LMFDB - Embedded newform 6015.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22966 q^{2} -1.00000 q^{3} -0.487935 q^{4} -1.00000 q^{5} +1.22966 q^{6} -1.61954 q^{7} +3.05932 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.22966 q^{2} -1.00000 q^{3} -0.487935 q^{4} -1.00000 q^{5} +1.22966 q^{6} -1.61954 q^{7} +3.05932 q^{8} +1.00000 q^{9} +1.22966 q^{10} +2.45183 q^{11} +0.487935 q^{12} +4.26013 q^{13} +1.99148 q^{14} +1.00000 q^{15} -2.78605 q^{16} -3.00769 q^{17} -1.22966 q^{18} +0.688977 q^{19} +0.487935 q^{20} +1.61954 q^{21} -3.01492 q^{22} +7.92405 q^{23} -3.05932 q^{24} +1.00000 q^{25} -5.23852 q^{26} -1.00000 q^{27} +0.790230 q^{28} +6.38753 q^{29} -1.22966 q^{30} +7.42579 q^{31} -2.69274 q^{32} -2.45183 q^{33} +3.69843 q^{34} +1.61954 q^{35} -0.487935 q^{36} +6.78966 q^{37} -0.847208 q^{38} -4.26013 q^{39} -3.05932 q^{40} -5.05598 q^{41} -1.99148 q^{42} +5.89535 q^{43} -1.19633 q^{44} -1.00000 q^{45} -9.74389 q^{46} -0.204157 q^{47} +2.78605 q^{48} -4.37710 q^{49} -1.22966 q^{50} +3.00769 q^{51} -2.07867 q^{52} +5.56014 q^{53} +1.22966 q^{54} -2.45183 q^{55} -4.95468 q^{56} -0.688977 q^{57} -7.85449 q^{58} +13.1102 q^{59} -0.487935 q^{60} -3.71562 q^{61} -9.13120 q^{62} -1.61954 q^{63} +8.88325 q^{64} -4.26013 q^{65} +3.01492 q^{66} -7.14071 q^{67} +1.46756 q^{68} -7.92405 q^{69} -1.99148 q^{70} +2.64267 q^{71} +3.05932 q^{72} +10.6282 q^{73} -8.34897 q^{74} -1.00000 q^{75} -0.336176 q^{76} -3.97083 q^{77} +5.23852 q^{78} -4.60197 q^{79} +2.78605 q^{80} +1.00000 q^{81} +6.21714 q^{82} -8.38811 q^{83} -0.790230 q^{84} +3.00769 q^{85} -7.24927 q^{86} -6.38753 q^{87} +7.50092 q^{88} -12.6023 q^{89} +1.22966 q^{90} -6.89945 q^{91} -3.86642 q^{92} -7.42579 q^{93} +0.251044 q^{94} -0.688977 q^{95} +2.69274 q^{96} +3.48515 q^{97} +5.38234 q^{98} +2.45183 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.22966	−0.869501	−0.434751	−	0.900551i	$-0.643163\pi$
$2$	−1.22966	−0.869501	−0.434751	+	0.900551i	$0.643163\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.487935	−0.243968
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.22966	0.502007
$7$	−1.61954	−0.612128	−0.306064	−	0.952011i	$-0.599012\pi$
$7$	−1.61954	−0.612128	−0.306064	+	0.952011i	$0.599012\pi$
$8$	3.05932	1.08163
$9$	1.00000	0.333333
$10$	1.22966	0.388853
$11$	2.45183	0.739255	0.369627	−	0.929180i	$-0.379485\pi$
$11$	2.45183	0.739255	0.369627	+	0.929180i	$0.379485\pi$
$12$	0.487935	0.140855
$13$	4.26013	1.18155	0.590774	−	0.806837i	$-0.298822\pi$
$13$	4.26013	1.18155	0.590774	+	0.806837i	$0.298822\pi$
$14$	1.99148	0.532246
$15$	1.00000	0.258199
$16$	−2.78605	−0.696512
$17$	−3.00769	−0.729471	−0.364736	−	0.931111i	$-0.618841\pi$
$17$	−3.00769	−0.729471	−0.364736	+	0.931111i	$0.618841\pi$
$18$	−1.22966	−0.289834
$19$	0.688977	0.158062	0.0790311	−	0.996872i	$-0.474817\pi$
$19$	0.688977	0.158062	0.0790311	+	0.996872i	$0.474817\pi$
$20$	0.487935	0.109106
$21$	1.61954	0.353412
$22$	−3.01492	−0.642783
$23$	7.92405	1.65228	0.826139	−	0.563466i	$-0.190532\pi$
$23$	7.92405	1.65228	0.826139	+	0.563466i	$0.190532\pi$
$24$	−3.05932	−0.624480
$25$	1.00000	0.200000
$26$	−5.23852	−1.02736
$27$	−1.00000	−0.192450
$28$	0.790230	0.149339
$29$	6.38753	1.18613	0.593067	−	0.805153i	$-0.297917\pi$
$29$	6.38753	1.18613	0.593067	+	0.805153i	$0.297917\pi$
$30$	−1.22966	−0.224504
$31$	7.42579	1.33371	0.666856	−	0.745187i	$-0.267640\pi$
$31$	7.42579	1.33371	0.666856	+	0.745187i	$0.267640\pi$
$32$	−2.69274	−0.476013
$33$	−2.45183	−0.426809
$34$	3.69843	0.634276
$35$	1.61954	0.273752
$36$	−0.487935	−0.0813226
$37$	6.78966	1.11621	0.558106	−	0.829769i	$-0.311528\pi$
$37$	6.78966	1.11621	0.558106	+	0.829769i	$0.311528\pi$
$38$	−0.847208	−0.137435
$39$	−4.26013	−0.682167
$40$	−3.05932	−0.483720
$41$	−5.05598	−0.789611	−0.394806	−	0.918765i	$-0.629188\pi$
$41$	−5.05598	−0.789611	−0.394806	+	0.918765i	$0.629188\pi$
$42$	−1.99148	−0.307292
$43$	5.89535	0.899032	0.449516	−	0.893272i	$-0.351596\pi$
$43$	5.89535	0.899032	0.449516	+	0.893272i	$0.351596\pi$
$44$	−1.19633	−0.180354
$45$	−1.00000	−0.149071
$46$	−9.74389	−1.43666
$47$	−0.204157	−0.0297794	−0.0148897	−	0.999889i	$-0.504740\pi$
$47$	−0.204157	−0.0297794	−0.0148897	+	0.999889i	$0.504740\pi$
$48$	2.78605	0.402131
$49$	−4.37710	−0.625299
$50$	−1.22966	−0.173900
$51$	3.00769	0.421161
$52$	−2.07867	−0.288260
$53$	5.56014	0.763743	0.381872	−	0.924215i	$-0.375280\pi$
$53$	5.56014	0.763743	0.381872	+	0.924215i	$0.375280\pi$
$54$	1.22966	0.167336
$55$	−2.45183	−0.330605
$56$	−4.95468	−0.662097
$57$	−0.688977	−0.0912573
$58$	−7.85449	−1.03134
$59$	13.1102	1.70680	0.853400	−	0.521257i	$-0.174537\pi$
$59$	13.1102	1.70680	0.853400	+	0.521257i	$0.174537\pi$
$60$	−0.487935	−0.0629922
$61$	−3.71562	−0.475736	−0.237868	−	0.971297i	$-0.576449\pi$
$61$	−3.71562	−0.475736	−0.237868	+	0.971297i	$0.576449\pi$
$62$	−9.13120	−1.15966
$63$	−1.61954	−0.204043
$64$	8.88325	1.11041
$65$	−4.26013	−0.528404
$66$	3.01492	0.371111
$67$	−7.14071	−0.872376	−0.436188	−	0.899856i	$-0.643672\pi$
$67$	−7.14071	−0.872376	−0.436188	+	0.899856i	$0.643672\pi$
$68$	1.46756	0.177967
$69$	−7.92405	−0.953943
$70$	−1.99148	−0.238028
$71$	2.64267	0.313627	0.156814	−	0.987628i	$-0.449878\pi$
$71$	2.64267	0.313627	0.156814	+	0.987628i	$0.449878\pi$
$72$	3.05932	0.360544
$73$	10.6282	1.24393	0.621966	−	0.783045i	$-0.286334\pi$
$73$	10.6282	1.24393	0.621966	+	0.783045i	$0.286334\pi$
$74$	−8.34897	−0.970549
$75$	−1.00000	−0.115470
$76$	−0.336176	−0.0385621
$77$	−3.97083	−0.452518
$78$	5.23852	0.593145
$79$	−4.60197	−0.517762	−0.258881	−	0.965909i	$-0.583354\pi$
$79$	−4.60197	−0.517762	−0.258881	+	0.965909i	$0.583354\pi$
$80$	2.78605	0.311490
$81$	1.00000	0.111111
$82$	6.21714	0.686568
$83$	−8.38811	−0.920715	−0.460358	−	0.887734i	$-0.652279\pi$
$83$	−8.38811	−0.920715	−0.460358	+	0.887734i	$0.652279\pi$
$84$	−0.790230	−0.0862211
$85$	3.00769	0.326230
$86$	−7.24927	−0.781709
$87$	−6.38753	−0.684815
$88$	7.50092	0.799601
$89$	−12.6023	−1.33584	−0.667922	−	0.744231i	$-0.732816\pi$
$89$	−12.6023	−1.33584	−0.667922	+	0.744231i	$0.732816\pi$
$90$	1.22966	0.129618
$91$	−6.89945	−0.723259
$92$	−3.86642	−0.403102
$93$	−7.42579	−0.770019
$94$	0.251044	0.0258933
$95$	−0.688977	−0.0706876
$96$	2.69274	0.274826
$97$	3.48515	0.353864	0.176932	−	0.984223i	$-0.443383\pi$
$97$	3.48515	0.353864	0.176932	+	0.984223i	$0.443383\pi$
$98$	5.38234	0.543699
$99$	2.45183	0.246418
$100$	−0.487935	−0.0487935
$101$	7.36756	0.733099	0.366550	−	0.930398i	$-0.380539\pi$
$101$	7.36756	0.733099	0.366550	+	0.930398i	$0.380539\pi$
$102$	−3.69843	−0.366200
$103$	16.5450	1.63023	0.815115	−	0.579300i	$-0.196674\pi$
$103$	16.5450	1.63023	0.815115	+	0.579300i	$0.196674\pi$
$104$	13.0331	1.27800
$105$	−1.61954	−0.158051
$106$	−6.83708	−0.664076
$107$	13.7818	1.33234	0.666169	−	0.745801i	$-0.267933\pi$
$107$	13.7818	1.33234	0.666169	+	0.745801i	$0.267933\pi$
$108$	0.487935	0.0469516
$109$	−4.67337	−0.447627	−0.223814	−	0.974632i	$-0.571851\pi$
$109$	−4.67337	−0.447627	−0.223814	+	0.974632i	$0.571851\pi$
$110$	3.01492	0.287461
$111$	−6.78966	−0.644446
$112$	4.51211	0.426354
$113$	−12.2852	−1.15569	−0.577845	−	0.816147i	$-0.696106\pi$
$113$	−12.2852	−1.15569	−0.577845	+	0.816147i	$0.696106\pi$
$114$	0.847208	0.0793483
$115$	−7.92405	−0.738921
$116$	−3.11670	−0.289378
$117$	4.26013	0.393849
$118$	−16.1211	−1.48406
$119$	4.87107	0.446530
$120$	3.05932	0.279276
$121$	−4.98853	−0.453503
$122$	4.56895	0.413653
$123$	5.05598	0.455882
$124$	−3.62331	−0.325382
$125$	−1.00000	−0.0894427
$126$	1.99148	0.177415
$127$	−16.4298	−1.45791	−0.728954	−	0.684562i	$-0.759993\pi$
$127$	−16.4298	−1.45791	−0.728954	+	0.684562i	$0.759993\pi$
$128$	−5.53791	−0.489486
$129$	−5.89535	−0.519056
$130$	5.23852	0.459448
$131$	−4.06338	−0.355019	−0.177510	−	0.984119i	$-0.556804\pi$
$131$	−4.06338	−0.355019	−0.177510	+	0.984119i	$0.556804\pi$
$132$	1.19633	0.104128
$133$	−1.11583	−0.0967543
$134$	8.78064	0.758532
$135$	1.00000	0.0860663
$136$	−9.20147	−0.789019
$137$	−17.6138	−1.50485	−0.752426	−	0.658677i	$-0.771117\pi$
$137$	−17.6138	−1.50485	−0.752426	+	0.658677i	$0.771117\pi$
$138$	9.74389	0.829455
$139$	−17.4219	−1.47770	−0.738851	−	0.673868i	$-0.764632\pi$
$139$	−17.4219	−1.47770	−0.738851	+	0.673868i	$0.764632\pi$
$140$	−0.790230	−0.0667866
$141$	0.204157	0.0171932
$142$	−3.24959	−0.272699
$143$	10.4451	0.873465
$144$	−2.78605	−0.232171
$145$	−6.38753	−0.530455
$146$	−13.0690	−1.08160
$147$	4.37710	0.361017
$148$	−3.31291	−0.272320
$149$	9.61539	0.787723	0.393862	−	0.919170i	$-0.371139\pi$
$149$	9.61539	0.787723	0.393862	+	0.919170i	$0.371139\pi$
$150$	1.22966	0.100401
$151$	−6.97598	−0.567697	−0.283849	−	0.958869i	$-0.591611\pi$
$151$	−6.97598	−0.567697	−0.283849	+	0.958869i	$0.591611\pi$
$152$	2.10780	0.170965
$153$	−3.00769	−0.243157
$154$	4.88278	0.393465
$155$	−7.42579	−0.596454
$156$	2.07867	0.166427
$157$	11.3837	0.908520	0.454260	−	0.890869i	$-0.349904\pi$
$157$	11.3837	0.908520	0.454260	+	0.890869i	$0.349904\pi$
$158$	5.65886	0.450195
$159$	−5.56014	−0.440947
$160$	2.69274	0.212880
$161$	−12.8333	−1.01141
$162$	−1.22966	−0.0966112
$163$	−6.54848	−0.512917	−0.256458	−	0.966555i	$-0.582556\pi$
$163$	−6.54848	−0.512917	−0.256458	+	0.966555i	$0.582556\pi$
$164$	2.46699	0.192640
$165$	2.45183	0.190875
$166$	10.3145	0.800563
$167$	7.73506	0.598557	0.299279	−	0.954166i	$-0.403254\pi$
$167$	7.73506	0.598557	0.299279	+	0.954166i	$0.403254\pi$
$168$	4.95468	0.382262
$169$	5.14874	0.396057
$170$	−3.69843	−0.283657
$171$	0.688977	0.0526874
$172$	−2.87655	−0.219335
$173$	−3.90579	−0.296952	−0.148476	−	0.988916i	$-0.547437\pi$
$173$	−3.90579	−0.296952	−0.148476	+	0.988916i	$0.547437\pi$
$174$	7.85449	0.595447
$175$	−1.61954	−0.122426
$176$	−6.83092	−0.514900
$177$	−13.1102	−0.985421
$178$	15.4966	1.16152
$179$	17.0400	1.27363	0.636814	−	0.771017i	$-0.280252\pi$
$179$	17.0400	1.27363	0.636814	+	0.771017i	$0.280252\pi$
$180$	0.487935	0.0363686
$181$	2.16332	0.160798	0.0803990	−	0.996763i	$-0.474381\pi$
$181$	2.16332	0.160798	0.0803990	+	0.996763i	$0.474381\pi$
$182$	8.48398	0.628874
$183$	3.71562	0.274666
$184$	24.2422	1.78716
$185$	−6.78966	−0.499186
$186$	9.13120	0.669532
$187$	−7.37434	−0.539265
$188$	0.0996157	0.00726522
$189$	1.61954	0.117804
$190$	0.847208	0.0614629
$191$	−15.5342	−1.12402	−0.562009	−	0.827131i	$-0.689971\pi$
$191$	−15.5342	−1.12402	−0.562009	+	0.827131i	$0.689971\pi$
$192$	−8.88325	−0.641093
$193$	−14.2773	−1.02770	−0.513852	−	0.857879i	$-0.671782\pi$
$193$	−14.2773	−1.02770	−0.513852	+	0.857879i	$0.671782\pi$
$194$	−4.28556	−0.307685
$195$	4.26013	0.305074
$196$	2.13574	0.152553
$197$	14.8489	1.05794	0.528972	−	0.848639i	$-0.322578\pi$
$197$	14.8489	1.05794	0.528972	+	0.848639i	$0.322578\pi$
$198$	−3.01492	−0.214261
$199$	−3.44106	−0.243930	−0.121965	−	0.992534i	$-0.538920\pi$
$199$	−3.44106	−0.243930	−0.121965	+	0.992534i	$0.538920\pi$
$200$	3.05932	0.216326
$201$	7.14071	0.503667
$202$	−9.05959	−0.637431
$203$	−10.3448	−0.726066
$204$	−1.46756	−0.102750
$205$	5.05598	0.353125
$206$	−20.3448	−1.41749
$207$	7.92405	0.550759
$208$	−11.8689	−0.822963
$209$	1.68926	0.116848
$210$	1.99148	0.137425
$211$	−2.52505	−0.173831	−0.0869157	−	0.996216i	$-0.527701\pi$
$211$	−2.52505	−0.173831	−0.0869157	+	0.996216i	$0.527701\pi$
$212$	−2.71299	−0.186329
$213$	−2.64267	−0.181073
$214$	−16.9469	−1.15847
$215$	−5.89535	−0.402059
$216$	−3.05932	−0.208160
$217$	−12.0264	−0.816402
$218$	5.74665	0.389213
$219$	−10.6282	−0.718184
$220$	1.19633	0.0806569
$221$	−12.8132	−0.861906
$222$	8.34897	0.560346
$223$	−4.17648	−0.279678	−0.139839	−	0.990174i	$-0.544659\pi$
$223$	−4.17648	−0.279678	−0.139839	+	0.990174i	$0.544659\pi$
$224$	4.36099	0.291381
$225$	1.00000	0.0666667
$226$	15.1066	1.00487
$227$	12.0738	0.801366	0.400683	−	0.916217i	$-0.368773\pi$
$227$	12.0738	0.801366	0.400683	+	0.916217i	$0.368773\pi$
$228$	0.336176	0.0222638
$229$	17.3943	1.14945	0.574724	−	0.818347i	$-0.305109\pi$
$229$	17.3943	1.14945	0.574724	+	0.818347i	$0.305109\pi$
$230$	9.74389	0.642493
$231$	3.97083	0.261262
$232$	19.5415	1.28296
$233$	26.0228	1.70481	0.852404	−	0.522883i	$-0.175144\pi$
$233$	26.0228	1.70481	0.852404	+	0.522883i	$0.175144\pi$
$234$	−5.23852	−0.342453
$235$	0.204157	0.0133178
$236$	−6.39692	−0.416404
$237$	4.60197	0.298930
$238$	−5.98976	−0.388258
$239$	−29.2525	−1.89219	−0.946095	−	0.323890i	$-0.895009\pi$
$239$	−29.2525	−1.89219	−0.946095	+	0.323890i	$0.895009\pi$
$240$	−2.78605	−0.179839
$241$	4.17067	0.268656	0.134328	−	0.990937i	$-0.457112\pi$
$241$	4.17067	0.268656	0.134328	+	0.990937i	$0.457112\pi$
$242$	6.13420	0.394321
$243$	−1.00000	−0.0641500
$244$	1.81298	0.116064
$245$	4.37710	0.279642
$246$	−6.21714	−0.396390
$247$	2.93514	0.186758
$248$	22.7178	1.44258
$249$	8.38811	0.531575
$250$	1.22966	0.0777706
$251$	−1.28677	−0.0812203	−0.0406101	−	0.999175i	$-0.512930\pi$
$251$	−1.28677	−0.0812203	−0.0406101	+	0.999175i	$0.512930\pi$
$252$	0.790230	0.0497798
$253$	19.4284	1.22145
$254$	20.2031	1.26765
$255$	−3.00769	−0.188349
$256$	−10.9568	−0.684797
$257$	−1.56120	−0.0973851	−0.0486926	−	0.998814i	$-0.515505\pi$
$257$	−1.56120	−0.0973851	−0.0486926	+	0.998814i	$0.515505\pi$
$258$	7.24927	0.451320
$259$	−10.9961	−0.683265
$260$	2.07867	0.128914
$261$	6.38753	0.395378
$262$	4.99658	0.308690
$263$	26.3639	1.62567	0.812833	−	0.582497i	$-0.197924\pi$
$263$	26.3639	1.62567	0.812833	+	0.582497i	$0.197924\pi$
$264$	−7.50092	−0.461650
$265$	−5.56014	−0.341556
$266$	1.37209	0.0841280
$267$	12.6023	0.771250
$268$	3.48420	0.212832
$269$	12.9378	0.788829	0.394415	−	0.918933i	$-0.370947\pi$
$269$	12.9378	0.788829	0.394415	+	0.918933i	$0.370947\pi$
$270$	−1.22966	−0.0748347
$271$	−12.6589	−0.768975	−0.384487	−	0.923130i	$-0.625622\pi$
$271$	−12.6589	−0.768975	−0.384487	+	0.923130i	$0.625622\pi$
$272$	8.37956	0.508086
$273$	6.89945	0.417574
$274$	21.6590	1.30847
$275$	2.45183	0.147851
$276$	3.86642	0.232731
$277$	19.5644	1.17551	0.587755	−	0.809039i	$-0.300012\pi$
$277$	19.5644	1.17551	0.587755	+	0.809039i	$0.300012\pi$
$278$	21.4230	1.28486
$279$	7.42579	0.444570
$280$	4.95468	0.296099
$281$	18.6326	1.11153	0.555763	−	0.831341i	$-0.312426\pi$
$281$	18.6326	1.11153	0.555763	+	0.831341i	$0.312426\pi$
$282$	−0.251044	−0.0149495
$283$	−6.68650	−0.397471	−0.198736	−	0.980053i	$-0.563683\pi$
$283$	−6.68650	−0.397471	−0.198736	+	0.980053i	$0.563683\pi$
$284$	−1.28945	−0.0765149
$285$	0.688977	0.0408115
$286$	−12.8440	−0.759479
$287$	8.18835	0.483343
$288$	−2.69274	−0.158671
$289$	−7.95381	−0.467871
$290$	7.85449	0.461231
$291$	−3.48515	−0.204303
$292$	−5.18585	−0.303479
$293$	14.0020	0.818007	0.409004	−	0.912533i	$-0.365876\pi$
$293$	14.0020	0.818007	0.409004	+	0.912533i	$0.365876\pi$
$294$	−5.38234	−0.313905
$295$	−13.1102	−0.763304
$296$	20.7717	1.20733
$297$	−2.45183	−0.142270
$298$	−11.8237	−0.684926
$299$	33.7575	1.95225
$300$	0.487935	0.0281710
$301$	−9.54774	−0.550323
$302$	8.57808	0.493613
$303$	−7.36756	−0.423255
$304$	−1.91952	−0.110092
$305$	3.71562	0.212756
$306$	3.69843	0.211425
$307$	−10.9316	−0.623897	−0.311949	−	0.950099i	$-0.600982\pi$
$307$	−10.9316	−0.623897	−0.311949	+	0.950099i	$0.600982\pi$
$308$	1.93751	0.110400
$309$	−16.5450	−0.941213
$310$	9.13120	0.518617
$311$	21.7392	1.23272	0.616359	−	0.787466i	$-0.288607\pi$
$311$	21.7392	1.23272	0.616359	+	0.787466i	$0.288607\pi$
$312$	−13.0331	−0.737854
$313$	7.23368	0.408872	0.204436	−	0.978880i	$-0.434464\pi$
$313$	7.23368	0.408872	0.204436	+	0.978880i	$0.434464\pi$
$314$	−13.9981	−0.789960
$315$	1.61954	0.0912506
$316$	2.24546	0.126317
$317$	12.8518	0.721828	0.360914	−	0.932599i	$-0.382465\pi$
$317$	12.8518	0.721828	0.360914	+	0.932599i	$0.382465\pi$
$318$	6.83708	0.383404
$319$	15.6611	0.876855
$320$	−8.88325	−0.496589
$321$	−13.7818	−0.769226
$322$	15.7806	0.879418
$323$	−2.07223	−0.115302
$324$	−0.487935	−0.0271075
$325$	4.26013	0.236310
$326$	8.05241	0.445982
$327$	4.67337	0.258438
$328$	−15.4678	−0.854068
$329$	0.330641	0.0182288
$330$	−3.01492	−0.165966
$331$	14.0960	0.774789	0.387394	−	0.921914i	$-0.373375\pi$
$331$	14.0960	0.774789	0.387394	+	0.921914i	$0.373375\pi$
$332$	4.09286	0.224625
$333$	6.78966	0.372071
$334$	−9.51150	−0.520446
$335$	7.14071	0.390139
$336$	−4.51211	−0.246156
$337$	12.8400	0.699438	0.349719	−	0.936855i	$-0.386277\pi$
$337$	12.8400	0.699438	0.349719	+	0.936855i	$0.386277\pi$
$338$	−6.33120	−0.344372
$339$	12.2852	0.667238
$340$	−1.46756	−0.0795895
$341$	18.2068	0.985952
$342$	−0.847208	−0.0458118
$343$	18.4256	0.994891
$344$	18.0357	0.972421
$345$	7.92405	0.426616
$346$	4.80279	0.258200
$347$	−12.1230	−0.650796	−0.325398	−	0.945577i	$-0.605498\pi$
$347$	−12.1230	−0.650796	−0.325398	+	0.945577i	$0.605498\pi$
$348$	3.11670	0.167073
$349$	−24.9934	−1.33787	−0.668934	−	0.743322i	$-0.733249\pi$
$349$	−24.9934	−1.33787	−0.668934	+	0.743322i	$0.733249\pi$
$350$	1.99148	0.106449
$351$	−4.26013	−0.227389
$352$	−6.60213	−0.351895
$353$	1.37219	0.0730342	0.0365171	−	0.999333i	$-0.488374\pi$
$353$	1.37219	0.0730342	0.0365171	+	0.999333i	$0.488374\pi$
$354$	16.1211	0.856825
$355$	−2.64267	−0.140258
$356$	6.14912	0.325903
$357$	−4.87107	−0.257804
$358$	−20.9534	−1.10742
$359$	23.1371	1.22113	0.610565	−	0.791967i	$-0.290943\pi$
$359$	23.1371	1.22113	0.610565	+	0.791967i	$0.290943\pi$
$360$	−3.05932	−0.161240
$361$	−18.5253	−0.975016
$362$	−2.66014	−0.139814
$363$	4.98853	0.261830
$364$	3.36648	0.176452
$365$	−10.6282	−0.556303
$366$	−4.56895	−0.238823
$367$	12.1825	0.635920	0.317960	−	0.948104i	$-0.397002\pi$
$367$	12.1825	0.635920	0.317960	+	0.948104i	$0.397002\pi$
$368$	−22.0768	−1.15083
$369$	−5.05598	−0.263204
$370$	8.34897	0.434042
$371$	−9.00485	−0.467509
$372$	3.62331	0.187860
$373$	−21.3904	−1.10756	−0.553778	−	0.832665i	$-0.686814\pi$
$373$	−21.3904	−1.10756	−0.553778	+	0.832665i	$0.686814\pi$
$374$	9.06793	0.468892
$375$	1.00000	0.0516398
$376$	−0.624582	−0.0322104
$377$	27.2117	1.40147
$378$	−1.99148	−0.102431
$379$	−28.6596	−1.47214	−0.736072	−	0.676904i	$-0.763321\pi$
$379$	−28.6596	−1.47214	−0.736072	+	0.676904i	$0.763321\pi$
$380$	0.336176	0.0172455
$381$	16.4298	0.841724
$382$	19.1018	0.977334
$383$	11.2226	0.573448	0.286724	−	0.958013i	$-0.407434\pi$
$383$	11.2226	0.573448	0.286724	+	0.958013i	$0.407434\pi$
$384$	5.53791	0.282605
$385$	3.97083	0.202372
$386$	17.5563	0.893590
$387$	5.89535	0.299677
$388$	−1.70053	−0.0863313
$389$	−3.67915	−0.186540	−0.0932702	−	0.995641i	$-0.529732\pi$
$389$	−3.67915	−0.186540	−0.0932702	+	0.995641i	$0.529732\pi$
$390$	−5.23852	−0.265263
$391$	−23.8331	−1.20529
$392$	−13.3909	−0.676344
$393$	4.06338	0.204970
$394$	−18.2592	−0.919883
$395$	4.60197	0.231550
$396$	−1.19633	−0.0601181
$397$	−8.66162	−0.434714	−0.217357	−	0.976092i	$-0.569744\pi$
$397$	−8.66162	−0.434714	−0.217357	+	0.976092i	$0.569744\pi$
$398$	4.23134	0.212098
$399$	1.11583	0.0558611
$400$	−2.78605	−0.139302
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−8.78064	−0.437939
$403$	31.6349	1.57584
$404$	−3.59489	−0.178853
$405$	−1.00000	−0.0496904
$406$	12.7206	0.631315
$407$	16.6471	0.825166
$408$	9.20147	0.455540
$409$	21.6302	1.06955	0.534773	−	0.844996i	$-0.320397\pi$
$409$	21.6302	1.06955	0.534773	+	0.844996i	$0.320397\pi$
$410$	−6.21714	−0.307042
$411$	17.6138	0.868827
$412$	−8.07290	−0.397723
$413$	−21.2324	−1.04478
$414$	−9.74389	−0.478886
$415$	8.38811	0.411756
$416$	−11.4714	−0.562433
$417$	17.4219	0.853152
$418$	−2.07721	−0.101600
$419$	14.1043	0.689041	0.344520	−	0.938779i	$-0.388042\pi$
$419$	14.1043	0.689041	0.344520	+	0.938779i	$0.388042\pi$
$420$	0.790230	0.0385593
$421$	−8.06799	−0.393210	−0.196605	−	0.980483i	$-0.562992\pi$
$421$	−8.06799	−0.393210	−0.196605	+	0.980483i	$0.562992\pi$
$422$	3.10495	0.151147
$423$	−0.204157	−0.00992648
$424$	17.0102	0.826089
$425$	−3.00769	−0.145894
$426$	3.24959	0.157443
$427$	6.01759	0.291211
$428$	−6.72463	−0.325047
$429$	−10.4451	−0.504295
$430$	7.24927	0.349591
$431$	−40.2469	−1.93863	−0.969313	−	0.245830i	$-0.920940\pi$
$431$	−40.2469	−1.93863	−0.969313	+	0.245830i	$0.920940\pi$
$432$	2.78605	0.134044
$433$	−16.8793	−0.811166	−0.405583	−	0.914058i	$-0.632931\pi$
$433$	−16.8793	−0.811166	−0.405583	+	0.914058i	$0.632931\pi$
$434$	14.7883	0.709862
$435$	6.38753	0.306258
$436$	2.28030	0.109207
$437$	5.45949	0.261163
$438$	13.0690	0.624462
$439$	−2.12052	−0.101207	−0.0506035	−	0.998719i	$-0.516114\pi$
$439$	−2.12052	−0.101207	−0.0506035	+	0.998719i	$0.516114\pi$
$440$	−7.50092	−0.357592
$441$	−4.37710	−0.208433
$442$	15.7558	0.749428
$443$	−38.4987	−1.82913	−0.914565	−	0.404440i	$-0.867467\pi$
$443$	−38.4987	−1.82913	−0.914565	+	0.404440i	$0.867467\pi$
$444$	3.31291	0.157224
$445$	12.6023	0.597408
$446$	5.13566	0.243180
$447$	−9.61539	−0.454792
$448$	−14.3868	−0.679711
$449$	−25.7389	−1.21469	−0.607346	−	0.794437i	$-0.707766\pi$
$449$	−25.7389	−1.21469	−0.607346	+	0.794437i	$0.707766\pi$
$450$	−1.22966	−0.0579667
$451$	−12.3964	−0.583724
$452$	5.99436	0.281951
$453$	6.97598	0.327760
$454$	−14.8467	−0.696789
$455$	6.89945	0.323451
$456$	−2.10780	−0.0987068
$457$	11.3920	0.532894	0.266447	−	0.963850i	$-0.414150\pi$
$457$	11.3920	0.532894	0.266447	+	0.963850i	$0.414150\pi$
$458$	−21.3891	−0.999446
$459$	3.00769	0.140387
$460$	3.86642	0.180273
$461$	25.2312	1.17513	0.587566	−	0.809176i	$-0.300086\pi$
$461$	25.2312	1.17513	0.587566	+	0.809176i	$0.300086\pi$
$462$	−4.88278	−0.227167
$463$	16.0952	0.748009	0.374005	−	0.927427i	$-0.377984\pi$
$463$	16.0952	0.748009	0.374005	+	0.927427i	$0.377984\pi$
$464$	−17.7960	−0.826157
$465$	7.42579	0.344363
$466$	−31.9992	−1.48233
$467$	39.6475	1.83467	0.917333	−	0.398121i	$-0.130337\pi$
$467$	39.6475	1.83467	0.917333	+	0.398121i	$0.130337\pi$
$468$	−2.07867	−0.0960865
$469$	11.5646	0.534006
$470$	−0.251044	−0.0115798
$471$	−11.3837	−0.524534
$472$	40.1082	1.84613
$473$	14.4544	0.664613
$474$	−5.65886	−0.259920
$475$	0.688977	0.0316125
$476$	−2.37676	−0.108939
$477$	5.56014	0.254581
$478$	35.9707	1.64526
$479$	−13.6195	−0.622290	−0.311145	−	0.950362i	$-0.600712\pi$
$479$	−13.6195	−0.622290	−0.311145	+	0.950362i	$0.600712\pi$
$480$	−2.69274	−0.122906
$481$	28.9248	1.31886
$482$	−5.12850	−0.233597
$483$	12.8333	0.583935
$484$	2.43408	0.110640
$485$	−3.48515	−0.158253
$486$	1.22966	0.0557785
$487$	−7.37810	−0.334334	−0.167167	−	0.985929i	$-0.553462\pi$
$487$	−7.37810	−0.334334	−0.167167	+	0.985929i	$0.553462\pi$
$488$	−11.3672	−0.514571
$489$	6.54848	0.296132
$490$	−5.38234	−0.243149
$491$	17.6095	0.794706	0.397353	−	0.917666i	$-0.369929\pi$
$491$	17.6095	0.794706	0.397353	+	0.917666i	$0.369929\pi$
$492$	−2.46699	−0.111221
$493$	−19.2117	−0.865251
$494$	−3.60922	−0.162386
$495$	−2.45183	−0.110202
$496$	−20.6886	−0.928946
$497$	−4.27991	−0.191980
$498$	−10.3145	−0.462205
$499$	−21.8885	−0.979863	−0.489932	−	0.871761i	$-0.662978\pi$
$499$	−21.8885	−0.979863	−0.489932	+	0.871761i	$0.662978\pi$
$500$	0.487935	0.0218211
$501$	−7.73506	−0.345577
$502$	1.58229	0.0706211
$503$	−29.3248	−1.30753	−0.653765	−	0.756698i	$-0.726812\pi$
$503$	−29.3248	−1.30753	−0.653765	+	0.756698i	$0.726812\pi$
$504$	−4.95468	−0.220699
$505$	−7.36756	−0.327852
$506$	−23.8904	−1.06206
$507$	−5.14874	−0.228663
$508$	8.01668	0.355683
$509$	27.0210	1.19768	0.598842	−	0.800867i	$-0.295628\pi$
$509$	27.0210	1.19768	0.598842	+	0.800867i	$0.295628\pi$
$510$	3.69843	0.163769
$511$	−17.2127	−0.761445
$512$	24.5489	1.08492
$513$	−0.688977	−0.0304191
$514$	1.91975	0.0846765
$515$	−16.5450	−0.729061
$516$	2.87655	0.126633
$517$	−0.500559	−0.0220146
$518$	13.5215	0.594100
$519$	3.90579	0.171445
$520$	−13.0331	−0.571539
$521$	12.1139	0.530719	0.265360	−	0.964149i	$-0.414509\pi$
$521$	12.1139	0.530719	0.265360	+	0.964149i	$0.414509\pi$
$522$	−7.85449	−0.343782
$523$	25.3733	1.10950	0.554748	−	0.832018i	$-0.312815\pi$
$523$	25.3733	1.10950	0.554748	+	0.832018i	$0.312815\pi$
$524$	1.98267	0.0866132
$525$	1.61954	0.0706824
$526$	−32.4186	−1.41352
$527$	−22.3345	−0.972904
$528$	6.83092	0.297278
$529$	39.7905	1.73002
$530$	6.83708	0.296984
$531$	13.1102	0.568933
$532$	0.544451	0.0236049
$533$	−21.5391	−0.932964
$534$	−15.4966	−0.670603
$535$	−13.7818	−0.595840
$536$	−21.8457	−0.943589
$537$	−17.0400	−0.735330
$538$	−15.9090	−0.685888
$539$	−10.7319	−0.462255
$540$	−0.487935	−0.0209974
$541$	1.51086	0.0649569	0.0324784	−	0.999472i	$-0.489660\pi$
$541$	1.51086	0.0649569	0.0324784	+	0.999472i	$0.489660\pi$
$542$	15.5662	0.668625
$543$	−2.16332	−0.0928368
$544$	8.09891	0.347238
$545$	4.67337	0.200185
$546$	−8.48398	−0.363081
$547$	−26.6479	−1.13938	−0.569691	−	0.821859i	$-0.692937\pi$
$547$	−26.6479	−1.13938	−0.569691	+	0.821859i	$0.692937\pi$
$548$	8.59442	0.367135
$549$	−3.71562	−0.158579
$550$	−3.01492	−0.128557
$551$	4.40086	0.187483
$552$	−24.2422	−1.03182
$553$	7.45306	0.316937
$554$	−24.0576	−1.02211
$555$	6.78966	0.288205
$556$	8.50074	0.360512
$557$	43.6278	1.84857	0.924285	−	0.381704i	$-0.124662\pi$
$557$	43.6278	1.84857	0.924285	+	0.381704i	$0.124662\pi$
$558$	−9.13120	−0.386555
$559$	25.1150	1.06225
$560$	−4.51211	−0.190672
$561$	7.37434	0.311345
$562$	−22.9117	−0.966472
$563$	40.3935	1.70238	0.851192	−	0.524854i	$-0.175880\pi$
$563$	40.3935	1.70238	0.851192	+	0.524854i	$0.175880\pi$
$564$	−0.0996157	−0.00419458
$565$	12.2852	0.516840
$566$	8.22212	0.345602
$567$	−1.61954	−0.0680142
$568$	8.08477	0.339229
$569$	8.22800	0.344936	0.172468	−	0.985015i	$-0.444826\pi$
$569$	8.22800	0.344936	0.172468	+	0.985015i	$0.444826\pi$
$570$	−0.847208	−0.0354857
$571$	−10.1467	−0.424627	−0.212313	−	0.977202i	$-0.568100\pi$
$571$	−10.1467	−0.424627	−0.212313	+	0.977202i	$0.568100\pi$
$572$	−5.09654	−0.213097
$573$	15.5342	0.648952
$574$	−10.0689	−0.420267
$575$	7.92405	0.330456
$576$	8.88325	0.370135
$577$	4.51840	0.188103	0.0940517	−	0.995567i	$-0.470018\pi$
$577$	4.51840	0.188103	0.0940517	+	0.995567i	$0.470018\pi$
$578$	9.78049	0.406815
$579$	14.2773	0.593345
$580$	3.11670	0.129414
$581$	13.5849	0.563595
$582$	4.28556	0.177642
$583$	13.6325	0.564601
$584$	32.5149	1.34548
$585$	−4.26013	−0.176135
$586$	−17.2177	−0.711258
$587$	25.1639	1.03863	0.519313	−	0.854584i	$-0.326188\pi$
$587$	25.1639	1.03863	0.519313	+	0.854584i	$0.326188\pi$
$588$	−2.13574	−0.0880764
$589$	5.11620	0.210809
$590$	16.1211	0.663694
$591$	−14.8489	−0.610804
$592$	−18.9163	−0.777456
$593$	19.7879	0.812593	0.406297	−	0.913741i	$-0.366820\pi$
$593$	19.7879	0.812593	0.406297	+	0.913741i	$0.366820\pi$
$594$	3.01492	0.123704
$595$	−4.87107	−0.199694
$596$	−4.69169	−0.192179
$597$	3.44106	0.140833
$598$	−41.5103	−1.69748
$599$	24.9222	1.01829	0.509147	−	0.860679i	$-0.329961\pi$
$599$	24.9222	1.01829	0.509147	+	0.860679i	$0.329961\pi$
$600$	−3.05932	−0.124896
$601$	7.67971	0.313262	0.156631	−	0.987657i	$-0.449937\pi$
$601$	7.67971	0.313262	0.156631	+	0.987657i	$0.449937\pi$
$602$	11.7405	0.478506
$603$	−7.14071	−0.290792
$604$	3.40383	0.138500
$605$	4.98853	0.202813
$606$	9.05959	0.368021
$607$	38.0667	1.54508	0.772539	−	0.634967i	$-0.218986\pi$
$607$	38.0667	1.54508	0.772539	+	0.634967i	$0.218986\pi$
$608$	−1.85524	−0.0752397
$609$	10.3448	0.419194
$610$	−4.56895	−0.184991
$611$	−0.869738	−0.0351858
$612$	1.46756	0.0593225
$613$	23.7474	0.959149	0.479575	−	0.877501i	$-0.340791\pi$
$613$	23.7474	0.959149	0.479575	+	0.877501i	$0.340791\pi$
$614$	13.4421	0.542479
$615$	−5.05598	−0.203877
$616$	−12.1480	−0.489458
$617$	9.71268	0.391018	0.195509	−	0.980702i	$-0.437364\pi$
$617$	9.71268	0.391018	0.195509	+	0.980702i	$0.437364\pi$
$618$	20.3448	0.818386
$619$	−37.9954	−1.52716	−0.763582	−	0.645711i	$-0.776561\pi$
$619$	−37.9954	−1.52716	−0.763582	+	0.645711i	$0.776561\pi$
$620$	3.62331	0.145515
$621$	−7.92405	−0.317981
$622$	−26.7318	−1.07185
$623$	20.4100	0.817707
$624$	11.8689	0.475138
$625$	1.00000	0.0400000
$626$	−8.89497	−0.355514
$627$	−1.68926	−0.0674624
$628$	−5.55452	−0.221650
$629$	−20.4212	−0.814245
$630$	−1.99148	−0.0793425
$631$	−41.5504	−1.65409	−0.827047	−	0.562133i	$-0.809981\pi$
$631$	−41.5504	−1.65409	−0.827047	+	0.562133i	$0.809981\pi$
$632$	−14.0789	−0.560028
$633$	2.52505	0.100362
$634$	−15.8033	−0.627630
$635$	16.4298	0.651997
$636$	2.71299	0.107577
$637$	−18.6470	−0.738822
$638$	−19.2579	−0.762426
$639$	2.64267	0.104542
$640$	5.53791	0.218905
$641$	−38.4851	−1.52007	−0.760035	−	0.649883i	$-0.774818\pi$
$641$	−38.4851	−1.52007	−0.760035	+	0.649883i	$0.774818\pi$
$642$	16.9469	0.668843
$643$	−14.5551	−0.573998	−0.286999	−	0.957931i	$-0.592658\pi$
$643$	−14.5551	−0.573998	−0.286999	+	0.957931i	$0.592658\pi$
$644$	6.26182	0.246750
$645$	5.89535	0.232129
$646$	2.54814	0.100255
$647$	−18.0017	−0.707720	−0.353860	−	0.935298i	$-0.615131\pi$
$647$	−18.0017	−0.707720	−0.353860	+	0.935298i	$0.615131\pi$
$648$	3.05932	0.120181
$649$	32.1439	1.26176
$650$	−5.23852	−0.205472
$651$	12.0264	0.471350
$652$	3.19523	0.125135
$653$	−0.926998	−0.0362762	−0.0181381	−	0.999835i	$-0.505774\pi$
$653$	−0.926998	−0.0362762	−0.0181381	+	0.999835i	$0.505774\pi$
$654$	−5.74665	−0.224712
$655$	4.06338	0.158769
$656$	14.0862	0.549974
$657$	10.6282	0.414644
$658$	−0.406576	−0.0158500
$659$	−33.5676	−1.30761	−0.653804	−	0.756664i	$-0.726828\pi$
$659$	−33.5676	−1.30761	−0.653804	+	0.756664i	$0.726828\pi$
$660$	−1.19633	−0.0465673
$661$	30.9991	1.20573	0.602863	−	0.797845i	$-0.294027\pi$
$661$	30.9991	1.20573	0.602863	+	0.797845i	$0.294027\pi$
$662$	−17.3333	−0.673680
$663$	12.8132	0.497622
$664$	−25.6619	−0.995874
$665$	1.11583	0.0432698
$666$	−8.34897	−0.323516
$667$	50.6151	1.95982
$668$	−3.77421	−0.146029
$669$	4.17648	0.161472
$670$	−8.78064	−0.339226
$671$	−9.11006	−0.351690
$672$	−4.36099	−0.168229
$673$	−36.0763	−1.39064	−0.695319	−	0.718701i	$-0.744737\pi$
$673$	−36.0763	−1.39064	−0.695319	+	0.718701i	$0.744737\pi$
$674$	−15.7888	−0.608162
$675$	−1.00000	−0.0384900
$676$	−2.51225	−0.0966250
$677$	43.3496	1.66606	0.833031	−	0.553227i	$-0.186604\pi$
$677$	43.3496	1.66606	0.833031	+	0.553227i	$0.186604\pi$
$678$	−15.1066	−0.580164
$679$	−5.64434	−0.216610
$680$	9.20147	0.352860
$681$	−12.0738	−0.462669
$682$	−22.3882	−0.857287
$683$	−31.5410	−1.20688	−0.603442	−	0.797407i	$-0.706204\pi$
$683$	−31.5410	−1.20688	−0.603442	+	0.797407i	$0.706204\pi$
$684$	−0.336176	−0.0128540
$685$	17.6138	0.672990
$686$	−22.6573	−0.865059
$687$	−17.3943	−0.663634
$688$	−16.4247	−0.626187
$689$	23.6869	0.902400
$690$	−9.74389	−0.370943
$691$	−27.3970	−1.04223	−0.521116	−	0.853486i	$-0.674484\pi$
$691$	−27.3970	−1.04223	−0.521116	+	0.853486i	$0.674484\pi$
$692$	1.90577	0.0724466
$693$	−3.97083	−0.150839
$694$	14.9072	0.565868
$695$	17.4219	0.660849
$696$	−19.5415	−0.740717
$697$	15.2068	0.575999
$698$	30.7334	1.16328
$699$	−26.0228	−0.984272
$700$	0.790230	0.0298679
$701$	12.3924	0.468053	0.234026	−	0.972230i	$-0.424810\pi$
$701$	12.3924	0.468053	0.234026	+	0.972230i	$0.424810\pi$
$702$	5.23852	0.197715
$703$	4.67792	0.176431
$704$	21.7802	0.820873
$705$	−0.204157	−0.00768902
$706$	−1.68732	−0.0635033
$707$	−11.9320	−0.448751
$708$	6.39692	0.240411
$709$	−6.93416	−0.260418	−0.130209	−	0.991487i	$-0.541565\pi$
$709$	−6.93416	−0.260418	−0.130209	+	0.991487i	$0.541565\pi$
$710$	3.24959	0.121955
$711$	−4.60197	−0.172587
$712$	−38.5545	−1.44489
$713$	58.8423	2.20366
$714$	5.98976	0.224161
$715$	−10.4451	−0.390625
$716$	−8.31441	−0.310724
$717$	29.2525	1.09246
$718$	−28.4508	−1.06177
$719$	10.5328	0.392806	0.196403	−	0.980523i	$-0.437074\pi$
$719$	10.5328	0.392806	0.196403	+	0.980523i	$0.437074\pi$
$720$	2.78605	0.103830
$721$	−26.7953	−0.997909
$722$	22.7798	0.847778
$723$	−4.17067	−0.155109
$724$	−1.05556	−0.0392295
$725$	6.38753	0.237227
$726$	−6.13420	−0.227661
$727$	12.2030	0.452584	0.226292	−	0.974060i	$-0.427340\pi$
$727$	12.2030	0.452584	0.226292	+	0.974060i	$0.427340\pi$
$728$	−21.1076	−0.782299
$729$	1.00000	0.0370370
$730$	13.0690	0.483706
$731$	−17.7314	−0.655818
$732$	−1.81298	−0.0670097
$733$	14.8705	0.549255	0.274628	−	0.961551i	$-0.411445\pi$
$733$	14.8705	0.549255	0.274628	+	0.961551i	$0.411445\pi$
$734$	−14.9803	−0.552933
$735$	−4.37710	−0.161452
$736$	−21.3374	−0.786506
$737$	−17.5078	−0.644908
$738$	6.21714	0.228856
$739$	−25.7368	−0.946742	−0.473371	−	0.880863i	$-0.656963\pi$
$739$	−25.7368	−0.946742	−0.473371	+	0.880863i	$0.656963\pi$
$740$	3.31291	0.121785
$741$	−2.93514	−0.107825
$742$	11.0729	0.406499
$743$	42.8850	1.57330	0.786650	−	0.617400i	$-0.211814\pi$
$743$	42.8850	1.57330	0.786650	+	0.617400i	$0.211814\pi$
$744$	−22.7178	−0.832876
$745$	−9.61539	−0.352281
$746$	26.3030	0.963021
$747$	−8.38811	−0.306905
$748$	3.59820	0.131563
$749$	−22.3202	−0.815561
$750$	−1.22966	−0.0449008
$751$	28.6331	1.04484	0.522418	−	0.852690i	$-0.325030\pi$
$751$	28.6331	1.04484	0.522418	+	0.852690i	$0.325030\pi$
$752$	0.568793	0.0207417
$753$	1.28677	0.0468926
$754$	−33.4612	−1.21858
$755$	6.97598	0.253882
$756$	−0.790230	−0.0287404
$757$	−31.2006	−1.13400	−0.567002	−	0.823716i	$-0.691897\pi$
$757$	−31.2006	−1.13400	−0.567002	+	0.823716i	$0.691897\pi$
$758$	35.2415	1.28003
$759$	−19.4284	−0.705207
$760$	−2.10780	−0.0764579
$761$	8.32080	0.301629	0.150814	−	0.988562i	$-0.451810\pi$
$761$	8.32080	0.301629	0.150814	+	0.988562i	$0.451810\pi$
$762$	−20.2031	−0.731880
$763$	7.56870	0.274005
$764$	7.57970	0.274224
$765$	3.00769	0.108743
$766$	−13.8000	−0.498614
$767$	55.8511	2.01667
$768$	10.9568	0.395368
$769$	−14.6765	−0.529248	−0.264624	−	0.964352i	$-0.585248\pi$
$769$	−14.6765	−0.529248	−0.264624	+	0.964352i	$0.585248\pi$
$770$	−4.88278	−0.175963
$771$	1.56120	0.0562253
$772$	6.96641	0.250727
$773$	21.5292	0.774350	0.387175	−	0.922006i	$-0.373451\pi$
$773$	21.5292	0.774350	0.387175	+	0.922006i	$0.373451\pi$
$774$	−7.24927	−0.260570
$775$	7.42579	0.266742
$776$	10.6622	0.382750
$777$	10.9961	0.394483
$778$	4.52411	0.162197
$779$	−3.48346	−0.124808
$780$	−2.07867	−0.0744283
$781$	6.47938	0.231850
$782$	29.3066	1.04800
$783$	−6.38753	−0.228272
$784$	12.1948	0.435529
$785$	−11.3837	−0.406303
$786$	−4.99658	−0.178222
$787$	6.29829	0.224510	0.112255	−	0.993679i	$-0.464193\pi$
$787$	6.29829	0.224510	0.112255	+	0.993679i	$0.464193\pi$
$788$	−7.24532	−0.258104
$789$	−26.3639	−0.938578
$790$	−5.65886	−0.201333
$791$	19.8963	0.707430
$792$	7.50092	0.266534
$793$	−15.8290	−0.562105
$794$	10.6509	0.377985
$795$	5.56014	0.197198
$796$	1.67902	0.0595111
$797$	−9.83563	−0.348396	−0.174198	−	0.984711i	$-0.555733\pi$
$797$	−9.83563	−0.348396	−0.174198	+	0.984711i	$0.555733\pi$
$798$	−1.37209	−0.0485713
$799$	0.614042	0.0217232
$800$	−2.69274	−0.0952026
$801$	−12.6023	−0.445281
$802$	−1.22966	−0.0434208
$803$	26.0584	0.919582
$804$	−3.48420	−0.122878
$805$	12.8333	0.452314
$806$	−38.9001	−1.37020
$807$	−12.9378	−0.455431
$808$	22.5397	0.792943
$809$	1.71773	0.0603921	0.0301960	−	0.999544i	$-0.490387\pi$
$809$	1.71773	0.0603921	0.0301960	+	0.999544i	$0.490387\pi$
$810$	1.22966	0.0432059
$811$	2.17498	0.0763738	0.0381869	−	0.999271i	$-0.487842\pi$
$811$	2.17498	0.0763738	0.0381869	+	0.999271i	$0.487842\pi$
$812$	5.04761	0.177137
$813$	12.6589	0.443968
$814$	−20.4703	−0.717482
$815$	6.54848	0.229383
$816$	−8.37956	−0.293343
$817$	4.06176	0.142103
$818$	−26.5978	−0.929972
$819$	−6.89945	−0.241086
$820$	−2.46699	−0.0861510
$821$	22.6125	0.789181	0.394590	−	0.918857i	$-0.370886\pi$
$821$	22.6125	0.789181	0.394590	+	0.918857i	$0.370886\pi$
$822$	−21.6590	−0.755446
$823$	42.7317	1.48953	0.744767	−	0.667324i	$-0.232560\pi$
$823$	42.7317	1.48953	0.744767	+	0.667324i	$0.232560\pi$
$824$	50.6164	1.76331
$825$	−2.45183	−0.0853618
$826$	26.1087	0.908437
$827$	13.7715	0.478882	0.239441	−	0.970911i	$-0.423036\pi$
$827$	13.7715	0.478882	0.239441	+	0.970911i	$0.423036\pi$
$828$	−3.86642	−0.134367
$829$	8.24959	0.286520	0.143260	−	0.989685i	$-0.454241\pi$
$829$	8.24959	0.286520	0.143260	+	0.989685i	$0.454241\pi$
$830$	−10.3145	−0.358023
$831$	−19.5644	−0.678681
$832$	37.8438	1.31200
$833$	13.1649	0.456138
$834$	−21.4230	−0.741817
$835$	−7.73506	−0.267683
$836$	−0.824247	−0.0285072
$837$	−7.42579	−0.256673
$838$	−17.3435	−0.599122
$839$	3.14191	0.108471	0.0542355	−	0.998528i	$-0.482728\pi$
$839$	3.14191	0.108471	0.0542355	+	0.998528i	$0.482728\pi$
$840$	−4.95468	−0.170953
$841$	11.8005	0.406913
$842$	9.92089	0.341896
$843$	−18.6326	−0.641739
$844$	1.23206	0.0424092
$845$	−5.14874	−0.177122
$846$	0.251044	0.00863108
$847$	8.07911	0.277602
$848$	−15.4908	−0.531957
$849$	6.68650	0.229480
$850$	3.69843	0.126855
$851$	53.8016	1.84429
$852$	1.28945	0.0441759
$853$	50.2078	1.71908	0.859541	−	0.511067i	$-0.170750\pi$
$853$	50.2078	1.71908	0.859541	+	0.511067i	$0.170750\pi$
$854$	−7.39959	−0.253209
$855$	−0.688977	−0.0235625
$856$	42.1629	1.44110
$857$	−52.5319	−1.79446	−0.897228	−	0.441568i	$-0.854422\pi$
$857$	−52.5319	−1.79446	−0.897228	+	0.441568i	$0.854422\pi$
$858$	12.8440	0.438485
$859$	22.6055	0.771289	0.385645	−	0.922647i	$-0.373979\pi$
$859$	22.6055	0.771289	0.385645	+	0.922647i	$0.373979\pi$
$860$	2.87655	0.0980895
$861$	−8.18835	−0.279058
$862$	49.4900	1.68564
$863$	−14.0547	−0.478428	−0.239214	−	0.970967i	$-0.576890\pi$
$863$	−14.0547	−0.478428	−0.239214	+	0.970967i	$0.576890\pi$
$864$	2.69274	0.0916088
$865$	3.90579	0.132801
$866$	20.7558	0.705310
$867$	7.95381	0.270126
$868$	5.86808	0.199176
$869$	−11.2832	−0.382758
$870$	−7.85449	−0.266292
$871$	−30.4204	−1.03075
$872$	−14.2973	−0.484168
$873$	3.48515	0.117955
$874$	−6.71332	−0.227081
$875$	1.61954	0.0547504
$876$	5.18585	0.175214
$877$	−44.0213	−1.48649	−0.743247	−	0.669017i	$-0.766715\pi$
$877$	−44.0213	−1.48649	−0.743247	+	0.669017i	$0.766715\pi$
$878$	2.60752	0.0879996
$879$	−14.0020	−0.472277
$880$	6.83092	0.230270
$881$	3.17377	0.106927	0.0534635	−	0.998570i	$-0.482974\pi$
$881$	3.17377	0.106927	0.0534635	+	0.998570i	$0.482974\pi$
$882$	5.38234	0.181233
$883$	−30.1355	−1.01414	−0.507069	−	0.861905i	$-0.669271\pi$
$883$	−30.1355	−1.01414	−0.507069	+	0.861905i	$0.669271\pi$
$884$	6.25199	0.210277
$885$	13.1102	0.440694
$886$	47.3404	1.59043
$887$	7.42551	0.249324	0.124662	−	0.992199i	$-0.460215\pi$
$887$	7.42551	0.249324	0.124662	+	0.992199i	$0.460215\pi$
$888$	−20.7717	−0.697053
$889$	26.6087	0.892426
$890$	−15.4966	−0.519447
$891$	2.45183	0.0821394
$892$	2.03785	0.0682324
$893$	−0.140660	−0.00470700
$894$	11.8237	0.395442
$895$	−17.0400	−0.569584
$896$	8.96885	0.299628
$897$	−33.7575	−1.12713
$898$	31.6501	1.05618
$899$	47.4324	1.58196
$900$	−0.487935	−0.0162645
$901$	−16.7232	−0.557129
$902$	15.2434	0.507548
$903$	9.54774	0.317729
$904$	−37.5842	−1.25003
$905$	−2.16332	−0.0719110
$906$	−8.57808	−0.284988
$907$	−58.7427	−1.95052	−0.975259	−	0.221066i	$-0.929046\pi$
$907$	−58.7427	−1.95052	−0.975259	+	0.221066i	$0.929046\pi$
$908$	−5.89123	−0.195507
$909$	7.36756	0.244366
$910$	−8.48398	−0.281241
$911$	−56.1844	−1.86147	−0.930736	−	0.365691i	$-0.880833\pi$
$911$	−56.1844	−1.86147	−0.930736	+	0.365691i	$0.880833\pi$
$912$	1.91952	0.0635618
$913$	−20.5662	−0.680643
$914$	−14.0083	−0.463352
$915$	−3.71562	−0.122835
$916$	−8.48730	−0.280428
$917$	6.58080	0.217317
$918$	−3.69843	−0.122067
$919$	28.7934	0.949806	0.474903	−	0.880038i	$-0.342483\pi$
$919$	28.7934	0.949806	0.474903	+	0.880038i	$0.342483\pi$
$920$	−24.2422	−0.799240
$921$	10.9316	0.360207
$922$	−31.0258	−1.02178
$923$	11.2581	0.370566
$924$	−1.93751	−0.0637394
$925$	6.78966	0.223243
$926$	−19.7917	−0.650395
$927$	16.5450	0.543410
$928$	−17.1999	−0.564615
$929$	−22.2414	−0.729717	−0.364858	−	0.931063i	$-0.618883\pi$
$929$	−22.2414	−0.729717	−0.364858	+	0.931063i	$0.618883\pi$
$930$	−9.13120	−0.299424
$931$	−3.01572	−0.0988363
$932$	−12.6974	−0.415918
$933$	−21.7392	−0.711710
$934$	−48.7529	−1.59524
$935$	7.37434	0.241167
$936$	13.0331	0.426000
$937$	8.21088	0.268238	0.134119	−	0.990965i	$-0.457180\pi$
$937$	8.21088	0.268238	0.134119	+	0.990965i	$0.457180\pi$
$938$	−14.2206	−0.464319
$939$	−7.23368	−0.236062
$940$	−0.0996157	−0.00324910
$941$	4.25451	0.138693	0.0693465	−	0.997593i	$-0.477909\pi$
$941$	4.25451	0.138693	0.0693465	+	0.997593i	$0.477909\pi$
$942$	13.9981	0.456083
$943$	−40.0638	−1.30466
$944$	−36.5256	−1.18881
$945$	−1.61954	−0.0526836
$946$	−17.7740	−0.577882
$947$	−18.0838	−0.587644	−0.293822	−	0.955860i	$-0.594927\pi$
$947$	−18.0838	−0.587644	−0.293822	+	0.955860i	$0.594927\pi$
$948$	−2.24546	−0.0729293
$949$	45.2774	1.46976
$950$	−0.847208	−0.0274871
$951$	−12.8518	−0.416747
$952$	14.9021	0.482981
$953$	−41.3951	−1.34092	−0.670460	−	0.741946i	$-0.733903\pi$
$953$	−41.3951	−1.34092	−0.670460	+	0.741946i	$0.733903\pi$
$954$	−6.83708	−0.221359
$955$	15.5342	0.502676
$956$	14.2733	0.461633
$957$	−15.6611	−0.506252
$958$	16.7473	0.541082
$959$	28.5263	0.921162
$960$	8.88325	0.286706
$961$	24.1424	0.778786
$962$	−35.5677	−1.14675
$963$	13.7818	0.444113
$964$	−2.03502	−0.0655434
$965$	14.2773	0.459603
$966$	−15.7806	−0.507732
$967$	21.6316	0.695626	0.347813	−	0.937564i	$-0.386924\pi$
$967$	21.6316	0.695626	0.347813	+	0.937564i	$0.386924\pi$
$968$	−15.2615	−0.490523
$969$	2.07223	0.0665696
$970$	4.28556	0.137601
$971$	−31.2371	−1.00245	−0.501223	−	0.865318i	$-0.667116\pi$
$971$	−31.2371	−1.00245	−0.501223	+	0.865318i	$0.667116\pi$
$972$	0.487935	0.0156505
$973$	28.2154	0.904543
$974$	9.07256	0.290703
$975$	−4.26013	−0.136433
$976$	10.3519	0.331356
$977$	−2.30841	−0.0738526	−0.0369263	−	0.999318i	$-0.511757\pi$
$977$	−2.30841	−0.0738526	−0.0369263	+	0.999318i	$0.511757\pi$
$978$	−8.05241	−0.257488
$979$	−30.8988	−0.987529
$980$	−2.13574	−0.0682237
$981$	−4.67337	−0.149209
$982$	−21.6537	−0.690998
$983$	−4.06049	−0.129509	−0.0647547	−	0.997901i	$-0.520627\pi$
$983$	−4.06049	−0.129509	−0.0647547	+	0.997901i	$0.520627\pi$
$984$	15.4678	0.493097
$985$	−14.8489	−0.473127
$986$	23.6238	0.752337
$987$	−0.330641	−0.0105244
$988$	−1.43216	−0.0455630
$989$	46.7150	1.48545
$990$	3.01492	0.0958204
$991$	−48.9448	−1.55478	−0.777392	−	0.629016i	$-0.783458\pi$
$991$	−48.9448	−1.55478	−0.777392	+	0.629016i	$0.783458\pi$
$992$	−19.9957	−0.634864
$993$	−14.0960	−0.447324
$994$	5.26283	0.166927
$995$	3.44106	0.109089
$996$	−4.09286	−0.129687
$997$	16.1207	0.510546	0.255273	−	0.966869i	$-0.417835\pi$
$997$	16.1207	0.510546	0.255273	+	0.966869i	$0.417835\pi$
$998$	26.9154	0.851992
$999$	−6.78966	−0.214815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.9	✓	31	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.22966 q^{2} -1.00000 q^{3} -0.487935 q^{4} -1.00000 q^{5} +1.22966 q^{6} -1.61954 q^{7} +3.05932 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.22966 q^{2} -1.00000 q^{3} -0.487935 q^{4} -1.00000 q^{5} +1.22966 q^{6} -1.61954 q^{7} +3.05932 q^{8} +1.00000 q^{9} +1.22966 q^{10} +2.45183 q^{11} +0.487935 q^{12} +4.26013 q^{13} +1.99148 q^{14} +1.00000 q^{15} -2.78605 q^{16} -3.00769 q^{17} -1.22966 q^{18} +0.688977 q^{19} +0.487935 q^{20} +1.61954 q^{21} -3.01492 q^{22} +7.92405 q^{23} -3.05932 q^{24} +1.00000 q^{25} -5.23852 q^{26} -1.00000 q^{27} +0.790230 q^{28} +6.38753 q^{29} -1.22966 q^{30} +7.42579 q^{31} -2.69274 q^{32} -2.45183 q^{33} +3.69843 q^{34} +1.61954 q^{35} -0.487935 q^{36} +6.78966 q^{37} -0.847208 q^{38} -4.26013 q^{39} -3.05932 q^{40} -5.05598 q^{41} -1.99148 q^{42} +5.89535 q^{43} -1.19633 q^{44} -1.00000 q^{45} -9.74389 q^{46} -0.204157 q^{47} +2.78605 q^{48} -4.37710 q^{49} -1.22966 q^{50} +3.00769 q^{51} -2.07867 q^{52} +5.56014 q^{53} +1.22966 q^{54} -2.45183 q^{55} -4.95468 q^{56} -0.688977 q^{57} -7.85449 q^{58} +13.1102 q^{59} -0.487935 q^{60} -3.71562 q^{61} -9.13120 q^{62} -1.61954 q^{63} +8.88325 q^{64} -4.26013 q^{65} +3.01492 q^{66} -7.14071 q^{67} +1.46756 q^{68} -7.92405 q^{69} -1.99148 q^{70} +2.64267 q^{71} +3.05932 q^{72} +10.6282 q^{73} -8.34897 q^{74} -1.00000 q^{75} -0.336176 q^{76} -3.97083 q^{77} +5.23852 q^{78} -4.60197 q^{79} +2.78605 q^{80} +1.00000 q^{81} +6.21714 q^{82} -8.38811 q^{83} -0.790230 q^{84} +3.00769 q^{85} -7.24927 q^{86} -6.38753 q^{87} +7.50092 q^{88} -12.6023 q^{89} +1.22966 q^{90} -6.89945 q^{91} -3.86642 q^{92} -7.42579 q^{93} +0.251044 q^{94} -0.688977 q^{95} +2.69274 q^{96} +3.48515 q^{97} +5.38234 q^{98} +2.45183 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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