LMFDB - Embedded newform 4033.2.a.d.1.66

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.66
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.91542 q^{2} +2.79623 q^{3} +1.66883 q^{4} -3.26142 q^{5} +5.35595 q^{6} -0.602359 q^{7} -0.634334 q^{8} +4.81890 q^{9} +O(q^{10})$	\(q+1.91542 q^{2} +2.79623 q^{3} +1.66883 q^{4} -3.26142 q^{5} +5.35595 q^{6} -0.602359 q^{7} -0.634334 q^{8} +4.81890 q^{9} -6.24698 q^{10} -2.65798 q^{11} +4.66642 q^{12} -4.14237 q^{13} -1.15377 q^{14} -9.11968 q^{15} -4.55267 q^{16} +0.128751 q^{17} +9.23020 q^{18} +0.738959 q^{19} -5.44275 q^{20} -1.68433 q^{21} -5.09115 q^{22} +3.86358 q^{23} -1.77374 q^{24} +5.63686 q^{25} -7.93438 q^{26} +5.08605 q^{27} -1.00523 q^{28} -4.88507 q^{29} -17.4680 q^{30} -7.33176 q^{31} -7.45160 q^{32} -7.43233 q^{33} +0.246612 q^{34} +1.96454 q^{35} +8.04191 q^{36} -1.00000 q^{37} +1.41541 q^{38} -11.5830 q^{39} +2.06883 q^{40} +4.66555 q^{41} -3.22620 q^{42} -5.51712 q^{43} -4.43571 q^{44} -15.7164 q^{45} +7.40038 q^{46} +2.26156 q^{47} -12.7303 q^{48} -6.63716 q^{49} +10.7970 q^{50} +0.360018 q^{51} -6.91290 q^{52} -5.06552 q^{53} +9.74192 q^{54} +8.66880 q^{55} +0.382097 q^{56} +2.06630 q^{57} -9.35695 q^{58} +12.5037 q^{59} -15.2192 q^{60} -5.33607 q^{61} -14.0434 q^{62} -2.90270 q^{63} -5.16759 q^{64} +13.5100 q^{65} -14.2360 q^{66} +4.80149 q^{67} +0.214863 q^{68} +10.8035 q^{69} +3.76293 q^{70} -15.1120 q^{71} -3.05679 q^{72} +3.06276 q^{73} -1.91542 q^{74} +15.7620 q^{75} +1.23319 q^{76} +1.60106 q^{77} -22.1863 q^{78} -9.75426 q^{79} +14.8482 q^{80} -0.234922 q^{81} +8.93647 q^{82} +3.65909 q^{83} -2.81086 q^{84} -0.419912 q^{85} -10.5676 q^{86} -13.6598 q^{87} +1.68605 q^{88} +1.75111 q^{89} -30.1036 q^{90} +2.49519 q^{91} +6.44765 q^{92} -20.5013 q^{93} +4.33184 q^{94} -2.41005 q^{95} -20.8364 q^{96} +6.48767 q^{97} -12.7129 q^{98} -12.8085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * 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 $

$2$	1.91542	1.35441	0.677203	−	0.735797i	$-0.263192\pi$
$2$	1.91542	1.35441	0.677203	+	0.735797i	$0.263192\pi$
$3$	2.79623	1.61440	0.807202	−	0.590276i	$-0.200981\pi$
$3$	2.79623	1.61440	0.807202	+	0.590276i	$0.200981\pi$
$4$	1.66883	0.834414
$5$	−3.26142	−1.45855	−0.729276	−	0.684220i	$-0.760143\pi$
$5$	−3.26142	−1.45855	−0.729276	+	0.684220i	$0.760143\pi$
$6$	5.35595	2.18656
$7$	−0.602359	−0.227670	−0.113835	−	0.993500i	$-0.536314\pi$
$7$	−0.602359	−0.227670	−0.113835	+	0.993500i	$0.536314\pi$
$8$	−0.634334	−0.224271
$9$	4.81890	1.60630
$10$	−6.24698	−1.97547
$11$	−2.65798	−0.801412	−0.400706	−	0.916207i	$-0.631235\pi$
$11$	−2.65798	−0.801412	−0.400706	+	0.916207i	$0.631235\pi$
$12$	4.66642	1.34708
$13$	−4.14237	−1.14889	−0.574444	−	0.818544i	$-0.694782\pi$
$13$	−4.14237	−1.14889	−0.574444	+	0.818544i	$0.694782\pi$
$14$	−1.15377	−0.308358
$15$	−9.11968	−2.35469
$16$	−4.55267	−1.13817
$17$	0.128751	0.0312267	0.0156134	−	0.999878i	$-0.495030\pi$
$17$	0.128751	0.0312267	0.0156134	+	0.999878i	$0.495030\pi$
$18$	9.23020	2.17558
$19$	0.738959	0.169529	0.0847644	−	0.996401i	$-0.472986\pi$
$19$	0.738959	0.169529	0.0847644	+	0.996401i	$0.472986\pi$
$20$	−5.44275	−1.21704
$21$	−1.68433	−0.367552
$22$	−5.09115	−1.08544
$23$	3.86358	0.805613	0.402806	−	0.915285i	$-0.368035\pi$
$23$	3.86358	0.805613	0.402806	+	0.915285i	$0.368035\pi$
$24$	−1.77374	−0.362064
$25$	5.63686	1.12737
$26$	−7.93438	−1.55606
$27$	5.08605	0.978811
$28$	−1.00523	−0.189971
$29$	−4.88507	−0.907135	−0.453567	−	0.891222i	$-0.649849\pi$
$29$	−4.88507	−0.907135	−0.453567	+	0.891222i	$0.649849\pi$
$30$	−17.4680	−3.18921
$31$	−7.33176	−1.31682	−0.658412	−	0.752658i	$-0.728771\pi$
$31$	−7.33176	−1.31682	−0.658412	+	0.752658i	$0.728771\pi$
$32$	−7.45160	−1.31727
$33$	−7.43233	−1.29380
$34$	0.246612	0.0422937
$35$	1.96454	0.332069
$36$	8.04191	1.34032
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	1.41541	0.229611
$39$	−11.5830	−1.85477
$40$	2.06883	0.327111
$41$	4.66555	0.728636	0.364318	−	0.931275i	$-0.381302\pi$
$41$	4.66555	0.728636	0.364318	+	0.931275i	$0.381302\pi$
$42$	−3.22620	−0.497814
$43$	−5.51712	−0.841354	−0.420677	−	0.907211i	$-0.638207\pi$
$43$	−5.51712	−0.841354	−0.420677	+	0.907211i	$0.638207\pi$
$44$	−4.43571	−0.668709
$45$	−15.7164	−2.34287
$46$	7.40038	1.09113
$47$	2.26156	0.329883	0.164941	−	0.986303i	$-0.447257\pi$
$47$	2.26156	0.329883	0.164941	+	0.986303i	$0.447257\pi$
$48$	−12.7303	−1.83746
$49$	−6.63716	−0.948166
$50$	10.7970	1.52692
$51$	0.360018	0.0504126
$52$	−6.91290	−0.958647
$53$	−5.06552	−0.695803	−0.347902	−	0.937531i	$-0.613106\pi$
$53$	−5.06552	−0.695803	−0.347902	+	0.937531i	$0.613106\pi$
$54$	9.74192	1.32571
$55$	8.66880	1.16890
$56$	0.382097	0.0510598
$57$	2.06630	0.273688
$58$	−9.35695	−1.22863
$59$	12.5037	1.62784	0.813919	−	0.580978i	$-0.197330\pi$
$59$	12.5037	1.62784	0.813919	+	0.580978i	$0.197330\pi$
$60$	−15.2192	−1.96479
$61$	−5.33607	−0.683214	−0.341607	−	0.939843i	$-0.610971\pi$
$61$	−5.33607	−0.683214	−0.341607	+	0.939843i	$0.610971\pi$
$62$	−14.0434	−1.78351
$63$	−2.90270	−0.365706
$64$	−5.16759	−0.645949
$65$	13.5100	1.67571
$66$	−14.2360	−1.75233
$67$	4.80149	0.586595	0.293297	−	0.956021i	$-0.405247\pi$
$67$	4.80149	0.586595	0.293297	+	0.956021i	$0.405247\pi$
$68$	0.214863	0.0260560
$69$	10.8035	1.30058
$70$	3.76293	0.449756
$71$	−15.1120	−1.79346	−0.896730	−	0.442578i	$-0.854064\pi$
$71$	−15.1120	−1.79346	−0.896730	+	0.442578i	$0.854064\pi$
$72$	−3.05679	−0.360246
$73$	3.06276	0.358469	0.179234	−	0.983806i	$-0.442638\pi$
$73$	3.06276	0.358469	0.179234	+	0.983806i	$0.442638\pi$
$74$	−1.91542	−0.222663
$75$	15.7620	1.82003
$76$	1.23319	0.141457
$77$	1.60106	0.182458
$78$	−22.1863	−2.51211
$79$	−9.75426	−1.09744	−0.548720	−	0.836006i	$-0.684885\pi$
$79$	−9.75426	−1.09744	−0.548720	+	0.836006i	$0.684885\pi$
$80$	14.8482	1.66008
$81$	−0.234922	−0.0261025
$82$	8.93647	0.986868
$83$	3.65909	0.401637	0.200819	−	0.979628i	$-0.435640\pi$
$83$	3.65909	0.401637	0.200819	+	0.979628i	$0.435640\pi$
$84$	−2.81086	−0.306690
$85$	−0.419912	−0.0455458
$86$	−10.5676	−1.13953
$87$	−13.6598	−1.46448
$88$	1.68605	0.179733
$89$	1.75111	0.185617	0.0928084	−	0.995684i	$-0.470416\pi$
$89$	1.75111	0.185617	0.0928084	+	0.995684i	$0.470416\pi$
$90$	−30.1036	−3.17320
$91$	2.49519	0.261567
$92$	6.44765	0.672214
$93$	−20.5013	−2.12588
$94$	4.33184	0.446795
$95$	−2.41005	−0.247266
$96$	−20.8364	−2.12660
$97$	6.48767	0.658723	0.329362	−	0.944204i	$-0.393166\pi$
$97$	6.48767	0.658723	0.329362	+	0.944204i	$0.393166\pi$
$98$	−12.7129	−1.28420
$99$	−12.8085	−1.28731
$100$	9.40695	0.940695
$101$	3.60538	0.358748	0.179374	−	0.983781i	$-0.442593\pi$
$101$	3.60538	0.358748	0.179374	+	0.983781i	$0.442593\pi$
$102$	0.689585	0.0682790
$103$	4.83759	0.476662	0.238331	−	0.971184i	$-0.423400\pi$
$103$	4.83759	0.476662	0.238331	+	0.971184i	$0.423400\pi$
$104$	2.62765	0.257662
$105$	5.49332	0.536093
$106$	−9.70260	−0.942400
$107$	12.1668	1.17621	0.588106	−	0.808784i	$-0.299874\pi$
$107$	12.1668	1.17621	0.588106	+	0.808784i	$0.299874\pi$
$108$	8.48774	0.816734
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	16.6044	1.58317
$111$	−2.79623	−0.265406
$112$	2.74234	0.259127
$113$	−6.89193	−0.648339	−0.324169	−	0.945999i	$-0.605085\pi$
$113$	−6.89193	−0.648339	−0.324169	+	0.945999i	$0.605085\pi$
$114$	3.95782	0.370684
$115$	−12.6008	−1.17503
$116$	−8.15234	−0.756926
$117$	−19.9617	−1.84546
$118$	23.9497	2.20475
$119$	−0.0775544	−0.00710940
$120$	5.78492	0.528089
$121$	−3.93513	−0.357739
$122$	−10.2208	−0.925348
$123$	13.0459	1.17631
$124$	−12.2354	−1.09878
$125$	−2.07708	−0.185780
$126$	−5.55989	−0.495315
$127$	−8.07281	−0.716346	−0.358173	−	0.933655i	$-0.616600\pi$
$127$	−8.07281	−0.716346	−0.358173	+	0.933655i	$0.616600\pi$
$128$	5.00510	0.442393
$129$	−15.4271	−1.35828
$130$	25.8773	2.26959
$131$	−14.0520	−1.22773	−0.613864	−	0.789412i	$-0.710386\pi$
$131$	−14.0520	−1.22773	−0.613864	+	0.789412i	$0.710386\pi$
$132$	−12.4033	−1.07957
$133$	−0.445118	−0.0385966
$134$	9.19686	0.794487
$135$	−16.5878	−1.42765
$136$	−0.0816712	−0.00700325
$137$	−5.53805	−0.473148	−0.236574	−	0.971614i	$-0.576025\pi$
$137$	−5.53805	−0.473148	−0.236574	+	0.971614i	$0.576025\pi$
$138$	20.6932	1.76152
$139$	20.4015	1.73043	0.865217	−	0.501397i	$-0.167181\pi$
$139$	20.4015	1.73043	0.865217	+	0.501397i	$0.167181\pi$
$140$	3.27849	0.277083
$141$	6.32384	0.532564
$142$	−28.9457	−2.42907
$143$	11.0104	0.920732
$144$	−21.9388	−1.82824
$145$	15.9323	1.32310
$146$	5.86646	0.485512
$147$	−18.5590	−1.53072
$148$	−1.66883	−0.137177
$149$	−0.748060	−0.0612834	−0.0306417	−	0.999530i	$-0.509755\pi$
$149$	−0.748060	−0.0612834	−0.0306417	+	0.999530i	$0.509755\pi$
$150$	30.1908	2.46506
$151$	16.1817	1.31685	0.658425	−	0.752646i	$-0.271223\pi$
$151$	16.1817	1.31685	0.658425	+	0.752646i	$0.271223\pi$
$152$	−0.468746	−0.0380204
$153$	0.620439	0.0501595
$154$	3.06670	0.247122
$155$	23.9120	1.92066
$156$	−19.3301	−1.54764
$157$	8.92367	0.712186	0.356093	−	0.934451i	$-0.384109\pi$
$157$	8.92367	0.712186	0.356093	+	0.934451i	$0.384109\pi$
$158$	−18.6835	−1.48638
$159$	−14.1644	−1.12331
$160$	24.3028	1.92130
$161$	−2.32726	−0.183414
$162$	−0.449974	−0.0353533
$163$	−5.35637	−0.419543	−0.209772	−	0.977750i	$-0.567272\pi$
$163$	−5.35637	−0.419543	−0.209772	+	0.977750i	$0.567272\pi$
$164$	7.78599	0.607984
$165$	24.2399	1.88708
$166$	7.00869	0.543980
$167$	−13.9815	−1.08192	−0.540962	−	0.841047i	$-0.681940\pi$
$167$	−13.9815	−1.08192	−0.540962	+	0.841047i	$0.681940\pi$
$168$	1.06843	0.0824311
$169$	4.15925	0.319942
$170$	−0.804306	−0.0616875
$171$	3.56097	0.272314
$172$	−9.20713	−0.702037
$173$	8.61587	0.655053	0.327526	−	0.944842i	$-0.393785\pi$
$173$	8.61587	0.655053	0.327526	+	0.944842i	$0.393785\pi$
$174$	−26.1642	−1.98350
$175$	−3.39541	−0.256669
$176$	12.1009	0.912141
$177$	34.9631	2.62799
$178$	3.35410	0.251400
$179$	−2.12041	−0.158487	−0.0792433	−	0.996855i	$-0.525250\pi$
$179$	−2.12041	−0.158487	−0.0792433	+	0.996855i	$0.525250\pi$
$180$	−26.2280	−1.95492
$181$	3.25547	0.241977	0.120989	−	0.992654i	$-0.461394\pi$
$181$	3.25547	0.241977	0.120989	+	0.992654i	$0.461394\pi$
$182$	4.77934	0.354268
$183$	−14.9209	−1.10298
$184$	−2.45080	−0.180676
$185$	3.26142	0.239784
$186$	−39.2685	−2.87931
$187$	−0.342218	−0.0250255
$188$	3.77416	0.275259
$189$	−3.06363	−0.222846
$190$	−4.61626	−0.334899
$191$	17.5728	1.27152	0.635762	−	0.771885i	$-0.280686\pi$
$191$	17.5728	1.27152	0.635762	+	0.771885i	$0.280686\pi$
$192$	−14.4498	−1.04282
$193$	9.55196	0.687565	0.343783	−	0.939049i	$-0.388292\pi$
$193$	9.55196	0.687565	0.343783	+	0.939049i	$0.388292\pi$
$194$	12.4266	0.892179
$195$	37.7771	2.70527
$196$	−11.0763	−0.791163
$197$	−1.89307	−0.134876	−0.0674379	−	0.997723i	$-0.521482\pi$
$197$	−1.89307	−0.134876	−0.0674379	+	0.997723i	$0.521482\pi$
$198$	−24.5337	−1.74354
$199$	11.5291	0.817278	0.408639	−	0.912696i	$-0.366003\pi$
$199$	11.5291	0.817278	0.408639	+	0.912696i	$0.366003\pi$
$200$	−3.57565	−0.252837
$201$	13.4261	0.947001
$202$	6.90581	0.485891
$203$	2.94256	0.206527
$204$	0.600807	0.0420649
$205$	−15.2163	−1.06275
$206$	9.26601	0.645594
$207$	18.6182	1.29405
$208$	18.8589	1.30763
$209$	−1.96414	−0.135862
$210$	10.5220	0.726087
$211$	6.11016	0.420641	0.210320	−	0.977633i	$-0.432549\pi$
$211$	6.11016	0.420641	0.210320	+	0.977633i	$0.432549\pi$
$212$	−8.45349	−0.580588
$213$	−42.2565	−2.89537
$214$	23.3046	1.59307
$215$	17.9937	1.22716
$216$	−3.22626	−0.219519
$217$	4.41635	0.299801
$218$	−1.91542	−0.129729
$219$	8.56417	0.578713
$220$	14.4667	0.975347
$221$	−0.533335	−0.0358760
$222$	−5.35595	−0.359468
$223$	5.61383	0.375930	0.187965	−	0.982176i	$-0.439811\pi$
$223$	5.61383	0.375930	0.187965	+	0.982176i	$0.439811\pi$
$224$	4.48854	0.299903
$225$	27.1635	1.81090
$226$	−13.2009	−0.878113
$227$	−12.3600	−0.820361	−0.410180	−	0.912004i	$-0.634534\pi$
$227$	−12.3600	−0.820361	−0.410180	+	0.912004i	$0.634534\pi$
$228$	3.44829	0.228369
$229$	−1.46264	−0.0966542	−0.0483271	−	0.998832i	$-0.515389\pi$
$229$	−1.46264	−0.0966542	−0.0483271	+	0.998832i	$0.515389\pi$
$230$	−24.1357	−1.59146
$231$	4.47693	0.294560
$232$	3.09877	0.203444
$233$	22.1255	1.44949	0.724745	−	0.689017i	$-0.241958\pi$
$233$	22.1255	1.44949	0.724745	+	0.689017i	$0.241958\pi$
$234$	−38.2349	−2.49950
$235$	−7.37590	−0.481151
$236$	20.8665	1.35829
$237$	−27.2751	−1.77171
$238$	−0.148549	−0.00962901
$239$	16.5663	1.07158	0.535792	−	0.844350i	$-0.320013\pi$
$239$	16.5663	1.07158	0.535792	+	0.844350i	$0.320013\pi$
$240$	41.5189	2.68003
$241$	−10.4401	−0.672503	−0.336251	−	0.941772i	$-0.609159\pi$
$241$	−10.4401	−0.672503	−0.336251	+	0.941772i	$0.609159\pi$
$242$	−7.53742	−0.484523
$243$	−15.9151	−1.02095
$244$	−8.90498	−0.570083
$245$	21.6466	1.38295
$246$	24.9884	1.59320
$247$	−3.06104	−0.194769
$248$	4.65079	0.295325
$249$	10.2317	0.648405
$250$	−3.97848	−0.251621
$251$	−27.0663	−1.70841	−0.854204	−	0.519938i	$-0.825955\pi$
$251$	−27.0663	−1.70841	−0.854204	+	0.519938i	$0.825955\pi$
$252$	−4.84411	−0.305150
$253$	−10.2693	−0.645628
$254$	−15.4628	−0.970223
$255$	−1.17417	−0.0735293
$256$	19.9220	1.24513
$257$	1.26251	0.0787529	0.0393765	−	0.999224i	$-0.487463\pi$
$257$	1.26251	0.0787529	0.0393765	+	0.999224i	$0.487463\pi$
$258$	−29.5494	−1.83967
$259$	0.602359	0.0374287
$260$	22.5459	1.39824
$261$	−23.5406	−1.45713
$262$	−26.9155	−1.66284
$263$	−29.3716	−1.81113	−0.905564	−	0.424209i	$-0.860552\pi$
$263$	−29.3716	−1.81113	−0.905564	+	0.424209i	$0.860552\pi$
$264$	4.71458	0.290162
$265$	16.5208	1.01486
$266$	−0.852587	−0.0522755
$267$	4.89649	0.299661
$268$	8.01285	0.489463
$269$	−28.5810	−1.74261	−0.871307	−	0.490738i	$-0.836727\pi$
$269$	−28.5810	−1.74261	−0.871307	+	0.490738i	$0.836727\pi$
$270$	−31.7725	−1.93361
$271$	−13.6198	−0.827346	−0.413673	−	0.910426i	$-0.635754\pi$
$271$	−13.6198	−0.827346	−0.413673	+	0.910426i	$0.635754\pi$
$272$	−0.586161	−0.0355413
$273$	6.97713	0.422275
$274$	−10.6077	−0.640834
$275$	−14.9827	−0.903490
$276$	18.0291	1.08523
$277$	14.9507	0.898299	0.449149	−	0.893457i	$-0.351727\pi$
$277$	14.9507	0.898299	0.449149	+	0.893457i	$0.351727\pi$
$278$	39.0774	2.34371
$279$	−35.3310	−2.11521
$280$	−1.24618	−0.0744734
$281$	−18.6892	−1.11490	−0.557452	−	0.830209i	$-0.688221\pi$
$281$	−18.6892	−1.11490	−0.557452	+	0.830209i	$0.688221\pi$
$282$	12.1128	0.721307
$283$	1.70128	0.101131	0.0505654	−	0.998721i	$-0.483898\pi$
$283$	1.70128	0.101131	0.0505654	+	0.998721i	$0.483898\pi$
$284$	−25.2193	−1.49649
$285$	−6.73906	−0.399188
$286$	21.0894	1.24704
$287$	−2.81033	−0.165889
$288$	−35.9085	−2.11593
$289$	−16.9834	−0.999025
$290$	30.5170	1.79202
$291$	18.1410	1.06345
$292$	5.11121	0.299111
$293$	−3.68885	−0.215505	−0.107752	−	0.994178i	$-0.534365\pi$
$293$	−3.68885	−0.215505	−0.107752	+	0.994178i	$0.534365\pi$
$294$	−35.5483	−2.07322
$295$	−40.7797	−2.37429
$296$	0.634334	0.0368699
$297$	−13.5186	−0.784431
$298$	−1.43285	−0.0830026
$299$	−16.0044	−0.925558
$300$	26.3040	1.51866
$301$	3.32329	0.191551
$302$	30.9948	1.78355
$303$	10.0815	0.579165
$304$	−3.36423	−0.192952
$305$	17.4032	0.996502
$306$	1.18840	0.0679363
$307$	−2.87995	−0.164367	−0.0821836	−	0.996617i	$-0.526189\pi$
$307$	−2.87995	−0.164367	−0.0821836	+	0.996617i	$0.526189\pi$
$308$	2.67189	0.152245
$309$	13.5270	0.769525
$310$	45.8014	2.60135
$311$	−24.2248	−1.37366	−0.686832	−	0.726816i	$-0.740999\pi$
$311$	−24.2248	−1.37366	−0.686832	+	0.726816i	$0.740999\pi$
$312$	7.34750	0.415970
$313$	−1.87235	−0.105832	−0.0529158	−	0.998599i	$-0.516852\pi$
$313$	−1.87235	−0.105832	−0.0529158	+	0.998599i	$0.516852\pi$
$314$	17.0926	0.964589
$315$	9.46694	0.533402
$316$	−16.2782	−0.915719
$317$	28.0037	1.57284	0.786422	−	0.617689i	$-0.211931\pi$
$317$	28.0037	1.57284	0.786422	+	0.617689i	$0.211931\pi$
$318$	−27.1307	−1.52141
$319$	12.9844	0.726988
$320$	16.8537	0.942150
$321$	34.0212	1.89888
$322$	−4.45768	−0.248417
$323$	0.0951418	0.00529383
$324$	−0.392045	−0.0217803
$325$	−23.3500	−1.29522
$326$	−10.2597	−0.568232
$327$	−2.79623	−0.154632
$328$	−2.95951	−0.163412
$329$	−1.36227	−0.0751044
$330$	46.4296	2.55587
$331$	1.21845	0.0669720	0.0334860	−	0.999439i	$-0.489339\pi$
$331$	1.21845	0.0669720	0.0334860	+	0.999439i	$0.489339\pi$
$332$	6.10639	0.335132
$333$	−4.81890	−0.264074
$334$	−26.7805	−1.46536
$335$	−15.6597	−0.855579
$336$	7.66821	0.418335
$337$	8.35708	0.455239	0.227620	−	0.973750i	$-0.426906\pi$
$337$	8.35708	0.455239	0.227620	+	0.973750i	$0.426906\pi$
$338$	7.96669	0.433331
$339$	−19.2714	−1.04668
$340$	−0.700760	−0.0380041
$341$	19.4877	1.05532
$342$	6.82074	0.368823
$343$	8.21446	0.443539
$344$	3.49970	0.188691
$345$	−35.2346	−1.89697
$346$	16.5030	0.887207
$347$	19.2090	1.03119	0.515597	−	0.856831i	$-0.327570\pi$
$347$	19.2090	1.03119	0.515597	+	0.856831i	$0.327570\pi$
$348$	−22.7958	−1.22198
$349$	−16.7692	−0.897636	−0.448818	−	0.893623i	$-0.648155\pi$
$349$	−16.7692	−0.897636	−0.448818	+	0.893623i	$0.648155\pi$
$350$	−6.50364	−0.347634
$351$	−21.0683	−1.12454
$352$	19.8062	1.05568
$353$	−17.2714	−0.919266	−0.459633	−	0.888109i	$-0.652019\pi$
$353$	−17.2714	−0.919266	−0.459633	+	0.888109i	$0.652019\pi$
$354$	66.9690	3.55936
$355$	49.2865	2.61585
$356$	2.92229	0.154881
$357$	−0.216860	−0.0114774
$358$	−4.06146	−0.214655
$359$	−8.78901	−0.463866	−0.231933	−	0.972732i	$-0.574505\pi$
$359$	−8.78901	−0.463866	−0.231933	+	0.972732i	$0.574505\pi$
$360$	9.96948	0.525438
$361$	−18.4539	−0.971260
$362$	6.23558	0.327735
$363$	−11.0035	−0.577535
$364$	4.16405	0.218255
$365$	−9.98894	−0.522845
$366$	−28.5797	−1.49389
$367$	6.65549	0.347413	0.173707	−	0.984797i	$-0.444426\pi$
$367$	6.65549	0.347413	0.173707	+	0.984797i	$0.444426\pi$
$368$	−17.5896	−0.916922
$369$	22.4828	1.17041
$370$	6.24698	0.324765
$371$	3.05126	0.158414
$372$	−34.2131	−1.77387
$373$	−23.3010	−1.20648	−0.603241	−	0.797559i	$-0.706124\pi$
$373$	−23.3010	−1.20648	−0.603241	+	0.797559i	$0.706124\pi$
$374$	−0.655491	−0.0338946
$375$	−5.80800	−0.299924
$376$	−1.43459	−0.0739831
$377$	20.2358	1.04220
$378$	−5.86813	−0.301824
$379$	12.4782	0.640963	0.320482	−	0.947255i	$-0.396155\pi$
$379$	12.4782	0.640963	0.320482	+	0.947255i	$0.396155\pi$
$380$	−4.02197	−0.206322
$381$	−22.5734	−1.15647
$382$	33.6593	1.72216
$383$	−15.8732	−0.811082	−0.405541	−	0.914077i	$-0.632917\pi$
$383$	−15.8732	−0.811082	−0.405541	+	0.914077i	$0.632917\pi$
$384$	13.9954	0.714200
$385$	−5.22173	−0.266124
$386$	18.2960	0.931242
$387$	−26.5865	−1.35147
$388$	10.8268	0.549648
$389$	3.77979	0.191643	0.0958215	−	0.995399i	$-0.469452\pi$
$389$	3.77979	0.191643	0.0958215	+	0.995399i	$0.469452\pi$
$390$	72.3590	3.66404
$391$	0.497441	0.0251567
$392$	4.21018	0.212646
$393$	−39.2926	−1.98205
$394$	−3.62603	−0.182677
$395$	31.8127	1.60067
$396$	−21.3753	−1.07415
$397$	29.5121	1.48117	0.740584	−	0.671964i	$-0.234549\pi$
$397$	29.5121	1.48117	0.740584	+	0.671964i	$0.234549\pi$
$398$	22.0831	1.10693
$399$	−1.24465	−0.0623105
$400$	−25.6628	−1.28314
$401$	−25.3411	−1.26548	−0.632738	−	0.774366i	$-0.718069\pi$
$401$	−25.3411	−1.26548	−0.632738	+	0.774366i	$0.718069\pi$
$402$	25.7165	1.28262
$403$	30.3709	1.51288
$404$	6.01675	0.299345
$405$	0.766180	0.0380718
$406$	5.63624	0.279722
$407$	2.65798	0.131751
$408$	−0.228371	−0.0113061
$409$	−17.5094	−0.865782	−0.432891	−	0.901446i	$-0.642507\pi$
$409$	−17.5094	−0.865782	−0.432891	+	0.901446i	$0.642507\pi$
$410$	−29.1456	−1.43940
$411$	−15.4857	−0.763851
$412$	8.07311	0.397733
$413$	−7.53169	−0.370610
$414$	35.6617	1.75267
$415$	−11.9338	−0.585809
$416$	30.8673	1.51339
$417$	57.0473	2.79362
$418$	−3.76215	−0.184013
$419$	−13.0326	−0.636682	−0.318341	−	0.947976i	$-0.603126\pi$
$419$	−13.0326	−0.636682	−0.318341	+	0.947976i	$0.603126\pi$
$420$	9.16740	0.447323
$421$	9.05284	0.441208	0.220604	−	0.975363i	$-0.429197\pi$
$421$	9.05284	0.441208	0.220604	+	0.975363i	$0.429197\pi$
$422$	11.7035	0.569718
$423$	10.8982	0.529890
$424$	3.21323	0.156048
$425$	0.725753	0.0352042
$426$	−80.9389	−3.92150
$427$	3.21423	0.155547
$428$	20.3043	0.981447
$429$	30.7875	1.48643
$430$	34.4654	1.66207
$431$	−16.4074	−0.790316	−0.395158	−	0.918613i	$-0.629310\pi$
$431$	−16.4074	−0.790316	−0.395158	+	0.918613i	$0.629310\pi$
$432$	−23.1551	−1.11405
$433$	14.3255	0.688441	0.344220	−	0.938889i	$-0.388143\pi$
$433$	14.3255	0.688441	0.344220	+	0.938889i	$0.388143\pi$
$434$	8.45916	0.406053
$435$	44.5503	2.13602
$436$	−1.66883	−0.0799223
$437$	2.85503	0.136574
$438$	16.4040	0.783812
$439$	−7.36175	−0.351357	−0.175679	−	0.984448i	$-0.556212\pi$
$439$	−7.36175	−0.351357	−0.175679	+	0.984448i	$0.556212\pi$
$440$	−5.49891	−0.262150
$441$	−31.9838	−1.52304
$442$	−1.02156	−0.0485906
$443$	35.3204	1.67812	0.839062	−	0.544036i	$-0.183105\pi$
$443$	35.3204	1.67812	0.839062	+	0.544036i	$0.183105\pi$
$444$	−4.66642	−0.221459
$445$	−5.71109	−0.270732
$446$	10.7528	0.509162
$447$	−2.09175	−0.0989362
$448$	3.11274	0.147063
$449$	2.06751	0.0975719	0.0487860	−	0.998809i	$-0.484465\pi$
$449$	2.06751	0.0975719	0.0487860	+	0.998809i	$0.484465\pi$
$450$	52.0294	2.45269
$451$	−12.4009	−0.583938
$452$	−11.5014	−0.540983
$453$	45.2478	2.12593
$454$	−23.6745	−1.11110
$455$	−8.13788	−0.381509
$456$	−1.31072	−0.0613802
$457$	17.8686	0.835859	0.417930	−	0.908479i	$-0.362756\pi$
$457$	17.8686	0.835859	0.417930	+	0.908479i	$0.362756\pi$
$458$	−2.80157	−0.130909
$459$	0.654835	0.0305651
$460$	−21.0285	−0.980459
$461$	21.9492	1.02227	0.511137	−	0.859499i	$-0.329224\pi$
$461$	21.9492	1.02227	0.511137	+	0.859499i	$0.329224\pi$
$462$	8.57519	0.398954
$463$	23.8228	1.10714	0.553570	−	0.832803i	$-0.313265\pi$
$463$	23.8228	1.10714	0.553570	+	0.832803i	$0.313265\pi$
$464$	22.2401	1.03247
$465$	66.8633	3.10071
$466$	42.3796	1.96320
$467$	−28.5833	−1.32268	−0.661338	−	0.750088i	$-0.730011\pi$
$467$	−28.5833	−1.32268	−0.661338	+	0.750088i	$0.730011\pi$
$468$	−33.3126	−1.53987
$469$	−2.89222	−0.133550
$470$	−14.1279	−0.651673
$471$	24.9526	1.14976
$472$	−7.93150	−0.365077
$473$	14.6644	0.674271
$474$	−52.2433	−2.39961
$475$	4.16541	0.191122
$476$	−0.129425	−0.00593218
$477$	−24.4102	−1.11767
$478$	31.7314	1.45136
$479$	−30.2982	−1.38436	−0.692180	−	0.721725i	$-0.743350\pi$
$479$	−30.2982	−1.38436	−0.692180	+	0.721725i	$0.743350\pi$
$480$	67.9562	3.10176
$481$	4.14237	0.188876
$482$	−19.9971	−0.910842
$483$	−6.50756	−0.296104
$484$	−6.56705	−0.298502
$485$	−21.1590	−0.960782
$486$	−30.4840	−1.38278
$487$	11.0631	0.501319	0.250660	−	0.968075i	$-0.419353\pi$
$487$	11.0631	0.501319	0.250660	+	0.968075i	$0.419353\pi$
$488$	3.38485	0.153225
$489$	−14.9776	−0.677312
$490$	41.4623	1.87307
$491$	−13.9105	−0.627774	−0.313887	−	0.949460i	$-0.601631\pi$
$491$	−13.9105	−0.627774	−0.313887	+	0.949460i	$0.601631\pi$
$492$	21.7714	0.981531
$493$	−0.628958	−0.0283269
$494$	−5.86317	−0.263797
$495$	41.7741	1.87760
$496$	33.3791	1.49877
$497$	9.10282	0.408317
$498$	19.5979	0.878203
$499$	12.9286	0.578762	0.289381	−	0.957214i	$-0.406551\pi$
$499$	12.9286	0.578762	0.289381	+	0.957214i	$0.406551\pi$
$500$	−3.46629	−0.155017
$501$	−39.0956	−1.74666
$502$	−51.8432	−2.31388
$503$	−15.9582	−0.711541	−0.355771	−	0.934573i	$-0.615782\pi$
$503$	−15.9582	−0.711541	−0.355771	+	0.934573i	$0.615782\pi$
$504$	1.84128	0.0820173
$505$	−11.7587	−0.523253
$506$	−19.6701	−0.874442
$507$	11.6302	0.516515
$508$	−13.4721	−0.597729
$509$	−35.3662	−1.56758	−0.783789	−	0.621027i	$-0.786716\pi$
$509$	−35.3662	−1.56758	−0.783789	+	0.621027i	$0.786716\pi$
$510$	−2.24903	−0.0995885
$511$	−1.84488	−0.0816126
$512$	28.1488	1.24401
$513$	3.75838	0.165937
$514$	2.41823	0.106663
$515$	−15.7774	−0.695236
$516$	−25.7452	−1.13337
$517$	−6.01119	−0.264372
$518$	1.15377	0.0506937
$519$	24.0920	1.05752
$520$	−8.56986	−0.375813
$521$	5.59464	0.245106	0.122553	−	0.992462i	$-0.460892\pi$
$521$	5.59464	0.245106	0.122553	+	0.992462i	$0.460892\pi$
$522$	−45.0902	−1.97354
$523$	−31.1107	−1.36038	−0.680189	−	0.733037i	$-0.738102\pi$
$523$	−31.1107	−1.36038	−0.680189	+	0.733037i	$0.738102\pi$
$524$	−23.4504	−1.02443
$525$	−9.49435	−0.414368
$526$	−56.2589	−2.45300
$527$	−0.943973	−0.0411201
$528$	33.8369	1.47256
$529$	−8.07273	−0.350988
$530$	31.6442	1.37454
$531$	60.2539	2.61479
$532$	−0.742825	−0.0322056
$533$	−19.3264	−0.837121
$534$	9.37883	0.405862
$535$	−39.6812	−1.71557
$536$	−3.04575	−0.131556
$537$	−5.92914	−0.255861
$538$	−54.7446	−2.36021
$539$	17.6415	0.759872
$540$	−27.6821	−1.19125
$541$	13.5110	0.580884	0.290442	−	0.956893i	$-0.406198\pi$
$541$	13.5110	0.580884	0.290442	+	0.956893i	$0.406198\pi$
$542$	−26.0877	−1.12056
$543$	9.10303	0.390649
$544$	−0.959402	−0.0411340
$545$	3.26142	0.139704
$546$	13.3641	0.571932
$547$	18.0338	0.771068	0.385534	−	0.922694i	$-0.374017\pi$
$547$	18.0338	0.771068	0.385534	+	0.922694i	$0.374017\pi$
$548$	−9.24205	−0.394801
$549$	−25.7140	−1.09745
$550$	−28.6981	−1.22369
$551$	−3.60986	−0.153785
$552$	−6.85300	−0.291683
$553$	5.87556	0.249854
$554$	28.6368	1.21666
$555$	9.11968	0.387109
$556$	34.0466	1.44390
$557$	−42.4248	−1.79760	−0.898799	−	0.438361i	$-0.855559\pi$
$557$	−42.4248	−1.79760	−0.898799	+	0.438361i	$0.855559\pi$
$558$	−67.6737	−2.86485
$559$	22.8540	0.966620
$560$	−8.94392	−0.377950
$561$	−0.956921	−0.0404012
$562$	−35.7976	−1.51003
$563$	−22.3016	−0.939899	−0.469949	−	0.882693i	$-0.655728\pi$
$563$	−22.3016	−0.939899	−0.469949	+	0.882693i	$0.655728\pi$
$564$	10.5534	0.444378
$565$	22.4775	0.945635
$566$	3.25867	0.136972
$567$	0.141507	0.00594275
$568$	9.58603	0.402221
$569$	−25.6736	−1.07630	−0.538148	−	0.842851i	$-0.680876\pi$
$569$	−25.6736	−1.07630	−0.538148	+	0.842851i	$0.680876\pi$
$570$	−12.9081	−0.540662
$571$	34.8643	1.45902	0.729512	−	0.683968i	$-0.239747\pi$
$571$	34.8643	1.45902	0.729512	+	0.683968i	$0.239747\pi$
$572$	18.3744	0.768271
$573$	49.1376	2.05275
$574$	−5.38296	−0.224680
$575$	21.7785	0.908226
$576$	−24.9021	−1.03759
$577$	−11.8626	−0.493847	−0.246924	−	0.969035i	$-0.579420\pi$
$577$	−11.8626	−0.493847	−0.246924	+	0.969035i	$0.579420\pi$
$578$	−32.5304	−1.35308
$579$	26.7095	1.11001
$580$	26.5882	1.10401
$581$	−2.20409	−0.0914409
$582$	34.7476	1.44034
$583$	13.4641	0.557625
$584$	−1.94281	−0.0803941
$585$	65.1034	2.69169
$586$	−7.06568	−0.291881
$587$	20.1803	0.832929	0.416465	−	0.909152i	$-0.363269\pi$
$587$	20.1803	0.832929	0.416465	+	0.909152i	$0.363269\pi$
$588$	−30.9718	−1.27726
$589$	−5.41787	−0.223239
$590$	−78.1102	−3.21575
$591$	−5.29346	−0.217744
$592$	4.55267	0.187114
$593$	15.2793	0.627445	0.313723	−	0.949515i	$-0.398424\pi$
$593$	15.2793	0.627445	0.313723	+	0.949515i	$0.398424\pi$
$594$	−25.8939	−1.06244
$595$	0.252937	0.0103694
$596$	−1.24838	−0.0511357
$597$	32.2381	1.31942
$598$	−30.6551	−1.25358
$599$	−14.4513	−0.590464	−0.295232	−	0.955426i	$-0.595397\pi$
$599$	−14.4513	−0.590464	−0.295232	+	0.955426i	$0.595397\pi$
$600$	−9.99835	−0.408181
$601$	1.52551	0.0622270	0.0311135	−	0.999516i	$-0.490095\pi$
$601$	1.52551	0.0622270	0.0311135	+	0.999516i	$0.490095\pi$
$602$	6.36549	0.259438
$603$	23.1379	0.942247
$604$	27.0045	1.09880
$605$	12.8341	0.521781
$606$	19.3102	0.784424
$607$	−19.8907	−0.807339	−0.403669	−	0.914905i	$-0.632265\pi$
$607$	−19.8907	−0.807339	−0.403669	+	0.914905i	$0.632265\pi$
$608$	−5.50642	−0.223315
$609$	8.22808	0.333419
$610$	33.3343	1.34967
$611$	−9.36823	−0.378998
$612$	1.03540	0.0418538
$613$	21.2936	0.860040	0.430020	−	0.902819i	$-0.358506\pi$
$613$	21.2936	0.860040	0.430020	+	0.902819i	$0.358506\pi$
$614$	−5.51630	−0.222620
$615$	−42.5483	−1.71571
$616$	−1.01561	−0.0409199
$617$	−16.1617	−0.650646	−0.325323	−	0.945603i	$-0.605473\pi$
$617$	−16.1617	−0.650646	−0.325323	+	0.945603i	$0.605473\pi$
$618$	25.9099	1.04225
$619$	−0.676625	−0.0271958	−0.0135979	−	0.999908i	$-0.504328\pi$
$619$	−0.676625	−0.0271958	−0.0135979	+	0.999908i	$0.504328\pi$
$620$	39.9049	1.60262
$621$	19.6504	0.788543
$622$	−46.4007	−1.86050
$623$	−1.05479	−0.0422594
$624$	52.7337	2.11104
$625$	−21.4101	−0.856403
$626$	−3.58634	−0.143339
$627$	−5.49218	−0.219337
$628$	14.8921	0.594258
$629$	−0.128751	−0.00513364
$630$	18.1331	0.722442
$631$	34.7390	1.38294	0.691470	−	0.722406i	$-0.256964\pi$
$631$	34.7390	1.38294	0.691470	+	0.722406i	$0.256964\pi$
$632$	6.18746	0.246124
$633$	17.0854	0.679084
$634$	53.6388	2.13027
$635$	26.3288	1.04483
$636$	−23.6379	−0.937303
$637$	27.4936	1.08934
$638$	24.8706	0.984637
$639$	−72.8230	−2.88083
$640$	−16.3237	−0.645252
$641$	−33.0777	−1.30649	−0.653246	−	0.757145i	$-0.726593\pi$
$641$	−33.0777	−1.30649	−0.653246	+	0.757145i	$0.726593\pi$
$642$	65.1649	2.57185
$643$	−13.4630	−0.530930	−0.265465	−	0.964121i	$-0.585525\pi$
$643$	−13.4630	−0.530930	−0.265465	+	0.964121i	$0.585525\pi$
$644$	−3.88380	−0.153043
$645$	50.3144	1.98113
$646$	0.182236	0.00716999
$647$	−38.4337	−1.51098	−0.755492	−	0.655158i	$-0.772602\pi$
$647$	−38.4337	−1.51098	−0.755492	+	0.655158i	$0.772602\pi$
$648$	0.149019	0.00585402
$649$	−33.2345	−1.30457
$650$	−44.7250	−1.75426
$651$	12.3491	0.484001
$652$	−8.93886	−0.350073
$653$	−12.9192	−0.505569	−0.252784	−	0.967523i	$-0.581346\pi$
$653$	−12.9192	−0.505569	−0.252784	+	0.967523i	$0.581346\pi$
$654$	−5.35595	−0.209434
$655$	45.8295	1.79071
$656$	−21.2407	−0.829310
$657$	14.7591	0.575808
$658$	−2.60932	−0.101722
$659$	16.2209	0.631877	0.315938	−	0.948780i	$-0.397681\pi$
$659$	16.2209	0.631877	0.315938	+	0.948780i	$0.397681\pi$
$660$	40.4523	1.57460
$661$	−28.7549	−1.11843	−0.559217	−	0.829021i	$-0.688898\pi$
$661$	−28.7549	−1.11843	−0.559217	+	0.829021i	$0.688898\pi$
$662$	2.33384	0.0907072
$663$	−1.49133	−0.0579184
$664$	−2.32109	−0.0900756
$665$	1.45172	0.0562952
$666$	−9.23020	−0.357663
$667$	−18.8739	−0.730799
$668$	−23.3328	−0.902772
$669$	15.6976	0.606903
$670$	−29.9948	−1.15880
$671$	14.1832	0.547536
$672$	12.5510	0.484164
$673$	13.6053	0.524446	0.262223	−	0.965007i	$-0.415544\pi$
$673$	13.6053	0.524446	0.262223	+	0.965007i	$0.415544\pi$
$674$	16.0073	0.616578
$675$	28.6694	1.10349
$676$	6.94106	0.266964
$677$	−22.2602	−0.855531	−0.427765	−	0.903890i	$-0.640699\pi$
$677$	−22.2602	−0.855531	−0.427765	+	0.903890i	$0.640699\pi$
$678$	−36.9128	−1.41763
$679$	−3.90791	−0.149972
$680$	0.266364	0.0102146
$681$	−34.5613	−1.32439
$682$	37.3271	1.42933
$683$	−13.2095	−0.505449	−0.252725	−	0.967538i	$-0.581327\pi$
$683$	−13.2095	−0.505449	−0.252725	+	0.967538i	$0.581327\pi$
$684$	5.94264	0.227222
$685$	18.0619	0.690110
$686$	15.7341	0.600732
$687$	−4.08988	−0.156039
$688$	25.1176	0.957601
$689$	20.9833	0.799399
$690$	−67.4891	−2.56926
$691$	39.3033	1.49517	0.747583	−	0.664168i	$-0.231214\pi$
$691$	39.3033	1.49517	0.747583	+	0.664168i	$0.231214\pi$
$692$	14.3784	0.546585
$693$	7.71534	0.293081
$694$	36.7933	1.39665
$695$	−66.5379	−2.52393
$696$	8.66486	0.328441
$697$	0.600694	0.0227529
$698$	−32.1201	−1.21576
$699$	61.8680	2.34006
$700$	−5.66636	−0.214168
$701$	−19.6621	−0.742626	−0.371313	−	0.928508i	$-0.621092\pi$
$701$	−19.6621	−0.742626	−0.371313	+	0.928508i	$0.621092\pi$
$702$	−40.3547	−1.52309
$703$	−0.738959	−0.0278703
$704$	13.7354	0.517671
$705$	−20.6247	−0.776772
$706$	−33.0820	−1.24506
$707$	−2.17173	−0.0816763
$708$	58.3474	2.19283
$709$	−19.4858	−0.731804	−0.365902	−	0.930653i	$-0.619239\pi$
$709$	−19.4858	−0.731804	−0.365902	+	0.930653i	$0.619239\pi$
$710$	94.4042	3.54293
$711$	−47.0048	−1.76282
$712$	−1.11079	−0.0416285
$713$	−28.3269	−1.06085
$714$	−0.415377	−0.0155451
$715$	−35.9094	−1.34294
$716$	−3.53859	−0.132243
$717$	46.3232	1.72997
$718$	−16.8346	−0.628263
$719$	45.6712	1.70325	0.851624	−	0.524153i	$-0.175618\pi$
$719$	45.6712	1.70325	0.851624	+	0.524153i	$0.175618\pi$
$720$	71.5518	2.66658
$721$	−2.91397	−0.108522
$722$	−35.3470	−1.31548
$723$	−29.1928	−1.08569
$724$	5.43281	0.201909
$725$	−27.5365	−1.02268
$726$	−21.0763	−0.782216
$727$	14.0047	0.519406	0.259703	−	0.965689i	$-0.416375\pi$
$727$	14.0047	0.519406	0.259703	+	0.965689i	$0.416375\pi$
$728$	−1.58279	−0.0586620
$729$	−43.7974	−1.62212
$730$	−19.1330	−0.708144
$731$	−0.710336	−0.0262727
$732$	−24.9004	−0.920344
$733$	44.8394	1.65618	0.828091	−	0.560594i	$-0.189427\pi$
$733$	44.8394	1.65618	0.828091	+	0.560594i	$0.189427\pi$
$734$	12.7480	0.470539
$735$	60.5288	2.23264
$736$	−28.7899	−1.06121
$737$	−12.7623	−0.470104
$738$	43.0639	1.58521
$739$	37.8132	1.39098	0.695491	−	0.718535i	$-0.255187\pi$
$739$	37.8132	1.39098	0.695491	+	0.718535i	$0.255187\pi$
$740$	5.44275	0.200079
$741$	−8.55937	−0.314436
$742$	5.84444	0.214556
$743$	21.8562	0.801827	0.400914	−	0.916116i	$-0.368693\pi$
$743$	21.8562	0.801827	0.400914	+	0.916116i	$0.368693\pi$
$744$	13.0047	0.476774
$745$	2.43974	0.0893850
$746$	−44.6312	−1.63407
$747$	17.6328	0.645150
$748$	−0.571103	−0.0208816
$749$	−7.32880	−0.267788
$750$	−11.1247	−0.406218
$751$	−42.0563	−1.53466	−0.767328	−	0.641255i	$-0.778414\pi$
$751$	−42.0563	−1.53466	−0.767328	+	0.641255i	$0.778414\pi$
$752$	−10.2961	−0.375462
$753$	−75.6835	−2.75806
$754$	38.7600	1.41155
$755$	−52.7754	−1.92069
$756$	−5.11267	−0.185946
$757$	−47.0539	−1.71020	−0.855101	−	0.518462i	$-0.826505\pi$
$757$	−47.0539	−1.71020	−0.855101	+	0.518462i	$0.826505\pi$
$758$	23.9010	0.868124
$759$	−28.7154	−1.04230
$760$	1.52878	0.0554547
$761$	−18.3168	−0.663984	−0.331992	−	0.943282i	$-0.607721\pi$
$761$	−18.3168	−0.663984	−0.331992	+	0.943282i	$0.607721\pi$
$762$	−43.2376	−1.56633
$763$	0.602359	0.0218068
$764$	29.3260	1.06098
$765$	−2.02351	−0.0731602
$766$	−30.4038	−1.09853
$767$	−51.7948	−1.87020
$768$	55.7066	2.01014
$769$	11.8025	0.425610	0.212805	−	0.977095i	$-0.431740\pi$
$769$	11.8025	0.425610	0.212805	+	0.977095i	$0.431740\pi$
$770$	−10.0018	−0.360439
$771$	3.53025	0.127139
$772$	15.9406	0.573714
$773$	−42.8725	−1.54202	−0.771008	−	0.636826i	$-0.780247\pi$
$773$	−42.8725	−1.54202	−0.771008	+	0.636826i	$0.780247\pi$
$774$	−50.9242	−1.83043
$775$	−41.3282	−1.48455
$776$	−4.11535	−0.147733
$777$	1.68433	0.0604251
$778$	7.23988	0.259562
$779$	3.44765	0.123525
$780$	63.0435	2.25732
$781$	40.1673	1.43730
$782$	0.952807	0.0340723
$783$	−24.8457	−0.887914
$784$	30.2168	1.07917
$785$	−29.1038	−1.03876
$786$	−75.2618	−2.68450
$787$	−27.1069	−0.966258	−0.483129	−	0.875549i	$-0.660500\pi$
$787$	−27.1069	−0.966258	−0.483129	+	0.875549i	$0.660500\pi$
$788$	−3.15921	−0.112542
$789$	−82.1297	−2.92389
$790$	60.9347	2.16796
$791$	4.15142	0.147607
$792$	8.12490	0.288706
$793$	22.1040	0.784936
$794$	56.5279	2.00610
$795$	46.1960	1.63840
$796$	19.2401	0.681948
$797$	−5.66719	−0.200742	−0.100371	−	0.994950i	$-0.532003\pi$
$797$	−5.66719	−0.200742	−0.100371	+	0.994950i	$0.532003\pi$
$798$	−2.38403	−0.0843937
$799$	0.291179	0.0103012
$800$	−42.0037	−1.48505
$801$	8.43840	0.298156
$802$	−48.5389	−1.71397
$803$	−8.14076	−0.287281
$804$	22.4058	0.790191
$805$	7.59018	0.267519
$806$	58.1730	2.04906
$807$	−79.9190	−2.81328
$808$	−2.28701	−0.0804568
$809$	−27.9680	−0.983302	−0.491651	−	0.870792i	$-0.663606\pi$
$809$	−27.9680	−0.983302	−0.491651	+	0.870792i	$0.663606\pi$
$810$	1.46756	0.0515646
$811$	5.70314	0.200264	0.100132	−	0.994974i	$-0.468073\pi$
$811$	5.70314	0.200264	0.100132	+	0.994974i	$0.468073\pi$
$812$	4.91063	0.172329
$813$	−38.0842	−1.33567
$814$	5.09115	0.178445
$815$	17.4694	0.611926
$816$	−1.63904	−0.0573779
$817$	−4.07693	−0.142634
$818$	−33.5378	−1.17262
$819$	12.0241	0.420155
$820$	−25.3934	−0.886776
$821$	6.11205	0.213312	0.106656	−	0.994296i	$-0.465986\pi$
$821$	6.11205	0.213312	0.106656	+	0.994296i	$0.465986\pi$
$822$	−29.6615	−1.03456
$823$	−7.16484	−0.249751	−0.124875	−	0.992172i	$-0.539853\pi$
$823$	−7.16484	−0.249751	−0.124875	+	0.992172i	$0.539853\pi$
$824$	−3.06865	−0.106901
$825$	−41.8950	−1.45860
$826$	−14.4263	−0.501956
$827$	−5.15899	−0.179396	−0.0896978	−	0.995969i	$-0.528590\pi$
$827$	−5.15899	−0.179396	−0.0896978	+	0.995969i	$0.528590\pi$
$828$	31.0706	1.07978
$829$	−35.5067	−1.23320	−0.616600	−	0.787277i	$-0.711490\pi$
$829$	−35.5067	−1.23320	−0.616600	+	0.787277i	$0.711490\pi$
$830$	−22.8583	−0.793423
$831$	41.8055	1.45022
$832$	21.4061	0.742122
$833$	−0.854542	−0.0296081
$834$	109.269	3.78369
$835$	45.5997	1.57804
$836$	−3.27781	−0.113365
$837$	−37.2897	−1.28892
$838$	−24.9628	−0.862326
$839$	38.6977	1.33599	0.667996	−	0.744165i	$-0.267152\pi$
$839$	38.6977	1.33599	0.667996	+	0.744165i	$0.267152\pi$
$840$	−3.48460	−0.120230
$841$	−5.13610	−0.177107
$842$	17.3400	0.597575
$843$	−52.2593	−1.79991
$844$	10.1968	0.350988
$845$	−13.5650	−0.466652
$846$	20.8747	0.717686
$847$	2.37036	0.0814465
$848$	23.0617	0.791941
$849$	4.75718	0.163266
$850$	1.39012	0.0476807
$851$	−3.86358	−0.132442
$852$	−70.5188	−2.41593
$853$	−11.3086	−0.387199	−0.193599	−	0.981081i	$-0.562016\pi$
$853$	−11.3086	−0.387199	−0.193599	+	0.981081i	$0.562016\pi$
$854$	6.15659	0.210674
$855$	−11.6138	−0.397184
$856$	−7.71783	−0.263790
$857$	−44.1854	−1.50935	−0.754673	−	0.656101i	$-0.772204\pi$
$857$	−44.1854	−1.50935	−0.754673	+	0.656101i	$0.772204\pi$
$858$	58.9709	2.01323
$859$	−9.07440	−0.309615	−0.154807	−	0.987945i	$-0.549476\pi$
$859$	−9.07440	−0.309615	−0.154807	+	0.987945i	$0.549476\pi$
$860$	30.0283	1.02396
$861$	−7.85833	−0.267811
$862$	−31.4270	−1.07041
$863$	−17.3463	−0.590474	−0.295237	−	0.955424i	$-0.595399\pi$
$863$	−17.3463	−0.590474	−0.295237	+	0.955424i	$0.595399\pi$
$864$	−37.8992	−1.28936
$865$	−28.1000	−0.955428
$866$	27.4394	0.932428
$867$	−47.4895	−1.61283
$868$	7.37013	0.250158
$869$	25.9266	0.879501
$870$	85.3324	2.89304
$871$	−19.8895	−0.673931
$872$	0.634334	0.0214813
$873$	31.2634	1.05811
$874$	5.46857	0.184977
$875$	1.25115	0.0422965
$876$	14.2921	0.482886
$877$	−17.9479	−0.606059	−0.303030	−	0.952981i	$-0.597998\pi$
$877$	−17.9479	−0.606059	−0.303030	+	0.952981i	$0.597998\pi$
$878$	−14.1008	−0.475880
$879$	−10.3149	−0.347912
$880$	−39.4662	−1.33040
$881$	−8.86877	−0.298796	−0.149398	−	0.988777i	$-0.547734\pi$
$881$	−8.86877	−0.298796	−0.149398	+	0.988777i	$0.547734\pi$
$882$	−61.2624	−2.06281
$883$	41.2733	1.38896	0.694479	−	0.719513i	$-0.255635\pi$
$883$	41.2733	1.38896	0.694479	+	0.719513i	$0.255635\pi$
$884$	−0.890044	−0.0299354
$885$	−114.029	−3.83306
$886$	67.6534	2.27286
$887$	40.7751	1.36909	0.684547	−	0.728968i	$-0.260000\pi$
$887$	40.7751	1.36909	0.684547	+	0.728968i	$0.260000\pi$
$888$	1.77374	0.0595229
$889$	4.86273	0.163091
$890$	−10.9391	−0.366681
$891$	0.624419	0.0209188
$892$	9.36852	0.313681
$893$	1.67120	0.0559246
$894$	−4.00657	−0.134000
$895$	6.91554	0.231161
$896$	−3.01487	−0.100720
$897$	−44.7520	−1.49422
$898$	3.96015	0.132152
$899$	35.8162	1.19454
$900$	45.3311	1.51104
$901$	−0.652192	−0.0217277
$902$	−23.7530	−0.790888
$903$	9.29267	0.309241
$904$	4.37179	0.145404
$905$	−10.6174	−0.352936
$906$	86.6685	2.87937
$907$	−46.1770	−1.53328	−0.766641	−	0.642075i	$-0.778074\pi$
$907$	−46.1770	−1.53328	−0.766641	+	0.642075i	$0.778074\pi$
$908$	−20.6267	−0.684520
$909$	17.3739	0.576257
$910$	−15.5874	−0.516718
$911$	31.7480	1.05186	0.525929	−	0.850528i	$-0.323718\pi$
$911$	31.7480	1.05186	0.525929	+	0.850528i	$0.323718\pi$
$912$	−9.40717	−0.311503
$913$	−9.72580	−0.321877
$914$	34.2259	1.13209
$915$	48.6632	1.60876
$916$	−2.44090	−0.0806496
$917$	8.46434	0.279517
$918$	1.25428	0.0413975
$919$	51.4334	1.69663	0.848316	−	0.529490i	$-0.177617\pi$
$919$	51.4334	1.69663	0.848316	+	0.529490i	$0.177617\pi$
$920$	7.99310	0.263525
$921$	−8.05299	−0.265355
$922$	42.0418	1.38457
$923$	62.5994	2.06048
$924$	7.47122	0.245785
$925$	−5.63686	−0.185339
$926$	45.6306	1.49952
$927$	23.3119	0.765662
$928$	36.4016	1.19494
$929$	−22.3106	−0.731986	−0.365993	−	0.930618i	$-0.619271\pi$
$929$	−22.3106	−0.731986	−0.365993	+	0.930618i	$0.619271\pi$
$930$	128.071	4.19962
$931$	−4.90459	−0.160741
$932$	36.9236	1.20947
$933$	−67.7382	−2.21765
$934$	−54.7489	−1.79144
$935$	1.11612	0.0365010
$936$	12.6624	0.413882
$937$	−5.86962	−0.191752	−0.0958760	−	0.995393i	$-0.530565\pi$
$937$	−5.86962	−0.191752	−0.0958760	+	0.995393i	$0.530565\pi$
$938$	−5.53981	−0.180881
$939$	−5.23553	−0.170855
$940$	−12.3091	−0.401479
$941$	29.8480	0.973017	0.486508	−	0.873676i	$-0.338270\pi$
$941$	29.8480	0.973017	0.486508	+	0.873676i	$0.338270\pi$
$942$	47.7947	1.55724
$943$	18.0257	0.586998
$944$	−56.9250	−1.85275
$945$	9.99178	0.325033
$946$	28.0885	0.913236
$947$	−31.0116	−1.00774	−0.503870	−	0.863779i	$-0.668091\pi$
$947$	−31.0116	−1.00774	−0.503870	+	0.863779i	$0.668091\pi$
$948$	−45.5175	−1.47834
$949$	−12.6871	−0.411840
$950$	7.97850	0.258857
$951$	78.3048	2.53921
$952$	0.0491954	0.00159443
$953$	−38.7509	−1.25526	−0.627632	−	0.778510i	$-0.715976\pi$
$953$	−38.7509	−1.25526	−0.627632	+	0.778510i	$0.715976\pi$
$954$	−46.7558	−1.51378
$955$	−57.3123	−1.85458
$956$	27.6463	0.894145
$957$	36.3074	1.17365
$958$	−58.0338	−1.87499
$959$	3.33589	0.107722
$960$	47.1268	1.52101
$961$	22.7547	0.734024
$962$	7.93438	0.255815
$963$	58.6307	1.88935
$964$	−17.4226	−0.561146
$965$	−31.1530	−1.00285
$966$	−12.4647	−0.401045
$967$	58.5578	1.88309	0.941547	−	0.336882i	$-0.109372\pi$
$967$	58.5578	1.88309	0.941547	+	0.336882i	$0.109372\pi$
$968$	2.49619	0.0802304
$969$	0.266038	0.00854638
$970$	−40.5284	−1.30129
$971$	1.90669	0.0611885	0.0305943	−	0.999532i	$-0.490260\pi$
$971$	1.90669	0.0611885	0.0305943	+	0.999532i	$0.490260\pi$
$972$	−26.5595	−0.851896
$973$	−12.2890	−0.393968
$974$	21.1906	0.678989
$975$	−65.2919	−2.09101
$976$	24.2934	0.777612
$977$	34.7429	1.11152	0.555762	−	0.831341i	$-0.312426\pi$
$977$	34.7429	1.11152	0.555762	+	0.831341i	$0.312426\pi$
$978$	−28.6885	−0.917356
$979$	−4.65441	−0.148756
$980$	36.1244	1.15395
$981$	−4.81890	−0.153856
$982$	−26.6445	−0.850261
$983$	−23.8301	−0.760062	−0.380031	−	0.924974i	$-0.624087\pi$
$983$	−23.8301	−0.760062	−0.380031	+	0.924974i	$0.624087\pi$
$984$	−8.27548	−0.263813
$985$	6.17411	0.196723
$986$	−1.20472	−0.0383660
$987$	−3.80922	−0.121249
$988$	−5.10835	−0.162518
$989$	−21.3159	−0.677805
$990$	80.0148	2.54304
$991$	20.0724	0.637620	0.318810	−	0.947819i	$-0.396717\pi$
$991$	20.0724	0.637620	0.318810	+	0.947819i	$0.396717\pi$
$992$	54.6334	1.73461
$993$	3.40706	0.108120
$994$	17.4357	0.553027
$995$	−37.6013	−1.19204
$996$	17.0749	0.541038
$997$	60.5392	1.91730	0.958648	−	0.284596i	$-0.0918594\pi$
$997$	60.5392	1.91730	0.958648	+	0.284596i	$0.0918594\pi$
$998$	24.7636	0.783878
$999$	−5.08605	−0.160916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.66	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.66	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+1.91542 q^{2} +2.79623 q^{3} +1.66883 q^{4} -3.26142 q^{5} +5.35595 q^{6} -0.602359 q^{7} -0.634334 q^{8} +4.81890 q^{9} +O(q^{10})\)	\(q+1.91542 q^{2} +2.79623 q^{3} +1.66883 q^{4} -3.26142 q^{5} +5.35595 q^{6} -0.602359 q^{7} -0.634334 q^{8} +4.81890 q^{9} -6.24698 q^{10} -2.65798 q^{11} +4.66642 q^{12} -4.14237 q^{13} -1.15377 q^{14} -9.11968 q^{15} -4.55267 q^{16} +0.128751 q^{17} +9.23020 q^{18} +0.738959 q^{19} -5.44275 q^{20} -1.68433 q^{21} -5.09115 q^{22} +3.86358 q^{23} -1.77374 q^{24} +5.63686 q^{25} -7.93438 q^{26} +5.08605 q^{27} -1.00523 q^{28} -4.88507 q^{29} -17.4680 q^{30} -7.33176 q^{31} -7.45160 q^{32} -7.43233 q^{33} +0.246612 q^{34} +1.96454 q^{35} +8.04191 q^{36} -1.00000 q^{37} +1.41541 q^{38} -11.5830 q^{39} +2.06883 q^{40} +4.66555 q^{41} -3.22620 q^{42} -5.51712 q^{43} -4.43571 q^{44} -15.7164 q^{45} +7.40038 q^{46} +2.26156 q^{47} -12.7303 q^{48} -6.63716 q^{49} +10.7970 q^{50} +0.360018 q^{51} -6.91290 q^{52} -5.06552 q^{53} +9.74192 q^{54} +8.66880 q^{55} +0.382097 q^{56} +2.06630 q^{57} -9.35695 q^{58} +12.5037 q^{59} -15.2192 q^{60} -5.33607 q^{61} -14.0434 q^{62} -2.90270 q^{63} -5.16759 q^{64} +13.5100 q^{65} -14.2360 q^{66} +4.80149 q^{67} +0.214863 q^{68} +10.8035 q^{69} +3.76293 q^{70} -15.1120 q^{71} -3.05679 q^{72} +3.06276 q^{73} -1.91542 q^{74} +15.7620 q^{75} +1.23319 q^{76} +1.60106 q^{77} -22.1863 q^{78} -9.75426 q^{79} +14.8482 q^{80} -0.234922 q^{81} +8.93647 q^{82} +3.65909 q^{83} -2.81086 q^{84} -0.419912 q^{85} -10.5676 q^{86} -13.6598 q^{87} +1.68605 q^{88} +1.75111 q^{89} -30.1036 q^{90} +2.49519 q^{91} +6.44765 q^{92} -20.5013 q^{93} +4.33184 q^{94} -2.41005 q^{95} -20.8364 q^{96} +6.48767 q^{97} -12.7129 q^{98} -12.8085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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