LMFDB - Embedded newform 4033.2.a.e.1.8

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:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.37038 q^{2} +1.65069 q^{3} +3.61871 q^{4} -2.32287 q^{5} -3.91275 q^{6} -2.51278 q^{7} -3.83696 q^{8} -0.275237 q^{9} +O(q^{10})$	\(q-2.37038 q^{2} +1.65069 q^{3} +3.61871 q^{4} -2.32287 q^{5} -3.91275 q^{6} -2.51278 q^{7} -3.83696 q^{8} -0.275237 q^{9} +5.50608 q^{10} -1.42719 q^{11} +5.97335 q^{12} +2.13674 q^{13} +5.95624 q^{14} -3.83432 q^{15} +1.85763 q^{16} +0.0765110 q^{17} +0.652417 q^{18} -4.14719 q^{19} -8.40578 q^{20} -4.14780 q^{21} +3.38299 q^{22} -1.71849 q^{23} -6.33361 q^{24} +0.395710 q^{25} -5.06489 q^{26} -5.40639 q^{27} -9.09300 q^{28} +3.03176 q^{29} +9.08881 q^{30} -2.42247 q^{31} +3.27061 q^{32} -2.35585 q^{33} -0.181360 q^{34} +5.83684 q^{35} -0.996003 q^{36} -1.00000 q^{37} +9.83042 q^{38} +3.52709 q^{39} +8.91274 q^{40} +10.4177 q^{41} +9.83188 q^{42} -7.12028 q^{43} -5.16459 q^{44} +0.639339 q^{45} +4.07348 q^{46} -7.20172 q^{47} +3.06637 q^{48} -0.685956 q^{49} -0.937984 q^{50} +0.126296 q^{51} +7.73225 q^{52} +4.17885 q^{53} +12.8152 q^{54} +3.31518 q^{55} +9.64141 q^{56} -6.84571 q^{57} -7.18642 q^{58} +3.15886 q^{59} -13.8753 q^{60} -4.72929 q^{61} +5.74219 q^{62} +0.691609 q^{63} -11.4679 q^{64} -4.96337 q^{65} +5.58425 q^{66} +7.80637 q^{67} +0.276871 q^{68} -2.83669 q^{69} -13.8355 q^{70} +6.51365 q^{71} +1.05607 q^{72} -9.23333 q^{73} +2.37038 q^{74} +0.653193 q^{75} -15.0075 q^{76} +3.58621 q^{77} -8.36055 q^{78} -2.35544 q^{79} -4.31504 q^{80} -8.09853 q^{81} -24.6939 q^{82} -12.8323 q^{83} -15.0097 q^{84} -0.177725 q^{85} +16.8778 q^{86} +5.00448 q^{87} +5.47607 q^{88} -17.2649 q^{89} -1.51548 q^{90} -5.36915 q^{91} -6.21871 q^{92} -3.99874 q^{93} +17.0708 q^{94} +9.63337 q^{95} +5.39875 q^{96} +7.03164 q^{97} +1.62598 q^{98} +0.392816 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.37038	−1.67611	−0.838056	−	0.545584i	$-0.816308\pi$
$2$	−2.37038	−1.67611	−0.838056	+	0.545584i	$0.816308\pi$
$3$	1.65069	0.953024	0.476512	−	0.879168i	$-0.341901\pi$
$3$	1.65069	0.953024	0.476512	+	0.879168i	$0.341901\pi$
$4$	3.61871	1.80935
$5$	−2.32287	−1.03882	−0.519409	−	0.854526i	$-0.673848\pi$
$5$	−2.32287	−1.03882	−0.519409	+	0.854526i	$0.673848\pi$
$6$	−3.91275	−1.59738
$7$	−2.51278	−0.949740	−0.474870	−	0.880056i	$-0.657505\pi$
$7$	−2.51278	−0.949740	−0.474870	+	0.880056i	$0.657505\pi$
$8$	−3.83696	−1.35657
$9$	−0.275237	−0.0917457
$10$	5.50608	1.74118
$11$	−1.42719	−0.430315	−0.215157	−	0.976579i	$-0.569026\pi$
$11$	−1.42719	−0.430315	−0.215157	+	0.976579i	$0.569026\pi$
$12$	5.97335	1.72436
$13$	2.13674	0.592626	0.296313	−	0.955091i	$-0.404243\pi$
$13$	2.13674	0.592626	0.296313	+	0.955091i	$0.404243\pi$
$14$	5.95624	1.59187
$15$	−3.83432	−0.990018
$16$	1.85763	0.464408
$17$	0.0765110	0.0185566	0.00927832	−	0.999957i	$-0.497047\pi$
$17$	0.0765110	0.0185566	0.00927832	+	0.999957i	$0.497047\pi$
$18$	0.652417	0.153776
$19$	−4.14719	−0.951431	−0.475715	−	0.879599i	$-0.657811\pi$
$19$	−4.14719	−0.951431	−0.475715	+	0.879599i	$0.657811\pi$
$20$	−8.40578	−1.87959
$21$	−4.14780	−0.905125
$22$	3.38299	0.721256
$23$	−1.71849	−0.358330	−0.179165	−	0.983819i	$-0.557340\pi$
$23$	−1.71849	−0.358330	−0.179165	+	0.983819i	$0.557340\pi$
$24$	−6.33361	−1.29284
$25$	0.395710	0.0791420
$26$	−5.06489	−0.993307
$27$	−5.40639	−1.04046
$28$	−9.09300	−1.71842
$29$	3.03176	0.562983	0.281492	−	0.959564i	$-0.409171\pi$
$29$	3.03176	0.562983	0.281492	+	0.959564i	$0.409171\pi$
$30$	9.08881	1.65938
$31$	−2.42247	−0.435089	−0.217545	−	0.976050i	$-0.569805\pi$
$31$	−2.42247	−0.435089	−0.217545	+	0.976050i	$0.569805\pi$
$32$	3.27061	0.578168
$33$	−2.35585	−0.410100
$34$	−0.181360	−0.0311030
$35$	5.83684	0.986607
$36$	−0.996003	−0.166000
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	9.83042	1.59471
$39$	3.52709	0.564786
$40$	8.91274	1.40923
$41$	10.4177	1.62697	0.813486	−	0.581585i	$-0.197567\pi$
$41$	10.4177	1.62697	0.813486	+	0.581585i	$0.197567\pi$
$42$	9.83188	1.51709
$43$	−7.12028	−1.08583	−0.542916	−	0.839787i	$-0.682680\pi$
$43$	−7.12028	−1.08583	−0.542916	+	0.839787i	$0.682680\pi$
$44$	−5.16459	−0.778592
$45$	0.639339	0.0953071
$46$	4.07348	0.600601
$47$	−7.20172	−1.05048	−0.525239	−	0.850955i	$-0.676024\pi$
$47$	−7.20172	−1.05048	−0.525239	+	0.850955i	$0.676024\pi$
$48$	3.06637	0.442592
$49$	−0.685956	−0.0979937
$50$	−0.937984	−0.132651
$51$	0.126296	0.0176849
$52$	7.73225	1.07227
$53$	4.17885	0.574009	0.287005	−	0.957929i	$-0.407340\pi$
$53$	4.17885	0.574009	0.287005	+	0.957929i	$0.407340\pi$
$54$	12.8152	1.74393
$55$	3.31518	0.447018
$56$	9.64141	1.28839
$57$	−6.84571	−0.906736
$58$	−7.18642	−0.943624
$59$	3.15886	0.411248	0.205624	−	0.978631i	$-0.434078\pi$
$59$	3.15886	0.411248	0.205624	+	0.978631i	$0.434078\pi$
$60$	−13.8753	−1.79129
$61$	−4.72929	−0.605523	−0.302762	−	0.953066i	$-0.597909\pi$
$61$	−4.72929	−0.605523	−0.302762	+	0.953066i	$0.597909\pi$
$62$	5.74219	0.729259
$63$	0.691609	0.0871346
$64$	−11.4679	−1.43348
$65$	−4.96337	−0.615630
$66$	5.58425	0.687374
$67$	7.80637	0.953700	0.476850	−	0.878985i	$-0.341779\pi$
$67$	7.80637	0.953700	0.476850	+	0.878985i	$0.341779\pi$
$68$	0.276871	0.0335755
$69$	−2.83669	−0.341497
$70$	−13.8355	−1.65366
$71$	6.51365	0.773028	0.386514	−	0.922284i	$-0.373679\pi$
$71$	6.51365	0.773028	0.386514	+	0.922284i	$0.373679\pi$
$72$	1.05607	0.124459
$73$	−9.23333	−1.08068	−0.540340	−	0.841447i	$-0.681704\pi$
$73$	−9.23333	−1.08068	−0.540340	+	0.841447i	$0.681704\pi$
$74$	2.37038	0.275551
$75$	0.653193	0.0754242
$76$	−15.0075	−1.72148
$77$	3.58621	0.408687
$78$	−8.36055	−0.946646
$79$	−2.35544	−0.265008	−0.132504	−	0.991182i	$-0.542302\pi$
$79$	−2.35544	−0.265008	−0.132504	+	0.991182i	$0.542302\pi$
$80$	−4.31504	−0.482436
$81$	−8.09853	−0.899837
$82$	−24.6939	−2.72699
$83$	−12.8323	−1.40853	−0.704264	−	0.709938i	$-0.748723\pi$
$83$	−12.8323	−1.40853	−0.704264	+	0.709938i	$0.748723\pi$
$84$	−15.0097	−1.63769
$85$	−0.177725	−0.0192770
$86$	16.8778	1.81998
$87$	5.00448	0.536537
$88$	5.47607	0.583752
$89$	−17.2649	−1.83008	−0.915038	−	0.403367i	$-0.867840\pi$
$89$	−17.2649	−1.83008	−0.915038	+	0.403367i	$0.867840\pi$
$90$	−1.51548	−0.159745
$91$	−5.36915	−0.562840
$92$	−6.21871	−0.648346
$93$	−3.99874	−0.414650
$94$	17.0708	1.76072
$95$	9.63337	0.988363
$96$	5.39875	0.551008
$97$	7.03164	0.713955	0.356978	−	0.934113i	$-0.383807\pi$
$97$	7.03164	0.713955	0.356978	+	0.934113i	$0.383807\pi$
$98$	1.62598	0.164248
$99$	0.392816	0.0394795
$100$	1.43196	0.143196
$101$	−6.54047	−0.650801	−0.325400	−	0.945576i	$-0.605499\pi$
$101$	−6.54047	−0.650801	−0.325400	+	0.945576i	$0.605499\pi$
$102$	−0.299369	−0.0296419
$103$	14.5249	1.43118	0.715590	−	0.698521i	$-0.246158\pi$
$103$	14.5249	1.43118	0.715590	+	0.698521i	$0.246158\pi$
$104$	−8.19859	−0.803938
$105$	9.63479	0.940260
$106$	−9.90547	−0.962104
$107$	19.0347	1.84015	0.920077	−	0.391739i	$-0.128126\pi$
$107$	19.0347	1.84015	0.920077	+	0.391739i	$0.128126\pi$
$108$	−19.5641	−1.88256
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−7.85824	−0.749253
$111$	−1.65069	−0.156676
$112$	−4.66782	−0.441067
$113$	14.2943	1.34469	0.672346	−	0.740237i	$-0.265287\pi$
$113$	14.2943	1.34469	0.672346	+	0.740237i	$0.265287\pi$
$114$	16.2269	1.51979
$115$	3.99182	0.372239
$116$	10.9711	1.01864
$117$	−0.588111	−0.0543709
$118$	−7.48769	−0.689298
$119$	−0.192255	−0.0176240
$120$	14.7121	1.34303
$121$	−8.96312	−0.814829
$122$	11.2102	1.01493
$123$	17.1964	1.55054
$124$	−8.76623	−0.787230
$125$	10.6952	0.956603
$126$	−1.63938	−0.146047
$127$	−6.33769	−0.562379	−0.281190	−	0.959652i	$-0.590729\pi$
$127$	−6.33769	−0.562379	−0.281190	+	0.959652i	$0.590729\pi$
$128$	20.6420	1.82451
$129$	−11.7533	−1.03482
$130$	11.7651	1.03187
$131$	19.7453	1.72515	0.862577	−	0.505927i	$-0.168849\pi$
$131$	19.7453	1.72515	0.862577	+	0.505927i	$0.168849\pi$
$132$	−8.52512	−0.742016
$133$	10.4210	0.903612
$134$	−18.5041	−1.59851
$135$	12.5583	1.08085
$136$	−0.293569	−0.0251734
$137$	4.62278	0.394951	0.197475	−	0.980308i	$-0.436726\pi$
$137$	4.62278	0.394951	0.197475	+	0.980308i	$0.436726\pi$
$138$	6.72403	0.572387
$139$	18.9433	1.60675	0.803376	−	0.595472i	$-0.203035\pi$
$139$	18.9433	1.60675	0.803376	+	0.595472i	$0.203035\pi$
$140$	21.1218	1.78512
$141$	−11.8878	−1.00113
$142$	−15.4398	−1.29568
$143$	−3.04954	−0.255016
$144$	−0.511290	−0.0426075
$145$	−7.04237	−0.584837
$146$	21.8865	1.81134
$147$	−1.13230	−0.0933903
$148$	−3.61871	−0.297456
$149$	−13.6762	−1.12040	−0.560200	−	0.828357i	$-0.689276\pi$
$149$	−13.6762	−1.12040	−0.560200	+	0.828357i	$0.689276\pi$
$150$	−1.54832	−0.126419
$151$	−4.84192	−0.394030	−0.197015	−	0.980400i	$-0.563125\pi$
$151$	−4.84192	−0.394030	−0.197015	+	0.980400i	$0.563125\pi$
$152$	15.9126	1.29068
$153$	−0.0210587	−0.00170249
$154$	−8.50070	−0.685006
$155$	5.62708	0.451978
$156$	12.7635	1.02190
$157$	0.531032	0.0423810	0.0211905	−	0.999775i	$-0.493254\pi$
$157$	0.531032	0.0423810	0.0211905	+	0.999775i	$0.493254\pi$
$158$	5.58330	0.444184
$159$	6.89797	0.547044
$160$	−7.59720	−0.600611
$161$	4.31818	0.340320
$162$	19.1966	1.50823
$163$	−16.9666	−1.32893	−0.664464	−	0.747320i	$-0.731340\pi$
$163$	−16.9666	−1.32893	−0.664464	+	0.747320i	$0.731340\pi$
$164$	37.6986	2.94377
$165$	5.47232	0.426019
$166$	30.4175	2.36085
$167$	−1.08110	−0.0836582	−0.0418291	−	0.999125i	$-0.513318\pi$
$167$	−1.08110	−0.0836582	−0.0418291	+	0.999125i	$0.513318\pi$
$168$	15.9149	1.22786
$169$	−8.43433	−0.648795
$170$	0.421276	0.0323104
$171$	1.14146	0.0872897
$172$	−25.7662	−1.96465
$173$	0.825152	0.0627351	0.0313676	−	0.999508i	$-0.490014\pi$
$173$	0.825152	0.0627351	0.0313676	+	0.999508i	$0.490014\pi$
$174$	−11.8625	−0.899296
$175$	−0.994331	−0.0751643
$176$	−2.65120	−0.199842
$177$	5.21428	0.391929
$178$	40.9244	3.06742
$179$	12.1615	0.908996	0.454498	−	0.890748i	$-0.349819\pi$
$179$	12.1615	0.908996	0.454498	+	0.890748i	$0.349819\pi$
$180$	2.31358	0.172444
$181$	4.73045	0.351611	0.175806	−	0.984425i	$-0.443747\pi$
$181$	4.73045	0.351611	0.175806	+	0.984425i	$0.443747\pi$
$182$	12.7269	0.943384
$183$	−7.80657	−0.577078
$184$	6.59377	0.486099
$185$	2.32287	0.170781
$186$	9.47855	0.695001
$187$	−0.109196	−0.00798520
$188$	−26.0609	−1.90069
$189$	13.5850	0.988166
$190$	−22.8348	−1.65661
$191$	22.0282	1.59391	0.796953	−	0.604041i	$-0.206444\pi$
$191$	22.0282	1.59391	0.796953	+	0.604041i	$0.206444\pi$
$192$	−18.9298	−1.36614
$193$	12.9288	0.930632	0.465316	−	0.885145i	$-0.345941\pi$
$193$	12.9288	0.930632	0.465316	+	0.885145i	$0.345941\pi$
$194$	−16.6677	−1.19667
$195$	−8.19296	−0.586710
$196$	−2.48227	−0.177305
$197$	23.5961	1.68115	0.840576	−	0.541694i	$-0.182217\pi$
$197$	23.5961	1.68115	0.840576	+	0.541694i	$0.182217\pi$
$198$	−0.931124	−0.0661721
$199$	14.1905	1.00594	0.502968	−	0.864305i	$-0.332241\pi$
$199$	14.1905	1.00594	0.502968	+	0.864305i	$0.332241\pi$
$200$	−1.51832	−0.107362
$201$	12.8859	0.908899
$202$	15.5034	1.09082
$203$	−7.61813	−0.534688
$204$	0.457027	0.0319983
$205$	−24.1989	−1.69013
$206$	−34.4295	−2.39882
$207$	0.472992	0.0328752
$208$	3.96928	0.275220
$209$	5.91884	0.409415
$210$	−22.8381	−1.57598
$211$	11.7361	0.807947	0.403973	−	0.914771i	$-0.367629\pi$
$211$	11.7361	0.807947	0.403973	+	0.914771i	$0.367629\pi$
$212$	15.1220	1.03859
$213$	10.7520	0.736714
$214$	−45.1195	−3.08430
$215$	16.5395	1.12798
$216$	20.7441	1.41146
$217$	6.08713	0.413222
$218$	−2.37038	−0.160542
$219$	−15.2413	−1.02991
$220$	11.9967	0.808815
$221$	0.163484	0.0109971
$222$	3.91275	0.262607
$223$	−11.8942	−0.796493	−0.398246	−	0.917278i	$-0.630381\pi$
$223$	−11.8942	−0.796493	−0.398246	+	0.917278i	$0.630381\pi$
$224$	−8.21832	−0.549109
$225$	−0.108914	−0.00726094
$226$	−33.8829	−2.25386
$227$	13.9596	0.926528	0.463264	−	0.886220i	$-0.346678\pi$
$227$	13.9596	0.926528	0.463264	+	0.886220i	$0.346678\pi$
$228$	−24.7726	−1.64061
$229$	−20.0195	−1.32293	−0.661464	−	0.749977i	$-0.730065\pi$
$229$	−20.0195	−1.32293	−0.661464	+	0.749977i	$0.730065\pi$
$230$	−9.46214	−0.623915
$231$	5.91971	0.389489
$232$	−11.6327	−0.763726
$233$	−8.51978	−0.558149	−0.279075	−	0.960269i	$-0.590028\pi$
$233$	−8.51978	−0.558149	−0.279075	+	0.960269i	$0.590028\pi$
$234$	1.39405	0.0911317
$235$	16.7286	1.09126
$236$	11.4310	0.744093
$237$	−3.88810	−0.252559
$238$	0.455718	0.0295398
$239$	−0.960800	−0.0621490	−0.0310745	−	0.999517i	$-0.509893\pi$
$239$	−0.960800	−0.0621490	−0.0310745	+	0.999517i	$0.509893\pi$
$240$	−7.12277	−0.459773
$241$	−0.0890788	−0.00573807	−0.00286904	−	0.999996i	$-0.500913\pi$
$241$	−0.0890788	−0.00573807	−0.00286904	+	0.999996i	$0.500913\pi$
$242$	21.2460	1.36575
$243$	2.85103	0.182894
$244$	−17.1139	−1.09561
$245$	1.59338	0.101798
$246$	−40.7619	−2.59888
$247$	−8.86148	−0.563842
$248$	9.29493	0.590228
$249$	−21.1821	−1.34236
$250$	−25.3516	−1.60338
$251$	23.5534	1.48668	0.743339	−	0.668915i	$-0.233241\pi$
$251$	23.5534	1.48668	0.743339	+	0.668915i	$0.233241\pi$
$252$	2.50273	0.157657
$253$	2.45262	0.154195
$254$	15.0227	0.942611
$255$	−0.293368	−0.0183714
$256$	−25.9937	−1.62460
$257$	12.4555	0.776954	0.388477	−	0.921458i	$-0.373001\pi$
$257$	12.4555	0.776954	0.388477	+	0.921458i	$0.373001\pi$
$258$	27.8599	1.73448
$259$	2.51278	0.156136
$260$	−17.9610	−1.11389
$261$	−0.834453	−0.0516513
$262$	−46.8038	−2.89155
$263$	−15.9868	−0.985791	−0.492895	−	0.870089i	$-0.664062\pi$
$263$	−15.9868	−0.985791	−0.492895	+	0.870089i	$0.664062\pi$
$264$	9.03928	0.556329
$265$	−9.70691	−0.596291
$266$	−24.7017	−1.51456
$267$	−28.4989	−1.74411
$268$	28.2490	1.72558
$269$	−13.3951	−0.816715	−0.408358	−	0.912822i	$-0.633898\pi$
$269$	−13.3951	−0.816715	−0.408358	+	0.912822i	$0.633898\pi$
$270$	−29.7680	−1.81162
$271$	18.9758	1.15270	0.576349	−	0.817203i	$-0.304477\pi$
$271$	18.9758	1.15270	0.576349	+	0.817203i	$0.304477\pi$
$272$	0.142129	0.00861786
$273$	−8.86279	−0.536400
$274$	−10.9577	−0.661982
$275$	−0.564754	−0.0340560
$276$	−10.2651	−0.617889
$277$	−3.48178	−0.209200	−0.104600	−	0.994514i	$-0.533356\pi$
$277$	−3.48178	−0.209200	−0.104600	+	0.994514i	$0.533356\pi$
$278$	−44.9029	−2.69310
$279$	0.666755	0.0399176
$280$	−22.3957	−1.33840
$281$	−7.00728	−0.418019	−0.209010	−	0.977914i	$-0.567024\pi$
$281$	−7.00728	−0.418019	−0.209010	+	0.977914i	$0.567024\pi$
$282$	28.1785	1.67801
$283$	9.19125	0.546363	0.273182	−	0.961962i	$-0.411924\pi$
$283$	9.19125	0.546363	0.273182	+	0.961962i	$0.411924\pi$
$284$	23.5710	1.39868
$285$	15.9017	0.941933
$286$	7.22858	0.427435
$287$	−26.1774	−1.54520
$288$	−0.900194	−0.0530444
$289$	−16.9941	−0.999656
$290$	16.6931	0.980253
$291$	11.6070	0.680416
$292$	−33.4127	−1.95533
$293$	−28.0100	−1.63636	−0.818180	−	0.574963i	$-0.805017\pi$
$293$	−28.0100	−1.63636	−0.818180	+	0.574963i	$0.805017\pi$
$294$	2.68398	0.156533
$295$	−7.33760	−0.427212
$296$	3.83696	0.223019
$297$	7.71595	0.447725
$298$	32.4179	1.87792
$299$	−3.67197	−0.212356
$300$	2.36371	0.136469
$301$	17.8917	1.03126
$302$	11.4772	0.660438
$303$	−10.7963	−0.620229
$304$	−7.70396	−0.441852
$305$	10.9855	0.629028
$306$	0.0499171	0.00285357
$307$	−25.4948	−1.45507	−0.727533	−	0.686073i	$-0.759333\pi$
$307$	−25.4948	−1.45507	−0.727533	+	0.686073i	$0.759333\pi$
$308$	12.9775	0.739460
$309$	23.9760	1.36395
$310$	−13.3383	−0.757567
$311$	10.5271	0.596936	0.298468	−	0.954420i	$-0.403524\pi$
$311$	10.5271	0.596936	0.298468	+	0.954420i	$0.403524\pi$
$312$	−13.5333	−0.766172
$313$	13.3424	0.754155	0.377077	−	0.926182i	$-0.376929\pi$
$313$	13.3424	0.754155	0.377077	+	0.926182i	$0.376929\pi$
$314$	−1.25875	−0.0710353
$315$	−1.60652	−0.0905169
$316$	−8.52367	−0.479494
$317$	−13.1301	−0.737461	−0.368730	−	0.929536i	$-0.620207\pi$
$317$	−13.1301	−0.737461	−0.368730	+	0.929536i	$0.620207\pi$
$318$	−16.3508	−0.916908
$319$	−4.32690	−0.242260
$320$	26.6383	1.48913
$321$	31.4203	1.75371
$322$	−10.2357	−0.570415
$323$	−0.317306	−0.0176554
$324$	−29.3062	−1.62812
$325$	0.845530	0.0469016
$326$	40.2174	2.22743
$327$	1.65069	0.0912831
$328$	−39.9723	−2.20710
$329$	18.0963	0.997681
$330$	−12.9715	−0.714056
$331$	−13.1805	−0.724463	−0.362232	−	0.932088i	$-0.617985\pi$
$331$	−13.1805	−0.724463	−0.362232	+	0.932088i	$0.617985\pi$
$332$	−46.4364	−2.54853
$333$	0.275237	0.0150829
$334$	2.56262	0.140221
$335$	−18.1332	−0.990720
$336$	−7.70510	−0.420348
$337$	13.9222	0.758393	0.379197	−	0.925316i	$-0.376200\pi$
$337$	13.9222	0.758393	0.379197	+	0.925316i	$0.376200\pi$
$338$	19.9926	1.08745
$339$	23.5953	1.28152
$340$	−0.643134	−0.0348789
$341$	3.45734	0.187225
$342$	−2.70570	−0.146307
$343$	19.3131	1.04281
$344$	27.3202	1.47301
$345$	6.58925	0.354753
$346$	−1.95592	−0.105151
$347$	6.41817	0.344545	0.172273	−	0.985049i	$-0.444889\pi$
$347$	6.41817	0.344545	0.172273	+	0.985049i	$0.444889\pi$
$348$	18.1098	0.970785
$349$	18.1823	0.973278	0.486639	−	0.873603i	$-0.338223\pi$
$349$	18.1823	0.973278	0.486639	+	0.873603i	$0.338223\pi$
$350$	2.35694	0.125984
$351$	−11.5521	−0.616603
$352$	−4.66779	−0.248794
$353$	11.3528	0.604247	0.302123	−	0.953269i	$-0.402305\pi$
$353$	11.3528	0.604247	0.302123	+	0.953269i	$0.402305\pi$
$354$	−12.3598	−0.656917
$355$	−15.1303	−0.803035
$356$	−62.4767	−3.31126
$357$	−0.317353	−0.0167961
$358$	−28.8275	−1.52358
$359$	20.4042	1.07689	0.538446	−	0.842660i	$-0.319012\pi$
$359$	20.4042	1.07689	0.538446	+	0.842660i	$0.319012\pi$
$360$	−2.45312	−0.129291
$361$	−1.80081	−0.0947797
$362$	−11.2130	−0.589340
$363$	−14.7953	−0.776552
$364$	−19.4294	−1.01838
$365$	21.4478	1.12263
$366$	18.5045	0.967248
$367$	29.3063	1.52978	0.764888	−	0.644163i	$-0.222794\pi$
$367$	29.3063	1.52978	0.764888	+	0.644163i	$0.222794\pi$
$368$	−3.19233	−0.166411
$369$	−2.86734	−0.149268
$370$	−5.50608	−0.286247
$371$	−10.5005	−0.545160
$372$	−14.4703	−0.750249
$373$	26.9619	1.39604	0.698018	−	0.716080i	$-0.254066\pi$
$373$	26.9619	1.39604	0.698018	+	0.716080i	$0.254066\pi$
$374$	0.258836	0.0133841
$375$	17.6543	0.911666
$376$	27.6327	1.42505
$377$	6.47809	0.333638
$378$	−32.2017	−1.65628
$379$	26.8519	1.37929	0.689644	−	0.724149i	$-0.257767\pi$
$379$	26.8519	1.37929	0.689644	+	0.724149i	$0.257767\pi$
$380$	34.8604	1.78830
$381$	−10.4615	−0.535961
$382$	−52.2153	−2.67157
$383$	−26.3010	−1.34392	−0.671959	−	0.740588i	$-0.734547\pi$
$383$	−26.3010	−1.34392	−0.671959	+	0.740588i	$0.734547\pi$
$384$	34.0734	1.73880
$385$	−8.33030	−0.424551
$386$	−30.6461	−1.55984
$387$	1.95976	0.0996204
$388$	25.4455	1.29180
$389$	−30.7796	−1.56059	−0.780295	−	0.625412i	$-0.784931\pi$
$389$	−30.7796	−1.56059	−0.780295	+	0.625412i	$0.784931\pi$
$390$	19.4204	0.983392
$391$	−0.131483	−0.00664940
$392$	2.63198	0.132935
$393$	32.5932	1.64411
$394$	−55.9317	−2.81780
$395$	5.47138	0.275295
$396$	1.42149	0.0714324
$397$	7.81345	0.392146	0.196073	−	0.980589i	$-0.437181\pi$
$397$	7.81345	0.392146	0.196073	+	0.980589i	$0.437181\pi$
$398$	−33.6368	−1.68606
$399$	17.2017	0.861164
$400$	0.735084	0.0367542
$401$	−19.5109	−0.974326	−0.487163	−	0.873311i	$-0.661968\pi$
$401$	−19.5109	−0.974326	−0.487163	+	0.873311i	$0.661968\pi$
$402$	−30.5444	−1.52342
$403$	−5.17620	−0.257845
$404$	−23.6680	−1.17753
$405$	18.8118	0.934767
$406$	18.0579	0.896197
$407$	1.42719	0.0707433
$408$	−0.484591	−0.0239908
$409$	−3.48916	−0.172528	−0.0862639	−	0.996272i	$-0.527493\pi$
$409$	−3.48916	−0.172528	−0.0862639	+	0.996272i	$0.527493\pi$
$410$	57.3607	2.83284
$411$	7.63075	0.376397
$412$	52.5613	2.58951
$413$	−7.93750	−0.390579
$414$	−1.12117	−0.0551026
$415$	29.8077	1.46320
$416$	6.98845	0.342637
$417$	31.2695	1.53127
$418$	−14.0299	−0.686225
$419$	−36.9002	−1.80269	−0.901347	−	0.433098i	$-0.857421\pi$
$419$	−36.9002	−1.80269	−0.901347	+	0.433098i	$0.857421\pi$
$420$	34.8655	1.70126
$421$	23.0888	1.12528	0.562640	−	0.826702i	$-0.309786\pi$
$421$	23.0888	1.12528	0.562640	+	0.826702i	$0.309786\pi$
$422$	−27.8190	−1.35421
$423$	1.98218	0.0963769
$424$	−16.0341	−0.778683
$425$	0.0302762	0.00146861
$426$	−25.4863	−1.23482
$427$	11.8836	0.575090
$428$	68.8810	3.32949
$429$	−5.03383	−0.243036
$430$	−39.2048	−1.89062
$431$	21.7340	1.04689	0.523445	−	0.852060i	$-0.324647\pi$
$431$	21.7340	1.04689	0.523445	+	0.852060i	$0.324647\pi$
$432$	−10.0431	−0.483198
$433$	7.71229	0.370629	0.185314	−	0.982679i	$-0.440670\pi$
$433$	7.71229	0.370629	0.185314	+	0.982679i	$0.440670\pi$
$434$	−14.4288	−0.692606
$435$	−11.6247	−0.557364
$436$	3.61871	0.173305
$437$	7.12690	0.340926
$438$	36.1277	1.72625
$439$	11.6279	0.554968	0.277484	−	0.960730i	$-0.410499\pi$
$439$	11.6279	0.554968	0.277484	+	0.960730i	$0.410499\pi$
$440$	−12.7202	−0.606411
$441$	0.188800	0.00899050
$442$	−0.387520	−0.0184325
$443$	29.2092	1.38777	0.693885	−	0.720086i	$-0.255898\pi$
$443$	29.2092	1.38777	0.693885	+	0.720086i	$0.255898\pi$
$444$	−5.97335	−0.283483
$445$	40.1041	1.90112
$446$	28.1937	1.33501
$447$	−22.5752	−1.06777
$448$	28.8162	1.36144
$449$	21.4712	1.01329	0.506644	−	0.862155i	$-0.330886\pi$
$449$	21.4712	1.01329	0.506644	+	0.862155i	$0.330886\pi$
$450$	0.258168	0.0121702
$451$	−14.8681	−0.700110
$452$	51.7268	2.43302
$453$	−7.99249	−0.375520
$454$	−33.0895	−1.55297
$455$	12.4718	0.584688
$456$	26.2667	1.23005
$457$	−12.5004	−0.584742	−0.292371	−	0.956305i	$-0.594444\pi$
$457$	−12.5004	−0.584742	−0.292371	+	0.956305i	$0.594444\pi$
$458$	47.4539	2.21738
$459$	−0.413648	−0.0193074
$460$	14.4452	0.673513
$461$	25.6243	1.19344	0.596721	−	0.802449i	$-0.296470\pi$
$461$	25.6243	1.19344	0.596721	+	0.802449i	$0.296470\pi$
$462$	−14.0320	−0.652827
$463$	−27.3134	−1.26936	−0.634680	−	0.772775i	$-0.718868\pi$
$463$	−27.3134	−1.26936	−0.634680	+	0.772775i	$0.718868\pi$
$464$	5.63190	0.261454
$465$	9.28855	0.430746
$466$	20.1951	0.935521
$467$	−6.92653	−0.320521	−0.160261	−	0.987075i	$-0.551233\pi$
$467$	−6.92653	−0.320521	−0.160261	+	0.987075i	$0.551233\pi$
$468$	−2.12820	−0.0983761
$469$	−19.6157	−0.905767
$470$	−39.6532	−1.82907
$471$	0.876567	0.0403901
$472$	−12.1204	−0.557886
$473$	10.1620	0.467249
$474$	9.21628	0.423318
$475$	−1.64108	−0.0752981
$476$	−0.695715	−0.0318880
$477$	−1.15017	−0.0526629
$478$	2.27746	0.104169
$479$	24.1242	1.10226	0.551132	−	0.834418i	$-0.314196\pi$
$479$	24.1242	1.10226	0.551132	+	0.834418i	$0.314196\pi$
$480$	−12.5406	−0.572397
$481$	−2.13674	−0.0974271
$482$	0.211151	0.00961765
$483$	7.12796	0.324333
$484$	−32.4349	−1.47431
$485$	−16.3336	−0.741669
$486$	−6.75802	−0.306550
$487$	16.0603	0.727760	0.363880	−	0.931446i	$-0.381452\pi$
$487$	16.0603	0.727760	0.363880	+	0.931446i	$0.381452\pi$
$488$	18.1461	0.821434
$489$	−28.0066	−1.26650
$490$	−3.77693	−0.170624
$491$	−1.00173	−0.0452076	−0.0226038	−	0.999745i	$-0.507196\pi$
$491$	−1.00173	−0.0452076	−0.0226038	+	0.999745i	$0.507196\pi$
$492$	62.2286	2.80548
$493$	0.231963	0.0104471
$494$	21.0051	0.945063
$495$	−0.912460	−0.0410120
$496$	−4.50007	−0.202059
$497$	−16.3673	−0.734175
$498$	50.2097	2.24995
$499$	−23.2845	−1.04236	−0.521179	−	0.853448i	$-0.674507\pi$
$499$	−23.2845	−1.04236	−0.521179	+	0.853448i	$0.674507\pi$
$500$	38.7026	1.73083
$501$	−1.78456	−0.0797282
$502$	−55.8305	−2.49184
$503$	7.02628	0.313286	0.156643	−	0.987655i	$-0.449933\pi$
$503$	7.02628	0.313286	0.156643	+	0.987655i	$0.449933\pi$
$504$	−2.65367	−0.118204
$505$	15.1926	0.676063
$506$	−5.81363	−0.258448
$507$	−13.9224	−0.618317
$508$	−22.9343	−1.01754
$509$	8.68160	0.384805	0.192402	−	0.981316i	$-0.438372\pi$
$509$	8.68160	0.384805	0.192402	+	0.981316i	$0.438372\pi$
$510$	0.695394	0.0307926
$511$	23.2013	1.02636
$512$	20.3309	0.898508
$513$	22.4213	0.989925
$514$	−29.5243	−1.30226
$515$	−33.7394	−1.48673
$516$	−42.5319	−1.87236
$517$	10.2782	0.452036
$518$	−5.95624	−0.261702
$519$	1.36207	0.0597881
$520$	19.0442	0.835145
$521$	14.4520	0.633155	0.316577	−	0.948567i	$-0.397466\pi$
$521$	14.4520	0.633155	0.316577	+	0.948567i	$0.397466\pi$
$522$	1.97797	0.0865734
$523$	24.5846	1.07501	0.537505	−	0.843260i	$-0.319367\pi$
$523$	24.5846	1.07501	0.537505	+	0.843260i	$0.319367\pi$
$524$	71.4524	3.12141
$525$	−1.64133	−0.0716334
$526$	37.8949	1.65230
$527$	−0.185346	−0.00807379
$528$	−4.37630	−0.190454
$529$	−20.0468	−0.871600
$530$	23.0091	0.999451
$531$	−0.869434	−0.0377302
$532$	37.7104	1.63495
$533$	22.2599	0.964185
$534$	67.5534	2.92332
$535$	−44.2151	−1.91158
$536$	−29.9527	−1.29376
$537$	20.0749	0.866294
$538$	31.7516	1.36891
$539$	0.978991	0.0421681
$540$	45.4449	1.95564
$541$	−6.84218	−0.294168	−0.147084	−	0.989124i	$-0.546989\pi$
$541$	−6.84218	−0.294168	−0.147084	+	0.989124i	$0.546989\pi$
$542$	−44.9799	−1.93205
$543$	7.80848	0.335094
$544$	0.250238	0.0107289
$545$	−2.32287	−0.0995007
$546$	21.0082	0.899067
$547$	−4.78992	−0.204802	−0.102401	−	0.994743i	$-0.532653\pi$
$547$	−4.78992	−0.204802	−0.102401	+	0.994743i	$0.532653\pi$
$548$	16.7285	0.714606
$549$	1.30168	0.0555542
$550$	1.33868	0.0570816
$551$	−12.5733	−0.535640
$552$	10.8842	0.463264
$553$	5.91871	0.251689
$554$	8.25315	0.350643
$555$	3.83432	0.162758
$556$	68.5504	2.90718
$557$	1.01644	0.0430681	0.0215341	−	0.999768i	$-0.493145\pi$
$557$	1.01644	0.0430681	0.0215341	+	0.999768i	$0.493145\pi$
$558$	−1.58046	−0.0669063
$559$	−15.2142	−0.643492
$560$	10.8427	0.458189
$561$	−0.180248	−0.00761008
$562$	16.6099	0.700648
$563$	27.7428	1.16922	0.584609	−	0.811315i	$-0.301248\pi$
$563$	27.7428	1.16922	0.584609	+	0.811315i	$0.301248\pi$
$564$	−43.0184	−1.81140
$565$	−33.2037	−1.39689
$566$	−21.7868	−0.915766
$567$	20.3498	0.854611
$568$	−24.9926	−1.04867
$569$	−39.4315	−1.65306	−0.826528	−	0.562896i	$-0.809687\pi$
$569$	−39.4315	−1.65306	−0.826528	+	0.562896i	$0.809687\pi$
$570$	−37.6930	−1.57879
$571$	7.84111	0.328140	0.164070	−	0.986449i	$-0.447538\pi$
$571$	7.84111	0.328140	0.164070	+	0.986449i	$0.447538\pi$
$572$	−11.0354	−0.461413
$573$	36.3617	1.51903
$574$	62.0503	2.58993
$575$	−0.680024	−0.0283589
$576$	3.15638	0.131516
$577$	−7.39793	−0.307980	−0.153990	−	0.988072i	$-0.549212\pi$
$577$	−7.39793	−0.307980	−0.153990	+	0.988072i	$0.549212\pi$
$578$	40.2826	1.67554
$579$	21.3413	0.886914
$580$	−25.4843	−1.05818
$581$	32.2447	1.33774
$582$	−27.5131	−1.14045
$583$	−5.96402	−0.247005
$584$	35.4279	1.46602
$585$	1.36610	0.0564814
$586$	66.3943	2.74272
$587$	35.2141	1.45344	0.726721	−	0.686933i	$-0.241043\pi$
$587$	35.2141	1.45344	0.726721	+	0.686933i	$0.241043\pi$
$588$	−4.09745	−0.168976
$589$	10.0465	0.413957
$590$	17.3929	0.716055
$591$	38.9497	1.60218
$592$	−1.85763	−0.0763483
$593$	−8.38492	−0.344328	−0.172164	−	0.985068i	$-0.555076\pi$
$593$	−8.38492	−0.344328	−0.172164	+	0.985068i	$0.555076\pi$
$594$	−18.2898	−0.750438
$595$	0.446583	0.0183081
$596$	−49.4903	−2.02720
$597$	23.4240	0.958681
$598$	8.70397	0.355932
$599$	34.6722	1.41667	0.708333	−	0.705878i	$-0.249447\pi$
$599$	34.6722	1.41667	0.708333	+	0.705878i	$0.249447\pi$
$600$	−2.50627	−0.102318
$601$	−9.45612	−0.385723	−0.192862	−	0.981226i	$-0.561777\pi$
$601$	−9.45612	−0.385723	−0.192862	+	0.981226i	$0.561777\pi$
$602$	−42.4101	−1.72851
$603$	−2.14860	−0.0874979
$604$	−17.5215	−0.712939
$605$	20.8201	0.846459
$606$	25.5912	1.03957
$607$	30.1795	1.22495	0.612474	−	0.790491i	$-0.290174\pi$
$607$	30.1795	1.22495	0.612474	+	0.790491i	$0.290174\pi$
$608$	−13.5639	−0.550087
$609$	−12.5751	−0.509570
$610$	−26.0398	−1.05432
$611$	−15.3882	−0.622540
$612$	−0.0762052	−0.00308041
$613$	−16.1735	−0.653242	−0.326621	−	0.945155i	$-0.605910\pi$
$613$	−16.1735	−0.653242	−0.326621	+	0.945155i	$0.605910\pi$
$614$	60.4324	2.43885
$615$	−39.9448	−1.61073
$616$	−13.7601	−0.554412
$617$	−0.420747	−0.0169387	−0.00846933	−	0.999964i	$-0.502696\pi$
$617$	−0.420747	−0.0169387	−0.00846933	+	0.999964i	$0.502696\pi$
$618$	−56.8323	−2.28613
$619$	−0.280082	−0.0112574	−0.00562872	−	0.999984i	$-0.501792\pi$
$619$	−0.280082	−0.0112574	−0.00562872	+	0.999984i	$0.501792\pi$
$620$	20.3628	0.817789
$621$	9.29082	0.372828
$622$	−24.9532	−1.00053
$623$	43.3829	1.73810
$624$	6.55204	0.262292
$625$	−26.8220	−1.07288
$626$	−31.6265	−1.26405
$627$	9.77014	0.390182
$628$	1.92165	0.0766822
$629$	−0.0765110	−0.00305069
$630$	3.80806	0.151717
$631$	0.696718	0.0277359	0.0138679	−	0.999904i	$-0.495586\pi$
$631$	0.696718	0.0277359	0.0138679	+	0.999904i	$0.495586\pi$
$632$	9.03774	0.359502
$633$	19.3726	0.769992
$634$	31.1234	1.23607
$635$	14.7216	0.584209
$636$	24.9617	0.989797
$637$	−1.46571	−0.0580736
$638$	10.2564	0.406055
$639$	−1.79280	−0.0709220
$640$	−47.9486	−1.89533
$641$	−2.41470	−0.0953749	−0.0476875	−	0.998862i	$-0.515185\pi$
$641$	−2.41470	−0.0953749	−0.0476875	+	0.998862i	$0.515185\pi$
$642$	−74.4781	−2.93942
$643$	−9.09862	−0.358815	−0.179407	−	0.983775i	$-0.557418\pi$
$643$	−9.09862	−0.358815	−0.179407	+	0.983775i	$0.557418\pi$
$644$	15.6262	0.615760
$645$	27.3014	1.07499
$646$	0.752135	0.0295924
$647$	24.8436	0.976702	0.488351	−	0.872647i	$-0.337599\pi$
$647$	24.8436	0.976702	0.488351	+	0.872647i	$0.337599\pi$
$648$	31.0737	1.22069
$649$	−4.50829	−0.176966
$650$	−2.00423	−0.0786123
$651$	10.0479	0.393810
$652$	−61.3973	−2.40450
$653$	−46.3204	−1.81266	−0.906328	−	0.422575i	$-0.861126\pi$
$653$	−46.3204	−1.81266	−0.906328	+	0.422575i	$0.861126\pi$
$654$	−3.91275	−0.153001
$655$	−45.8657	−1.79212
$656$	19.3523	0.755580
$657$	2.54135	0.0991477
$658$	−42.8951	−1.67223
$659$	−50.6211	−1.97192	−0.985960	−	0.166984i	$-0.946597\pi$
$659$	−50.6211	−1.97192	−0.985960	+	0.166984i	$0.946597\pi$
$660$	19.8027	0.770820
$661$	31.4667	1.22391	0.611956	−	0.790892i	$-0.290383\pi$
$661$	31.4667	1.22391	0.611956	+	0.790892i	$0.290383\pi$
$662$	31.2427	1.21428
$663$	0.269861	0.0104805
$664$	49.2370	1.91077
$665$	−24.2065	−0.938688
$666$	−0.652417	−0.0252806
$667$	−5.21005	−0.201734
$668$	−3.91219	−0.151367
$669$	−19.6335	−0.759077
$670$	42.9825	1.66056
$671$	6.74960	0.260566
$672$	−13.5659	−0.523314
$673$	−2.88992	−0.111398	−0.0556992	−	0.998448i	$-0.517739\pi$
$673$	−2.88992	−0.111398	−0.0556992	+	0.998448i	$0.517739\pi$
$674$	−33.0010	−1.27115
$675$	−2.13936	−0.0823441
$676$	−30.5214	−1.17390
$677$	8.00775	0.307763	0.153881	−	0.988089i	$-0.450823\pi$
$677$	8.00775	0.307763	0.153881	+	0.988089i	$0.450823\pi$
$678$	−55.9300	−2.14798
$679$	−17.6689	−0.678072
$680$	0.681923	0.0261505
$681$	23.0428	0.883003
$682$	−8.19521	−0.313811
$683$	7.69561	0.294464	0.147232	−	0.989102i	$-0.452964\pi$
$683$	7.69561	0.294464	0.147232	+	0.989102i	$0.452964\pi$
$684$	4.13061	0.157938
$685$	−10.7381	−0.410282
$686$	−45.7794	−1.74786
$687$	−33.0459	−1.26078
$688$	−13.2269	−0.504270
$689$	8.92913	0.340173
$690$	−15.6190	−0.594606
$691$	−16.1535	−0.614508	−0.307254	−	0.951628i	$-0.599410\pi$
$691$	−16.1535	−0.614508	−0.307254	+	0.951628i	$0.599410\pi$
$692$	2.98598	0.113510
$693$	−0.987059	−0.0374953
$694$	−15.2135	−0.577497
$695$	−44.0028	−1.66912
$696$	−19.2020	−0.727849
$697$	0.797069	0.0301911
$698$	−43.0990	−1.63132
$699$	−14.0635	−0.531929
$700$	−3.59819	−0.135999
$701$	18.2117	0.687846	0.343923	−	0.938998i	$-0.388244\pi$
$701$	18.2117	0.687846	0.343923	+	0.938998i	$0.388244\pi$
$702$	27.3828	1.03350
$703$	4.14719	0.156414
$704$	16.3668	0.616849
$705$	27.6137	1.03999
$706$	−26.9104	−1.01279
$707$	16.4347	0.618092
$708$	18.8690	0.709139
$709$	16.1664	0.607141	0.303571	−	0.952809i	$-0.401821\pi$
$709$	16.1664	0.607141	0.303571	+	0.952809i	$0.401821\pi$
$710$	35.8647	1.34598
$711$	0.648306	0.0243134
$712$	66.2447	2.48263
$713$	4.16300	0.155905
$714$	0.752247	0.0281521
$715$	7.08368	0.264915
$716$	44.0090	1.64469
$717$	−1.58598	−0.0592294
$718$	−48.3657	−1.80499
$719$	−15.8318	−0.590426	−0.295213	−	0.955432i	$-0.595391\pi$
$719$	−15.8318	−0.590426	−0.295213	+	0.955432i	$0.595391\pi$
$720$	1.18766	0.0442614
$721$	−36.4978	−1.35925
$722$	4.26862	0.158861
$723$	−0.147041	−0.00546852
$724$	17.1181	0.636189
$725$	1.19970	0.0445556
$726$	35.0705	1.30159
$727$	23.8933	0.886152	0.443076	−	0.896484i	$-0.353887\pi$
$727$	23.8933	0.886152	0.443076	+	0.896484i	$0.353887\pi$
$728$	20.6012	0.763532
$729$	29.0018	1.07414
$730$	−50.8394	−1.88165
$731$	−0.544779	−0.0201494
$732$	−28.2497	−1.04414
$733$	17.7310	0.654908	0.327454	−	0.944867i	$-0.393809\pi$
$733$	17.7310	0.654908	0.327454	+	0.944867i	$0.393809\pi$
$734$	−69.4671	−2.56408
$735$	2.63018	0.0970155
$736$	−5.62051	−0.207175
$737$	−11.1412	−0.410391
$738$	6.79669	0.250190
$739$	−30.0702	−1.10615	−0.553076	−	0.833131i	$-0.686546\pi$
$739$	−30.0702	−1.10615	−0.553076	+	0.833131i	$0.686546\pi$
$740$	8.40578	0.309003
$741$	−14.6275	−0.537355
$742$	24.8902	0.913749
$743$	−29.9438	−1.09853	−0.549267	−	0.835647i	$-0.685093\pi$
$743$	−29.9438	−1.09853	−0.549267	+	0.835647i	$0.685093\pi$
$744$	15.3430	0.562502
$745$	31.7681	1.16389
$746$	−63.9101	−2.33991
$747$	3.53193	0.129226
$748$	−0.395148	−0.0144480
$749$	−47.8299	−1.74767
$750$	−41.8475	−1.52805
$751$	40.0192	1.46032	0.730161	−	0.683275i	$-0.239445\pi$
$751$	40.0192	1.46032	0.730161	+	0.683275i	$0.239445\pi$
$752$	−13.3782	−0.487851
$753$	38.8793	1.41684
$754$	−15.3555	−0.559216
$755$	11.2471	0.409325
$756$	49.1603	1.78794
$757$	34.2356	1.24432	0.622158	−	0.782892i	$-0.286256\pi$
$757$	34.2356	1.24432	0.622158	+	0.782892i	$0.286256\pi$
$758$	−63.6492	−2.31184
$759$	4.04850	0.146951
$760$	−36.9628	−1.34078
$761$	−53.9375	−1.95523	−0.977616	−	0.210397i	$-0.932524\pi$
$761$	−53.9375	−1.95523	−0.977616	+	0.210397i	$0.932524\pi$
$762$	24.7978	0.898331
$763$	−2.51278	−0.0909686
$764$	79.7137	2.88394
$765$	0.0489165	0.00176858
$766$	62.3434	2.25256
$767$	6.74966	0.243716
$768$	−42.9074	−1.54829
$769$	−14.4020	−0.519351	−0.259676	−	0.965696i	$-0.583616\pi$
$769$	−14.4020	−0.519351	−0.259676	+	0.965696i	$0.583616\pi$
$770$	19.7460	0.711596
$771$	20.5601	0.740455
$772$	46.7854	1.68384
$773$	34.1241	1.22736	0.613680	−	0.789555i	$-0.289689\pi$
$773$	34.1241	1.22736	0.613680	+	0.789555i	$0.289689\pi$
$774$	−4.64539	−0.166975
$775$	−0.958597	−0.0344338
$776$	−26.9801	−0.968529
$777$	4.14780	0.148802
$778$	72.9595	2.61572
$779$	−43.2042	−1.54795
$780$	−29.6479	−1.06157
$781$	−9.29623	−0.332645
$782$	0.311666	0.0111451
$783$	−16.3909	−0.585762
$784$	−1.27425	−0.0455091
$785$	−1.23352	−0.0440261
$786$	−77.2584	−2.75572
$787$	4.32058	0.154012	0.0770060	−	0.997031i	$-0.475464\pi$
$787$	4.32058	0.154012	0.0770060	+	0.997031i	$0.475464\pi$
$788$	85.3874	3.04180
$789$	−26.3893	−0.939482
$790$	−12.9693	−0.461426
$791$	−35.9183	−1.27711
$792$	−1.50722	−0.0535567
$793$	−10.1053	−0.358849
$794$	−18.5209	−0.657280
$795$	−16.0231	−0.568279
$796$	51.3512	1.82009
$797$	21.5039	0.761709	0.380854	−	0.924635i	$-0.375630\pi$
$797$	21.5039	0.761709	0.380854	+	0.924635i	$0.375630\pi$
$798$	−40.7747	−1.44341
$799$	−0.551010	−0.0194933
$800$	1.29421	0.0457574
$801$	4.75194	0.167902
$802$	46.2482	1.63308
$803$	13.1777	0.465032
$804$	46.6302	1.64452
$805$	−10.0306	−0.353531
$806$	12.2696	0.432177
$807$	−22.1111	−0.778349
$808$	25.0955	0.882856
$809$	−24.0271	−0.844749	−0.422374	−	0.906421i	$-0.638803\pi$
$809$	−24.0271	−0.844749	−0.422374	+	0.906421i	$0.638803\pi$
$810$	−44.5912	−1.56677
$811$	−26.1172	−0.917100	−0.458550	−	0.888669i	$-0.651631\pi$
$811$	−26.1172	−0.917100	−0.458550	+	0.888669i	$0.651631\pi$
$812$	−27.5678	−0.967440
$813$	31.3231	1.09855
$814$	−3.38299	−0.118574
$815$	39.4112	1.38051
$816$	0.234611	0.00821303
$817$	29.5291	1.03309
$818$	8.27064	0.289176
$819$	1.47779	0.0516382
$820$	−87.5689	−3.05804
$821$	32.3824	1.13016	0.565078	−	0.825038i	$-0.308846\pi$
$821$	32.3824	1.13016	0.565078	+	0.825038i	$0.308846\pi$
$822$	−18.0878	−0.630884
$823$	52.9387	1.84533	0.922663	−	0.385608i	$-0.126008\pi$
$823$	52.9387	1.84533	0.922663	+	0.385608i	$0.126008\pi$
$824$	−55.7314	−1.94149
$825$	−0.932232	−0.0324561
$826$	18.8149	0.654654
$827$	−25.6051	−0.890376	−0.445188	−	0.895437i	$-0.646863\pi$
$827$	−25.6051	−0.890376	−0.445188	+	0.895437i	$0.646863\pi$
$828$	1.71162	0.0594829
$829$	−18.6091	−0.646321	−0.323160	−	0.946344i	$-0.604745\pi$
$829$	−18.6091	−0.646321	−0.323160	+	0.946344i	$0.604745\pi$
$830$	−70.6557	−2.45250
$831$	−5.74733	−0.199373
$832$	−24.5039	−0.849519
$833$	−0.0524832	−0.00181843
$834$	−74.1206	−2.56659
$835$	2.51125	0.0869056
$836$	21.4185	0.740776
$837$	13.0968	0.452693
$838$	87.4676	3.02152
$839$	−8.47893	−0.292725	−0.146363	−	0.989231i	$-0.546757\pi$
$839$	−8.47893	−0.292725	−0.146363	+	0.989231i	$0.546757\pi$
$840$	−36.9683	−1.27553
$841$	−19.8084	−0.683050
$842$	−54.7293	−1.88609
$843$	−11.5668	−0.398382
$844$	42.4695	1.46186
$845$	19.5918	0.673979
$846$	−4.69852	−0.161539
$847$	22.5223	0.773876
$848$	7.76277	0.266575
$849$	15.1719	0.520697
$850$	−0.0717661	−0.00246156
$851$	1.71849	0.0589091
$852$	38.9083	1.33298
$853$	−36.2360	−1.24070	−0.620348	−	0.784327i	$-0.713009\pi$
$853$	−36.2360	−1.24070	−0.620348	+	0.784327i	$0.713009\pi$
$854$	−28.1688	−0.963915
$855$	−2.65146	−0.0906781
$856$	−73.0353	−2.49629
$857$	21.3296	0.728604	0.364302	−	0.931281i	$-0.381308\pi$
$857$	21.3296	0.728604	0.364302	+	0.931281i	$0.381308\pi$
$858$	11.9321	0.407355
$859$	−50.3707	−1.71863	−0.859314	−	0.511449i	$-0.829109\pi$
$859$	−50.3707	−1.71863	−0.859314	+	0.511449i	$0.829109\pi$
$860$	59.8515	2.04092
$861$	−43.2106	−1.47261
$862$	−51.5179	−1.75471
$863$	22.3563	0.761019	0.380509	−	0.924777i	$-0.375749\pi$
$863$	22.3563	0.761019	0.380509	+	0.924777i	$0.375749\pi$
$864$	−17.6822	−0.601560
$865$	−1.91672	−0.0651704
$866$	−18.2811	−0.621216
$867$	−28.0520	−0.952696
$868$	22.0276	0.747664
$869$	3.36167	0.114037
$870$	27.5551	0.934204
$871$	16.6802	0.565187
$872$	−3.83696	−0.129936
$873$	−1.93537	−0.0655023
$874$	−16.8935	−0.571431
$875$	−26.8745	−0.908525
$876$	−55.1539	−1.86348
$877$	−5.56329	−0.187859	−0.0939295	−	0.995579i	$-0.529943\pi$
$877$	−5.56329	−0.187859	−0.0939295	+	0.995579i	$0.529943\pi$
$878$	−27.5625	−0.930189
$879$	−46.2356	−1.55949
$880$	6.15839	0.207599
$881$	1.48582	0.0500587	0.0250293	−	0.999687i	$-0.492032\pi$
$881$	1.48582	0.0500587	0.0250293	+	0.999687i	$0.492032\pi$
$882$	−0.447529	−0.0150691
$883$	−42.5796	−1.43292	−0.716460	−	0.697629i	$-0.754239\pi$
$883$	−42.5796	−1.43292	−0.716460	+	0.697629i	$0.754239\pi$
$884$	0.591602	0.0198977
$885$	−12.1121	−0.407143
$886$	−69.2369	−2.32606
$887$	−25.5624	−0.858300	−0.429150	−	0.903233i	$-0.641187\pi$
$887$	−25.5624	−0.858300	−0.429150	+	0.903233i	$0.641187\pi$
$888$	6.33361	0.212542
$889$	15.9252	0.534114
$890$	−95.0620	−3.18649
$891$	11.5582	0.387213
$892$	−43.0416	−1.44114
$893$	29.8669	0.999457
$894$	53.5117	1.78970
$895$	−28.2496	−0.944281
$896$	−51.8687	−1.73281
$897$	−6.06127	−0.202380
$898$	−50.8949	−1.69838
$899$	−7.34436	−0.244948
$900$	−0.394128	−0.0131376
$901$	0.319728	0.0106517
$902$	35.2430	1.17346
$903$	29.5335	0.982814
$904$	−54.8465	−1.82417
$905$	−10.9882	−0.365260
$906$	18.9452	0.629413
$907$	−5.08782	−0.168938	−0.0844691	−	0.996426i	$-0.526919\pi$
$907$	−5.08782	−0.168938	−0.0844691	+	0.996426i	$0.526919\pi$
$908$	50.5156	1.67642
$909$	1.80018	0.0597082
$910$	−29.5630	−0.980004
$911$	38.2342	1.26676	0.633378	−	0.773843i	$-0.281668\pi$
$911$	38.2342	1.26676	0.633378	+	0.773843i	$0.281668\pi$
$912$	−12.7168	−0.421096
$913$	18.3142	0.606111
$914$	29.6306	0.980094
$915$	18.1336	0.599479
$916$	−72.4448	−2.39364
$917$	−49.6155	−1.63845
$918$	0.980504	0.0323614
$919$	−59.5153	−1.96323	−0.981614	−	0.190876i	$-0.938867\pi$
$919$	−59.5153	−1.96323	−0.981614	+	0.190876i	$0.938867\pi$
$920$	−15.3165	−0.504968
$921$	−42.0839	−1.38671
$922$	−60.7393	−2.00034
$923$	13.9180	0.458116
$924$	21.4217	0.704723
$925$	−0.395710	−0.0130109
$926$	64.7431	2.12759
$927$	−3.99779	−0.131305
$928$	9.91571	0.325499
$929$	−22.3911	−0.734628	−0.367314	−	0.930097i	$-0.619723\pi$
$929$	−22.3911	−0.734628	−0.367314	+	0.930097i	$0.619723\pi$
$930$	−22.0174	−0.721979
$931$	2.84479	0.0932342
$932$	−30.8306	−1.00989
$933$	17.3769	0.568894
$934$	16.4185	0.537230
$935$	0.253648	0.00829516
$936$	2.25656	0.0737578
$937$	−6.31678	−0.206360	−0.103180	−	0.994663i	$-0.532902\pi$
$937$	−6.31678	−0.206360	−0.103180	+	0.994663i	$0.532902\pi$
$938$	46.4966	1.51817
$939$	22.0240	0.718728
$940$	60.5360	1.97447
$941$	−18.8825	−0.615553	−0.307776	−	0.951459i	$-0.599585\pi$
$941$	−18.8825	−0.615553	−0.307776	+	0.951459i	$0.599585\pi$
$942$	−2.07780	−0.0676983
$943$	−17.9027	−0.582993
$944$	5.86800	0.190987
$945$	−31.5562	−1.02652
$946$	−24.0878	−0.783163
$947$	51.0886	1.66016	0.830078	−	0.557648i	$-0.188296\pi$
$947$	51.0886	1.66016	0.830078	+	0.557648i	$0.188296\pi$
$948$	−14.0699	−0.456969
$949$	−19.7292	−0.640438
$950$	3.89000	0.126208
$951$	−21.6737	−0.702817
$952$	0.737674	0.0239082
$953$	−17.2528	−0.558871	−0.279436	−	0.960164i	$-0.590147\pi$
$953$	−17.2528	−0.558871	−0.279436	+	0.960164i	$0.590147\pi$
$954$	2.72635	0.0882689
$955$	−51.1686	−1.65578
$956$	−3.47685	−0.112449
$957$	−7.14236	−0.230880
$958$	−57.1836	−1.84752
$959$	−11.6160	−0.375100
$960$	43.9715	1.41917
$961$	−25.1316	−0.810697
$962$	5.06489	0.163299
$963$	−5.23905	−0.168826
$964$	−0.322350	−0.0103822
$965$	−30.0318	−0.966757
$966$	−16.8960	−0.543619
$967$	37.7109	1.21270	0.606351	−	0.795197i	$-0.292633\pi$
$967$	37.7109	1.21270	0.606351	+	0.795197i	$0.292633\pi$
$968$	34.3911	1.10537
$969$	−0.523772	−0.0168260
$970$	38.7168	1.24312
$971$	0.0828538	0.00265890	0.00132945	−	0.999999i	$-0.499577\pi$
$971$	0.0828538	0.00265890	0.00132945	+	0.999999i	$0.499577\pi$
$972$	10.3170	0.330919
$973$	−47.6003	−1.52600
$974$	−38.0690	−1.21981
$975$	1.39570	0.0446983
$976$	−8.78529	−0.281210
$977$	−4.71496	−0.150845	−0.0754225	−	0.997152i	$-0.524031\pi$
$977$	−4.71496	−0.150845	−0.0754225	+	0.997152i	$0.524031\pi$
$978$	66.3862	2.12280
$979$	24.6403	0.787509
$980$	5.76599	0.184188
$981$	−0.275237	−0.00878765
$982$	2.37449	0.0757730
$983$	48.6584	1.55196	0.775980	−	0.630757i	$-0.217256\pi$
$983$	48.6584	1.55196	0.775980	+	0.630757i	$0.217256\pi$
$984$	−65.9817	−2.10342
$985$	−54.8106	−1.74641
$986$	−0.549841	−0.0175105
$987$	29.8713	0.950814
$988$	−32.0671	−1.02019
$989$	12.2361	0.389086
$990$	2.16288	0.0687408
$991$	42.7979	1.35952	0.679761	−	0.733434i	$-0.262084\pi$
$991$	42.7979	1.35952	0.679761	+	0.733434i	$0.262084\pi$
$992$	−7.92297	−0.251555
$993$	−21.7568	−0.690431
$994$	38.7968	1.23056
$995$	−32.9626	−1.04498
$996$	−76.6519	−2.42881
$997$	−1.65659	−0.0524648	−0.0262324	−	0.999656i	$-0.508351\pi$
$997$	−1.65659	−0.0524648	−0.0262324	+	0.999656i	$0.508351\pi$
$998$	55.1931	1.74711
$999$	5.40639	0.171051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.8	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.8	✓	82	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)

\(f(q)\)	\(=\)	\(q-2.37038 q^{2} +1.65069 q^{3} +3.61871 q^{4} -2.32287 q^{5} -3.91275 q^{6} -2.51278 q^{7} -3.83696 q^{8} -0.275237 q^{9} +O(q^{10})\)	\(q-2.37038 q^{2} +1.65069 q^{3} +3.61871 q^{4} -2.32287 q^{5} -3.91275 q^{6} -2.51278 q^{7} -3.83696 q^{8} -0.275237 q^{9} +5.50608 q^{10} -1.42719 q^{11} +5.97335 q^{12} +2.13674 q^{13} +5.95624 q^{14} -3.83432 q^{15} +1.85763 q^{16} +0.0765110 q^{17} +0.652417 q^{18} -4.14719 q^{19} -8.40578 q^{20} -4.14780 q^{21} +3.38299 q^{22} -1.71849 q^{23} -6.33361 q^{24} +0.395710 q^{25} -5.06489 q^{26} -5.40639 q^{27} -9.09300 q^{28} +3.03176 q^{29} +9.08881 q^{30} -2.42247 q^{31} +3.27061 q^{32} -2.35585 q^{33} -0.181360 q^{34} +5.83684 q^{35} -0.996003 q^{36} -1.00000 q^{37} +9.83042 q^{38} +3.52709 q^{39} +8.91274 q^{40} +10.4177 q^{41} +9.83188 q^{42} -7.12028 q^{43} -5.16459 q^{44} +0.639339 q^{45} +4.07348 q^{46} -7.20172 q^{47} +3.06637 q^{48} -0.685956 q^{49} -0.937984 q^{50} +0.126296 q^{51} +7.73225 q^{52} +4.17885 q^{53} +12.8152 q^{54} +3.31518 q^{55} +9.64141 q^{56} -6.84571 q^{57} -7.18642 q^{58} +3.15886 q^{59} -13.8753 q^{60} -4.72929 q^{61} +5.74219 q^{62} +0.691609 q^{63} -11.4679 q^{64} -4.96337 q^{65} +5.58425 q^{66} +7.80637 q^{67} +0.276871 q^{68} -2.83669 q^{69} -13.8355 q^{70} +6.51365 q^{71} +1.05607 q^{72} -9.23333 q^{73} +2.37038 q^{74} +0.653193 q^{75} -15.0075 q^{76} +3.58621 q^{77} -8.36055 q^{78} -2.35544 q^{79} -4.31504 q^{80} -8.09853 q^{81} -24.6939 q^{82} -12.8323 q^{83} -15.0097 q^{84} -0.177725 q^{85} +16.8778 q^{86} +5.00448 q^{87} +5.47607 q^{88} -17.2649 q^{89} -1.51548 q^{90} -5.36915 q^{91} -6.21871 q^{92} -3.99874 q^{93} +17.0708 q^{94} +9.63337 q^{95} +5.39875 q^{96} +7.03164 q^{97} +1.62598 q^{98} +0.392816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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