LMFDB - Embedded newform 4033.2.a.e.1.15

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			1.15
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)

$f(q)$	$=$	$q-1.75361 q^{2} -2.25140 q^{3} +1.07516 q^{4} -3.95285 q^{5} +3.94809 q^{6} +2.44850 q^{7} +1.62182 q^{8} +2.06881 q^{9} +O(q^{10})$	\(q-1.75361 q^{2} -2.25140 q^{3} +1.07516 q^{4} -3.95285 q^{5} +3.94809 q^{6} +2.44850 q^{7} +1.62182 q^{8} +2.06881 q^{9} +6.93177 q^{10} +0.580727 q^{11} -2.42061 q^{12} -2.49536 q^{13} -4.29372 q^{14} +8.89945 q^{15} -4.99435 q^{16} +5.64768 q^{17} -3.62789 q^{18} +4.90923 q^{19} -4.24994 q^{20} -5.51255 q^{21} -1.01837 q^{22} +5.41485 q^{23} -3.65136 q^{24} +10.6250 q^{25} +4.37590 q^{26} +2.09649 q^{27} +2.63252 q^{28} +6.07723 q^{29} -15.6062 q^{30} +3.17848 q^{31} +5.51453 q^{32} -1.30745 q^{33} -9.90385 q^{34} -9.67855 q^{35} +2.22429 q^{36} -1.00000 q^{37} -8.60889 q^{38} +5.61807 q^{39} -6.41079 q^{40} +11.6203 q^{41} +9.66688 q^{42} -3.65478 q^{43} +0.624373 q^{44} -8.17768 q^{45} -9.49555 q^{46} +11.2633 q^{47} +11.2443 q^{48} -1.00486 q^{49} -18.6322 q^{50} -12.7152 q^{51} -2.68291 q^{52} -2.20708 q^{53} -3.67643 q^{54} -2.29553 q^{55} +3.97101 q^{56} -11.0527 q^{57} -10.6571 q^{58} -11.5454 q^{59} +9.56831 q^{60} +6.34807 q^{61} -5.57383 q^{62} +5.06547 q^{63} +0.318357 q^{64} +9.86380 q^{65} +2.29276 q^{66} +2.32188 q^{67} +6.07215 q^{68} -12.1910 q^{69} +16.9724 q^{70} +12.2184 q^{71} +3.35522 q^{72} +4.77830 q^{73} +1.75361 q^{74} -23.9212 q^{75} +5.27820 q^{76} +1.42191 q^{77} -9.85191 q^{78} +13.3469 q^{79} +19.7419 q^{80} -10.9265 q^{81} -20.3775 q^{82} -8.67043 q^{83} -5.92686 q^{84} -22.3244 q^{85} +6.40908 q^{86} -13.6823 q^{87} +0.941832 q^{88} +9.98744 q^{89} +14.3405 q^{90} -6.10989 q^{91} +5.82182 q^{92} -7.15604 q^{93} -19.7515 q^{94} -19.4055 q^{95} -12.4154 q^{96} +4.10122 q^{97} +1.76213 q^{98} +1.20141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.75361	−1.23999	−0.619996	−	0.784605i	$-0.712866\pi$
$2$	−1.75361	−1.23999	−0.619996	+	0.784605i	$0.712866\pi$
$3$	−2.25140	−1.29985	−0.649924	−	0.760000i	$-0.725199\pi$
$3$	−2.25140	−1.29985	−0.649924	+	0.760000i	$0.725199\pi$
$4$	1.07516	0.537579
$5$	−3.95285	−1.76777	−0.883884	−	0.467706i	$-0.845081\pi$
$5$	−3.95285	−1.76777	−0.883884	+	0.467706i	$0.845081\pi$
$6$	3.94809	1.61180
$7$	2.44850	0.925445	0.462723	−	0.886503i	$-0.346873\pi$
$7$	2.44850	0.925445	0.462723	+	0.886503i	$0.346873\pi$
$8$	1.62182	0.573398
$9$	2.06881	0.689602
$10$	6.93177	2.19202
$11$	0.580727	0.175096	0.0875479	−	0.996160i	$-0.472097\pi$
$11$	0.580727	0.175096	0.0875479	+	0.996160i	$0.472097\pi$
$12$	−2.42061	−0.698770
$13$	−2.49536	−0.692089	−0.346045	−	0.938218i	$-0.612475\pi$
$13$	−2.49536	−0.692089	−0.346045	+	0.938218i	$0.612475\pi$
$14$	−4.29372	−1.14754
$15$	8.89945	2.29783
$16$	−4.99435	−1.24859
$17$	5.64768	1.36976	0.684882	−	0.728654i	$-0.259854\pi$
$17$	5.64768	1.36976	0.684882	+	0.728654i	$0.259854\pi$
$18$	−3.62789	−0.855101
$19$	4.90923	1.12626	0.563128	−	0.826370i	$-0.309598\pi$
$19$	4.90923	1.12626	0.563128	+	0.826370i	$0.309598\pi$
$20$	−4.24994	−0.950315
$21$	−5.51255	−1.20294
$22$	−1.01837	−0.217117
$23$	5.41485	1.12907	0.564537	−	0.825408i	$-0.309055\pi$
$23$	5.41485	1.12907	0.564537	+	0.825408i	$0.309055\pi$
$24$	−3.65136	−0.745330
$25$	10.6250	2.12501
$26$	4.37590	0.858185
$27$	2.09649	0.403470
$28$	2.63252	0.497500
$29$	6.07723	1.12851	0.564257	−	0.825599i	$-0.309163\pi$
$29$	6.07723	1.12851	0.564257	+	0.825599i	$0.309163\pi$
$30$	−15.6062	−2.84929
$31$	3.17848	0.570872	0.285436	−	0.958398i	$-0.407862\pi$
$31$	3.17848	0.570872	0.285436	+	0.958398i	$0.407862\pi$
$32$	5.51453	0.974840
$33$	−1.30745	−0.227598
$34$	−9.90385	−1.69850
$35$	−9.67855	−1.63597
$36$	2.22429	0.370716
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−8.60889	−1.39655
$39$	5.61807	0.899610
$40$	−6.41079	−1.01364
$41$	11.6203	1.81479	0.907393	−	0.420284i	$-0.138070\pi$
$41$	11.6203	1.81479	0.907393	+	0.420284i	$0.138070\pi$
$42$	9.66688	1.49163
$43$	−3.65478	−0.557349	−0.278675	−	0.960386i	$-0.589895\pi$
$43$	−3.65478	−0.557349	−0.278675	+	0.960386i	$0.589895\pi$
$44$	0.624373	0.0941278
$45$	−8.17768	−1.21906
$46$	−9.49555	−1.40004
$47$	11.2633	1.64293	0.821463	−	0.570262i	$-0.193158\pi$
$47$	11.2633	1.64293	0.821463	+	0.570262i	$0.193158\pi$
$48$	11.2443	1.62297
$49$	−1.00486	−0.143551
$50$	−18.6322	−2.63499
$51$	−12.7152	−1.78048
$52$	−2.68291	−0.372053
$53$	−2.20708	−0.303165	−0.151583	−	0.988445i	$-0.548437\pi$
$53$	−2.20708	−0.303165	−0.151583	+	0.988445i	$0.548437\pi$
$54$	−3.67643	−0.500299
$55$	−2.29553	−0.309529
$56$	3.97101	0.530649
$57$	−11.0527	−1.46396
$58$	−10.6571	−1.39935
$59$	−11.5454	−1.50308	−0.751541	−	0.659686i	$-0.770689\pi$
$59$	−11.5454	−1.50308	−0.751541	+	0.659686i	$0.770689\pi$
$60$	9.56831	1.23526
$61$	6.34807	0.812787	0.406394	−	0.913698i	$-0.366786\pi$
$61$	6.34807	0.812787	0.406394	+	0.913698i	$0.366786\pi$
$62$	−5.57383	−0.707877
$63$	5.06547	0.638189
$64$	0.318357	0.0397946
$65$	9.86380	1.22345
$66$	2.29276	0.282219
$67$	2.32188	0.283663	0.141832	−	0.989891i	$-0.454701\pi$
$67$	2.32188	0.283663	0.141832	+	0.989891i	$0.454701\pi$
$68$	6.07215	0.736356
$69$	−12.1910	−1.46762
$70$	16.9724	2.02859
$71$	12.2184	1.45005	0.725027	−	0.688721i	$-0.241827\pi$
$71$	12.2184	1.45005	0.725027	+	0.688721i	$0.241827\pi$
$72$	3.35522	0.395417
$73$	4.77830	0.559257	0.279629	−	0.960108i	$-0.409789\pi$
$73$	4.77830	0.559257	0.279629	+	0.960108i	$0.409789\pi$
$74$	1.75361	0.203853
$75$	−23.9212	−2.76218
$76$	5.27820	0.605451
$77$	1.42191	0.162042
$78$	−9.85191	−1.11551
$79$	13.3469	1.50165	0.750823	−	0.660503i	$-0.229657\pi$
$79$	13.3469	1.50165	0.750823	+	0.660503i	$0.229657\pi$
$80$	19.7419	2.20721
$81$	−10.9265	−1.21405
$82$	−20.3775	−2.25032
$83$	−8.67043	−0.951703	−0.475852	−	0.879526i	$-0.657860\pi$
$83$	−8.67043	−0.951703	−0.475852	+	0.879526i	$0.657860\pi$
$84$	−5.92686	−0.646674
$85$	−22.3244	−2.42143
$86$	6.40908	0.691108
$87$	−13.6823	−1.46689
$88$	0.941832	0.100400
$89$	9.98744	1.05867	0.529333	−	0.848414i	$-0.322442\pi$
$89$	9.98744	1.05867	0.529333	+	0.848414i	$0.322442\pi$
$90$	14.3405	1.51162
$91$	−6.10989	−0.640491
$92$	5.82182	0.606967
$93$	−7.15604	−0.742046
$94$	−19.7515	−2.03721
$95$	−19.4055	−1.99096
$96$	−12.4154	−1.26714
$97$	4.10122	0.416415	0.208208	−	0.978085i	$-0.433237\pi$
$97$	4.10122	0.416415	0.208208	+	0.978085i	$0.433237\pi$
$98$	1.76213	0.178002
$99$	1.20141	0.120746
$100$	11.4236	1.14236
$101$	−7.78802	−0.774937	−0.387469	−	0.921883i	$-0.626650\pi$
$101$	−7.78802	−0.774937	−0.387469	+	0.921883i	$0.626650\pi$
$102$	22.2975	2.20779
$103$	−11.2467	−1.10817	−0.554086	−	0.832460i	$-0.686932\pi$
$103$	−11.2467	−1.10817	−0.554086	+	0.832460i	$0.686932\pi$
$104$	−4.04702	−0.396843
$105$	21.7903	2.12651
$106$	3.87036	0.375922
$107$	13.6691	1.32145	0.660723	−	0.750630i	$-0.270250\pi$
$107$	13.6691	1.32145	0.660723	+	0.750630i	$0.270250\pi$
$108$	2.25406	0.216897
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	4.02547	0.383813
$111$	2.25140	0.213694
$112$	−12.2287	−1.15550
$113$	−6.42335	−0.604258	−0.302129	−	0.953267i	$-0.597697\pi$
$113$	−6.42335	−0.604258	−0.302129	+	0.953267i	$0.597697\pi$
$114$	19.3821	1.81530
$115$	−21.4041	−1.99594
$116$	6.53398	0.606665
$117$	−5.16243	−0.477266
$118$	20.2462	1.86381
$119$	13.8283	1.26764
$120$	14.4333	1.31757
$121$	−10.6628	−0.969341
$122$	−11.1321	−1.00785
$123$	−26.1619	−2.35894
$124$	3.41737	0.306889
$125$	−22.2349	−1.98875
$126$	−8.88287	−0.791349
$127$	−10.4531	−0.927559	−0.463780	−	0.885951i	$-0.653507\pi$
$127$	−10.4531	−0.927559	−0.463780	+	0.885951i	$0.653507\pi$
$128$	−11.5873	−1.02418
$129$	8.22839	0.724469
$130$	−17.2973	−1.51707
$131$	−7.25367	−0.633756	−0.316878	−	0.948466i	$-0.602635\pi$
$131$	−7.25367	−0.633756	−0.316878	+	0.948466i	$0.602635\pi$
$132$	−1.40571	−0.122352
$133$	12.0202	1.04229
$134$	−4.07168	−0.351740
$135$	−8.28711	−0.713241
$136$	9.15950	0.785421
$137$	16.1782	1.38220	0.691100	−	0.722759i	$-0.257126\pi$
$137$	16.1782	1.38220	0.691100	+	0.722759i	$0.257126\pi$
$138$	21.3783	1.81984
$139$	−15.1134	−1.28190	−0.640949	−	0.767583i	$-0.721459\pi$
$139$	−15.1134	−1.28190	−0.640949	+	0.767583i	$0.721459\pi$
$140$	−10.4060	−0.879464
$141$	−25.3583	−2.13555
$142$	−21.4263	−1.79805
$143$	−1.44913	−0.121182
$144$	−10.3323	−0.861029
$145$	−24.0224	−1.99495
$146$	−8.37928	−0.693474
$147$	2.26234	0.186595
$148$	−1.07516	−0.0883774
$149$	13.0787	1.07145	0.535726	−	0.844392i	$-0.320038\pi$
$149$	13.0787	1.07145	0.535726	+	0.844392i	$0.320038\pi$
$150$	41.9485	3.42508
$151$	−23.8692	−1.94245	−0.971225	−	0.238164i	$-0.923455\pi$
$151$	−23.8692	−1.94245	−0.971225	+	0.238164i	$0.923455\pi$
$152$	7.96187	0.645793
$153$	11.6840	0.944593
$154$	−2.49348	−0.200930
$155$	−12.5641	−1.00917
$156$	6.04031	0.483612
$157$	8.97798	0.716521	0.358260	−	0.933622i	$-0.383370\pi$
$157$	8.97798	0.716521	0.358260	+	0.933622i	$0.383370\pi$
$158$	−23.4053	−1.86203
$159$	4.96901	0.394069
$160$	−21.7981	−1.72329
$161$	13.2583	1.04490
$162$	19.1608	1.50541
$163$	12.7920	1.00195	0.500973	−	0.865463i	$-0.332976\pi$
$163$	12.7920	1.00195	0.500973	+	0.865463i	$0.332976\pi$
$164$	12.4936	0.975590
$165$	5.16815	0.402340
$166$	15.2046	1.18010
$167$	−15.6736	−1.21286	−0.606428	−	0.795138i	$-0.707398\pi$
$167$	−15.6736	−1.21286	−0.606428	+	0.795138i	$0.707398\pi$
$168$	−8.94034	−0.689762
$169$	−6.77316	−0.521012
$170$	39.1484	3.00255
$171$	10.1563	0.776668
$172$	−3.92947	−0.299619
$173$	15.2860	1.16217	0.581087	−	0.813841i	$-0.302627\pi$
$173$	15.2860	1.16217	0.581087	+	0.813841i	$0.302627\pi$
$174$	23.9934	1.81894
$175$	26.0154	1.96658
$176$	−2.90036	−0.218623
$177$	25.9933	1.95378
$178$	−17.5141	−1.31274
$179$	−4.49554	−0.336012	−0.168006	−	0.985786i	$-0.553733\pi$
$179$	−4.49554	−0.336012	−0.168006	+	0.985786i	$0.553733\pi$
$180$	−8.79230	−0.655339
$181$	−4.94768	−0.367758	−0.183879	−	0.982949i	$-0.558866\pi$
$181$	−4.94768	−0.367758	−0.183879	+	0.982949i	$0.558866\pi$
$182$	10.7144	0.794203
$183$	−14.2921	−1.05650
$184$	8.78189	0.647409
$185$	3.95285	0.290619
$186$	12.5489	0.920131
$187$	3.27976	0.239840
$188$	12.1099	0.883202
$189$	5.13325	0.373389
$190$	34.0297	2.46877
$191$	12.5893	0.910930	0.455465	−	0.890254i	$-0.349473\pi$
$191$	12.5893	0.910930	0.455465	+	0.890254i	$0.349473\pi$
$192$	−0.716749	−0.0517269
$193$	−14.4088	−1.03717	−0.518585	−	0.855026i	$-0.673541\pi$
$193$	−14.4088	−1.03717	−0.518585	+	0.855026i	$0.673541\pi$
$194$	−7.19195	−0.516352
$195$	−22.2074	−1.59030
$196$	−1.08038	−0.0771701
$197$	6.79317	0.483993	0.241997	−	0.970277i	$-0.422198\pi$
$197$	6.79317	0.483993	0.241997	+	0.970277i	$0.422198\pi$
$198$	−2.10681	−0.149725
$199$	16.1764	1.14671	0.573357	−	0.819306i	$-0.305641\pi$
$199$	16.1764	1.14671	0.573357	+	0.819306i	$0.305641\pi$
$200$	17.2318	1.21847
$201$	−5.22749	−0.368719
$202$	13.6572	0.960916
$203$	14.8801	1.04438
$204$	−13.6708	−0.957151
$205$	−45.9333	−3.20812
$206$	19.7224	1.37412
$207$	11.2023	0.778612
$208$	12.4627	0.864134
$209$	2.85093	0.197203
$210$	−38.2117	−2.63686
$211$	0.799497	0.0550396	0.0275198	−	0.999621i	$-0.491239\pi$
$211$	0.799497	0.0550396	0.0275198	+	0.999621i	$0.491239\pi$
$212$	−2.37296	−0.162975
$213$	−27.5084	−1.88485
$214$	−23.9704	−1.63858
$215$	14.4468	0.985265
$216$	3.40012	0.231349
$217$	7.78251	0.528311
$218$	−1.75361	−0.118770
$219$	−10.7579	−0.726949
$220$	−2.46805	−0.166396
$221$	−14.0930	−0.947999
$222$	−3.94809	−0.264978
$223$	11.6205	0.778163	0.389082	−	0.921203i	$-0.372792\pi$
$223$	11.6205	0.778163	0.389082	+	0.921203i	$0.372792\pi$
$224$	13.5023	0.902161
$225$	21.9811	1.46541
$226$	11.2641	0.749275
$227$	21.5402	1.42967	0.714835	−	0.699293i	$-0.246502\pi$
$227$	21.5402	1.42967	0.714835	+	0.699293i	$0.246502\pi$
$228$	−11.8833	−0.786994
$229$	16.7847	1.10916	0.554582	−	0.832129i	$-0.312878\pi$
$229$	16.7847	1.10916	0.554582	+	0.832129i	$0.312878\pi$
$230$	37.5345	2.47495
$231$	−3.20129	−0.210629
$232$	9.85615	0.647088
$233$	10.2463	0.671259	0.335629	−	0.941994i	$-0.391051\pi$
$233$	10.2463	0.671259	0.335629	+	0.941994i	$0.391051\pi$
$234$	9.05290	0.591806
$235$	−44.5223	−2.90431
$236$	−12.4131	−0.808025
$237$	−30.0493	−1.95191
$238$	−24.2496	−1.57187
$239$	−29.9376	−1.93651	−0.968253	−	0.249974i	$-0.919578\pi$
$239$	−29.9376	−1.93651	−0.968253	+	0.249974i	$0.919578\pi$
$240$	−44.4470	−2.86904
$241$	20.7893	1.33916	0.669578	−	0.742742i	$-0.266475\pi$
$241$	20.7893	1.33916	0.669578	+	0.742742i	$0.266475\pi$
$242$	18.6983	1.20198
$243$	18.3104	1.17461
$244$	6.82518	0.436937
$245$	3.97205	0.253765
$246$	45.8779	2.92507
$247$	−12.2503	−0.779470
$248$	5.15491	0.327337
$249$	19.5206	1.23707
$250$	38.9914	2.46603
$251$	22.8423	1.44179	0.720897	−	0.693043i	$-0.243730\pi$
$251$	22.8423	1.44179	0.720897	+	0.693043i	$0.243730\pi$
$252$	5.44618	0.343077
$253$	3.14455	0.197696
$254$	18.3306	1.15017
$255$	50.2613	3.14748
$256$	19.6830	1.23019
$257$	16.6528	1.03877	0.519386	−	0.854540i	$-0.326161\pi$
$257$	16.6528	1.03877	0.519386	+	0.854540i	$0.326161\pi$
$258$	−14.4294	−0.898335
$259$	−2.44850	−0.152142
$260$	10.6051	0.657703
$261$	12.5726	0.778225
$262$	12.7201	0.785852
$263$	−14.3414	−0.884328	−0.442164	−	0.896934i	$-0.645789\pi$
$263$	−14.3414	−0.884328	−0.442164	+	0.896934i	$0.645789\pi$
$264$	−2.12044	−0.130504
$265$	8.72424	0.535926
$266$	−21.0789	−1.29243
$267$	−22.4857	−1.37610
$268$	2.49639	0.152491
$269$	−8.78050	−0.535356	−0.267678	−	0.963508i	$-0.586256\pi$
$269$	−8.78050	−0.535356	−0.267678	+	0.963508i	$0.586256\pi$
$270$	14.5324	0.884412
$271$	12.6105	0.766034	0.383017	−	0.923741i	$-0.374885\pi$
$271$	12.6105	0.766034	0.383017	+	0.923741i	$0.374885\pi$
$272$	−28.2065	−1.71027
$273$	13.7558	0.832540
$274$	−28.3704	−1.71392
$275$	6.17024	0.372080
$276$	−13.1072	−0.788964
$277$	7.66897	0.460784	0.230392	−	0.973098i	$-0.425999\pi$
$277$	7.66897	0.460784	0.230392	+	0.973098i	$0.425999\pi$
$278$	26.5030	1.58954
$279$	6.57566	0.393675
$280$	−15.6968	−0.938064
$281$	2.89506	0.172705	0.0863523	−	0.996265i	$-0.472479\pi$
$281$	2.89506	0.172705	0.0863523	+	0.996265i	$0.472479\pi$
$282$	44.4686	2.64807
$283$	17.2572	1.02584	0.512918	−	0.858438i	$-0.328565\pi$
$283$	17.2572	1.02584	0.512918	+	0.858438i	$0.328565\pi$
$284$	13.1367	0.779518
$285$	43.6895	2.58794
$286$	2.54121	0.150265
$287$	28.4523	1.67948
$288$	11.4085	0.672252
$289$	14.8963	0.876254
$290$	42.1260	2.47372
$291$	−9.23348	−0.541276
$292$	5.13742	0.300645
$293$	12.9405	0.755993	0.377997	−	0.925807i	$-0.376613\pi$
$293$	12.9405	0.755993	0.377997	+	0.925807i	$0.376613\pi$
$294$	−3.96727	−0.231376
$295$	45.6372	2.65710
$296$	−1.62182	−0.0942661
$297$	1.21749	0.0706458
$298$	−22.9350	−1.32859
$299$	−13.5120	−0.781421
$300$	−25.7191	−1.48489
$301$	−8.94873	−0.515796
$302$	41.8574	2.40862
$303$	17.5340	1.00730
$304$	−24.5184	−1.40623
$305$	−25.0930	−1.43682
$306$	−20.4892	−1.17129
$307$	−4.06283	−0.231878	−0.115939	−	0.993256i	$-0.536988\pi$
$307$	−4.06283	−0.231878	−0.115939	+	0.993256i	$0.536988\pi$
$308$	1.52878	0.0871101
$309$	25.3209	1.44045
$310$	22.0325	1.25136
$311$	−0.343231	−0.0194628	−0.00973142	−	0.999953i	$-0.503098\pi$
$311$	−0.343231	−0.0194628	−0.00973142	+	0.999953i	$0.503098\pi$
$312$	9.11146	0.515835
$313$	−7.45664	−0.421474	−0.210737	−	0.977543i	$-0.567586\pi$
$313$	−7.45664	−0.421474	−0.210737	+	0.977543i	$0.567586\pi$
$314$	−15.7439	−0.888480
$315$	−20.0230	−1.12817
$316$	14.3500	0.807253
$317$	11.3866	0.639534	0.319767	−	0.947496i	$-0.396395\pi$
$317$	11.3866	0.639534	0.319767	+	0.947496i	$0.396395\pi$
$318$	−8.71373	−0.488642
$319$	3.52921	0.197598
$320$	−1.25842	−0.0703476
$321$	−30.7747	−1.71768
$322$	−23.2498	−1.29566
$323$	27.7258	1.54270
$324$	−11.7477	−0.652648
$325$	−26.5133	−1.47069
$326$	−22.4322	−1.24240
$327$	−2.25140	−0.124503
$328$	18.8460	1.04059
$329$	27.5782	1.52044
$330$	−9.06294	−0.498898
$331$	−35.3874	−1.94506	−0.972532	−	0.232767i	$-0.925222\pi$
$331$	−35.3874	−1.94506	−0.972532	+	0.232767i	$0.925222\pi$
$332$	−9.32208	−0.511616
$333$	−2.06881	−0.113370
$334$	27.4854	1.50393
$335$	−9.17806	−0.501451
$336$	27.5316	1.50197
$337$	−31.9752	−1.74180	−0.870900	−	0.491461i	$-0.836463\pi$
$337$	−31.9752	−1.74180	−0.870900	+	0.491461i	$0.836463\pi$
$338$	11.8775	0.646051
$339$	14.4615	0.785443
$340$	−24.0023	−1.30171
$341$	1.84583	0.0999573
$342$	−17.8101	−0.963062
$343$	−19.5999	−1.05829
$344$	−5.92739	−0.319583
$345$	48.1892	2.59442
$346$	−26.8058	−1.44109
$347$	34.7743	1.86678	0.933392	−	0.358860i	$-0.116834\pi$
$347$	34.7743	1.86678	0.933392	+	0.358860i	$0.116834\pi$
$348$	−14.7106	−0.788572
$349$	−2.58144	−0.138181	−0.0690907	−	0.997610i	$-0.522010\pi$
$349$	−2.58144	−0.138181	−0.0690907	+	0.997610i	$0.522010\pi$
$350$	−45.6209	−2.43854
$351$	−5.23150	−0.279237
$352$	3.20244	0.170690
$353$	15.3943	0.819355	0.409677	−	0.912230i	$-0.365641\pi$
$353$	15.3943	0.819355	0.409677	+	0.912230i	$0.365641\pi$
$354$	−45.5822	−2.42267
$355$	−48.2974	−2.56336
$356$	10.7381	0.569117
$357$	−31.1331	−1.64774
$358$	7.88344	0.416652
$359$	−24.3838	−1.28693	−0.643464	−	0.765476i	$-0.722504\pi$
$359$	−24.3838	−1.28693	−0.643464	+	0.765476i	$0.722504\pi$
$360$	−13.2627	−0.699005
$361$	5.10057	0.268451
$362$	8.67632	0.456017
$363$	24.0061	1.26000
$364$	−6.56910	−0.344314
$365$	−18.8879	−0.988637
$366$	25.0627	1.31005
$367$	−8.74115	−0.456284	−0.228142	−	0.973628i	$-0.573265\pi$
$367$	−8.74115	−0.456284	−0.228142	+	0.973628i	$0.573265\pi$
$368$	−27.0437	−1.40975
$369$	24.0401	1.25148
$370$	−6.93177	−0.360366
$371$	−5.40402	−0.280563
$372$	−7.69387	−0.398908
$373$	−11.4072	−0.590644	−0.295322	−	0.955398i	$-0.595427\pi$
$373$	−11.4072	−0.590644	−0.295322	+	0.955398i	$0.595427\pi$
$374$	−5.75143	−0.297400
$375$	50.0597	2.58507
$376$	18.2670	0.942050
$377$	−15.1649	−0.781032
$378$	−9.00173	−0.462999
$379$	23.0334	1.18315	0.591574	−	0.806251i	$-0.298507\pi$
$379$	23.0334	1.18315	0.591574	+	0.806251i	$0.298507\pi$
$380$	−20.8639	−1.07030
$381$	23.5340	1.20569
$382$	−22.0768	−1.12954
$383$	18.3193	0.936072	0.468036	−	0.883709i	$-0.344962\pi$
$383$	18.3193	0.936072	0.468036	+	0.883709i	$0.344962\pi$
$384$	26.0877	1.33128
$385$	−5.62059	−0.286452
$386$	25.2675	1.28608
$387$	−7.56104	−0.384349
$388$	4.40945	0.223856
$389$	−27.3239	−1.38538	−0.692689	−	0.721236i	$-0.743574\pi$
$389$	−27.3239	−1.38538	−0.692689	+	0.721236i	$0.743574\pi$
$390$	38.9431	1.97196
$391$	30.5814	1.54657
$392$	−1.62969	−0.0823120
$393$	16.3309	0.823786
$394$	−11.9126	−0.600148
$395$	−52.7584	−2.65456
$396$	1.29171	0.0649108
$397$	22.2305	1.11571	0.557857	−	0.829937i	$-0.311624\pi$
$397$	22.2305	1.11571	0.557857	+	0.829937i	$0.311624\pi$
$398$	−28.3671	−1.42192
$399$	−27.0624	−1.35481
$400$	−53.0651	−2.65326
$401$	35.9299	1.79426	0.897128	−	0.441771i	$-0.145650\pi$
$401$	35.9299	1.79426	0.897128	+	0.441771i	$0.145650\pi$
$402$	9.16700	0.457208
$403$	−7.93147	−0.395095
$404$	−8.37335	−0.416590
$405$	43.1907	2.14616
$406$	−26.0939	−1.29502
$407$	−0.580727	−0.0287856
$408$	−20.6217	−1.02093
$409$	−16.4266	−0.812243	−0.406121	−	0.913819i	$-0.633119\pi$
$409$	−16.4266	−0.812243	−0.406121	+	0.913819i	$0.633119\pi$
$410$	80.5492	3.97804
$411$	−36.4237	−1.79665
$412$	−12.0920	−0.595729
$413$	−28.2689	−1.39102
$414$	−19.6445	−0.965473
$415$	34.2729	1.68239
$416$	−13.7608	−0.674676
$417$	34.0262	1.66627
$418$	−4.99942	−0.244530
$419$	−26.8669	−1.31254	−0.656268	−	0.754528i	$-0.727866\pi$
$419$	−26.8669	−1.31254	−0.656268	+	0.754528i	$0.727866\pi$
$420$	23.4280	1.14317
$421$	−29.0214	−1.41442	−0.707208	−	0.707006i	$-0.750046\pi$
$421$	−29.0214	−1.41442	−0.707208	+	0.707006i	$0.750046\pi$
$422$	−1.40201	−0.0682487
$423$	23.3016	1.13296
$424$	−3.57947	−0.173834
$425$	60.0068	2.91076
$426$	48.2392	2.33719
$427$	15.5432	0.752190
$428$	14.6965	0.710381
$429$	3.26256	0.157518
$430$	−25.3341	−1.22172
$431$	30.1787	1.45366	0.726829	−	0.686819i	$-0.240993\pi$
$431$	30.1787	1.45366	0.726829	+	0.686819i	$0.240993\pi$
$432$	−10.4706	−0.503767
$433$	−21.2866	−1.02297	−0.511484	−	0.859293i	$-0.670904\pi$
$433$	−21.2866	−1.02297	−0.511484	+	0.859293i	$0.670904\pi$
$434$	−13.6475	−0.655101
$435$	54.0840	2.59313
$436$	1.07516	0.0514907
$437$	26.5828	1.27163
$438$	18.8651	0.901410
$439$	0.747652	0.0356835	0.0178417	−	0.999841i	$-0.494320\pi$
$439$	0.747652	0.0356835	0.0178417	+	0.999841i	$0.494320\pi$
$440$	−3.72292	−0.177483
$441$	−2.07886	−0.0989932
$442$	24.7137	1.17551
$443$	16.0368	0.761930	0.380965	−	0.924589i	$-0.375592\pi$
$443$	16.0368	0.761930	0.380965	+	0.924589i	$0.375592\pi$
$444$	2.42061	0.114877
$445$	−39.4788	−1.87148
$446$	−20.3778	−0.964916
$447$	−29.4455	−1.39272
$448$	0.779496	0.0368277
$449$	1.43522	0.0677323	0.0338661	−	0.999426i	$-0.489218\pi$
$449$	1.43522	0.0677323	0.0338661	+	0.999426i	$0.489218\pi$
$450$	−38.5464	−1.81709
$451$	6.74822	0.317761
$452$	−6.90612	−0.324836
$453$	53.7392	2.52489
$454$	−37.7731	−1.77278
$455$	24.1515	1.13224
$456$	−17.9254	−0.839432
$457$	7.16118	0.334986	0.167493	−	0.985873i	$-0.446433\pi$
$457$	7.16118	0.334986	0.167493	+	0.985873i	$0.446433\pi$
$458$	−29.4338	−1.37535
$459$	11.8403	0.552658
$460$	−23.0128	−1.07298
$461$	−25.2119	−1.17423	−0.587117	−	0.809502i	$-0.699737\pi$
$461$	−25.2119	−1.17423	−0.587117	+	0.809502i	$0.699737\pi$
$462$	5.61382	0.261179
$463$	12.0694	0.560911	0.280455	−	0.959867i	$-0.409515\pi$
$463$	12.0694	0.560911	0.280455	+	0.959867i	$0.409515\pi$
$464$	−30.3518	−1.40905
$465$	28.2867	1.31177
$466$	−17.9681	−0.832355
$467$	0.908387	0.0420351	0.0210176	−	0.999779i	$-0.493309\pi$
$467$	0.908387	0.0420351	0.0210176	+	0.999779i	$0.493309\pi$
$468$	−5.55042	−0.256568
$469$	5.68513	0.262515
$470$	78.0748	3.60132
$471$	−20.2130	−0.931368
$472$	−18.7245	−0.861865
$473$	−2.12243	−0.0975896
$474$	52.6948	2.42035
$475$	52.1607	2.39330
$476$	14.8676	0.681457
$477$	−4.56602	−0.209063
$478$	52.4990	2.40125
$479$	−39.0476	−1.78413	−0.892066	−	0.451905i	$-0.850745\pi$
$479$	−39.0476	−1.78413	−0.892066	+	0.451905i	$0.850745\pi$
$480$	49.0763	2.24002
$481$	2.49536	0.113779
$482$	−36.4564	−1.66054
$483$	−29.8496	−1.35821
$484$	−11.4641	−0.521097
$485$	−16.2115	−0.736126
$486$	−32.1093	−1.45651
$487$	−23.9332	−1.08452	−0.542259	−	0.840211i	$-0.682431\pi$
$487$	−23.9332	−1.08452	−0.542259	+	0.840211i	$0.682431\pi$
$488$	10.2954	0.466051
$489$	−28.7999	−1.30238
$490$	−6.96544	−0.314667
$491$	0.0106982	0.000482805 0	0.000241402	−	1.00000i	$-0.499923\pi$
$491$	0.0106982	0.000482805 0	0.000241402		1.00000i	$0.499923\pi$
$492$	−28.1282	−1.26812
$493$	34.3223	1.54580
$494$	21.4823	0.966536
$495$	−4.74900	−0.213452
$496$	−15.8745	−0.712784
$497$	29.9166	1.34194
$498$	−34.2316	−1.53395
$499$	5.86004	0.262331	0.131166	−	0.991360i	$-0.458128\pi$
$499$	5.86004	0.262331	0.131166	+	0.991360i	$0.458128\pi$
$500$	−23.9060	−1.06911
$501$	35.2875	1.57653
$502$	−40.0566	−1.78781
$503$	−20.2130	−0.901255	−0.450628	−	0.892712i	$-0.648800\pi$
$503$	−20.2130	−0.901255	−0.450628	+	0.892712i	$0.648800\pi$
$504$	8.21526	0.365937
$505$	30.7849	1.36991
$506$	−5.51432	−0.245142
$507$	15.2491	0.677236
$508$	−11.2387	−0.498636
$509$	33.1764	1.47052	0.735258	−	0.677787i	$-0.237061\pi$
$509$	33.1764	1.47052	0.735258	+	0.677787i	$0.237061\pi$
$510$	−88.1388	−3.90285
$511$	11.6996	0.517562
$512$	−11.3417	−0.501235
$513$	10.2922	0.454410
$514$	−29.2026	−1.28807
$515$	44.4566	1.95899
$516$	8.84681	0.389459
$517$	6.54092	0.287669
$518$	4.29372	0.188655
$519$	−34.4150	−1.51065
$520$	15.9973	0.701526
$521$	15.6108	0.683923	0.341962	−	0.939714i	$-0.388909\pi$
$521$	15.6108	0.683923	0.341962	+	0.939714i	$0.388909\pi$
$522$	−22.0475	−0.964993
$523$	−16.5832	−0.725132	−0.362566	−	0.931958i	$-0.618099\pi$
$523$	−16.5832	−0.725132	−0.362566	+	0.931958i	$0.618099\pi$
$524$	−7.79884	−0.340694
$525$	−58.5710	−2.55625
$526$	25.1492	1.09656
$527$	17.9511	0.781960
$528$	6.52986	0.284176
$529$	6.32061	0.274809
$530$	−15.2989	−0.664544
$531$	−23.8852	−1.03653
$532$	12.9237	0.560312
$533$	−28.9969	−1.25599
$534$	39.4313	1.70636
$535$	−54.0321	−2.33601
$536$	3.76567	0.162652
$537$	10.1213	0.436765
$538$	15.3976	0.663837
$539$	−0.583548	−0.0251352
$540$	−8.90995	−0.383423
$541$	−11.6384	−0.500374	−0.250187	−	0.968198i	$-0.580492\pi$
$541$	−11.6384	−0.500374	−0.250187	+	0.968198i	$0.580492\pi$
$542$	−22.1139	−0.949875
$543$	11.1392	0.478030
$544$	31.1443	1.33530
$545$	−3.95285	−0.169322
$546$	−24.1224	−1.03234
$547$	5.63410	0.240897	0.120448	−	0.992720i	$-0.461567\pi$
$547$	5.63410	0.240897	0.120448	+	0.992720i	$0.461567\pi$
$548$	17.3942	0.743041
$549$	13.1329	0.560500
$550$	−10.8202	−0.461376
$551$	29.8345	1.27099
$552$	−19.7716	−0.841533
$553$	32.6799	1.38969
$554$	−13.4484	−0.571368
$555$	−8.89945	−0.377761
$556$	−16.2492	−0.689122
$557$	−44.8534	−1.90050	−0.950251	−	0.311487i	$-0.899173\pi$
$557$	−44.8534	−1.90050	−0.950251	+	0.311487i	$0.899173\pi$
$558$	−11.5312	−0.488153
$559$	9.12002	0.385736
$560$	48.3381	2.04266
$561$	−7.38406	−0.311755
$562$	−5.07681	−0.214152
$563$	−15.9548	−0.672414	−0.336207	−	0.941788i	$-0.609144\pi$
$563$	−15.9548	−0.672414	−0.336207	+	0.941788i	$0.609144\pi$
$564$	−27.2641	−1.14803
$565$	25.3906	1.06819
$566$	−30.2625	−1.27203
$567$	−26.7534	−1.12354
$568$	19.8159	0.831458
$569$	−27.8355	−1.16693	−0.583463	−	0.812140i	$-0.698302\pi$
$569$	−27.8355	−1.16693	−0.583463	+	0.812140i	$0.698302\pi$
$570$	−76.6144	−3.20903
$571$	−14.2502	−0.596352	−0.298176	−	0.954511i	$-0.596378\pi$
$571$	−14.2502	−0.596352	−0.298176	+	0.954511i	$0.596378\pi$
$572$	−1.55804	−0.0651449
$573$	−28.3436	−1.18407
$574$	−49.8943	−2.08255
$575$	57.5329	2.39929
$576$	0.658619	0.0274424
$577$	27.2671	1.13514	0.567572	−	0.823323i	$-0.307883\pi$
$577$	27.2671	1.13514	0.567572	+	0.823323i	$0.307883\pi$
$578$	−26.1224	−1.08655
$579$	32.4401	1.34816
$580$	−25.8279	−1.07244
$581$	−21.2295	−0.880749
$582$	16.1920	0.671178
$583$	−1.28171	−0.0530830
$584$	7.74951	0.320677
$585$	20.4063	0.843697
$586$	−22.6927	−0.937425
$587$	−9.66362	−0.398860	−0.199430	−	0.979912i	$-0.563909\pi$
$587$	−9.66362	−0.398860	−0.199430	+	0.979912i	$0.563909\pi$
$588$	2.43237	0.100309
$589$	15.6039	0.642948
$590$	−80.0300	−3.29478
$591$	−15.2942	−0.629117
$592$	4.99435	0.205267
$593$	−10.4853	−0.430579	−0.215290	−	0.976550i	$-0.569070\pi$
$593$	−10.4853	−0.430579	−0.215290	+	0.976550i	$0.569070\pi$
$594$	−2.13500	−0.0876002
$595$	−54.6614	−2.24090
$596$	14.0617	0.575990
$597$	−36.4196	−1.49055
$598$	23.6949	0.968955
$599$	−4.77642	−0.195159	−0.0975796	−	0.995228i	$-0.531110\pi$
$599$	−4.77642	−0.195159	−0.0975796	+	0.995228i	$0.531110\pi$
$600$	−38.7958	−1.58383
$601$	−30.0871	−1.22728	−0.613638	−	0.789587i	$-0.710295\pi$
$601$	−30.0871	−1.22728	−0.613638	+	0.789587i	$0.710295\pi$
$602$	15.6926	0.639583
$603$	4.80353	0.195615
$604$	−25.6632	−1.04422
$605$	42.1483	1.71357
$606$	−30.7478	−1.24904
$607$	24.0965	0.978048	0.489024	−	0.872270i	$-0.337353\pi$
$607$	24.0965	0.978048	0.489024	+	0.872270i	$0.337353\pi$
$608$	27.0721	1.09792
$609$	−33.5010	−1.35753
$610$	44.0034	1.78164
$611$	−28.1061	−1.13705
$612$	12.5621	0.507793
$613$	13.7573	0.555651	0.277825	−	0.960632i	$-0.410386\pi$
$613$	13.7573	0.555651	0.277825	+	0.960632i	$0.410386\pi$
$614$	7.12463	0.287527
$615$	103.414	4.17007
$616$	2.30607	0.0929144
$617$	−32.4995	−1.30838	−0.654191	−	0.756329i	$-0.726991\pi$
$617$	−32.4995	−1.30838	−0.654191	+	0.756329i	$0.726991\pi$
$618$	−44.4030	−1.78615
$619$	−19.0764	−0.766745	−0.383372	−	0.923594i	$-0.625237\pi$
$619$	−19.0764	−0.766745	−0.383372	+	0.923594i	$0.625237\pi$
$620$	−13.5083	−0.542508
$621$	11.3522	0.455547
$622$	0.601894	0.0241338
$623$	24.4542	0.979738
$624$	−28.0586	−1.12324
$625$	34.7661	1.39064
$626$	13.0761	0.522625
$627$	−6.41858	−0.256333
$628$	9.65275	0.385186
$629$	−5.64768	−0.225188
$630$	35.1127	1.39892
$631$	−9.15342	−0.364392	−0.182196	−	0.983262i	$-0.558321\pi$
$631$	−9.15342	−0.364392	−0.182196	+	0.983262i	$0.558321\pi$
$632$	21.6462	0.861041
$633$	−1.79999	−0.0715431
$634$	−19.9677	−0.793017
$635$	41.3194	1.63971
$636$	5.34247	0.211843
$637$	2.50749	0.0993502
$638$	−6.18887	−0.245020
$639$	25.2774	0.999960
$640$	45.8030	1.81052
$641$	−18.6547	−0.736815	−0.368407	−	0.929664i	$-0.620097\pi$
$641$	−18.6547	−0.736815	−0.368407	+	0.929664i	$0.620097\pi$
$642$	53.9669	2.12991
$643$	30.5958	1.20658	0.603291	−	0.797521i	$-0.293856\pi$
$643$	30.5958	1.20658	0.603291	+	0.797521i	$0.293856\pi$
$644$	14.2547	0.561714
$645$	−32.5256	−1.28069
$646$	−48.6203	−1.91294
$647$	5.95826	0.234244	0.117122	−	0.993118i	$-0.462633\pi$
$647$	5.95826	0.234244	0.117122	+	0.993118i	$0.462633\pi$
$648$	−17.7207	−0.696135
$649$	−6.70473	−0.263183
$650$	46.4941	1.82365
$651$	−17.5215	−0.686723
$652$	13.7534	0.538625
$653$	15.4629	0.605112	0.302556	−	0.953132i	$-0.402160\pi$
$653$	15.4629	0.605112	0.302556	+	0.953132i	$0.402160\pi$
$654$	3.94809	0.154382
$655$	28.6727	1.12033
$656$	−58.0358	−2.26592
$657$	9.88537	0.385665
$658$	−48.3615	−1.88533
$659$	−10.4064	−0.405374	−0.202687	−	0.979244i	$-0.564967\pi$
$659$	−10.4064	−0.405374	−0.202687	+	0.979244i	$0.564967\pi$
$660$	5.55658	0.216290
$661$	−6.04463	−0.235109	−0.117554	−	0.993066i	$-0.537505\pi$
$661$	−6.04463	−0.235109	−0.117554	+	0.993066i	$0.537505\pi$
$662$	62.0557	2.41186
$663$	31.7291	1.23225
$664$	−14.0618	−0.545705
$665$	−47.5142	−1.84252
$666$	3.62789	0.140578
$667$	32.9073	1.27418
$668$	−16.8515	−0.652006
$669$	−26.1623	−1.01149
$670$	16.0948	0.621795
$671$	3.68650	0.142316
$672$	−30.3991	−1.17267
$673$	14.6256	0.563774	0.281887	−	0.959448i	$-0.409040\pi$
$673$	14.6256	0.563774	0.281887	+	0.959448i	$0.409040\pi$
$674$	56.0721	2.15982
$675$	22.2753	0.857375
$676$	−7.28221	−0.280085
$677$	8.01089	0.307884	0.153942	−	0.988080i	$-0.450803\pi$
$677$	8.01089	0.307884	0.153942	+	0.988080i	$0.450803\pi$
$678$	−25.3599	−0.973943
$679$	10.0418	0.385370
$680$	−36.2061	−1.38844
$681$	−48.4955	−1.85835
$682$	−3.23687	−0.123946
$683$	−12.2258	−0.467806	−0.233903	−	0.972260i	$-0.575150\pi$
$683$	−12.2258	−0.467806	−0.233903	+	0.972260i	$0.575150\pi$
$684$	10.9196	0.417520
$685$	−63.9501	−2.44341
$686$	34.3706	1.31228
$687$	−37.7891	−1.44174
$688$	18.2533	0.695900
$689$	5.50746	0.209818
$690$	−84.5052	−3.21706
$691$	−5.07971	−0.193241	−0.0966206	−	0.995321i	$-0.530803\pi$
$691$	−5.07971	−0.193241	−0.0966206	+	0.995321i	$0.530803\pi$
$692$	16.4349	0.624760
$693$	2.94166	0.111744
$694$	−60.9807	−2.31480
$695$	59.7409	2.26610
$696$	−22.1901	−0.841115
$697$	65.6277	2.48583
$698$	4.52685	0.171344
$699$	−23.0686	−0.872534
$700$	27.9706	1.05719
$701$	−13.9344	−0.526296	−0.263148	−	0.964756i	$-0.584761\pi$
$701$	−13.9344	−0.526296	−0.263148	+	0.964756i	$0.584761\pi$
$702$	9.17403	0.346252
$703$	−4.90923	−0.185155
$704$	0.184878	0.00696787
$705$	100.237	3.77516
$706$	−26.9956	−1.01599
$707$	−19.0690	−0.717162
$708$	27.9469	1.05031
$709$	−14.9690	−0.562173	−0.281087	−	0.959682i	$-0.590695\pi$
$709$	−14.9690	−0.562173	−0.281087	+	0.959682i	$0.590695\pi$
$710$	84.6949	3.17854
$711$	27.6122	1.03554
$712$	16.1978	0.607037
$713$	17.2110	0.644557
$714$	54.5955	2.04318
$715$	5.72818	0.214222
$716$	−4.83341	−0.180633
$717$	67.4016	2.51716
$718$	42.7598	1.59578
$719$	21.0091	0.783507	0.391753	−	0.920070i	$-0.371869\pi$
$719$	21.0091	0.783507	0.391753	+	0.920070i	$0.371869\pi$
$720$	40.8422	1.52210
$721$	−27.5375	−1.02555
$722$	−8.94443	−0.332877
$723$	−46.8050	−1.74070
$724$	−5.31954	−0.197699
$725$	64.5707	2.39810
$726$	−42.0975	−1.56238
$727$	44.3052	1.64319	0.821594	−	0.570073i	$-0.193085\pi$
$727$	44.3052	1.64319	0.821594	+	0.570073i	$0.193085\pi$
$728$	−9.90912	−0.367256
$729$	−8.44462	−0.312764
$730$	33.1220	1.22590
$731$	−20.6411	−0.763437
$732$	−15.3662	−0.567952
$733$	−38.0343	−1.40483	−0.702415	−	0.711768i	$-0.747895\pi$
$733$	−38.0343	−1.40483	−0.702415	+	0.711768i	$0.747895\pi$
$734$	15.3286	0.565789
$735$	−8.94269	−0.329856
$736$	29.8603	1.10067
$737$	1.34838	0.0496683
$738$	−42.1571	−1.55182
$739$	−9.16423	−0.337112	−0.168556	−	0.985692i	$-0.553910\pi$
$739$	−9.16423	−0.337112	−0.168556	+	0.985692i	$0.553910\pi$
$740$	4.24994	0.156231
$741$	27.5804	1.01319
$742$	9.47656	0.347896
$743$	−17.3797	−0.637601	−0.318800	−	0.947822i	$-0.603280\pi$
$743$	−17.3797	−0.637601	−0.318800	+	0.947822i	$0.603280\pi$
$744$	−11.6058	−0.425488
$745$	−51.6983	−1.89408
$746$	20.0039	0.732394
$747$	−17.9374	−0.656297
$748$	3.52626	0.128933
$749$	33.4689	1.22293
$750$	−87.7853	−3.20546
$751$	−37.2618	−1.35970	−0.679851	−	0.733350i	$-0.737956\pi$
$751$	−37.2618	−1.35970	−0.679851	+	0.733350i	$0.737956\pi$
$752$	−56.2530	−2.05134
$753$	−51.4272	−1.87411
$754$	26.5934	0.968473
$755$	94.3515	3.43380
$756$	5.51905	0.200726
$757$	46.6296	1.69478	0.847390	−	0.530971i	$-0.178173\pi$
$757$	46.6296	1.69478	0.847390	+	0.530971i	$0.178173\pi$
$758$	−40.3917	−1.46709
$759$	−7.07965	−0.256975
$760$	−31.4721	−1.14161
$761$	−43.4697	−1.57578	−0.787888	−	0.615818i	$-0.788826\pi$
$761$	−43.4697	−1.57578	−0.787888	+	0.615818i	$0.788826\pi$
$762$	−41.2696	−1.49504
$763$	2.44850	0.0886416
$764$	13.5355	0.489696
$765$	−46.1850	−1.66982
$766$	−32.1249	−1.16072
$767$	28.8100	1.04027
$768$	−44.3143	−1.59905
$769$	−23.7140	−0.855150	−0.427575	−	0.903980i	$-0.640632\pi$
$769$	−23.7140	−0.855150	−0.427575	+	0.903980i	$0.640632\pi$
$770$	9.85635	0.355198
$771$	−37.4921	−1.35025
$772$	−15.4918	−0.557561
$773$	7.56260	0.272008	0.136004	−	0.990708i	$-0.456574\pi$
$773$	7.56260	0.272008	0.136004	+	0.990708i	$0.456574\pi$
$774$	13.2591	0.476590
$775$	33.7715	1.21311
$776$	6.65142	0.238772
$777$	5.51255	0.197762
$778$	47.9156	1.71786
$779$	57.0467	2.04391
$780$	−23.8764	−0.854913
$781$	7.09554	0.253898
$782$	−53.6279	−1.91773
$783$	12.7408	0.455321
$784$	5.01861	0.179236
$785$	−35.4886	−1.26664
$786$	−28.6381	−1.02149
$787$	31.1082	1.10889	0.554443	−	0.832221i	$-0.312931\pi$
$787$	31.1082	1.10889	0.554443	+	0.832221i	$0.312931\pi$
$788$	7.30373	0.260185
$789$	32.2882	1.14949
$790$	92.5178	3.29164
$791$	−15.7276	−0.559208
$792$	1.94847	0.0692358
$793$	−15.8408	−0.562522
$794$	−38.9836	−1.38348
$795$	−19.6418	−0.696622
$796$	17.3922	0.616449
$797$	4.63664	0.164238	0.0821191	−	0.996623i	$-0.473831\pi$
$797$	4.63664	0.164238	0.0821191	+	0.996623i	$0.473831\pi$
$798$	47.4570	1.67996
$799$	63.6117	2.25042
$800$	58.5920	2.07154
$801$	20.6621	0.730059
$802$	−63.0072	−2.22486
$803$	2.77489	0.0979236
$804$	−5.62038	−0.198215
$805$	−52.4079	−1.84714
$806$	13.9087	0.489914
$807$	19.7684	0.695881
$808$	−12.6307	−0.444348
$809$	−14.4468	−0.507923	−0.253962	−	0.967214i	$-0.581734\pi$
$809$	−14.4468	−0.507923	−0.253962	+	0.967214i	$0.581734\pi$
$810$	−75.7397	−2.66122
$811$	−17.0591	−0.599025	−0.299512	−	0.954092i	$-0.596824\pi$
$811$	−17.0591	−0.599025	−0.299512	+	0.954092i	$0.596824\pi$
$812$	15.9984	0.561435
$813$	−28.3913	−0.995727
$814$	1.01837	0.0356939
$815$	−50.5648	−1.77121
$816$	63.5042	2.22309
$817$	−17.9422	−0.627718
$818$	28.8059	1.00717
$819$	−12.6402	−0.441684
$820$	−49.3855	−1.72462
$821$	48.0003	1.67522	0.837611	−	0.546267i	$-0.183952\pi$
$821$	48.0003	1.67522	0.837611	+	0.546267i	$0.183952\pi$
$822$	63.8731	2.22783
$823$	43.3251	1.51022	0.755109	−	0.655599i	$-0.227584\pi$
$823$	43.3251	1.51022	0.755109	+	0.655599i	$0.227584\pi$
$824$	−18.2401	−0.635423
$825$	−13.8917	−0.483647
$826$	49.5727	1.72485
$827$	41.8936	1.45678	0.728391	−	0.685162i	$-0.240268\pi$
$827$	41.8936	1.45678	0.728391	+	0.685162i	$0.240268\pi$
$828$	12.0442	0.418566
$829$	52.1876	1.81255	0.906274	−	0.422690i	$-0.138914\pi$
$829$	52.1876	1.81255	0.906274	+	0.422690i	$0.138914\pi$
$830$	−60.1014	−2.08615
$831$	−17.2659	−0.598949
$832$	−0.794416	−0.0275414
$833$	−5.67512	−0.196631
$834$	−59.6689	−2.06616
$835$	61.9552	2.14405
$836$	3.06519	0.106012
$837$	6.66365	0.230330
$838$	47.1142	1.62753
$839$	27.6622	0.955006	0.477503	−	0.878630i	$-0.341542\pi$
$839$	27.6622	0.955006	0.477503	+	0.878630i	$0.341542\pi$
$840$	35.3398	1.21934
$841$	7.93273	0.273542
$842$	50.8923	1.75386
$843$	−6.51793	−0.224490
$844$	0.859585	0.0295881
$845$	26.7733	0.921029
$846$	−40.8621	−1.40487
$847$	−26.1077	−0.897072
$848$	11.0229	0.378529
$849$	−38.8529	−1.33343
$850$	−105.229	−3.60931
$851$	−5.41485	−0.185619
$852$	−29.5759	−1.01325
$853$	36.9352	1.26464	0.632319	−	0.774708i	$-0.282103\pi$
$853$	36.9352	1.26464	0.632319	+	0.774708i	$0.282103\pi$
$854$	−27.2568	−0.932709
$855$	−40.1462	−1.37297
$856$	22.1688	0.757715
$857$	35.2352	1.20361	0.601806	−	0.798642i	$-0.294448\pi$
$857$	35.2352	1.20361	0.601806	+	0.798642i	$0.294448\pi$
$858$	−5.72127	−0.195321
$859$	−12.2440	−0.417761	−0.208881	−	0.977941i	$-0.566982\pi$
$859$	−12.2440	−0.417761	−0.208881	+	0.977941i	$0.566982\pi$
$860$	15.5326	0.529657
$861$	−64.0575	−2.18307
$862$	−52.9218	−1.80252
$863$	−44.1691	−1.50353	−0.751767	−	0.659429i	$-0.770798\pi$
$863$	−44.1691	−1.50353	−0.751767	+	0.659429i	$0.770798\pi$
$864$	11.5611	0.393318
$865$	−60.4233	−2.05446
$866$	37.3284	1.26847
$867$	−33.5376	−1.13900
$868$	8.36742	0.284009
$869$	7.75092	0.262932
$870$	−94.8424	−3.21546
$871$	−5.79395	−0.196320
$872$	1.62182	0.0549216
$873$	8.48463	0.287161
$874$	−46.6159	−1.57681
$875$	−54.4421	−1.84048
$876$	−11.5664	−0.390792
$877$	−37.0327	−1.25051	−0.625253	−	0.780422i	$-0.715004\pi$
$877$	−37.0327	−1.25051	−0.625253	+	0.780422i	$0.715004\pi$
$878$	−1.31109	−0.0442472
$879$	−29.1343	−0.982676
$880$	11.4647	0.386474
$881$	−0.291969	−0.00983668	−0.00491834	−	0.999988i	$-0.501566\pi$
$881$	−0.291969	−0.00983668	−0.00491834	+	0.999988i	$0.501566\pi$
$882$	3.64551	0.122751
$883$	−45.0779	−1.51699	−0.758496	−	0.651678i	$-0.774065\pi$
$883$	−45.0779	−1.51699	−0.758496	+	0.651678i	$0.774065\pi$
$884$	−15.1522	−0.509624
$885$	−102.748	−3.45383
$886$	−28.1223	−0.944787
$887$	−30.5605	−1.02612	−0.513061	−	0.858352i	$-0.671489\pi$
$887$	−30.5605	−1.02612	−0.513061	+	0.858352i	$0.671489\pi$
$888$	3.65136	0.122532
$889$	−25.5943	−0.858405
$890$	69.2306	2.32062
$891$	−6.34529	−0.212575
$892$	12.4938	0.418324
$893$	55.2943	1.85035
$894$	51.6360	1.72696
$895$	17.7702	0.593992
$896$	−28.3716	−0.947827
$897$	30.4210	1.01573
$898$	−2.51682	−0.0839875
$899$	19.3164	0.644237
$900$	23.6332	0.787773
$901$	−12.4649	−0.415265
$902$	−11.8338	−0.394021
$903$	20.1472	0.670456
$904$	−10.4175	−0.346481
$905$	19.5575	0.650112
$906$	−94.2378	−3.13084
$907$	−5.37352	−0.178425	−0.0892124	−	0.996013i	$-0.528435\pi$
$907$	−5.37352	−0.178425	−0.0892124	+	0.996013i	$0.528435\pi$
$908$	23.1591	0.768561
$909$	−16.1119	−0.534399
$910$	−42.3524	−1.40397
$911$	−21.8289	−0.723222	−0.361611	−	0.932329i	$-0.617773\pi$
$911$	−21.8289	−0.723222	−0.361611	+	0.932329i	$0.617773\pi$
$912$	55.2008	1.82788
$913$	−5.03515	−0.166639
$914$	−12.5579	−0.415380
$915$	56.4944	1.86765
$916$	18.0462	0.596263
$917$	−17.7606	−0.586507
$918$	−20.7633	−0.685291
$919$	14.5263	0.479179	0.239589	−	0.970874i	$-0.422987\pi$
$919$	14.5263	0.479179	0.239589	+	0.970874i	$0.422987\pi$
$920$	−34.7135	−1.14447
$921$	9.14706	0.301406
$922$	44.2118	1.45604
$923$	−30.4893	−1.00357
$924$	−3.44189	−0.113230
$925$	−10.6250	−0.349349
$926$	−21.1650	−0.695525
$927$	−23.2673	−0.764197
$928$	33.5131	1.10012
$929$	−22.2840	−0.731115	−0.365558	−	0.930789i	$-0.619122\pi$
$929$	−22.2840	−0.731115	−0.365558	+	0.930789i	$0.619122\pi$
$930$	−49.6040	−1.62658
$931$	−4.93308	−0.161675
$932$	11.0164	0.360855
$933$	0.772750	0.0252987
$934$	−1.59296	−0.0521232
$935$	−12.9644	−0.423982
$936$	−8.37250	−0.273664
$937$	−35.0576	−1.14528	−0.572641	−	0.819806i	$-0.694081\pi$
$937$	−35.0576	−1.14528	−0.572641	+	0.819806i	$0.694081\pi$
$938$	−9.96951	−0.325516
$939$	16.7879	0.547852
$940$	−47.8684	−1.56130
$941$	−40.9274	−1.33419	−0.667097	−	0.744971i	$-0.732463\pi$
$941$	−40.9274	−1.33419	−0.667097	+	0.744971i	$0.732463\pi$
$942$	35.4458	1.15489
$943$	62.9222	2.04903
$944$	57.6618	1.87673
$945$	−20.2910	−0.660065
$946$	3.72192	0.121010
$947$	−21.1363	−0.686837	−0.343419	−	0.939182i	$-0.611585\pi$
$947$	−21.1363	−0.686837	−0.343419	+	0.939182i	$0.611585\pi$
$948$	−32.3077	−1.04931
$949$	−11.9236	−0.387056
$950$	−91.4697	−2.96767
$951$	−25.6358	−0.831297
$952$	22.4270	0.726864
$953$	−50.7678	−1.64453	−0.822265	−	0.569105i	$-0.807290\pi$
$953$	−50.7678	−1.64453	−0.822265	+	0.569105i	$0.807290\pi$
$954$	8.00702	0.259237
$955$	−49.7636	−1.61031
$956$	−32.1877	−1.04102
$957$	−7.94567	−0.256847
$958$	68.4744	2.21231
$959$	39.6124	1.27915
$960$	2.83320	0.0914412
$961$	−20.8973	−0.674105
$962$	−4.37590	−0.141085
$963$	28.2788	0.911272
$964$	22.3518	0.719902
$965$	56.9560	1.83348
$966$	52.3447	1.68416
$967$	33.4714	1.07637	0.538184	−	0.842828i	$-0.319111\pi$
$967$	33.4714	1.07637	0.538184	+	0.842828i	$0.319111\pi$
$968$	−17.2930	−0.555819
$969$	−62.4219	−2.00528
$970$	28.4287	0.912790
$971$	54.5090	1.74928	0.874639	−	0.484776i	$-0.161099\pi$
$971$	54.5090	1.74928	0.874639	+	0.484776i	$0.161099\pi$
$972$	19.6865	0.631446
$973$	−37.0050	−1.18633
$974$	41.9696	1.34479
$975$	59.6921	1.91168
$976$	−31.7045	−1.01484
$977$	35.8365	1.14651	0.573256	−	0.819377i	$-0.305680\pi$
$977$	35.8365	1.14651	0.573256	+	0.819377i	$0.305680\pi$
$978$	50.5038	1.61493
$979$	5.79998	0.185368
$980$	4.27058	0.136419
$981$	2.06881	0.0660519
$982$	−0.0187606	−0.000598674 0
$983$	1.46628	0.0467671	0.0233835	−	0.999727i	$-0.492556\pi$
$983$	1.46628	0.0467671	0.0233835	+	0.999727i	$0.492556\pi$
$984$	−42.4298	−1.35261
$985$	−26.8524	−0.855588
$986$	−60.1880	−1.91678
$987$	−62.0897	−1.97634
$988$	−13.1710	−0.419026
$989$	−19.7901	−0.629289
$990$	8.32791	0.264678
$991$	−8.05871	−0.255993	−0.127997	−	0.991775i	$-0.540855\pi$
$991$	−8.05871	−0.255993	−0.127997	+	0.991775i	$0.540855\pi$
$992$	17.5278	0.556509
$993$	79.6711	2.52829
$994$	−52.4622	−1.66400
$995$	−63.9429	−2.02713
$996$	20.9877	0.665022
$997$	−39.8242	−1.26125	−0.630623	−	0.776089i	$-0.717201\pi$
$997$	−39.8242	−1.26125	−0.630623	+	0.776089i	$0.717201\pi$
$998$	−10.2762	−0.325289
$999$	−2.09649	−0.0663300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.15	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.75361 q^{2} -2.25140 q^{3} +1.07516 q^{4} -3.95285 q^{5} +3.94809 q^{6} +2.44850 q^{7} +1.62182 q^{8} +2.06881 q^{9} +O(q^{10})\)	\(q-1.75361 q^{2} -2.25140 q^{3} +1.07516 q^{4} -3.95285 q^{5} +3.94809 q^{6} +2.44850 q^{7} +1.62182 q^{8} +2.06881 q^{9} +6.93177 q^{10} +0.580727 q^{11} -2.42061 q^{12} -2.49536 q^{13} -4.29372 q^{14} +8.89945 q^{15} -4.99435 q^{16} +5.64768 q^{17} -3.62789 q^{18} +4.90923 q^{19} -4.24994 q^{20} -5.51255 q^{21} -1.01837 q^{22} +5.41485 q^{23} -3.65136 q^{24} +10.6250 q^{25} +4.37590 q^{26} +2.09649 q^{27} +2.63252 q^{28} +6.07723 q^{29} -15.6062 q^{30} +3.17848 q^{31} +5.51453 q^{32} -1.30745 q^{33} -9.90385 q^{34} -9.67855 q^{35} +2.22429 q^{36} -1.00000 q^{37} -8.60889 q^{38} +5.61807 q^{39} -6.41079 q^{40} +11.6203 q^{41} +9.66688 q^{42} -3.65478 q^{43} +0.624373 q^{44} -8.17768 q^{45} -9.49555 q^{46} +11.2633 q^{47} +11.2443 q^{48} -1.00486 q^{49} -18.6322 q^{50} -12.7152 q^{51} -2.68291 q^{52} -2.20708 q^{53} -3.67643 q^{54} -2.29553 q^{55} +3.97101 q^{56} -11.0527 q^{57} -10.6571 q^{58} -11.5454 q^{59} +9.56831 q^{60} +6.34807 q^{61} -5.57383 q^{62} +5.06547 q^{63} +0.318357 q^{64} +9.86380 q^{65} +2.29276 q^{66} +2.32188 q^{67} +6.07215 q^{68} -12.1910 q^{69} +16.9724 q^{70} +12.2184 q^{71} +3.35522 q^{72} +4.77830 q^{73} +1.75361 q^{74} -23.9212 q^{75} +5.27820 q^{76} +1.42191 q^{77} -9.85191 q^{78} +13.3469 q^{79} +19.7419 q^{80} -10.9265 q^{81} -20.3775 q^{82} -8.67043 q^{83} -5.92686 q^{84} -22.3244 q^{85} +6.40908 q^{86} -13.6823 q^{87} +0.941832 q^{88} +9.98744 q^{89} +14.3405 q^{90} -6.10989 q^{91} +5.82182 q^{92} -7.15604 q^{93} -19.7515 q^{94} -19.4055 q^{95} -12.4154 q^{96} +4.10122 q^{97} +1.76213 q^{98} +1.20141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 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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