LMFDB - Embedded newform 6035.2.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.03393 q^{2} +2.68090 q^{3} -0.930989 q^{4} +1.00000 q^{5} -2.77186 q^{6} +1.41622 q^{7} +3.03044 q^{8} +4.18720 q^{9} +O(q^{10})$	\(q-1.03393 q^{2} +2.68090 q^{3} -0.930989 q^{4} +1.00000 q^{5} -2.77186 q^{6} +1.41622 q^{7} +3.03044 q^{8} +4.18720 q^{9} -1.03393 q^{10} +1.78846 q^{11} -2.49588 q^{12} -7.19809 q^{13} -1.46427 q^{14} +2.68090 q^{15} -1.27128 q^{16} +1.00000 q^{17} -4.32927 q^{18} -3.87404 q^{19} -0.930989 q^{20} +3.79673 q^{21} -1.84915 q^{22} -3.40234 q^{23} +8.12429 q^{24} +1.00000 q^{25} +7.44232 q^{26} +3.18276 q^{27} -1.31848 q^{28} -0.0953703 q^{29} -2.77186 q^{30} -7.77708 q^{31} -4.74646 q^{32} +4.79469 q^{33} -1.03393 q^{34} +1.41622 q^{35} -3.89824 q^{36} -1.05865 q^{37} +4.00549 q^{38} -19.2973 q^{39} +3.03044 q^{40} -2.57994 q^{41} -3.92556 q^{42} -1.04642 q^{43} -1.66504 q^{44} +4.18720 q^{45} +3.51778 q^{46} -12.2869 q^{47} -3.40817 q^{48} -4.99432 q^{49} -1.03393 q^{50} +2.68090 q^{51} +6.70134 q^{52} -1.00091 q^{53} -3.29075 q^{54} +1.78846 q^{55} +4.29176 q^{56} -10.3859 q^{57} +0.0986062 q^{58} -4.98390 q^{59} -2.49588 q^{60} -2.65363 q^{61} +8.04095 q^{62} +5.92999 q^{63} +7.45007 q^{64} -7.19809 q^{65} -4.95737 q^{66} +7.29534 q^{67} -0.930989 q^{68} -9.12132 q^{69} -1.46427 q^{70} -1.00000 q^{71} +12.6890 q^{72} +3.76564 q^{73} +1.09457 q^{74} +2.68090 q^{75} +3.60669 q^{76} +2.53286 q^{77} +19.9521 q^{78} +7.37615 q^{79} -1.27128 q^{80} -4.02895 q^{81} +2.66747 q^{82} -11.9085 q^{83} -3.53472 q^{84} +1.00000 q^{85} +1.08192 q^{86} -0.255678 q^{87} +5.41983 q^{88} -8.48287 q^{89} -4.32927 q^{90} -10.1941 q^{91} +3.16754 q^{92} -20.8495 q^{93} +12.7038 q^{94} -3.87404 q^{95} -12.7248 q^{96} +17.6413 q^{97} +5.16378 q^{98} +7.48866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * 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 $

$2$	−1.03393	−0.731099	−0.365549	−	0.930792i	$-0.619119\pi$
$2$	−1.03393	−0.731099	−0.365549	+	0.930792i	$0.619119\pi$
$3$	2.68090	1.54782	0.773908	−	0.633298i	$-0.218299\pi$
$3$	2.68090	1.54782	0.773908	+	0.633298i	$0.218299\pi$
$4$	−0.930989	−0.465495
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.77186	−1.13161
$7$	1.41622	0.535280	0.267640	−	0.963519i	$-0.413756\pi$
$7$	1.41622	0.535280	0.267640	+	0.963519i	$0.413756\pi$
$8$	3.03044	1.07142
$9$	4.18720	1.39573
$10$	−1.03393	−0.326957
$11$	1.78846	0.539242	0.269621	−	0.962966i	$-0.413102\pi$
$11$	1.78846	0.539242	0.269621	+	0.962966i	$0.413102\pi$
$12$	−2.49588	−0.720500
$13$	−7.19809	−1.99639	−0.998195	−	0.0600520i	$-0.980873\pi$
$13$	−7.19809	−1.99639	−0.998195	+	0.0600520i	$0.980873\pi$
$14$	−1.46427	−0.391343
$15$	2.68090	0.692204
$16$	−1.27128	−0.317820
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−4.32927	−1.02042
$19$	−3.87404	−0.888767	−0.444383	−	0.895837i	$-0.646577\pi$
$19$	−3.87404	−0.888767	−0.444383	+	0.895837i	$0.646577\pi$
$20$	−0.930989	−0.208175
$21$	3.79673	0.828515
$22$	−1.84915	−0.394239
$23$	−3.40234	−0.709437	−0.354719	−	0.934973i	$-0.615423\pi$
$23$	−3.40234	−0.709437	−0.354719	+	0.934973i	$0.615423\pi$
$24$	8.12429	1.65836
$25$	1.00000	0.200000
$26$	7.44232	1.45956
$27$	3.18276	0.612523
$28$	−1.31848	−0.249170
$29$	−0.0953703	−0.0177098	−0.00885491	−	0.999961i	$-0.502819\pi$
$29$	−0.0953703	−0.0177098	−0.00885491	+	0.999961i	$0.502819\pi$
$30$	−2.77186	−0.506070
$31$	−7.77708	−1.39680	−0.698402	−	0.715706i	$-0.746105\pi$
$31$	−7.77708	−1.39680	−0.698402	+	0.715706i	$0.746105\pi$
$32$	−4.74646	−0.839063
$33$	4.79469	0.834648
$34$	−1.03393	−0.177318
$35$	1.41622	0.239385
$36$	−3.89824	−0.649706
$37$	−1.05865	−0.174041	−0.0870206	−	0.996207i	$-0.527735\pi$
$37$	−1.05865	−0.174041	−0.0870206	+	0.996207i	$0.527735\pi$
$38$	4.00549	0.649776
$39$	−19.2973	−3.09004
$40$	3.03044	0.479154
$41$	−2.57994	−0.402918	−0.201459	−	0.979497i	$-0.564568\pi$
$41$	−2.57994	−0.402918	−0.201459	+	0.979497i	$0.564568\pi$
$42$	−3.92556	−0.605727
$43$	−1.04642	−0.159577	−0.0797885	−	0.996812i	$-0.525424\pi$
$43$	−1.04642	−0.159577	−0.0797885	+	0.996812i	$0.525424\pi$
$44$	−1.66504	−0.251014
$45$	4.18720	0.624191
$46$	3.51778	0.518669
$47$	−12.2869	−1.79223	−0.896114	−	0.443824i	$-0.853621\pi$
$47$	−12.2869	−1.79223	−0.896114	+	0.443824i	$0.853621\pi$
$48$	−3.40817	−0.491927
$49$	−4.99432	−0.713475
$50$	−1.03393	−0.146220
$51$	2.68090	0.375400
$52$	6.70134	0.929309
$53$	−1.00091	−0.137486	−0.0687431	−	0.997634i	$-0.521899\pi$
$53$	−1.00091	−0.137486	−0.0687431	+	0.997634i	$0.521899\pi$
$54$	−3.29075	−0.447815
$55$	1.78846	0.241156
$56$	4.29176	0.573511
$57$	−10.3859	−1.37565
$58$	0.0986062	0.0129476
$59$	−4.98390	−0.648848	−0.324424	−	0.945912i	$-0.605170\pi$
$59$	−4.98390	−0.648848	−0.324424	+	0.945912i	$0.605170\pi$
$60$	−2.49588	−0.322217
$61$	−2.65363	−0.339762	−0.169881	−	0.985465i	$-0.554338\pi$
$61$	−2.65363	−0.339762	−0.169881	+	0.985465i	$0.554338\pi$
$62$	8.04095	1.02120
$63$	5.92999	0.747109
$64$	7.45007	0.931258
$65$	−7.19809	−0.892813
$66$	−4.95737	−0.610210
$67$	7.29534	0.891268	0.445634	−	0.895215i	$-0.352978\pi$
$67$	7.29534	0.891268	0.445634	+	0.895215i	$0.352978\pi$
$68$	−0.930989	−0.112899
$69$	−9.12132	−1.09808
$70$	−1.46427	−0.175014
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	12.6890	1.49542
$73$	3.76564	0.440735	0.220368	−	0.975417i	$-0.429274\pi$
$73$	3.76564	0.440735	0.220368	+	0.975417i	$0.429274\pi$
$74$	1.09457	0.127241
$75$	2.68090	0.309563
$76$	3.60669	0.413716
$77$	2.53286	0.288646
$78$	19.9521	2.25913
$79$	7.37615	0.829882	0.414941	−	0.909848i	$-0.363802\pi$
$79$	7.37615	0.829882	0.414941	+	0.909848i	$0.363802\pi$
$80$	−1.27128	−0.142134
$81$	−4.02895	−0.447661
$82$	2.66747	0.294573
$83$	−11.9085	−1.30713	−0.653563	−	0.756872i	$-0.726727\pi$
$83$	−11.9085	−1.30713	−0.653563	+	0.756872i	$0.726727\pi$
$84$	−3.53472	−0.385669
$85$	1.00000	0.108465
$86$	1.08192	0.116667
$87$	−0.255678	−0.0274115
$88$	5.41983	0.577756
$89$	−8.48287	−0.899182	−0.449591	−	0.893235i	$-0.648430\pi$
$89$	−8.48287	−0.899182	−0.449591	+	0.893235i	$0.648430\pi$
$90$	−4.32927	−0.456345
$91$	−10.1941	−1.06863
$92$	3.16754	0.330239
$93$	−20.8495	−2.16200
$94$	12.7038	1.31030
$95$	−3.87404	−0.397469
$96$	−12.7248	−1.29872
$97$	17.6413	1.79121	0.895603	−	0.444855i	$-0.146745\pi$
$97$	17.6413	1.79121	0.895603	+	0.444855i	$0.146745\pi$
$98$	5.16378	0.521621
$99$	7.48866	0.752639
$100$	−0.930989	−0.0930989
$101$	−0.388930	−0.0387000	−0.0193500	−	0.999813i	$-0.506160\pi$
$101$	−0.388930	−0.0387000	−0.0193500	+	0.999813i	$0.506160\pi$
$102$	−2.77186	−0.274455
$103$	−9.37944	−0.924183	−0.462092	−	0.886832i	$-0.652901\pi$
$103$	−9.37944	−0.924183	−0.462092	+	0.886832i	$0.652901\pi$
$104$	−21.8134	−2.13898
$105$	3.79673	0.370523
$106$	1.03488	0.100516
$107$	−0.586756	−0.0567238	−0.0283619	−	0.999598i	$-0.509029\pi$
$107$	−0.586756	−0.0567238	−0.0283619	+	0.999598i	$0.509029\pi$
$108$	−2.96312	−0.285126
$109$	−11.6473	−1.11561	−0.557803	−	0.829974i	$-0.688355\pi$
$109$	−11.6473	−1.11561	−0.557803	+	0.829974i	$0.688355\pi$
$110$	−1.84915	−0.176309
$111$	−2.83813	−0.269384
$112$	−1.80041	−0.170123
$113$	−10.0292	−0.943466	−0.471733	−	0.881741i	$-0.656371\pi$
$113$	−10.0292	−0.943466	−0.471733	+	0.881741i	$0.656371\pi$
$114$	10.7383	1.00573
$115$	−3.40234	−0.317270
$116$	0.0887887	0.00824382
$117$	−30.1398	−2.78643
$118$	5.15300	0.474372
$119$	1.41622	0.129825
$120$	8.12429	0.741642
$121$	−7.80140	−0.709218
$122$	2.74367	0.248400
$123$	−6.91654	−0.623643
$124$	7.24037	0.650205
$125$	1.00000	0.0894427
$126$	−6.13120	−0.546210
$127$	13.0247	1.15575	0.577877	−	0.816124i	$-0.303881\pi$
$127$	13.0247	1.15575	0.577877	+	0.816124i	$0.303881\pi$
$128$	1.79007	0.158221
$129$	−2.80533	−0.246996
$130$	7.44232	0.652734
$131$	−2.31350	−0.202131	−0.101066	−	0.994880i	$-0.532225\pi$
$131$	−2.31350	−0.202131	−0.101066	+	0.994880i	$0.532225\pi$
$132$	−4.46380	−0.388524
$133$	−5.48649	−0.475739
$134$	−7.54287	−0.651605
$135$	3.18276	0.273929
$136$	3.03044	0.259858
$137$	8.34510	0.712970	0.356485	−	0.934301i	$-0.383975\pi$
$137$	8.34510	0.712970	0.356485	+	0.934301i	$0.383975\pi$
$138$	9.43081	0.802804
$139$	12.0444	1.02159	0.510794	−	0.859703i	$-0.329351\pi$
$139$	12.0444	1.02159	0.510794	+	0.859703i	$0.329351\pi$
$140$	−1.31848	−0.111432
$141$	−32.9399	−2.77404
$142$	1.03393	0.0867655
$143$	−12.8735	−1.07654
$144$	−5.32311	−0.443593
$145$	−0.0953703	−0.00792007
$146$	−3.89341	−0.322221
$147$	−13.3893	−1.10433
$148$	0.985593	0.0810152
$149$	5.44465	0.446043	0.223022	−	0.974814i	$-0.428408\pi$
$149$	5.44465	0.446043	0.223022	+	0.974814i	$0.428408\pi$
$150$	−2.77186	−0.226321
$151$	0.257916	0.0209889	0.0104945	−	0.999945i	$-0.496659\pi$
$151$	0.257916	0.0209889	0.0104945	+	0.999945i	$0.496659\pi$
$152$	−11.7400	−0.952244
$153$	4.18720	0.338515
$154$	−2.61880	−0.211029
$155$	−7.77708	−0.624670
$156$	17.9656	1.43840
$157$	−6.55001	−0.522748	−0.261374	−	0.965238i	$-0.584176\pi$
$157$	−6.55001	−0.522748	−0.261374	+	0.965238i	$0.584176\pi$
$158$	−7.62642	−0.606725
$159$	−2.68335	−0.212803
$160$	−4.74646	−0.375240
$161$	−4.81846	−0.379748
$162$	4.16565	0.327284
$163$	20.9028	1.63723	0.818617	−	0.574340i	$-0.194741\pi$
$163$	20.9028	1.63723	0.818617	+	0.574340i	$0.194741\pi$
$164$	2.40189	0.187556
$165$	4.79469	0.373266
$166$	12.3125	0.955639
$167$	15.5734	1.20511	0.602553	−	0.798079i	$-0.294150\pi$
$167$	15.5734	1.20511	0.602553	+	0.798079i	$0.294150\pi$
$168$	11.5058	0.887689
$169$	38.8125	2.98558
$170$	−1.03393	−0.0792988
$171$	−16.2214	−1.24048
$172$	0.974202	0.0742822
$173$	−12.0165	−0.913596	−0.456798	−	0.889570i	$-0.651004\pi$
$173$	−12.0165	−0.913596	−0.456798	+	0.889570i	$0.651004\pi$
$174$	0.264353	0.0200405
$175$	1.41622	0.107056
$176$	−2.27364	−0.171382
$177$	−13.3613	−1.00430
$178$	8.77069	0.657391
$179$	17.1797	1.28407	0.642036	−	0.766675i	$-0.278090\pi$
$179$	17.1797	1.28407	0.642036	+	0.766675i	$0.278090\pi$
$180$	−3.89824	−0.290558
$181$	−13.0802	−0.972245	−0.486122	−	0.873891i	$-0.661589\pi$
$181$	−13.0802	−0.972245	−0.486122	+	0.873891i	$0.661589\pi$
$182$	10.5400	0.781273
$183$	−7.11410	−0.525890
$184$	−10.3106	−0.760106
$185$	−1.05865	−0.0778336
$186$	21.5569	1.58063
$187$	1.78846	0.130785
$188$	11.4390	0.834272
$189$	4.50749	0.327871
$190$	4.00549	0.290589
$191$	20.0620	1.45164	0.725819	−	0.687886i	$-0.241461\pi$
$191$	20.0620	1.45164	0.725819	+	0.687886i	$0.241461\pi$
$192$	19.9729	1.44142
$193$	−0.0678429	−0.00488344	−0.00244172	−	0.999997i	$-0.500777\pi$
$193$	−0.0678429	−0.00488344	−0.00244172	+	0.999997i	$0.500777\pi$
$194$	−18.2399	−1.30955
$195$	−19.2973	−1.38191
$196$	4.64966	0.332119
$197$	0.425225	0.0302960	0.0151480	−	0.999885i	$-0.495178\pi$
$197$	0.425225	0.0302960	0.0151480	+	0.999885i	$0.495178\pi$
$198$	−7.74275	−0.550253
$199$	13.9725	0.990483	0.495241	−	0.868755i	$-0.335080\pi$
$199$	13.9725	0.990483	0.495241	+	0.868755i	$0.335080\pi$
$200$	3.03044	0.214284
$201$	19.5581	1.37952
$202$	0.402127	0.0282935
$203$	−0.135065	−0.00947972
$204$	−2.49588	−0.174747
$205$	−2.57994	−0.180190
$206$	9.69768	0.675669
$207$	−14.2463	−0.990186
$208$	9.15079	0.634493
$209$	−6.92859	−0.479261
$210$	−3.92556	−0.270889
$211$	−12.8893	−0.887338	−0.443669	−	0.896191i	$-0.646323\pi$
$211$	−12.8893	−0.887338	−0.443669	+	0.896191i	$0.646323\pi$
$212$	0.931841	0.0639991
$213$	−2.68090	−0.183692
$214$	0.606664	0.0414707
$215$	−1.04642	−0.0713650
$216$	9.64516	0.656270
$217$	−11.0140	−0.747682
$218$	12.0425	0.815618
$219$	10.0953	0.682177
$220$	−1.66504	−0.112257
$221$	−7.19809	−0.484196
$222$	2.93443	0.196946
$223$	−10.4272	−0.698254	−0.349127	−	0.937075i	$-0.613522\pi$
$223$	−10.4272	−0.698254	−0.349127	+	0.937075i	$0.613522\pi$
$224$	−6.72202	−0.449134
$225$	4.18720	0.279147
$226$	10.3695	0.689767
$227$	−5.79010	−0.384302	−0.192151	−	0.981365i	$-0.561546\pi$
$227$	−5.79010	−0.384302	−0.192151	+	0.981365i	$0.561546\pi$
$228$	9.66917	0.640356
$229$	2.61873	0.173051	0.0865254	−	0.996250i	$-0.472424\pi$
$229$	2.61873	0.173051	0.0865254	+	0.996250i	$0.472424\pi$
$230$	3.51778	0.231956
$231$	6.79032	0.446770
$232$	−0.289014	−0.0189747
$233$	−12.7545	−0.835577	−0.417789	−	0.908544i	$-0.637195\pi$
$233$	−12.7545	−0.835577	−0.417789	+	0.908544i	$0.637195\pi$
$234$	31.1625	2.03716
$235$	−12.2869	−0.801509
$236$	4.63995	0.302035
$237$	19.7747	1.28450
$238$	−1.46427	−0.0949146
$239$	4.89362	0.316542	0.158271	−	0.987396i	$-0.449408\pi$
$239$	4.89362	0.316542	0.158271	+	0.987396i	$0.449408\pi$
$240$	−3.40817	−0.219997
$241$	20.0151	1.28929	0.644643	−	0.764484i	$-0.277006\pi$
$241$	20.0151	1.28929	0.644643	+	0.764484i	$0.277006\pi$
$242$	8.06610	0.518508
$243$	−20.3495	−1.30542
$244$	2.47050	0.158158
$245$	−4.99432	−0.319076
$246$	7.15121	0.455945
$247$	27.8857	1.77433
$248$	−23.5679	−1.49657
$249$	−31.9254	−2.02319
$250$	−1.03393	−0.0653915
$251$	11.4084	0.720089	0.360044	−	0.932935i	$-0.382762\pi$
$251$	11.4084	0.720089	0.360044	+	0.932935i	$0.382762\pi$
$252$	−5.52076	−0.347775
$253$	−6.08497	−0.382559
$254$	−13.4666	−0.844971
$255$	2.68090	0.167884
$256$	−16.7509	−1.04693
$257$	0.194424	0.0121278	0.00606392	−	0.999982i	$-0.498070\pi$
$257$	0.194424	0.0121278	0.00606392	+	0.999982i	$0.498070\pi$
$258$	2.90052	0.180578
$259$	−1.49928	−0.0931609
$260$	6.70134	0.415600
$261$	−0.399334	−0.0247182
$262$	2.39199	0.147778
$263$	−5.80169	−0.357747	−0.178874	−	0.983872i	$-0.557245\pi$
$263$	−5.80169	−0.357747	−0.178874	+	0.983872i	$0.557245\pi$
$264$	14.5300	0.894259
$265$	−1.00091	−0.0614857
$266$	5.67265	0.347813
$267$	−22.7417	−1.39177
$268$	−6.79188	−0.414880
$269$	4.27212	0.260476	0.130238	−	0.991483i	$-0.458426\pi$
$269$	4.27212	0.260476	0.130238	+	0.991483i	$0.458426\pi$
$270$	−3.29075	−0.200269
$271$	−21.2954	−1.29360	−0.646802	−	0.762658i	$-0.723894\pi$
$271$	−21.2954	−1.29360	−0.646802	+	0.762658i	$0.723894\pi$
$272$	−1.27128	−0.0770827
$273$	−27.3292	−1.65404
$274$	−8.62824	−0.521251
$275$	1.78846	0.107848
$276$	8.49185	0.511149
$277$	2.91626	0.175221	0.0876104	−	0.996155i	$-0.472077\pi$
$277$	2.91626	0.175221	0.0876104	+	0.996155i	$0.472077\pi$
$278$	−12.4530	−0.746882
$279$	−32.5642	−1.94957
$280$	4.29176	0.256482
$281$	−2.78504	−0.166141	−0.0830707	−	0.996544i	$-0.526473\pi$
$281$	−2.78504	−0.166141	−0.0830707	+	0.996544i	$0.526473\pi$
$282$	34.0575	2.02810
$283$	−0.246545	−0.0146556	−0.00732779	−	0.999973i	$-0.502333\pi$
$283$	−0.246545	−0.0146556	−0.00732779	+	0.999973i	$0.502333\pi$
$284$	0.930989	0.0552440
$285$	−10.3859	−0.615208
$286$	13.3103	0.787056
$287$	−3.65375	−0.215674
$288$	−19.8744	−1.17111
$289$	1.00000	0.0588235
$290$	0.0986062	0.00579035
$291$	47.2946	2.77246
$292$	−3.50577	−0.205160
$293$	7.91946	0.462660	0.231330	−	0.972875i	$-0.425692\pi$
$293$	7.91946	0.462660	0.231330	+	0.972875i	$0.425692\pi$
$294$	13.8436	0.807373
$295$	−4.98390	−0.290174
$296$	−3.20818	−0.186472
$297$	5.69226	0.330298
$298$	−5.62939	−0.326102
$299$	24.4904	1.41631
$300$	−2.49588	−0.144100
$301$	−1.48195	−0.0854184
$302$	−0.266667	−0.0153450
$303$	−1.04268	−0.0599005
$304$	4.92500	0.282468
$305$	−2.65363	−0.151946
$306$	−4.32927	−0.247488
$307$	24.2425	1.38359	0.691796	−	0.722093i	$-0.256820\pi$
$307$	24.2425	1.38359	0.691796	+	0.722093i	$0.256820\pi$
$308$	−2.35806	−0.134363
$309$	−25.1453	−1.43047
$310$	8.04095	0.456695
$311$	21.9148	1.24268	0.621338	−	0.783543i	$-0.286589\pi$
$311$	21.9148	1.24268	0.621338	+	0.783543i	$0.286589\pi$
$312$	−58.4793	−3.31074
$313$	9.83369	0.555833	0.277916	−	0.960605i	$-0.410356\pi$
$313$	9.83369	0.555833	0.277916	+	0.960605i	$0.410356\pi$
$314$	6.77225	0.382180
$315$	5.92999	0.334117
$316$	−6.86711	−0.386305
$317$	33.1705	1.86304	0.931520	−	0.363690i	$-0.118483\pi$
$317$	33.1705	1.86304	0.931520	+	0.363690i	$0.118483\pi$
$318$	2.77439	0.155580
$319$	−0.170566	−0.00954988
$320$	7.45007	0.416471
$321$	−1.57303	−0.0877980
$322$	4.98195	0.277633
$323$	−3.87404	−0.215558
$324$	3.75091	0.208384
$325$	−7.19809	−0.399278
$326$	−21.6120	−1.19698
$327$	−31.2251	−1.72675
$328$	−7.81833	−0.431695
$329$	−17.4009	−0.959344
$330$	−4.95737	−0.272894
$331$	24.3007	1.33569	0.667845	−	0.744300i	$-0.267217\pi$
$331$	24.3007	1.33569	0.667845	+	0.744300i	$0.267217\pi$
$332$	11.0867	0.608460
$333$	−4.43279	−0.242915
$334$	−16.1018	−0.881051
$335$	7.29534	0.398587
$336$	−4.82672	−0.263319
$337$	9.44868	0.514703	0.257351	−	0.966318i	$-0.417150\pi$
$337$	9.44868	0.514703	0.257351	+	0.966318i	$0.417150\pi$
$338$	−40.1294	−2.18275
$339$	−26.8872	−1.46031
$340$	−0.930989	−0.0504900
$341$	−13.9090	−0.753216
$342$	16.7718	0.906915
$343$	−16.9866	−0.917189
$344$	−3.17110	−0.170974
$345$	−9.12132	−0.491076
$346$	12.4242	0.667929
$347$	−19.3515	−1.03884	−0.519420	−	0.854519i	$-0.673852\pi$
$347$	−19.3515	−1.03884	−0.519420	+	0.854519i	$0.673852\pi$
$348$	0.238033	0.0127599
$349$	−15.4216	−0.825498	−0.412749	−	0.910845i	$-0.635431\pi$
$349$	−15.4216	−0.825498	−0.412749	+	0.910845i	$0.635431\pi$
$350$	−1.46427	−0.0782686
$351$	−22.9098	−1.22283
$352$	−8.48887	−0.452458
$353$	−23.8492	−1.26936	−0.634682	−	0.772773i	$-0.718869\pi$
$353$	−23.8492	−1.26936	−0.634682	+	0.772773i	$0.718869\pi$
$354$	13.8147	0.734241
$355$	−1.00000	−0.0530745
$356$	7.89746	0.418564
$357$	3.79673	0.200944
$358$	−17.7626	−0.938783
$359$	−15.1953	−0.801975	−0.400988	−	0.916083i	$-0.631333\pi$
$359$	−15.1953	−0.801975	−0.400988	+	0.916083i	$0.631333\pi$
$360$	12.6890	0.668772
$361$	−3.99178	−0.210093
$362$	13.5240	0.710807
$363$	−20.9147	−1.09774
$364$	9.49057	0.497441
$365$	3.76564	0.197103
$366$	7.35548	0.384477
$367$	−32.1556	−1.67851	−0.839255	−	0.543738i	$-0.817008\pi$
$367$	−32.1556	−1.67851	−0.839255	+	0.543738i	$0.817008\pi$
$368$	4.32533	0.225474
$369$	−10.8027	−0.562367
$370$	1.09457	0.0569041
$371$	−1.41751	−0.0735937
$372$	19.4107	1.00640
$373$	−7.98223	−0.413304	−0.206652	−	0.978414i	$-0.566257\pi$
$373$	−7.98223	−0.413304	−0.206652	+	0.978414i	$0.566257\pi$
$374$	−1.84915	−0.0956171
$375$	2.68090	0.138441
$376$	−37.2347	−1.92023
$377$	0.686484	0.0353557
$378$	−4.66043	−0.239706
$379$	−30.9129	−1.58789	−0.793944	−	0.607991i	$-0.791976\pi$
$379$	−30.9129	−1.58789	−0.793944	+	0.607991i	$0.791976\pi$
$380$	3.60669	0.185019
$381$	34.9178	1.78890
$382$	−20.7427	−1.06129
$383$	−17.0361	−0.870504	−0.435252	−	0.900309i	$-0.643341\pi$
$383$	−17.0361	−0.870504	−0.435252	+	0.900309i	$0.643341\pi$
$384$	4.79899	0.244897
$385$	2.53286	0.129086
$386$	0.0701448	0.00357028
$387$	−4.38155	−0.222727
$388$	−16.4239	−0.833796
$389$	−12.0828	−0.612620	−0.306310	−	0.951932i	$-0.599094\pi$
$389$	−12.0828	−0.612620	−0.306310	+	0.951932i	$0.599094\pi$
$390$	19.9521	1.01031
$391$	−3.40234	−0.172064
$392$	−15.1350	−0.764432
$393$	−6.20224	−0.312862
$394$	−0.439653	−0.0221494
$395$	7.37615	0.371134
$396$	−6.97186	−0.350349
$397$	−2.26728	−0.113791	−0.0568957	−	0.998380i	$-0.518120\pi$
$397$	−2.26728	−0.113791	−0.0568957	+	0.998380i	$0.518120\pi$
$398$	−14.4466	−0.724141
$399$	−14.7087	−0.736357
$400$	−1.27128	−0.0635641
$401$	21.3985	1.06859	0.534295	−	0.845298i	$-0.320577\pi$
$401$	21.3985	1.06859	0.534295	+	0.845298i	$0.320577\pi$
$402$	−20.2217	−1.00856
$403$	55.9801	2.78857
$404$	0.362090	0.0180146
$405$	−4.02895	−0.200200
$406$	0.139648	0.00693061
$407$	−1.89336	−0.0938504
$408$	8.12429	0.402212
$409$	−21.9000	−1.08288	−0.541442	−	0.840738i	$-0.682122\pi$
$409$	−21.9000	−1.08288	−0.541442	+	0.840738i	$0.682122\pi$
$410$	2.66747	0.131737
$411$	22.3723	1.10355
$412$	8.73215	0.430202
$413$	−7.05829	−0.347316
$414$	14.7297	0.723924
$415$	−11.9085	−0.584565
$416$	34.1654	1.67510
$417$	32.2897	1.58123
$418$	7.16368	0.350387
$419$	−8.28162	−0.404583	−0.202292	−	0.979325i	$-0.564839\pi$
$419$	−8.28162	−0.404583	−0.202292	+	0.979325i	$0.564839\pi$
$420$	−3.53472	−0.172477
$421$	12.3081	0.599858	0.299929	−	0.953961i	$-0.403037\pi$
$421$	12.3081	0.599858	0.299929	+	0.953961i	$0.403037\pi$
$422$	13.3267	0.648732
$423$	−51.4477	−2.50147
$424$	−3.03321	−0.147306
$425$	1.00000	0.0485071
$426$	2.77186	0.134297
$427$	−3.75812	−0.181868
$428$	0.546263	0.0264046
$429$	−34.5126	−1.66628
$430$	1.08192	0.0521749
$431$	0.626242	0.0301650	0.0150825	−	0.999886i	$-0.495199\pi$
$431$	0.626242	0.0301650	0.0150825	+	0.999886i	$0.495199\pi$
$432$	−4.04619	−0.194672
$433$	26.6717	1.28176	0.640881	−	0.767640i	$-0.278569\pi$
$433$	26.6717	1.28176	0.640881	+	0.767640i	$0.278569\pi$
$434$	11.3877	0.546629
$435$	−0.255678	−0.0122588
$436$	10.8435	0.519308
$437$	13.1808	0.630524
$438$	−10.4378	−0.498739
$439$	−4.80489	−0.229325	−0.114662	−	0.993405i	$-0.536579\pi$
$439$	−4.80489	−0.229325	−0.114662	+	0.993405i	$0.536579\pi$
$440$	5.41983	0.258380
$441$	−20.9122	−0.995821
$442$	7.44232	0.353995
$443$	−25.4836	−1.21076	−0.605380	−	0.795936i	$-0.706979\pi$
$443$	−25.4836	−1.21076	−0.605380	+	0.795936i	$0.706979\pi$
$444$	2.64227	0.125397
$445$	−8.48287	−0.402126
$446$	10.7809	0.510493
$447$	14.5965	0.690393
$448$	10.5509	0.498484
$449$	19.5067	0.920578	0.460289	−	0.887769i	$-0.347746\pi$
$449$	19.5067	0.920578	0.460289	+	0.887769i	$0.347746\pi$
$450$	−4.32927	−0.204084
$451$	−4.61412	−0.217271
$452$	9.33706	0.439178
$453$	0.691446	0.0324870
$454$	5.98655	0.280963
$455$	−10.1941	−0.477905
$456$	−31.4738	−1.47390
$457$	6.45913	0.302145	0.151073	−	0.988523i	$-0.451727\pi$
$457$	6.45913	0.302145	0.151073	+	0.988523i	$0.451727\pi$
$458$	−2.70759	−0.126517
$459$	3.18276	0.148559
$460$	3.16754	0.147687
$461$	−1.15607	−0.0538437	−0.0269218	−	0.999638i	$-0.508571\pi$
$461$	−1.15607	−0.0538437	−0.0269218	+	0.999638i	$0.508571\pi$
$462$	−7.02072	−0.326633
$463$	−36.8347	−1.71185	−0.855926	−	0.517098i	$-0.827012\pi$
$463$	−36.8347	−1.71185	−0.855926	+	0.517098i	$0.827012\pi$
$464$	0.121242	0.00562854
$465$	−20.8495	−0.966874
$466$	13.1873	0.610890
$467$	2.43831	0.112832	0.0564158	−	0.998407i	$-0.482033\pi$
$467$	2.43831	0.112832	0.0564158	+	0.998407i	$0.482033\pi$
$468$	28.0599	1.29707
$469$	10.3318	0.477078
$470$	12.7038	0.585982
$471$	−17.5599	−0.809118
$472$	−15.1034	−0.695190
$473$	−1.87148	−0.0860506
$474$	−20.4456	−0.939099
$475$	−3.87404	−0.177753
$476$	−1.31848	−0.0604326
$477$	−4.19103	−0.191894
$478$	−5.05966	−0.231423
$479$	25.3999	1.16055	0.580275	−	0.814421i	$-0.302945\pi$
$479$	25.3999	1.16055	0.580275	+	0.814421i	$0.302945\pi$
$480$	−12.7248	−0.580803
$481$	7.62027	0.347454
$482$	−20.6942	−0.942595
$483$	−12.9178	−0.587780
$484$	7.26301	0.330137
$485$	17.6413	0.801051
$486$	21.0399	0.954391
$487$	−35.9026	−1.62690	−0.813451	−	0.581633i	$-0.802414\pi$
$487$	−35.9026	−1.62690	−0.813451	+	0.581633i	$0.802414\pi$
$488$	−8.04166	−0.364029
$489$	56.0382	2.53414
$490$	5.16378	0.233276
$491$	21.5881	0.974258	0.487129	−	0.873330i	$-0.338044\pi$
$491$	21.5881	0.974258	0.487129	+	0.873330i	$0.338044\pi$
$492$	6.43922	0.290302
$493$	−0.0953703	−0.00429526
$494$	−28.8319	−1.29721
$495$	7.48866	0.336590
$496$	9.88685	0.443933
$497$	−1.41622	−0.0635261
$498$	33.0086	1.47915
$499$	−16.3518	−0.732006	−0.366003	−	0.930614i	$-0.619274\pi$
$499$	−16.3518	−0.732006	−0.366003	+	0.930614i	$0.619274\pi$
$500$	−0.930989	−0.0416351
$501$	41.7506	1.86528
$502$	−11.7954	−0.526456
$503$	13.6410	0.608222	0.304111	−	0.952637i	$-0.401641\pi$
$503$	13.6410	0.608222	0.304111	+	0.952637i	$0.401641\pi$
$504$	17.9705	0.800468
$505$	−0.388930	−0.0173072
$506$	6.29143	0.279688
$507$	104.052	4.62112
$508$	−12.1258	−0.537997
$509$	15.7102	0.696341	0.348171	−	0.937431i	$-0.386803\pi$
$509$	15.7102	0.696341	0.348171	+	0.937431i	$0.386803\pi$
$510$	−2.77186	−0.122740
$511$	5.33298	0.235917
$512$	13.7392	0.607191
$513$	−12.3302	−0.544390
$514$	−0.201021	−0.00886665
$515$	−9.37944	−0.413307
$516$	2.61173	0.114975
$517$	−21.9747	−0.966445
$518$	1.55015	0.0681098
$519$	−32.2149	−1.41408
$520$	−21.8134	−0.956579
$521$	−11.2603	−0.493322	−0.246661	−	0.969102i	$-0.579333\pi$
$521$	−11.2603	−0.493322	−0.246661	+	0.969102i	$0.579333\pi$
$522$	0.412884	0.0180714
$523$	2.42744	0.106145	0.0530724	−	0.998591i	$-0.483099\pi$
$523$	2.42744	0.106145	0.0530724	+	0.998591i	$0.483099\pi$
$524$	2.15384	0.0940909
$525$	3.79673	0.165703
$526$	5.99854	0.261549
$527$	−7.77708	−0.338775
$528$	−6.09539	−0.265268
$529$	−11.4241	−0.496699
$530$	1.03488	0.0449521
$531$	−20.8686	−0.905619
$532$	5.10787	0.221454
$533$	18.5706	0.804382
$534$	23.5133	1.01752
$535$	−0.586756	−0.0253677
$536$	22.1081	0.954924
$537$	46.0570	1.98751
$538$	−4.41707	−0.190434
$539$	−8.93217	−0.384736
$540$	−2.96312	−0.127512
$541$	−13.6514	−0.586919	−0.293459	−	0.955972i	$-0.594807\pi$
$541$	−13.6514	−0.586919	−0.293459	+	0.955972i	$0.594807\pi$
$542$	22.0179	0.945752
$543$	−35.0667	−1.50486
$544$	−4.74646	−0.203503
$545$	−11.6473	−0.498914
$546$	28.2565	1.20927
$547$	24.6845	1.05543	0.527717	−	0.849420i	$-0.323048\pi$
$547$	24.6845	1.05543	0.527717	+	0.849420i	$0.323048\pi$
$548$	−7.76919	−0.331883
$549$	−11.1113	−0.474218
$550$	−1.84915	−0.0788479
$551$	0.369469	0.0157399
$552$	−27.6416	−1.17650
$553$	10.4462	0.444219
$554$	−3.01520	−0.128104
$555$	−2.83813	−0.120472
$556$	−11.2132	−0.475544
$557$	−9.35023	−0.396182	−0.198091	−	0.980184i	$-0.563474\pi$
$557$	−9.35023	−0.396182	−0.198091	+	0.980184i	$0.563474\pi$
$558$	33.6691	1.42533
$559$	7.53220	0.318578
$560$	−1.80041	−0.0760813
$561$	4.79469	0.202432
$562$	2.87953	0.121466
$563$	−31.7834	−1.33951	−0.669755	−	0.742582i	$-0.733601\pi$
$563$	−31.7834	−1.33951	−0.669755	+	0.742582i	$0.733601\pi$
$564$	30.6667	1.29130
$565$	−10.0292	−0.421931
$566$	0.254910	0.0107147
$567$	−5.70587	−0.239624
$568$	−3.03044	−0.127154
$569$	27.1281	1.13727	0.568634	−	0.822590i	$-0.307472\pi$
$569$	27.1281	1.13727	0.568634	+	0.822590i	$0.307472\pi$
$570$	10.7383	0.449778
$571$	−7.70329	−0.322373	−0.161186	−	0.986924i	$-0.551532\pi$
$571$	−7.70329	−0.322373	−0.161186	+	0.986924i	$0.551532\pi$
$572$	11.9851	0.501123
$573$	53.7842	2.24687
$574$	3.77772	0.157679
$575$	−3.40234	−0.141887
$576$	31.1949	1.29979
$577$	−2.28179	−0.0949921	−0.0474960	−	0.998871i	$-0.515124\pi$
$577$	−2.28179	−0.0949921	−0.0474960	+	0.998871i	$0.515124\pi$
$578$	−1.03393	−0.0430058
$579$	−0.181880	−0.00755867
$580$	0.0887887	0.00368675
$581$	−16.8650	−0.699679
$582$	−48.8993	−2.02694
$583$	−1.79010	−0.0741384
$584$	11.4115	0.472213
$585$	−30.1398	−1.24613
$586$	−8.18816	−0.338250
$587$	−26.1346	−1.07869	−0.539345	−	0.842085i	$-0.681328\pi$
$587$	−26.1346	−1.07869	−0.539345	+	0.842085i	$0.681328\pi$
$588$	12.4653	0.514059
$589$	30.1287	1.24143
$590$	5.15300	0.212146
$591$	1.13998	0.0468927
$592$	1.34584	0.0553138
$593$	21.6579	0.889383	0.444692	−	0.895684i	$-0.353313\pi$
$593$	21.6579	0.889383	0.444692	+	0.895684i	$0.353313\pi$
$594$	−5.88539	−0.241481
$595$	1.41622	0.0580593
$596$	−5.06891	−0.207631
$597$	37.4588	1.53308
$598$	−25.3213	−1.03547
$599$	−20.7988	−0.849817	−0.424908	−	0.905236i	$-0.639694\pi$
$599$	−20.7988	−0.849817	−0.424908	+	0.905236i	$0.639694\pi$
$600$	8.12429	0.331673
$601$	5.36559	0.218867	0.109433	−	0.993994i	$-0.465096\pi$
$601$	5.36559	0.218867	0.109433	+	0.993994i	$0.465096\pi$
$602$	1.53224	0.0624493
$603$	30.5471	1.24397
$604$	−0.240117	−0.00977023
$605$	−7.80140	−0.317172
$606$	1.07806	0.0437932
$607$	−17.0754	−0.693069	−0.346534	−	0.938037i	$-0.612642\pi$
$607$	−17.0754	−0.693069	−0.346534	+	0.938037i	$0.612642\pi$
$608$	18.3880	0.745732
$609$	−0.362096	−0.0146729
$610$	2.74367	0.111088
$611$	88.4422	3.57799
$612$	−3.89824	−0.157577
$613$	−41.2459	−1.66591	−0.832953	−	0.553344i	$-0.813352\pi$
$613$	−41.2459	−1.66591	−0.832953	+	0.553344i	$0.813352\pi$
$614$	−25.0650	−1.01154
$615$	−6.91654	−0.278902
$616$	7.67566	0.309261
$617$	13.0255	0.524386	0.262193	−	0.965015i	$-0.415554\pi$
$617$	13.0255	0.524386	0.262193	+	0.965015i	$0.415554\pi$
$618$	25.9985	1.04581
$619$	21.1174	0.848780	0.424390	−	0.905479i	$-0.360489\pi$
$619$	21.1174	0.848780	0.424390	+	0.905479i	$0.360489\pi$
$620$	7.24037	0.290780
$621$	−10.8288	−0.434547
$622$	−22.6584	−0.908519
$623$	−12.0136	−0.481314
$624$	24.5323	0.982079
$625$	1.00000	0.0400000
$626$	−10.1673	−0.406369
$627$	−18.5748	−0.741807
$628$	6.09799	0.243336
$629$	−1.05865	−0.0422112
$630$	−6.13120	−0.244273
$631$	−31.5985	−1.25792	−0.628958	−	0.777439i	$-0.716518\pi$
$631$	−31.5985	−1.25792	−0.628958	+	0.777439i	$0.716518\pi$
$632$	22.3530	0.889153
$633$	−34.5550	−1.37344
$634$	−34.2960	−1.36207
$635$	13.0247	0.516869
$636$	2.49817	0.0990588
$637$	35.9496	1.42437
$638$	0.176354	0.00698191
$639$	−4.18720	−0.165643
$640$	1.79007	0.0707587
$641$	−43.4454	−1.71599	−0.857995	−	0.513658i	$-0.828290\pi$
$641$	−43.4454	−1.71599	−0.857995	+	0.513658i	$0.828290\pi$
$642$	1.62640	0.0641890
$643$	0.506772	0.0199851	0.00999257	−	0.999950i	$-0.496819\pi$
$643$	0.506772	0.0199851	0.00999257	+	0.999950i	$0.496819\pi$
$644$	4.48593	0.176771
$645$	−2.80533	−0.110460
$646$	4.00549	0.157594
$647$	22.0882	0.868377	0.434189	−	0.900822i	$-0.357035\pi$
$647$	22.0882	0.868377	0.434189	+	0.900822i	$0.357035\pi$
$648$	−12.2095	−0.479634
$649$	−8.91352	−0.349886
$650$	7.44232	0.291912
$651$	−29.5275	−1.15727
$652$	−19.4603	−0.762123
$653$	−8.94988	−0.350236	−0.175118	−	0.984547i	$-0.556031\pi$
$653$	−8.94988	−0.350236	−0.175118	+	0.984547i	$0.556031\pi$
$654$	32.2846	1.26243
$655$	−2.31350	−0.0903958
$656$	3.27982	0.128056
$657$	15.7675	0.615149
$658$	17.9913	0.701375
$659$	−17.3104	−0.674318	−0.337159	−	0.941448i	$-0.609466\pi$
$659$	−17.3104	−0.674318	−0.337159	+	0.941448i	$0.609466\pi$
$660$	−4.46380	−0.173753
$661$	29.1609	1.13423	0.567114	−	0.823639i	$-0.308060\pi$
$661$	29.1609	1.13423	0.567114	+	0.823639i	$0.308060\pi$
$662$	−25.1253	−0.976521
$663$	−19.2973	−0.749446
$664$	−36.0879	−1.40048
$665$	−5.48649	−0.212757
$666$	4.58319	0.177595
$667$	0.324482	0.0125640
$668$	−14.4987	−0.560970
$669$	−27.9541	−1.08077
$670$	−7.54287	−0.291407
$671$	−4.74592	−0.183214
$672$	−18.0210	−0.695177
$673$	9.79781	0.377678	0.188839	−	0.982008i	$-0.439528\pi$
$673$	9.79781	0.377678	0.188839	+	0.982008i	$0.439528\pi$
$674$	−9.76927	−0.376298
$675$	3.18276	0.122505
$676$	−36.1340	−1.38977
$677$	39.2817	1.50972	0.754859	−	0.655887i	$-0.227705\pi$
$677$	39.2817	1.50972	0.754859	+	0.655887i	$0.227705\pi$
$678$	27.7995	1.06763
$679$	24.9840	0.958797
$680$	3.03044	0.116212
$681$	−15.5226	−0.594829
$682$	14.3810	0.550675
$683$	−8.34624	−0.319360	−0.159680	−	0.987169i	$-0.551046\pi$
$683$	−8.34624	−0.319360	−0.159680	+	0.987169i	$0.551046\pi$
$684$	15.1020	0.577438
$685$	8.34510	0.318850
$686$	17.5629	0.670556
$687$	7.02055	0.267851
$688$	1.33029	0.0507168
$689$	7.20467	0.274476
$690$	9.43081	0.359025
$691$	10.5208	0.400231	0.200115	−	0.979772i	$-0.435868\pi$
$691$	10.5208	0.400231	0.200115	+	0.979772i	$0.435868\pi$
$692$	11.1872	0.425274
$693$	10.6056	0.402873
$694$	20.0080	0.759495
$695$	12.0444	0.456868
$696$	−0.774815	−0.0293693
$697$	−2.57994	−0.0977220
$698$	15.9448	0.603521
$699$	−34.1936	−1.29332
$700$	−1.31848	−0.0498340
$701$	−20.1890	−0.762530	−0.381265	−	0.924466i	$-0.624511\pi$
$701$	−20.1890	−0.762530	−0.381265	+	0.924466i	$0.624511\pi$
$702$	23.6871	0.894013
$703$	4.10126	0.154682
$704$	13.3242	0.502174
$705$	−32.9399	−1.24059
$706$	24.6584	0.928030
$707$	−0.550810	−0.0207154
$708$	12.4392	0.467495
$709$	−18.4674	−0.693557	−0.346778	−	0.937947i	$-0.612724\pi$
$709$	−18.4674	−0.693557	−0.346778	+	0.937947i	$0.612724\pi$
$710$	1.03393	0.0388027
$711$	30.8854	1.15829
$712$	−25.7068	−0.963403
$713$	26.4603	0.990945
$714$	−3.92556	−0.146910
$715$	−12.8735	−0.481442
$716$	−15.9941	−0.597728
$717$	13.1193	0.489948
$718$	15.7108	0.586323
$719$	−24.2155	−0.903084	−0.451542	−	0.892250i	$-0.649126\pi$
$719$	−24.2155	−0.903084	−0.451542	+	0.892250i	$0.649126\pi$
$720$	−5.32311	−0.198381
$721$	−13.2833	−0.494697
$722$	4.12722	0.153599
$723$	53.6584	1.99558
$724$	12.1775	0.452575
$725$	−0.0953703	−0.00354196
$726$	21.6244	0.802555
$727$	11.4721	0.425475	0.212738	−	0.977109i	$-0.431762\pi$
$727$	11.4721	0.425475	0.212738	+	0.977109i	$0.431762\pi$
$728$	−30.8925	−1.14495
$729$	−42.4680	−1.57289
$730$	−3.89341	−0.144102
$731$	−1.04642	−0.0387031
$732$	6.62315	0.244799
$733$	39.1741	1.44693	0.723465	−	0.690361i	$-0.242548\pi$
$733$	39.1741	1.44693	0.723465	+	0.690361i	$0.242548\pi$
$734$	33.2467	1.22716
$735$	−13.3893	−0.493870
$736$	16.1491	0.595263
$737$	13.0475	0.480609
$738$	11.1692	0.411146
$739$	−9.70742	−0.357093	−0.178547	−	0.983931i	$-0.557140\pi$
$739$	−9.70742	−0.357093	−0.178547	+	0.983931i	$0.557140\pi$
$740$	0.985593	0.0362311
$741$	74.7587	2.74633
$742$	1.46561	0.0538043
$743$	−1.89747	−0.0696114	−0.0348057	−	0.999394i	$-0.511081\pi$
$743$	−1.89747	−0.0696114	−0.0348057	+	0.999394i	$0.511081\pi$
$744$	−63.1832	−2.31641
$745$	5.44465	0.199477
$746$	8.25307	0.302166
$747$	−49.8632	−1.82440
$748$	−1.66504	−0.0608799
$749$	−0.830975	−0.0303632
$750$	−2.77186	−0.101214
$751$	−11.1154	−0.405608	−0.202804	−	0.979219i	$-0.565005\pi$
$751$	−11.1154	−0.405608	−0.202804	+	0.979219i	$0.565005\pi$
$752$	15.6201	0.569606
$753$	30.5846	1.11457
$754$	−0.709776	−0.0258485
$755$	0.257916	0.00938653
$756$	−4.19642	−0.152622
$757$	14.7445	0.535899	0.267950	−	0.963433i	$-0.413654\pi$
$757$	14.7445	0.535899	0.267950	+	0.963433i	$0.413654\pi$
$758$	31.9617	1.16090
$759$	−16.3132	−0.592130
$760$	−11.7400	−0.425856
$761$	4.48970	0.162752	0.0813758	−	0.996683i	$-0.474069\pi$
$761$	4.48970	0.162752	0.0813758	+	0.996683i	$0.474069\pi$
$762$	−36.1026	−1.30786
$763$	−16.4951	−0.597162
$764$	−18.6775	−0.675730
$765$	4.18720	0.151389
$766$	17.6141	0.636425
$767$	35.8745	1.29535
$768$	−44.9075	−1.62046
$769$	9.52790	0.343585	0.171792	−	0.985133i	$-0.445044\pi$
$769$	9.52790	0.343585	0.171792	+	0.985133i	$0.445044\pi$
$770$	−2.61880	−0.0943749
$771$	0.521231	0.0187717
$772$	0.0631610	0.00227321
$773$	−3.21748	−0.115725	−0.0578624	−	0.998325i	$-0.518428\pi$
$773$	−3.21748	−0.115725	−0.0578624	+	0.998325i	$0.518428\pi$
$774$	4.53022	0.162835
$775$	−7.77708	−0.279361
$776$	53.4609	1.91914
$777$	−4.01942	−0.144196
$778$	12.4927	0.447886
$779$	9.99479	0.358100
$780$	17.9656	0.643272
$781$	−1.78846	−0.0639963
$782$	3.51778	0.125796
$783$	−0.303541	−0.0108477
$784$	6.34919	0.226757
$785$	−6.55001	−0.233780
$786$	6.41268	0.228733
$787$	28.6199	1.02019	0.510094	−	0.860119i	$-0.329611\pi$
$787$	28.6199	1.02019	0.510094	+	0.860119i	$0.329611\pi$
$788$	−0.395880	−0.0141026
$789$	−15.5537	−0.553727
$790$	−7.62642	−0.271336
$791$	−14.2035	−0.505019
$792$	22.6939	0.806393
$793$	19.1011	0.678298
$794$	2.34420	0.0831927
$795$	−2.68335	−0.0951686
$796$	−13.0082	−0.461064
$797$	−10.9180	−0.386734	−0.193367	−	0.981127i	$-0.561941\pi$
$797$	−10.9180	−0.386734	−0.193367	+	0.981127i	$0.561941\pi$
$798$	15.2078	0.538350
$799$	−12.2869	−0.434679
$800$	−4.74646	−0.167813
$801$	−35.5195	−1.25502
$802$	−22.1245	−0.781245
$803$	6.73472	0.237663
$804$	−18.2083	−0.642158
$805$	−4.81846	−0.169828
$806$	−57.8795	−2.03872
$807$	11.4531	0.403168
$808$	−1.17863	−0.0414640
$809$	−48.3301	−1.69920	−0.849598	−	0.527431i	$-0.823155\pi$
$809$	−48.3301	−1.69920	−0.849598	+	0.527431i	$0.823155\pi$
$810$	4.16565	0.146366
$811$	−44.8056	−1.57334	−0.786669	−	0.617375i	$-0.788196\pi$
$811$	−44.8056	−1.57334	−0.786669	+	0.617375i	$0.788196\pi$
$812$	0.125744	0.00441276
$813$	−57.0907	−2.00226
$814$	1.95760	0.0686139
$815$	20.9028	0.732193
$816$	−3.40817	−0.119310
$817$	4.05386	0.141827
$818$	22.6430	0.791696
$819$	−42.6846	−1.49152
$820$	2.40189	0.0838777
$821$	7.55058	0.263517	0.131759	−	0.991282i	$-0.457938\pi$
$821$	7.55058	0.263517	0.131759	+	0.991282i	$0.457938\pi$
$822$	−23.1314	−0.806801
$823$	26.0807	0.909116	0.454558	−	0.890717i	$-0.349797\pi$
$823$	26.0807	0.909116	0.454558	+	0.890717i	$0.349797\pi$
$824$	−28.4238	−0.990190
$825$	4.79469	0.166930
$826$	7.29777	0.253922
$827$	−7.67719	−0.266962	−0.133481	−	0.991051i	$-0.542616\pi$
$827$	−7.67719	−0.266962	−0.133481	+	0.991051i	$0.542616\pi$
$828$	13.2631	0.460926
$829$	0.0911866	0.00316704	0.00158352	−	0.999999i	$-0.499496\pi$
$829$	0.0911866	0.00316704	0.00158352	+	0.999999i	$0.499496\pi$
$830$	12.3125	0.427375
$831$	7.81818	0.271210
$832$	−53.6262	−1.85916
$833$	−4.99432	−0.173043
$834$	−33.3852	−1.15604
$835$	15.5734	0.538940
$836$	6.45044	0.223093
$837$	−24.7526	−0.855574
$838$	8.56261	0.295790
$839$	−37.4560	−1.29312	−0.646562	−	0.762862i	$-0.723794\pi$
$839$	−37.4560	−1.29312	−0.646562	+	0.762862i	$0.723794\pi$
$840$	11.5058	0.396987
$841$	−28.9909	−0.999686
$842$	−12.7257	−0.438556
$843$	−7.46639	−0.257156
$844$	11.9998	0.413051
$845$	38.8125	1.33519
$846$	53.1933	1.82882
$847$	−11.0485	−0.379630
$848$	1.27244	0.0436959
$849$	−0.660962	−0.0226841
$850$	−1.03393	−0.0354635
$851$	3.60189	0.123471
$852$	2.49588	0.0855076
$853$	6.24773	0.213918	0.106959	−	0.994263i	$-0.465889\pi$
$853$	6.24773	0.213918	0.106959	+	0.994263i	$0.465889\pi$
$854$	3.88563	0.132964
$855$	−16.2214	−0.554760
$856$	−1.77813	−0.0607751
$857$	−16.9567	−0.579228	−0.289614	−	0.957143i	$-0.593527\pi$
$857$	−16.9567	−0.579228	−0.289614	+	0.957143i	$0.593527\pi$
$858$	35.6836	1.21822
$859$	−51.1944	−1.74673	−0.873366	−	0.487065i	$-0.838068\pi$
$859$	−51.1944	−1.74673	−0.873366	+	0.487065i	$0.838068\pi$
$860$	0.974202	0.0332200
$861$	−9.79533	−0.333824
$862$	−0.647490	−0.0220536
$863$	35.4505	1.20675	0.603374	−	0.797458i	$-0.293823\pi$
$863$	35.4505	1.20675	0.603374	+	0.797458i	$0.293823\pi$
$864$	−15.1069	−0.513945
$865$	−12.0165	−0.408573
$866$	−27.5767	−0.937095
$867$	2.68090	0.0910480
$868$	10.2540	0.348042
$869$	13.1920	0.447507
$870$	0.264353	0.00896240
$871$	−52.5125	−1.77932
$872$	−35.2963	−1.19528
$873$	73.8678	2.50005
$874$	−13.6280	−0.460976
$875$	1.41622	0.0478769
$876$	−9.39861	−0.317550
$877$	−28.3882	−0.958602	−0.479301	−	0.877651i	$-0.659110\pi$
$877$	−28.3882	−0.958602	−0.479301	+	0.877651i	$0.659110\pi$
$878$	4.96792	0.167659
$879$	21.2312	0.716112
$880$	−2.27364	−0.0766444
$881$	−42.8481	−1.44359	−0.721795	−	0.692107i	$-0.756683\pi$
$881$	−42.8481	−1.44359	−0.721795	+	0.692107i	$0.756683\pi$
$882$	21.6218	0.728044
$883$	19.0481	0.641018	0.320509	−	0.947245i	$-0.396146\pi$
$883$	19.0481	0.641018	0.320509	+	0.947245i	$0.396146\pi$
$884$	6.70134	0.225391
$885$	−13.3613	−0.449135
$886$	26.3482	0.885186
$887$	10.2621	0.344567	0.172283	−	0.985047i	$-0.444886\pi$
$887$	10.2621	0.344567	0.172283	+	0.985047i	$0.444886\pi$
$888$	−8.60079	−0.288624
$889$	18.4458	0.618653
$890$	8.77069	0.293994
$891$	−7.20563	−0.241398
$892$	9.70757	0.325033
$893$	47.6000	1.59287
$894$	−15.0918	−0.504745
$895$	17.1797	0.574254
$896$	2.53513	0.0846928
$897$	65.6561	2.19219
$898$	−20.1686	−0.673034
$899$	0.741702	0.0247371
$900$	−3.89824	−0.129941
$901$	−1.00091	−0.0333453
$902$	4.77068	0.158846
$903$	−3.97296	−0.132212
$904$	−30.3928	−1.01085
$905$	−13.0802	−0.434801
$906$	−0.714907	−0.0237512
$907$	11.6524	0.386911	0.193456	−	0.981109i	$-0.438030\pi$
$907$	11.6524	0.386911	0.193456	+	0.981109i	$0.438030\pi$
$908$	5.39052	0.178891
$909$	−1.62853	−0.0540149
$910$	10.5400	0.349396
$911$	−19.8368	−0.657221	−0.328611	−	0.944465i	$-0.606580\pi$
$911$	−19.8368	−0.657221	−0.328611	+	0.944465i	$0.606580\pi$
$912$	13.2034	0.437209
$913$	−21.2979	−0.704858
$914$	−6.67829	−0.220898
$915$	−7.11410	−0.235185
$916$	−2.43801	−0.0805542
$917$	−3.27642	−0.108197
$918$	−3.29075	−0.108611
$919$	−24.1845	−0.797772	−0.398886	−	0.917001i	$-0.630603\pi$
$919$	−24.1845	−0.797772	−0.398886	+	0.917001i	$0.630603\pi$
$920$	−10.3106	−0.339930
$921$	64.9916	2.14155
$922$	1.19530	0.0393650
$923$	7.19809	0.236928
$924$	−6.32172	−0.207969
$925$	−1.05865	−0.0348082
$926$	38.0845	1.25153
$927$	−39.2736	−1.28991
$928$	0.452671	0.0148597
$929$	−3.16620	−0.103880	−0.0519398	−	0.998650i	$-0.516540\pi$
$929$	−3.16620	−0.103880	−0.0519398	+	0.998650i	$0.516540\pi$
$930$	21.5569	0.706880
$931$	19.3482	0.634113
$932$	11.8743	0.388957
$933$	58.7514	1.92343
$934$	−2.52104	−0.0824911
$935$	1.78846	0.0584890
$936$	−91.3369	−2.98544
$937$	21.6444	0.707091	0.353546	−	0.935417i	$-0.384976\pi$
$937$	21.6444	0.707091	0.353546	+	0.935417i	$0.384976\pi$
$938$	−10.6824	−0.348791
$939$	26.3631	0.860327
$940$	11.4390	0.373098
$941$	−31.8835	−1.03937	−0.519687	−	0.854357i	$-0.673951\pi$
$941$	−31.8835	−1.03937	−0.519687	+	0.854357i	$0.673951\pi$
$942$	18.1557	0.591545
$943$	8.77782	0.285845
$944$	6.33593	0.206217
$945$	4.50749	0.146629
$946$	1.93498	0.0629115
$947$	35.2195	1.14448	0.572239	−	0.820087i	$-0.306075\pi$
$947$	35.2195	1.14448	0.572239	+	0.820087i	$0.306075\pi$
$948$	−18.4100	−0.597929
$949$	−27.1054	−0.879880
$950$	4.00549	0.129955
$951$	88.9266	2.88364
$952$	4.29176	0.139097
$953$	32.6849	1.05877	0.529384	−	0.848382i	$-0.322423\pi$
$953$	32.6849	1.05877	0.529384	+	0.848382i	$0.322423\pi$
$954$	4.33323	0.140294
$955$	20.0620	0.649192
$956$	−4.55590	−0.147348
$957$	−0.457270	−0.0147815
$958$	−26.2617	−0.848476
$959$	11.8185	0.381639
$960$	19.9729	0.644621
$961$	29.4829	0.951061
$962$	−7.87882	−0.254023
$963$	−2.45686	−0.0791714
$964$	−18.6338	−0.600155
$965$	−0.0678429	−0.00218394
$966$	13.3561	0.429725
$967$	8.31302	0.267329	0.133664	−	0.991027i	$-0.457326\pi$
$967$	8.31302	0.267329	0.133664	+	0.991027i	$0.457326\pi$
$968$	−23.6416	−0.759871
$969$	−10.3859	−0.333643
$970$	−18.2399	−0.585648
$971$	7.36908	0.236485	0.118243	−	0.992985i	$-0.462274\pi$
$971$	7.36908	0.236485	0.118243	+	0.992985i	$0.462274\pi$
$972$	18.9451	0.607666
$973$	17.0574	0.546836
$974$	37.1208	1.18943
$975$	−19.2973	−0.618009
$976$	3.37351	0.107983
$977$	−30.6535	−0.980692	−0.490346	−	0.871528i	$-0.663130\pi$
$977$	−30.6535	−0.980692	−0.490346	+	0.871528i	$0.663130\pi$
$978$	−57.9396	−1.85270
$979$	−15.1713	−0.484877
$980$	4.64966	0.148528
$981$	−48.7694	−1.55709
$982$	−22.3206	−0.712279
$983$	−36.5090	−1.16446	−0.582228	−	0.813025i	$-0.697819\pi$
$983$	−36.5090	−1.16446	−0.582228	+	0.813025i	$0.697819\pi$
$984$	−20.9601	−0.668185
$985$	0.425225	0.0135488
$986$	0.0986062	0.00314026
$987$	−46.6501	−1.48489
$988$	−25.9613	−0.825939
$989$	3.56027	0.113210
$990$	−7.74275	−0.246081
$991$	−7.33711	−0.233071	−0.116536	−	0.993187i	$-0.537179\pi$
$991$	−7.33711	−0.233071	−0.116536	+	0.993187i	$0.537179\pi$
$992$	36.9136	1.17201
$993$	65.1478	2.06740
$994$	1.46427	0.0464438
$995$	13.9725	0.442957
$996$	29.7222	0.941784
$997$	21.5967	0.683973	0.341987	−	0.939705i	$-0.388900\pi$
$997$	21.5967	0.683973	0.341987	+	0.939705i	$0.388900\pi$
$998$	16.9066	0.535169
$999$	−3.36944	−0.106604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.13	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.03393 q^{2} +2.68090 q^{3} -0.930989 q^{4} +1.00000 q^{5} -2.77186 q^{6} +1.41622 q^{7} +3.03044 q^{8} +4.18720 q^{9} +O(q^{10})\)	\(q-1.03393 q^{2} +2.68090 q^{3} -0.930989 q^{4} +1.00000 q^{5} -2.77186 q^{6} +1.41622 q^{7} +3.03044 q^{8} +4.18720 q^{9} -1.03393 q^{10} +1.78846 q^{11} -2.49588 q^{12} -7.19809 q^{13} -1.46427 q^{14} +2.68090 q^{15} -1.27128 q^{16} +1.00000 q^{17} -4.32927 q^{18} -3.87404 q^{19} -0.930989 q^{20} +3.79673 q^{21} -1.84915 q^{22} -3.40234 q^{23} +8.12429 q^{24} +1.00000 q^{25} +7.44232 q^{26} +3.18276 q^{27} -1.31848 q^{28} -0.0953703 q^{29} -2.77186 q^{30} -7.77708 q^{31} -4.74646 q^{32} +4.79469 q^{33} -1.03393 q^{34} +1.41622 q^{35} -3.89824 q^{36} -1.05865 q^{37} +4.00549 q^{38} -19.2973 q^{39} +3.03044 q^{40} -2.57994 q^{41} -3.92556 q^{42} -1.04642 q^{43} -1.66504 q^{44} +4.18720 q^{45} +3.51778 q^{46} -12.2869 q^{47} -3.40817 q^{48} -4.99432 q^{49} -1.03393 q^{50} +2.68090 q^{51} +6.70134 q^{52} -1.00091 q^{53} -3.29075 q^{54} +1.78846 q^{55} +4.29176 q^{56} -10.3859 q^{57} +0.0986062 q^{58} -4.98390 q^{59} -2.49588 q^{60} -2.65363 q^{61} +8.04095 q^{62} +5.92999 q^{63} +7.45007 q^{64} -7.19809 q^{65} -4.95737 q^{66} +7.29534 q^{67} -0.930989 q^{68} -9.12132 q^{69} -1.46427 q^{70} -1.00000 q^{71} +12.6890 q^{72} +3.76564 q^{73} +1.09457 q^{74} +2.68090 q^{75} +3.60669 q^{76} +2.53286 q^{77} +19.9521 q^{78} +7.37615 q^{79} -1.27128 q^{80} -4.02895 q^{81} +2.66747 q^{82} -11.9085 q^{83} -3.53472 q^{84} +1.00000 q^{85} +1.08192 q^{86} -0.255678 q^{87} +5.41983 q^{88} -8.48287 q^{89} -4.32927 q^{90} -10.1941 q^{91} +3.16754 q^{92} -20.8495 q^{93} +12.7038 q^{94} -3.87404 q^{95} -12.7248 q^{96} +17.6413 q^{97} +5.16378 q^{98} +7.48866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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