184	−0.710920	−	0.703273i	$-0.751721\pi$
$499$	−31.7615	−1.42184	−0.710920	+	0.703273i	$0.751721\pi$
$500$	−26.1457	−1.16927
$501$	12.9097	0.576762
$502$	6.21367	0.277330
$503$	−15.7227	−0.701040	−0.350520	−	0.936555i	$-0.613995\pi$
$503$	−15.7227	−0.701040	−0.350520	+	0.936555i	$0.613995\pi$
$504$	0.597407	0.0266106
$505$	28.8121	1.28212
$506$	6.23844	0.277332
$507$	−8.27069	−0.367314
$508$	17.1233	0.759721
$509$	35.0443	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$509$	35.0443	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$510$	3.49154	0.154608
$511$	9.03154	0.399532
$512$	−31.5536	−1.39449
$513$	−25.2904	−1.11660
$514$	−37.6993	−1.66284
$515$	17.2831	0.761582
$516$	14.6204	0.643628
$517$	−1.30619	−0.0574464
$518$	−12.8686	−0.565415
$519$	4.13522	0.181516
$520$	1.75275	0.0768630
$521$	−7.16921	−0.314089	−0.157044	−	0.987592i	$-0.550197\pi$
$521$	−7.16921	−0.314089	−0.157044	+	0.987592i	$0.550197\pi$
$522$	−27.5958	−1.20784
$523$	−36.1288	−1.57980	−0.789901	−	0.613234i	$-0.789868\pi$
$523$	−36.1288	−1.57980	−0.789901	+	0.613234i	$0.789868\pi$
$524$	0.0835874	0.00365153
$525$	−2.09538	−0.0914498
$526$	−14.2334	−0.620606
$527$	8.37503	0.364822
$528$	7.50070	0.326426
$529$	−20.5518	−0.893555
$530$	−9.46366	−0.411075
$531$	4.39190	0.190592
$532$	7.44253	0.322675
$533$	−25.0382	−1.08453
$534$	4.23839	0.183413
$535$	22.3668	0.967003
$536$	−3.21731	−0.138967
$537$	16.9042	0.729470
$538$	−64.4310	−2.77782
$539$	12.6149	0.543364
$540$	−18.0409	−0.776357
$541$	−7.47367	−0.321318	−0.160659	−	0.987010i	$-0.551362\pi$
$541$	−7.47367	−0.321318	−0.160659	+	0.987010i	$0.551362\pi$
$542$	18.3912	0.789969
$543$	18.0935	0.776468
$544$	−8.11797	−0.348055
$545$	17.2950	0.740836
$546$	3.79085	0.162233
$547$	−27.5627	−1.17850	−0.589249	−	0.807952i	$-0.700576\pi$
$547$	−27.5627	−1.17850	−0.589249	+	0.807952i	$0.700576\pi$
$548$	20.5661	0.878541
$549$	1.66737	0.0711618
$550$	−10.7243	−0.457286
$551$	−36.4195	−1.55152
$552$	−0.851763	−0.0362534
$553$	−1.86393	−0.0792623
$554$	45.0450	1.91378
$555$	15.1920	0.644865
$556$	39.4864	1.67459
$557$	39.4876	1.67315	0.836573	−	0.547856i	$-0.184556\pi$
$557$	39.4876	1.67315	0.836573	+	0.547856i	$0.184556\pi$
$558$	−30.2467	−1.28045
$559$	−13.8453	−0.585592
$560$	−3.68145	−0.155570
$561$	2.16165	0.0912649
$562$	−0.422568	−0.0178250
$563$	3.95955	0.166875	0.0834375	−	0.996513i	$-0.473410\pi$
$563$	3.95955	0.166875	0.0834375	+	0.996513i	$0.473410\pi$
$564$	1.68349	0.0708879
$565$	−3.11200	−0.130923
$566$	52.0820	2.18917
$567$	−0.459268	−0.0192874
$568$	4.51815	0.189577
$569$	−18.2593	−0.765468	−0.382734	−	0.923859i	$-0.625017\pi$
$569$	−18.2593	−0.765468	−0.382734	+	0.923859i	$0.625017\pi$
$570$	−16.6417	−0.697045
$571$	3.18097	0.133119	0.0665596	−	0.997782i	$-0.478798\pi$
$571$	3.18097	0.133119	0.0665596	+	0.997782i	$0.478798\pi$
$572$	10.2435	0.428303
$573$	−0.133951	−0.00559589
$574$	−15.2175	−0.635166
$575$	−4.20869	−0.175515
$576$	17.1422	0.714258
$577$	12.6248	0.525576	0.262788	−	0.964854i	$-0.415358\pi$
$577$	12.6248	0.525576	0.262788	+	0.964854i	$0.415358\pi$
$578$	−2.05839	−0.0856178
$579$	−14.3145	−0.594890
$580$	−25.9799	−1.07876
$581$	3.69325	0.153222
$582$	19.3040	0.800176
$583$	−5.85906	−0.242658
$584$	−6.31119	−0.261159
$585$	6.30457	0.260662
$586$	0.524504	0.0216671
$587$	11.8006	0.487064	0.243532	−	0.969893i	$-0.421694\pi$
$587$	11.8006	0.487064	0.243532	+	0.969893i	$0.421694\pi$
$588$	−16.2588	−0.670503
$589$	−39.9179	−1.64479
$590$	7.83143	0.322415
$591$	9.29924	0.382520
$592$	−31.0773	−1.27727
$593$	40.6908	1.67097	0.835486	−	0.549511i	$-0.185186\pi$
$593$	40.6908	1.67097	0.835486	+	0.549511i	$0.185186\pi$
$594$	−21.1554	−0.868018
$595$	−1.06097	−0.0434955
$596$	34.4498	1.41112
$597$	8.59975	0.351964
$598$	7.61415	0.311366
$599$	−3.73676	−0.152680	−0.0763400	−	0.997082i	$-0.524323\pi$
$599$	−3.73676	−0.152680	−0.0763400	+	0.997082i	$0.524323\pi$
$600$	1.46424	0.0597773
$601$	45.5779	1.85916	0.929581	−	0.368617i	$-0.120169\pi$
$601$	45.5779	1.85916	0.929581	+	0.368617i	$0.120169\pi$
$602$	−8.41474	−0.342959
$603$	−11.5726	−0.471271
$604$	26.3151	1.07075
$605$	−11.0167	−0.447894
$606$	−43.5454	−1.76891
$607$	−15.1723	−0.615826	−0.307913	−	0.951414i	$-0.599631\pi$
$607$	−15.1723	−0.615826	−0.307913	+	0.951414i	$0.599631\pi$
$608$	38.6927	1.56920
$609$	−5.95242	−0.241204
$610$	2.97318	0.120381
$611$	−1.59424	−0.0644960
$612$	3.92487	0.158653
$613$	−3.79629	−0.153331	−0.0766653	−	0.997057i	$-0.524427\pi$
$613$	−3.79629	−0.153331	−0.0766653	+	0.997057i	$0.524427\pi$
$614$	−24.0317	−0.969839
$615$	17.9650	0.724417
$616$	0.659519	0.0265728
$617$	17.8501	0.718618	0.359309	−	0.933219i	$-0.383012\pi$
$617$	17.8501	0.718618	0.359309	+	0.933219i	$0.383012\pi$
$618$	−26.1209	−1.05074
$619$	−29.4096	−1.18207	−0.591035	−	0.806646i	$-0.701280\pi$
$619$	−29.4096	−1.18207	−0.591035	+	0.806646i	$0.701280\pi$
$620$	−28.4755	−1.14360
$621$	−8.30233	−0.333161
$622$	14.2556	0.571598
$623$	−1.28792	−0.0515992
$624$	9.15477	0.366484
$625$	−4.31596	−0.172638
$626$	10.3430	0.413390
$627$	−10.3031	−0.411466
$628$	27.8293	1.11051
$629$	−8.95625	−0.357109
$630$	3.83173	0.152660
$631$	6.35272	0.252898	0.126449	−	0.991973i	$-0.459642\pi$
$631$	6.35272	0.252898	0.126449	+	0.991973i	$0.459642\pi$
$632$	1.30250	0.0518108
$633$	−20.6852	−0.822163
$634$	25.5242	1.01370
$635$	11.6346	0.461703
$636$	7.55147	0.299435
$637$	15.3968	0.610044
$638$	−30.4650	−1.20612
$639$	16.2516	0.642905
$640$	5.88956	0.232805
$641$	31.6173	1.24881	0.624404	−	0.781102i	$-0.285342\pi$
$641$	31.6173	1.24881	0.624404	+	0.781102i	$0.285342\pi$
$642$	−33.8043	−1.33415
$643$	21.7533	0.857865	0.428932	−	0.903337i	$-0.358890\pi$
$643$	21.7533	0.857865	0.428932	+	0.903337i	$0.358890\pi$
$644$	2.44324	0.0962771
$645$	9.93398	0.391150
$646$	9.81092	0.386005
$647$	17.5815	0.691199	0.345600	−	0.938382i	$-0.387676\pi$
$647$	17.5815	0.691199	0.345600	+	0.938382i	$0.387676\pi$
$648$	0.320934	0.0126075
$649$	4.84852	0.190321
$650$	−13.0893	−0.513403
$651$	−6.52422	−0.255704
$652$	14.1985	0.556056
$653$	33.9790	1.32970	0.664850	−	0.746977i	$-0.268495\pi$
$653$	33.9790	1.32970	0.664850	+	0.746977i	$0.268495\pi$
$654$	−26.1389	−1.02211
$655$	0.0567943	0.00221914
$656$	−36.7497	−1.43483
$657$	−22.7012	−0.885656
$658$	−0.968930	−0.0377728
$659$	21.1350	0.823301	0.411651	−	0.911342i	$-0.364952\pi$
$659$	21.1350	0.823301	0.411651	+	0.911342i	$0.364952\pi$
$660$	−7.34972	−0.286088
$661$	−2.86376	−0.111387	−0.0556937	−	0.998448i	$-0.517737\pi$
$661$	−2.86376	−0.111387	−0.0556937	+	0.998448i	$0.517737\pi$
$662$	−53.0414	−2.06151
$663$	2.63834	0.102465
$664$	−2.58082	−0.100155
$665$	5.05690	0.196098
$666$	32.3458	1.25338
$667$	−11.9558	−0.462930
$668$	25.8769	1.00121
$669$	−13.3263	−0.515226
$670$	−20.6356	−0.797224
$671$	1.84073	0.0710606
$672$	6.32397	0.243952
$673$	−17.5002	−0.674584	−0.337292	−	0.941400i	$-0.609511\pi$
$673$	−17.5002	−0.674584	−0.337292	+	0.941400i	$0.609511\pi$
$674$	−25.1681	−0.969440
$675$	14.2723	0.549340
$676$	−16.5782	−0.637624
$677$	−23.5578	−0.905400	−0.452700	−	0.891663i	$-0.649539\pi$
$677$	−23.5578	−0.905400	−0.452700	+	0.891663i	$0.649539\pi$
$678$	4.70334	0.180631
$679$	−5.86588	−0.225112
$680$	0.741400	0.0284314
$681$	−15.7224	−0.602483
$682$	−33.3915	−1.27863
$683$	−21.8814	−0.837267	−0.418634	−	0.908155i	$-0.637491\pi$
$683$	−21.8814	−0.837267	−0.418634	+	0.908155i	$0.637491\pi$
$684$	−18.7071	−0.715285
$685$	13.9738	0.533913
$686$	19.4155	0.741289
$687$	−24.4862	−0.934209
$688$	−20.3213	−0.774742
$689$	−7.15111	−0.272436
$690$	−5.46316	−0.207979
$691$	−14.4794	−0.550821	−0.275411	−	0.961327i	$-0.588814\pi$
$691$	−14.4794	−0.550821	−0.275411	+	0.961327i	$0.588814\pi$
$692$	8.28886	0.315095
$693$	2.37227	0.0901150
$694$	22.9553	0.871370
$695$	26.8294	1.01770
$696$	4.15952	0.157666
$697$	−10.5910	−0.401163
$698$	16.6628	0.630698
$699$	26.1717	0.989903
$700$	−4.20010	−0.158749
$701$	−23.5084	−0.887899	−0.443949	−	0.896052i	$-0.646423\pi$
$701$	−23.5084	−0.887899	−0.443949	+	0.896052i	$0.646423\pi$
$702$	−25.8207	−0.974539
$703$	42.6882	1.61002
$704$	18.9245	0.713242
$705$	1.14387	0.0430805
$706$	−2.05839	−0.0774686
$707$	13.2321	0.497644
$708$	−6.24904	−0.234853
$709$	9.39454	0.352819	0.176410	−	0.984317i	$-0.443552\pi$
$709$	9.39454	0.352819	0.176410	+	0.984317i	$0.443552\pi$
$710$	28.9791	1.08757
$711$	4.68506	0.175704
$712$	0.899988	0.0337285
$713$	−13.1043	−0.490759
$714$	1.60350	0.0600096
$715$	6.96005	0.260291
$716$	33.8837	1.26629
$717$	−13.2426	−0.494553
$718$	55.1808	2.05933
$719$	19.9708	0.744783	0.372392	−	0.928076i	$-0.378538\pi$
$719$	19.9708	0.744783	0.372392	+	0.928076i	$0.378538\pi$
$720$	9.25349	0.344857
$721$	7.93732	0.295601
$722$	−7.65240	−0.284793
$723$	−32.1561	−1.19590
$724$	36.2677	1.34788
$725$	20.5528	0.763313
$726$	16.6502	0.617949
$727$	10.1861	0.377782	0.188891	−	0.981998i	$-0.439511\pi$
$727$	10.1861	0.377782	0.188891	+	0.981998i	$0.439511\pi$
$728$	0.804957	0.0298337
$729$	18.9191	0.700708
$730$	−40.4796	−1.49822
$731$	−5.85645	−0.216609
$732$	−2.37243	−0.0876876
$733$	−12.3558	−0.456372	−0.228186	−	0.973618i	$-0.573279\pi$
$733$	−12.3558	−0.456372	−0.228186	+	0.973618i	$0.573279\pi$
$734$	31.6428	1.16796
$735$	−11.0472	−0.407483
$736$	12.7021	0.468204
$737$	−12.7758	−0.470601
$738$	38.2498	1.40800
$739$	−5.10687	−0.187859	−0.0939296	−	0.995579i	$-0.529943\pi$
$739$	−5.10687	−0.187859	−0.0939296	+	0.995579i	$0.529943\pi$
$740$	30.4517	1.11943
$741$	−12.5751	−0.461959
$742$	−4.34623	−0.159555
$743$	−8.26763	−0.303310	−0.151655	−	0.988434i	$-0.548460\pi$
$743$	−8.26763	−0.303310	−0.151655	+	0.988434i	$0.548460\pi$
$744$	4.55909	0.167144
$745$	23.4072	0.857575
$746$	−46.5050	−1.70267
$747$	−9.28313	−0.339652
$748$	4.33293	0.158428
$749$	10.2721	0.375333
$750$	26.8492	0.980395
$751$	44.0290	1.60664	0.803321	−	0.595546i	$-0.203064\pi$
$751$	44.0290	1.60664	0.803321	+	0.595546i	$0.203064\pi$
$752$	−2.33993	−0.0853285
$753$	−3.36887	−0.122768
$754$	−37.1831	−1.35413
$755$	17.8801	0.650722
$756$	−8.28537	−0.301336
$757$	−27.2903	−0.991881	−0.495941	−	0.868356i	$-0.665177\pi$
$757$	−27.2903	−0.991881	−0.495941	+	0.868356i	$0.665177\pi$
$758$	−12.4709	−0.452962
$759$	−3.38230	−0.122770
$760$	−3.53374	−0.128182
$761$	−40.7593	−1.47752	−0.738761	−	0.673967i	$-0.764589\pi$
$761$	−40.7593	−1.47752	−0.738761	+	0.673967i	$0.764589\pi$
$762$	−17.5840	−0.637001
$763$	7.94281	0.287549
$764$	−0.268499	−0.00971396
$765$	2.66679	0.0964180
$766$	32.5583	1.17638
$767$	5.91773	0.213677
$768$	12.9058	0.465697
$769$	−39.6699	−1.43053	−0.715267	−	0.698851i	$-0.753695\pi$
$769$	−39.6699	−1.43053	−0.715267	+	0.698851i	$0.753695\pi$
$770$	4.23011	0.152443
$771$	20.4395	0.736109
$772$	−28.6928	−1.03268
$773$	−6.75644	−0.243012	−0.121506	−	0.992591i	$-0.538772\pi$
$773$	−6.75644	−0.243012	−0.121506	+	0.992591i	$0.538772\pi$
$774$	21.1508	0.760250
$775$	22.5272	0.809200
$776$	4.09905	0.147147
$777$	6.97700	0.250298
$778$	−9.85750	−0.353409
$779$	50.4800	1.80863
$780$	−8.97049	−0.321195
$781$	17.9413	0.641991
$782$	3.22073	0.115173
$783$	40.5438	1.44892
$784$	22.5986	0.807091
$785$	18.9089	0.674887
$786$	−0.0858365	−0.00306169
$787$	48.9885	1.74625	0.873126	−	0.487495i	$-0.162089\pi$
$787$	48.9885	1.74625	0.873126	+	0.487495i	$0.162089\pi$
$788$	18.6399	0.664020
$789$	7.71695	0.274731
$790$	8.35418	0.297228
$791$	−1.42920	−0.0508165
$792$	−1.65773	−0.0589048
$793$	2.24665	0.0797809
$794$	−46.8899	−1.66406
$795$	5.13092	0.181975
$796$	17.2378	0.610979
$797$	36.1239	1.27957	0.639787	−	0.768552i	$-0.279022\pi$
$797$	36.1239	1.27957	0.639787	+	0.768552i	$0.279022\pi$
$798$	−7.64279	−0.270552
$799$	−0.674352	−0.0238568
$800$	−21.8357	−0.772010
$801$	3.23723	0.114382
$802$	31.1094	1.09851
$803$	−25.0614	−0.884397
$804$	16.4661	0.580714
$805$	1.66008	0.0585102
$806$	−40.7550	−1.43553
$807$	34.9326	1.22969
$808$	−9.24651	−0.325291
$809$	15.1148	0.531407	0.265703	−	0.964055i	$-0.414396\pi$
$809$	15.1148	0.531407	0.265703	+	0.964055i	$0.414396\pi$
$810$	2.05845	0.0723266
$811$	47.1920	1.65713	0.828567	−	0.559890i	$-0.189157\pi$
$811$	47.1920	1.65713	0.828567	+	0.559890i	$0.189157\pi$
$812$	−11.9314	−0.418709
$813$	−9.97117	−0.349704
$814$	35.7088	1.25159
$815$	9.64731	0.337931
$816$	3.87240	0.135561
$817$	27.9136	0.976574
$818$	22.1340	0.773898
$819$	2.89540	0.101174
$820$	36.0100	1.25752
$821$	−19.7804	−0.690341	−0.345170	−	0.938540i	$-0.612179\pi$
$821$	−19.7804	−0.690341	−0.345170	+	0.938540i	$0.612179\pi$
$822$	−21.1195	−0.736627
$823$	20.6295	0.719098	0.359549	−	0.933126i	$-0.382930\pi$
$823$	20.6295	0.719098	0.359549	+	0.933126i	$0.382930\pi$
$824$	−5.54656	−0.193224
$825$	5.81441	0.202432
$826$	3.59662	0.125142
$827$	6.87781	0.239165	0.119583	−	0.992824i	$-0.461844\pi$
$827$	6.87781	0.239165	0.119583	+	0.992824i	$0.461844\pi$
$828$	−6.14118	−0.213421
$829$	−34.8587	−1.21069	−0.605346	−	0.795962i	$-0.706965\pi$
$829$	−34.8587	−1.21069	−0.605346	+	0.795962i	$0.706965\pi$
$830$	−16.5532	−0.574571
$831$	−24.4221	−0.847192
$832$	23.0977	0.800769
$833$	6.51275	0.225653
$834$	−40.5488	−1.40409
$835$	17.5823	0.608461
$836$	−20.6521	−0.714267
$837$	44.4385	1.53602
$838$	−24.1778	−0.835208
$839$	45.0848	1.55650	0.778250	−	0.627954i	$-0.216107\pi$
$839$	45.0848	1.55650	0.778250	+	0.627954i	$0.216107\pi$
$840$	−0.577557	−0.0199276
$841$	29.3853	1.01328
$842$	−57.2827	−1.97409
$843$	0.229104	0.00789077
$844$	−41.4626	−1.42720
$845$	−11.2642	−0.387502
$846$	2.43545	0.0837324
$847$	−5.05949	−0.173846
$848$	−10.4960	−0.360434
$849$	−28.2373	−0.969103
$850$	−5.53666	−0.189906
$851$	14.0137	0.480384
$852$	−23.1237	−0.792206
$853$	36.0523	1.23441	0.617204	−	0.786803i	$-0.288265\pi$
$853$	36.0523	1.23441	0.617204	+	0.786803i	$0.288265\pi$
$854$	1.36545	0.0467246
$855$	−12.7107	−0.434698
$856$	−7.17807	−0.245341
$857$	55.4949	1.89567	0.947835	−	0.318763i	$-0.103267\pi$
$857$	55.4949	1.89567	0.947835	+	0.318763i	$0.103267\pi$
$858$	−10.5191	−0.359117
$859$	−8.86383	−0.302430	−0.151215	−	0.988501i	$-0.548319\pi$
$859$	−8.86383	−0.302430	−0.151215	+	0.988501i	$0.548319\pi$
$860$	19.9122	0.679002
$861$	8.25049	0.281176
$862$	69.2244	2.35779
$863$	39.2546	1.33624	0.668122	−	0.744052i	$-0.267098\pi$
$863$	39.2546	1.33624	0.668122	+	0.744052i	$0.267098\pi$
$864$	−43.0745	−1.46543
$865$	5.63195	0.191492
$866$	28.3722	0.964126
$867$	1.11600	0.0379013
$868$	−13.0775	−0.443880
$869$	5.17217	0.175454
$870$	26.6789	0.904500
$871$	−15.5931	−0.528351
$872$	−5.55039	−0.187960
$873$	14.7441	0.499013
$874$	−15.3510	−0.519255
$875$	−8.15864	−0.275812
$876$	32.3005	1.09133
$877$	−18.6157	−0.628609	−0.314304	−	0.949322i	$-0.601771\pi$
$877$	−18.6157	−0.628609	−0.314304	+	0.949322i	$0.601771\pi$
$878$	2.20207	0.0743162
$879$	−0.284371	−0.00959159
$880$	10.2156	0.344367
$881$	−32.7915	−1.10477	−0.552387	−	0.833588i	$-0.686283\pi$
$881$	−32.7915	−1.10477	−0.552387	+	0.833588i	$0.686283\pi$
$882$	−23.5210	−0.791994
$883$	−20.5932	−0.693016	−0.346508	−	0.938047i	$-0.612633\pi$
$883$	−20.5932	−0.693016	−0.346508	+	0.938047i	$0.612633\pi$
$884$	5.28844	0.177869
$885$	−4.24597	−0.142727
$886$	−49.0638	−1.64833
$887$	−2.72336	−0.0914415	−0.0457207	−	0.998954i	$-0.514558\pi$
$887$	−2.72336	−0.0914415	−0.0457207	+	0.998954i	$0.514558\pi$
$888$	−4.87549	−0.163611
$889$	5.34322	0.179206
$890$	5.77247	0.193494
$891$	1.27441	0.0426943
$892$	−26.7121	−0.894386
$893$	3.21417	0.107558
$894$	−35.3767	−1.18318
$895$	23.0226	0.769562
$896$	2.70481	0.0903613
$897$	−4.12817	−0.137836
$898$	57.7128	1.92590
$899$	63.9938	2.13431
$900$	10.5571	0.351904
$901$	−3.02487	−0.100773
$902$	42.2266	1.40599
$903$	4.56223	0.151821
$904$	0.998717	0.0332168
$905$	24.6425	0.819143
$906$	−27.0232	−0.897785
$907$	−25.5716	−0.849092	−0.424546	−	0.905406i	$-0.639566\pi$
$907$	−25.5716	−0.849092	−0.424546	+	0.905406i	$0.639566\pi$
$908$	−31.5148	−1.04586
$909$	−33.2594	−1.10314
$910$	5.16294	0.171150
$911$	17.6413	0.584483	0.292241	−	0.956345i	$-0.405599\pi$
$911$	17.6413	0.584483	0.292241	+	0.956345i	$0.405599\pi$
$912$	−18.4571	−0.611174
$913$	−10.2483	−0.339169
$914$	−46.5527	−1.53982
$915$	−1.61197	−0.0532902
$916$	−49.0816	−1.62170
$917$	0.0260830	0.000861338 0
$918$	−10.9220	−0.360479
$919$	14.9719	0.493878	0.246939	−	0.969031i	$-0.420575\pi$
$919$	14.9719	0.493878	0.246939	+	0.969031i	$0.420575\pi$
$920$	−1.16006	−0.0382459
$921$	13.0293	0.429329
$922$	−18.2550	−0.601195
$923$	21.8978	0.720774
$924$	−3.37539	−0.111042
$925$	−24.0905	−0.792092
$926$	30.7108	1.00922
$927$	−19.9508	−0.655270
$928$	−62.0296	−2.03622
$929$	28.3112	0.928859	0.464430	−	0.885610i	$-0.346259\pi$
$929$	28.3112	0.928859	0.464430	+	0.885610i	$0.346259\pi$
$930$	29.2417	0.958874
$931$	−31.0417	−1.01735
$932$	52.4600	1.71838
$933$	−7.72898	−0.253035
$934$	−44.5065	−1.45630
$935$	2.94405	0.0962809
$936$	−2.02329	−0.0661334
$937$	17.0072	0.555600	0.277800	−	0.960639i	$-0.410395\pi$
$937$	17.0072	0.555600	0.277800	+	0.960639i	$0.410395\pi$
$938$	−9.47701	−0.309435
$939$	−5.60768	−0.183000
$940$	2.29283	0.0747839
$941$	45.4041	1.48013	0.740066	−	0.672534i	$-0.234794\pi$
$941$	45.4041	1.48013	0.740066	+	0.672534i	$0.234794\pi$
$942$	−28.5781	−0.931125
$943$	16.5716	0.539645
$944$	8.68570	0.282695
$945$	−5.62958	−0.183130
$946$	23.3498	0.759168
$947$	−35.2823	−1.14652	−0.573260	−	0.819373i	$-0.694322\pi$
$947$	−35.2823	−1.14652	−0.573260	+	0.819373i	$0.694322\pi$
$948$	−6.66617	−0.216507
$949$	−30.5879	−0.992927
$950$	26.3894	0.856186
$951$	−13.8385	−0.448744
$952$	0.340491	0.0110354
$953$	13.4397	0.435354	0.217677	−	0.976021i	$-0.430152\pi$
$953$	13.4397	0.435354	0.217677	+	0.976021i	$0.430152\pi$
$954$	10.9244	0.353692
$955$	−0.182434	−0.00590344
$956$	−26.5442	−0.858500
$957$	16.5172	0.533926
$958$	−30.2633	−0.977764
$959$	6.41755	0.207234
$960$	−16.5726	−0.534879
$961$	39.1411	1.26262
$962$	43.5834	1.40518
$963$	−25.8193	−0.832015
$964$	−64.4554	−2.07597
$965$	−19.4956	−0.627585
$966$	−2.50898	−0.0807251
$967$	−30.8518	−0.992128	−0.496064	−	0.868286i	$-0.665222\pi$
$967$	−30.8518	−0.992128	−0.496064	+	0.868286i	$0.665222\pi$
$968$	3.53555	0.113637
$969$	−5.31920	−0.170877
$970$	26.2910	0.844154
$971$	10.6513	0.341815	0.170908	−	0.985287i	$-0.445330\pi$
$971$	10.6513	0.341815	0.170908	+	0.985287i	$0.445330\pi$
$972$	33.9661	1.08946
$973$	12.3215	0.395010
$974$	−61.3013	−1.96422
$975$	7.09661	0.227273
$976$	3.29750	0.105551
$977$	−9.65099	−0.308763	−0.154381	−	0.988011i	$-0.549338\pi$
$977$	−9.65099	−0.308763	−0.154381	+	0.988011i	$0.549338\pi$
$978$	−14.5805	−0.466234
$979$	3.57380	0.114219
$980$	−22.1437	−0.707354
$981$	−19.9646	−0.637420
$982$	−57.0006	−1.81896
$983$	3.77430	0.120381	0.0601907	−	0.998187i	$-0.480829\pi$
$983$	3.77430	0.120381	0.0601907	+	0.998187i	$0.480829\pi$
$984$	−5.76540	−0.183794
$985$	12.6651	0.403543
$986$	−15.7282	−0.500888
$987$	0.525326	0.0167213
$988$	−25.2063	−0.801920
$989$	9.16350	0.291382
$990$	−10.6326	−0.337925
$991$	−21.4457	−0.681245	−0.340623	−	0.940200i	$-0.610638\pi$
$991$	−21.4457	−0.681245	−0.340623	+	0.940200i	$0.610638\pi$
$992$	−67.9883	−2.15863
$993$	28.7575	0.912592
$994$	13.3088	0.422130
$995$	11.7124	0.371308
$996$	13.2086	0.418529
$997$	−20.5970	−0.652315	−0.326157	−	0.945315i	$-0.605754\pi$
$997$	−20.5970	−0.652315	−0.326157	+	0.945315i	$0.605754\pi$
$998$	65.3776	2.06949
$999$	−47.5225	−1.50355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.19	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.19	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05839 q^{2} +1.11600 q^{3} +2.23697 q^{4} +1.51993 q^{5} -2.29716 q^{6} +0.698036 q^{7} -0.487784 q^{8} -1.75454 q^{9} +O(q^{10})\)	\(q-2.05839 q^{2} +1.11600 q^{3} +2.23697 q^{4} +1.51993 q^{5} -2.29716 q^{6} +0.698036 q^{7} -0.487784 q^{8} -1.75454 q^{9} -3.12862 q^{10} -1.93696 q^{11} +2.49646 q^{12} -2.36410 q^{13} -1.43683 q^{14} +1.69625 q^{15} -3.46990 q^{16} -1.00000 q^{17} +3.61154 q^{18} +4.76630 q^{19} +3.40005 q^{20} +0.779009 q^{21} +3.98703 q^{22} +1.56468 q^{23} -0.544367 q^{24} -2.68980 q^{25} +4.86625 q^{26} -5.30607 q^{27} +1.56149 q^{28} -7.64102 q^{29} -3.49154 q^{30} -8.37503 q^{31} +8.11797 q^{32} -2.16165 q^{33} +2.05839 q^{34} +1.06097 q^{35} -3.92487 q^{36} +8.95625 q^{37} -9.81092 q^{38} -2.63834 q^{39} -0.741400 q^{40} +10.5910 q^{41} -1.60350 q^{42} +5.85645 q^{43} -4.33293 q^{44} -2.66679 q^{45} -3.22073 q^{46} +0.674352 q^{47} -3.87240 q^{48} -6.51275 q^{49} +5.53666 q^{50} -1.11600 q^{51} -5.28844 q^{52} +3.02487 q^{53} +10.9220 q^{54} -2.94405 q^{55} -0.340491 q^{56} +5.31920 q^{57} +15.7282 q^{58} -2.50316 q^{59} +3.79446 q^{60} -0.950318 q^{61} +17.2391 q^{62} -1.22474 q^{63} -9.77017 q^{64} -3.59328 q^{65} +4.44952 q^{66} +6.59576 q^{67} -2.23697 q^{68} +1.74619 q^{69} -2.18389 q^{70} -9.26260 q^{71} +0.855839 q^{72} +12.9385 q^{73} -18.4355 q^{74} -3.00182 q^{75} +10.6621 q^{76} -1.35207 q^{77} +5.43074 q^{78} -2.67025 q^{79} -5.27401 q^{80} -0.657942 q^{81} -21.8004 q^{82} +5.29091 q^{83} +1.74262 q^{84} -1.51993 q^{85} -12.0549 q^{86} -8.52738 q^{87} +0.944820 q^{88} -1.84505 q^{89} +5.48930 q^{90} -1.65023 q^{91} +3.50016 q^{92} -9.34653 q^{93} -1.38808 q^{94} +7.24447 q^{95} +9.05966 q^{96} -8.40340 q^{97} +13.4058 q^{98} +3.39849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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