LMFDB - Embedded newform 4015.2.a.g.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.01115 q^{2} -3.15685 q^{3} +2.04473 q^{4} -1.00000 q^{5} +6.34891 q^{6} -3.03904 q^{7} -0.0899564 q^{8} +6.96573 q^{9} +O(q^{10})$	\(q-2.01115 q^{2} -3.15685 q^{3} +2.04473 q^{4} -1.00000 q^{5} +6.34891 q^{6} -3.03904 q^{7} -0.0899564 q^{8} +6.96573 q^{9} +2.01115 q^{10} -1.00000 q^{11} -6.45491 q^{12} -1.14946 q^{13} +6.11196 q^{14} +3.15685 q^{15} -3.90854 q^{16} -2.57905 q^{17} -14.0091 q^{18} +8.45936 q^{19} -2.04473 q^{20} +9.59380 q^{21} +2.01115 q^{22} -8.20572 q^{23} +0.283979 q^{24} +1.00000 q^{25} +2.31174 q^{26} -12.5192 q^{27} -6.21401 q^{28} -4.47747 q^{29} -6.34891 q^{30} +1.28758 q^{31} +8.04058 q^{32} +3.15685 q^{33} +5.18686 q^{34} +3.03904 q^{35} +14.2430 q^{36} -2.29939 q^{37} -17.0131 q^{38} +3.62867 q^{39} +0.0899564 q^{40} -7.85135 q^{41} -19.2946 q^{42} +2.62322 q^{43} -2.04473 q^{44} -6.96573 q^{45} +16.5029 q^{46} +8.57395 q^{47} +12.3387 q^{48} +2.23574 q^{49} -2.01115 q^{50} +8.14169 q^{51} -2.35033 q^{52} +5.00103 q^{53} +25.1781 q^{54} +1.00000 q^{55} +0.273381 q^{56} -26.7050 q^{57} +9.00487 q^{58} -11.0363 q^{59} +6.45491 q^{60} -14.2803 q^{61} -2.58951 q^{62} -21.1691 q^{63} -8.35374 q^{64} +1.14946 q^{65} -6.34891 q^{66} -1.23132 q^{67} -5.27346 q^{68} +25.9043 q^{69} -6.11196 q^{70} +14.7506 q^{71} -0.626612 q^{72} -1.00000 q^{73} +4.62442 q^{74} -3.15685 q^{75} +17.2971 q^{76} +3.03904 q^{77} -7.29781 q^{78} +3.49986 q^{79} +3.90854 q^{80} +18.6242 q^{81} +15.7903 q^{82} +13.3475 q^{83} +19.6167 q^{84} +2.57905 q^{85} -5.27569 q^{86} +14.1347 q^{87} +0.0899564 q^{88} +14.3041 q^{89} +14.0091 q^{90} +3.49325 q^{91} -16.7785 q^{92} -4.06469 q^{93} -17.2435 q^{94} -8.45936 q^{95} -25.3829 q^{96} +2.95564 q^{97} -4.49642 q^{98} -6.96573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−2.01115	−1.42210	−0.711049	−	0.703142i	$-0.751780\pi$
$2$	−2.01115	−1.42210	−0.711049	+	0.703142i	$0.751780\pi$
$3$	−3.15685	−1.82261	−0.911305	−	0.411731i	$-0.864924\pi$
$3$	−3.15685	−1.82261	−0.911305	+	0.411731i	$0.864924\pi$
$4$	2.04473	1.02236
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.34891	2.59193
$7$	−3.03904	−1.14865	−0.574324	−	0.818628i	$-0.694735\pi$
$7$	−3.03904	−1.14865	−0.574324	+	0.818628i	$0.694735\pi$
$8$	−0.0899564	−0.0318044
$9$	6.96573	2.32191
$10$	2.01115	0.635982
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−6.45491	−1.86337
$13$	−1.14946	−0.318802	−0.159401	−	0.987214i	$-0.550956\pi$
$13$	−1.14946	−0.318802	−0.159401	+	0.987214i	$0.550956\pi$
$14$	6.11196	1.63349
$15$	3.15685	0.815096
$16$	−3.90854	−0.977135
$17$	−2.57905	−0.625512	−0.312756	−	0.949833i	$-0.601252\pi$
$17$	−2.57905	−0.625512	−0.312756	+	0.949833i	$0.601252\pi$
$18$	−14.0091	−3.30199
$19$	8.45936	1.94071	0.970355	−	0.241682i	$-0.0776992\pi$
$19$	8.45936	1.94071	0.970355	+	0.241682i	$0.0776992\pi$
$20$	−2.04473	−0.457215
$21$	9.59380	2.09354
$22$	2.01115	0.428779
$23$	−8.20572	−1.71101	−0.855505	−	0.517794i	$-0.826753\pi$
$23$	−8.20572	−1.71101	−0.855505	+	0.517794i	$0.826753\pi$
$24$	0.283979	0.0579670
$25$	1.00000	0.200000
$26$	2.31174	0.453369
$27$	−12.5192	−2.40933
$28$	−6.21401	−1.17434
$29$	−4.47747	−0.831446	−0.415723	−	0.909491i	$-0.636471\pi$
$29$	−4.47747	−0.831446	−0.415723	+	0.909491i	$0.636471\pi$
$30$	−6.34891	−1.15915
$31$	1.28758	0.231255	0.115628	−	0.993293i	$-0.463112\pi$
$31$	1.28758	0.231255	0.115628	+	0.993293i	$0.463112\pi$
$32$	8.04058	1.42139
$33$	3.15685	0.549538
$34$	5.18686	0.889540
$35$	3.03904	0.513691
$36$	14.2430	2.37384
$37$	−2.29939	−0.378017	−0.189009	−	0.981975i	$-0.560527\pi$
$37$	−2.29939	−0.378017	−0.189009	+	0.981975i	$0.560527\pi$
$38$	−17.0131	−2.75988
$39$	3.62867	0.581053
$40$	0.0899564	0.0142234
$41$	−7.85135	−1.22617	−0.613087	−	0.790015i	$-0.710073\pi$
$41$	−7.85135	−1.22617	−0.613087	+	0.790015i	$0.710073\pi$
$42$	−19.2946	−2.97722
$43$	2.62322	0.400037	0.200019	−	0.979792i	$-0.435900\pi$
$43$	2.62322	0.400037	0.200019	+	0.979792i	$0.435900\pi$
$44$	−2.04473	−0.308254
$45$	−6.96573	−1.03839
$46$	16.5029	2.43323
$47$	8.57395	1.25064	0.625320	−	0.780369i	$-0.284968\pi$
$47$	8.57395	1.25064	0.625320	+	0.780369i	$0.284968\pi$
$48$	12.3387	1.78094
$49$	2.23574	0.319392
$50$	−2.01115	−0.284420
$51$	8.14169	1.14007
$52$	−2.35033	−0.325932
$53$	5.00103	0.686944	0.343472	−	0.939163i	$-0.388397\pi$
$53$	5.00103	0.686944	0.343472	+	0.939163i	$0.388397\pi$
$54$	25.1781	3.42630
$55$	1.00000	0.134840
$56$	0.273381	0.0365320
$57$	−26.7050	−3.53716
$58$	9.00487	1.18240
$59$	−11.0363	−1.43680	−0.718402	−	0.695628i	$-0.755126\pi$
$59$	−11.0363	−1.43680	−0.718402	+	0.695628i	$0.755126\pi$
$60$	6.45491	0.833325
$61$	−14.2803	−1.82840	−0.914200	−	0.405263i	$-0.867180\pi$
$61$	−14.2803	−1.82840	−0.914200	+	0.405263i	$0.867180\pi$
$62$	−2.58951	−0.328868
$63$	−21.1691	−2.66706
$64$	−8.35374	−1.04422
$65$	1.14946	0.142573
$66$	−6.34891	−0.781497
$67$	−1.23132	−0.150429	−0.0752147	−	0.997167i	$-0.523964\pi$
$67$	−1.23132	−0.150429	−0.0752147	+	0.997167i	$0.523964\pi$
$68$	−5.27346	−0.639501
$69$	25.9043	3.11851
$70$	−6.11196	−0.730519
$71$	14.7506	1.75058	0.875288	−	0.483603i	$-0.160672\pi$
$71$	14.7506	1.75058	0.875288	+	0.483603i	$0.160672\pi$
$72$	−0.626612	−0.0738469
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	4.62442	0.537578
$75$	−3.15685	−0.364522
$76$	17.2971	1.98411
$77$	3.03904	0.346330
$78$	−7.29781	−0.826314
$79$	3.49986	0.393765	0.196883	−	0.980427i	$-0.436918\pi$
$79$	3.49986	0.393765	0.196883	+	0.980427i	$0.436918\pi$
$80$	3.90854	0.436988
$81$	18.6242	2.06936
$82$	15.7903	1.74374
$83$	13.3475	1.46508	0.732538	−	0.680726i	$-0.238336\pi$
$83$	13.3475	1.46508	0.732538	+	0.680726i	$0.238336\pi$
$84$	19.6167	2.14036
$85$	2.57905	0.279737
$86$	−5.27569	−0.568892
$87$	14.1347	1.51540
$88$	0.0899564	0.00958939
$89$	14.3041	1.51623	0.758115	−	0.652120i	$-0.226120\pi$
$89$	14.3041	1.51623	0.758115	+	0.652120i	$0.226120\pi$
$90$	14.0091	1.47669
$91$	3.49325	0.366192
$92$	−16.7785	−1.74928
$93$	−4.06469	−0.421488
$94$	−17.2435	−1.77853
$95$	−8.45936	−0.867912
$96$	−25.3829	−2.59064
$97$	2.95564	0.300100	0.150050	−	0.988678i	$-0.452057\pi$
$97$	2.95564	0.300100	0.150050	+	0.988678i	$0.452057\pi$
$98$	−4.49642	−0.454207
$99$	−6.96573	−0.700082
$100$	2.04473	0.204473
$101$	−2.66500	−0.265177	−0.132589	−	0.991171i	$-0.542329\pi$
$101$	−2.66500	−0.265177	−0.132589	+	0.991171i	$0.542329\pi$
$102$	−16.3742	−1.62128
$103$	9.55277	0.941263	0.470631	−	0.882330i	$-0.344026\pi$
$103$	9.55277	0.941263	0.470631	+	0.882330i	$0.344026\pi$
$104$	0.103401	0.0101393
$105$	−9.59380	−0.936259
$106$	−10.0578	−0.976902
$107$	−2.92323	−0.282599	−0.141300	−	0.989967i	$-0.545128\pi$
$107$	−2.92323	−0.282599	−0.141300	+	0.989967i	$0.545128\pi$
$108$	−25.5984	−2.46321
$109$	12.7210	1.21845	0.609226	−	0.792996i	$-0.291480\pi$
$109$	12.7210	1.21845	0.609226	+	0.792996i	$0.291480\pi$
$110$	−2.01115	−0.191756
$111$	7.25884	0.688979
$112$	11.8782	1.12238
$113$	−5.75958	−0.541816	−0.270908	−	0.962605i	$-0.587324\pi$
$113$	−5.75958	−0.541816	−0.270908	+	0.962605i	$0.587324\pi$
$114$	53.7077	5.03019
$115$	8.20572	0.765187
$116$	−9.15522	−0.850040
$117$	−8.00682	−0.740231
$118$	22.1957	2.04328
$119$	7.83783	0.718493
$120$	−0.283979	−0.0259236
$121$	1.00000	0.0909091
$122$	28.7198	2.60017
$123$	24.7856	2.23484
$124$	2.63274	0.236427
$125$	−1.00000	−0.0894427
$126$	42.5743	3.79282
$127$	11.7155	1.03958	0.519790	−	0.854294i	$-0.326010\pi$
$127$	11.7155	1.03958	0.519790	+	0.854294i	$0.326010\pi$
$128$	0.719471	0.0635929
$129$	−8.28112	−0.729112
$130$	−2.31174	−0.202753
$131$	−0.882785	−0.0771293	−0.0385646	−	0.999256i	$-0.512279\pi$
$131$	−0.882785	−0.0771293	−0.0385646	+	0.999256i	$0.512279\pi$
$132$	6.45491	0.561828
$133$	−25.7083	−2.22919
$134$	2.47637	0.213926
$135$	12.5192	1.07748
$136$	0.232002	0.0198940
$137$	−11.2979	−0.965241	−0.482621	−	0.875829i	$-0.660315\pi$
$137$	−11.2979	−0.965241	−0.482621	+	0.875829i	$0.660315\pi$
$138$	−52.0974	−4.43482
$139$	10.1414	0.860186	0.430093	−	0.902785i	$-0.358481\pi$
$139$	10.1414	0.860186	0.430093	+	0.902785i	$0.358481\pi$
$140$	6.21401	0.525179
$141$	−27.0667	−2.27943
$142$	−29.6657	−2.48949
$143$	1.14946	0.0961226
$144$	−27.2258	−2.26882
$145$	4.47747	0.371834
$146$	2.01115	0.166444
$147$	−7.05791	−0.582127
$148$	−4.70163	−0.386472
$149$	17.4183	1.42697	0.713483	−	0.700673i	$-0.247117\pi$
$149$	17.4183	1.42697	0.713483	+	0.700673i	$0.247117\pi$
$150$	6.34891	0.518386
$151$	−6.27794	−0.510892	−0.255446	−	0.966823i	$-0.582222\pi$
$151$	−6.27794	−0.510892	−0.255446	+	0.966823i	$0.582222\pi$
$152$	−0.760974	−0.0617231
$153$	−17.9650	−1.45238
$154$	−6.11196	−0.492516
$155$	−1.28758	−0.103421
$156$	7.41965	0.594048
$157$	17.7344	1.41536	0.707681	−	0.706533i	$-0.249742\pi$
$157$	17.7344	1.41536	0.707681	+	0.706533i	$0.249742\pi$
$158$	−7.03875	−0.559973
$159$	−15.7875	−1.25203
$160$	−8.04058	−0.635664
$161$	24.9375	1.96535
$162$	−37.4561	−2.94283
$163$	9.08833	0.711853	0.355927	−	0.934514i	$-0.384165\pi$
$163$	9.08833	0.711853	0.355927	+	0.934514i	$0.384165\pi$
$164$	−16.0539	−1.25360
$165$	−3.15685	−0.245761
$166$	−26.8438	−2.08348
$167$	14.3046	1.10692	0.553460	−	0.832876i	$-0.313307\pi$
$167$	14.3046	1.10692	0.553460	+	0.832876i	$0.313307\pi$
$168$	−0.863023	−0.0665837
$169$	−11.6787	−0.898365
$170$	−5.18686	−0.397814
$171$	58.9256	4.50616
$172$	5.36377	0.408984
$173$	−13.6756	−1.03974	−0.519868	−	0.854246i	$-0.674019\pi$
$173$	−13.6756	−1.03974	−0.519868	+	0.854246i	$0.674019\pi$
$174$	−28.4271	−2.15505
$175$	−3.03904	−0.229730
$176$	3.90854	0.294617
$177$	34.8400	2.61873
$178$	−28.7677	−2.15623
$179$	−22.1684	−1.65695	−0.828473	−	0.560028i	$-0.810790\pi$
$179$	−22.1684	−1.65695	−0.828473	+	0.560028i	$0.810790\pi$
$180$	−14.2430	−1.06161
$181$	7.40181	0.550172	0.275086	−	0.961420i	$-0.411294\pi$
$181$	7.40181	0.550172	0.275086	+	0.961420i	$0.411294\pi$
$182$	−7.02545	−0.520761
$183$	45.0807	3.33246
$184$	0.738157	0.0544177
$185$	2.29939	0.169055
$186$	8.17470	0.599398
$187$	2.57905	0.188599
$188$	17.5314	1.27861
$189$	38.0464	2.76747
$190$	17.0131	1.23426
$191$	26.8282	1.94122	0.970611	−	0.240654i	$-0.0773619\pi$
$191$	26.8282	1.94122	0.970611	+	0.240654i	$0.0773619\pi$
$192$	26.3715	1.90320
$193$	12.0850	0.869894	0.434947	−	0.900456i	$-0.356767\pi$
$193$	12.0850	0.869894	0.434947	+	0.900456i	$0.356767\pi$
$194$	−5.94423	−0.426771
$195$	−3.62867	−0.259855
$196$	4.57149	0.326535
$197$	−5.85831	−0.417387	−0.208694	−	0.977981i	$-0.566921\pi$
$197$	−5.85831	−0.417387	−0.208694	+	0.977981i	$0.566921\pi$
$198$	14.0091	0.995586
$199$	−4.13460	−0.293094	−0.146547	−	0.989204i	$-0.546816\pi$
$199$	−4.13460	−0.293094	−0.146547	+	0.989204i	$0.546816\pi$
$200$	−0.0899564	−0.00636088
$201$	3.88709	0.274174
$202$	5.35971	0.377108
$203$	13.6072	0.955038
$204$	16.6476	1.16556
$205$	7.85135	0.548362
$206$	−19.2121	−1.33857
$207$	−57.1588	−3.97281
$208$	4.49271	0.311513
$209$	−8.45936	−0.585146
$210$	19.2946	1.33145
$211$	16.0791	1.10693	0.553464	−	0.832873i	$-0.313305\pi$
$211$	16.0791	1.10693	0.553464	+	0.832873i	$0.313305\pi$
$212$	10.2257	0.702307
$213$	−46.5655	−3.19062
$214$	5.87906	0.401884
$215$	−2.62322	−0.178902
$216$	1.12619	0.0766272
$217$	−3.91299	−0.265631
$218$	−25.5839	−1.73276
$219$	3.15685	0.213320
$220$	2.04473	0.137856
$221$	2.96451	0.199415
$222$	−14.5986	−0.979795
$223$	4.67472	0.313042	0.156521	−	0.987675i	$-0.449972\pi$
$223$	4.67472	0.313042	0.156521	+	0.987675i	$0.449972\pi$
$224$	−24.4356	−1.63267
$225$	6.96573	0.464382
$226$	11.5834	0.770516
$227$	19.6425	1.30372	0.651860	−	0.758340i	$-0.273989\pi$
$227$	19.6425	1.30372	0.651860	+	0.758340i	$0.273989\pi$
$228$	−54.6044	−3.61627
$229$	12.4356	0.821765	0.410883	−	0.911688i	$-0.365221\pi$
$229$	12.4356	0.821765	0.410883	+	0.911688i	$0.365221\pi$
$230$	−16.5029	−1.08817
$231$	−9.59380	−0.631225
$232$	0.402777	0.0264436
$233$	−1.42071	−0.0930736	−0.0465368	−	0.998917i	$-0.514818\pi$
$233$	−1.42071	−0.0930736	−0.0465368	+	0.998917i	$0.514818\pi$
$234$	16.1029	1.05268
$235$	−8.57395	−0.559303
$236$	−22.5662	−1.46894
$237$	−11.0486	−0.717680
$238$	−15.7631	−1.02177
$239$	−10.3413	−0.668922	−0.334461	−	0.942410i	$-0.608554\pi$
$239$	−10.3413	−0.668922	−0.334461	+	0.942410i	$0.608554\pi$
$240$	−12.3387	−0.796459
$241$	6.65478	0.428672	0.214336	−	0.976760i	$-0.431241\pi$
$241$	6.65478	0.428672	0.214336	+	0.976760i	$0.431241\pi$
$242$	−2.01115	−0.129282
$243$	−21.2362	−1.36230
$244$	−29.1993	−1.86929
$245$	−2.23574	−0.142836
$246$	−49.8475	−3.17816
$247$	−9.72369	−0.618703
$248$	−0.115826	−0.00735494
$249$	−42.1360	−2.67026
$250$	2.01115	0.127196
$251$	−16.7222	−1.05549	−0.527747	−	0.849401i	$-0.676963\pi$
$251$	−16.7222	−1.05549	−0.527747	+	0.849401i	$0.676963\pi$
$252$	−43.2851	−2.72670
$253$	8.20572	0.515889
$254$	−23.5616	−1.47838
$255$	−8.14169	−0.509853
$256$	15.2605	0.953782
$257$	−14.5062	−0.904871	−0.452435	−	0.891797i	$-0.649445\pi$
$257$	−14.5062	−0.904871	−0.452435	+	0.891797i	$0.649445\pi$
$258$	16.6546	1.03687
$259$	6.98793	0.434209
$260$	2.35033	0.145761
$261$	−31.1889	−1.93054
$262$	1.77541	0.109685
$263$	−14.5455	−0.896914	−0.448457	−	0.893805i	$-0.648026\pi$
$263$	−14.5455	−0.896914	−0.448457	+	0.893805i	$0.648026\pi$
$264$	−0.283979	−0.0174777
$265$	−5.00103	−0.307211
$266$	51.7033	3.17013
$267$	−45.1559	−2.76350
$268$	−2.51771	−0.153794
$269$	−20.2047	−1.23190	−0.615950	−	0.787785i	$-0.711228\pi$
$269$	−20.2047	−1.23190	−0.615950	+	0.787785i	$0.711228\pi$
$270$	−25.1781	−1.53229
$271$	−21.4015	−1.30005	−0.650025	−	0.759913i	$-0.725242\pi$
$271$	−21.4015	−1.30005	−0.650025	+	0.759913i	$0.725242\pi$
$272$	10.0803	0.611210
$273$	−11.0277	−0.667425
$274$	22.7217	1.37267
$275$	−1.00000	−0.0603023
$276$	52.9672	3.18825
$277$	−12.6103	−0.757680	−0.378840	−	0.925462i	$-0.623677\pi$
$277$	−12.6103	−0.757680	−0.378840	+	0.925462i	$0.623677\pi$
$278$	−20.3960	−1.22327
$279$	8.96890	0.536954
$280$	−0.273381	−0.0163376
$281$	−0.981511	−0.0585520	−0.0292760	−	0.999571i	$-0.509320\pi$
$281$	−0.981511	−0.0585520	−0.0292760	+	0.999571i	$0.509320\pi$
$282$	54.4353	3.24157
$283$	10.2251	0.607821	0.303911	−	0.952701i	$-0.401708\pi$
$283$	10.2251	0.607821	0.303911	+	0.952701i	$0.401708\pi$
$284$	30.1610	1.78973
$285$	26.7050	1.58187
$286$	−2.31174	−0.136696
$287$	23.8605	1.40844
$288$	56.0085	3.30033
$289$	−10.3485	−0.608735
$290$	−9.00487	−0.528784
$291$	−9.33052	−0.546965
$292$	−2.04473	−0.119659
$293$	−2.11004	−0.123270	−0.0616350	−	0.998099i	$-0.519631\pi$
$293$	−2.11004	−0.123270	−0.0616350	+	0.998099i	$0.519631\pi$
$294$	14.1945	0.827842
$295$	11.0363	0.642558
$296$	0.206845	0.0120226
$297$	12.5192	0.726440
$298$	−35.0309	−2.02929
$299$	9.43214	0.545474
$300$	−6.45491	−0.372674
$301$	−7.97206	−0.459502
$302$	12.6259	0.726539
$303$	8.41300	0.483314
$304$	−33.0638	−1.89634
$305$	14.2803	0.817686
$306$	36.1303	2.06543
$307$	9.76875	0.557532	0.278766	−	0.960359i	$-0.410075\pi$
$307$	9.76875	0.557532	0.278766	+	0.960359i	$0.410075\pi$
$308$	6.21401	0.354076
$309$	−30.1567	−1.71556
$310$	2.58951	0.147074
$311$	−11.0732	−0.627905	−0.313952	−	0.949439i	$-0.601653\pi$
$311$	−11.0732	−0.627905	−0.313952	+	0.949439i	$0.601653\pi$
$312$	−0.326422	−0.0184800
$313$	6.12585	0.346253	0.173127	−	0.984900i	$-0.444613\pi$
$313$	6.12585	0.346253	0.173127	+	0.984900i	$0.444613\pi$
$314$	−35.6666	−2.01278
$315$	21.1691	1.19274
$316$	7.15627	0.402571
$317$	25.7625	1.44697	0.723483	−	0.690342i	$-0.242540\pi$
$317$	25.7625	1.44697	0.723483	+	0.690342i	$0.242540\pi$
$318$	31.7511	1.78051
$319$	4.47747	0.250690
$320$	8.35374	0.466988
$321$	9.22822	0.515069
$322$	−50.1530	−2.79492
$323$	−21.8171	−1.21394
$324$	38.0815	2.11564
$325$	−1.14946	−0.0637605
$326$	−18.2780	−1.01233
$327$	−40.1584	−2.22077
$328$	0.706279	0.0389978
$329$	−26.0566	−1.43654
$330$	6.34891	0.349496
$331$	25.9908	1.42859	0.714293	−	0.699847i	$-0.246748\pi$
$331$	25.9908	1.42859	0.714293	+	0.699847i	$0.246748\pi$
$332$	27.2920	1.49784
$333$	−16.0169	−0.877722
$334$	−28.7686	−1.57415
$335$	1.23132	0.0672741
$336$	−37.4978	−2.04567
$337$	−30.4320	−1.65774	−0.828868	−	0.559445i	$-0.811014\pi$
$337$	−30.4320	−1.65774	−0.828868	+	0.559445i	$0.811014\pi$
$338$	23.4877	1.27756
$339$	18.1822	0.987520
$340$	5.27346	0.285994
$341$	−1.28758	−0.0697261
$342$	−118.508	−6.40820
$343$	14.4788	0.781779
$344$	−0.235975	−0.0127229
$345$	−25.9043	−1.39464
$346$	27.5037	1.47861
$347$	2.66512	0.143071	0.0715355	−	0.997438i	$-0.477210\pi$
$347$	2.66512	0.143071	0.0715355	+	0.997438i	$0.477210\pi$
$348$	28.9017	1.54929
$349$	−25.0159	−1.33907	−0.669534	−	0.742781i	$-0.733506\pi$
$349$	−25.0159	−1.33907	−0.669534	+	0.742781i	$0.733506\pi$
$350$	6.11196	0.326698
$351$	14.3903	0.768100
$352$	−8.04058	−0.428564
$353$	−29.1750	−1.55283	−0.776415	−	0.630222i	$-0.782964\pi$
$353$	−29.1750	−1.55283	−0.776415	+	0.630222i	$0.782964\pi$
$354$	−70.0685	−3.72410
$355$	−14.7506	−0.782881
$356$	29.2480	1.55014
$357$	−24.7429	−1.30953
$358$	44.5841	2.35634
$359$	−24.1149	−1.27273	−0.636367	−	0.771386i	$-0.719564\pi$
$359$	−24.1149	−1.27273	−0.636367	+	0.771386i	$0.719564\pi$
$360$	0.626612	0.0330254
$361$	52.5608	2.76636
$362$	−14.8862	−0.782399
$363$	−3.15685	−0.165692
$364$	7.14274	0.374381
$365$	1.00000	0.0523424
$366$	−90.6641	−4.73909
$367$	−25.8058	−1.34705	−0.673527	−	0.739163i	$-0.735221\pi$
$367$	−25.8058	−1.34705	−0.673527	+	0.739163i	$0.735221\pi$
$368$	32.0724	1.67189
$369$	−54.6904	−2.84707
$370$	−4.62442	−0.240412
$371$	−15.1983	−0.789057
$372$	−8.31118	−0.430915
$373$	−14.7841	−0.765490	−0.382745	−	0.923854i	$-0.625021\pi$
$373$	−14.7841	−0.765490	−0.382745	+	0.923854i	$0.625021\pi$
$374$	−5.18686	−0.268206
$375$	3.15685	0.163019
$376$	−0.771282	−0.0397758
$377$	5.14667	0.265067
$378$	−76.5171	−3.93561
$379$	10.3593	0.532124	0.266062	−	0.963956i	$-0.414277\pi$
$379$	10.3593	0.532124	0.266062	+	0.963956i	$0.414277\pi$
$380$	−17.2971	−0.887323
$381$	−36.9840	−1.89475
$382$	−53.9556	−2.76061
$383$	−0.577573	−0.0295126	−0.0147563	−	0.999891i	$-0.504697\pi$
$383$	−0.577573	−0.0295126	−0.0147563	+	0.999891i	$0.504697\pi$
$384$	−2.27127	−0.115905
$385$	−3.03904	−0.154884
$386$	−24.3047	−1.23708
$387$	18.2726	0.928850
$388$	6.04348	0.306811
$389$	13.9646	0.708031	0.354016	−	0.935240i	$-0.384816\pi$
$389$	13.9646	0.708031	0.354016	+	0.935240i	$0.384816\pi$
$390$	7.29781	0.369539
$391$	21.1630	1.07026
$392$	−0.201119	−0.0101581
$393$	2.78682	0.140577
$394$	11.7819	0.593566
$395$	−3.49986	−0.176097
$396$	−14.2430	−0.715739
$397$	18.0700	0.906910	0.453455	−	0.891279i	$-0.350191\pi$
$397$	18.0700	0.906910	0.453455	+	0.891279i	$0.350191\pi$
$398$	8.31530	0.416808
$399$	81.1574	4.06295
$400$	−3.90854	−0.195427
$401$	14.9180	0.744969	0.372485	−	0.928038i	$-0.378506\pi$
$401$	14.9180	0.744969	0.372485	+	0.928038i	$0.378506\pi$
$402$	−7.81753	−0.389903
$403$	−1.48001	−0.0737248
$404$	−5.44919	−0.271108
$405$	−18.6242	−0.925444
$406$	−27.3661	−1.35816
$407$	2.29939	0.113977
$408$	−0.732397	−0.0362591
$409$	−20.9777	−1.03728	−0.518641	−	0.854992i	$-0.673562\pi$
$409$	−20.9777	−1.03728	−0.518641	+	0.854992i	$0.673562\pi$
$410$	−15.7903	−0.779825
$411$	35.6657	1.75926
$412$	19.5328	0.962313
$413$	33.5397	1.65038
$414$	114.955	5.64973
$415$	−13.3475	−0.655202
$416$	−9.24232	−0.453142
$417$	−32.0150	−1.56778
$418$	17.0131	0.832136
$419$	−20.0307	−0.978565	−0.489283	−	0.872125i	$-0.662741\pi$
$419$	−20.0307	−0.978565	−0.489283	+	0.872125i	$0.662741\pi$
$420$	−19.6167	−0.957197
$421$	0.950520	0.0463255	0.0231627	−	0.999732i	$-0.492626\pi$
$421$	0.950520	0.0463255	0.0231627	+	0.999732i	$0.492626\pi$
$422$	−32.3374	−1.57416
$423$	59.7239	2.90387
$424$	−0.449875	−0.0218478
$425$	−2.57905	−0.125102
$426$	93.6503	4.53737
$427$	43.3982	2.10019
$428$	−5.97721	−0.288920
$429$	−3.62867	−0.175194
$430$	5.27569	0.254416
$431$	26.4477	1.27394	0.636970	−	0.770889i	$-0.280187\pi$
$431$	26.4477	1.27394	0.636970	+	0.770889i	$0.280187\pi$
$432$	48.9319	2.35424
$433$	−5.17286	−0.248592	−0.124296	−	0.992245i	$-0.539667\pi$
$433$	−5.17286	−0.248592	−0.124296	+	0.992245i	$0.539667\pi$
$434$	7.86961	0.377753
$435$	−14.1347	−0.677708
$436$	26.0110	1.24570
$437$	−69.4152	−3.32058
$438$	−6.34891	−0.303363
$439$	31.0165	1.48034	0.740168	−	0.672422i	$-0.234746\pi$
$439$	31.0165	1.48034	0.740168	+	0.672422i	$0.234746\pi$
$440$	−0.0899564	−0.00428850
$441$	15.5736	0.741599
$442$	−5.96209	−0.283587
$443$	−11.3727	−0.540334	−0.270167	−	0.962813i	$-0.587079\pi$
$443$	−11.3727	−0.540334	−0.270167	+	0.962813i	$0.587079\pi$
$444$	14.8424	0.704387
$445$	−14.3041	−0.678079
$446$	−9.40157	−0.445177
$447$	−54.9872	−2.60080
$448$	25.3873	1.19944
$449$	−36.5328	−1.72409	−0.862044	−	0.506834i	$-0.830816\pi$
$449$	−36.5328	−1.72409	−0.862044	+	0.506834i	$0.830816\pi$
$450$	−14.0091	−0.660397
$451$	7.85135	0.369706
$452$	−11.7768	−0.553933
$453$	19.8186	0.931157
$454$	−39.5041	−1.85402
$455$	−3.49325	−0.163766
$456$	2.40228	0.112497
$457$	17.1947	0.804336	0.402168	−	0.915566i	$-0.368257\pi$
$457$	17.1947	0.804336	0.402168	+	0.915566i	$0.368257\pi$
$458$	−25.0098	−1.16863
$459$	32.2878	1.50706
$460$	16.7785	0.782300
$461$	9.33877	0.434950	0.217475	−	0.976066i	$-0.430218\pi$
$461$	9.33877	0.434950	0.217475	+	0.976066i	$0.430218\pi$
$462$	19.2946	0.897665
$463$	−8.96532	−0.416654	−0.208327	−	0.978059i	$-0.566802\pi$
$463$	−8.96532	−0.416654	−0.208327	+	0.978059i	$0.566802\pi$
$464$	17.5004	0.812435
$465$	4.06469	0.188495
$466$	2.85726	0.132360
$467$	−38.6125	−1.78677	−0.893386	−	0.449290i	$-0.851677\pi$
$467$	−38.6125	−1.78677	−0.893386	+	0.449290i	$0.851677\pi$
$468$	−16.3718	−0.756785
$469$	3.74202	0.172790
$470$	17.2435	0.795384
$471$	−55.9850	−2.57965
$472$	0.992786	0.0456967
$473$	−2.62322	−0.120616
$474$	22.2203	1.02061
$475$	8.45936	0.388142
$476$	16.0262	0.734562
$477$	34.8358	1.59502
$478$	20.7979	0.951273
$479$	−7.78433	−0.355675	−0.177838	−	0.984060i	$-0.556910\pi$
$479$	−7.78433	−0.355675	−0.177838	+	0.984060i	$0.556910\pi$
$480$	25.3829	1.15857
$481$	2.64305	0.120513
$482$	−13.3838	−0.609614
$483$	−78.7240	−3.58207
$484$	2.04473	0.0929422
$485$	−2.95564	−0.134209
$486$	42.7092	1.93733
$487$	−24.0673	−1.09060	−0.545298	−	0.838242i	$-0.683583\pi$
$487$	−24.0673	−1.09060	−0.545298	+	0.838242i	$0.683583\pi$
$488$	1.28460	0.0581512
$489$	−28.6905	−1.29743
$490$	4.49642	0.203127
$491$	−7.93227	−0.357978	−0.178989	−	0.983851i	$-0.557283\pi$
$491$	−7.93227	−0.357978	−0.178989	+	0.983851i	$0.557283\pi$
$492$	50.6798	2.28482
$493$	11.5476	0.520079
$494$	19.5558	0.879857
$495$	6.96573	0.313086
$496$	−5.03254	−0.225968
$497$	−44.8276	−2.01079
$498$	84.7419	3.79738
$499$	26.0330	1.16540	0.582698	−	0.812689i	$-0.301997\pi$
$499$	26.0330	1.16540	0.582698	+	0.812689i	$0.301997\pi$
$500$	−2.04473	−0.0914431
$501$	−45.1574	−2.01749
$502$	33.6308	1.50102
$503$	25.5719	1.14019	0.570097	−	0.821577i	$-0.306906\pi$
$503$	25.5719	1.14019	0.570097	+	0.821577i	$0.306906\pi$
$504$	1.90430	0.0848241
$505$	2.66500	0.118591
$506$	−16.5029	−0.733645
$507$	36.8681	1.63737
$508$	23.9550	1.06283
$509$	−26.9606	−1.19501	−0.597504	−	0.801866i	$-0.703841\pi$
$509$	−26.9606	−1.19501	−0.597504	+	0.801866i	$0.703841\pi$
$510$	16.3742	0.725061
$511$	3.03904	0.134439
$512$	−32.1301	−1.41997
$513$	−105.905	−4.67581
$514$	29.1741	1.28682
$515$	−9.55277	−0.420945
$516$	−16.9326	−0.745418
$517$	−8.57395	−0.377082
$518$	−14.0538	−0.617488
$519$	43.1719	1.89504
$520$	−0.103401	−0.00453444
$521$	−14.9187	−0.653601	−0.326801	−	0.945093i	$-0.605971\pi$
$521$	−14.9187	−0.653601	−0.326801	+	0.945093i	$0.605971\pi$
$522$	62.7255	2.74542
$523$	22.3877	0.978946	0.489473	−	0.872018i	$-0.337189\pi$
$523$	22.3877	0.978946	0.489473	+	0.872018i	$0.337189\pi$
$524$	−1.80506	−0.0788542
$525$	9.59380	0.418708
$526$	29.2532	1.27550
$527$	−3.32072	−0.144653
$528$	−12.3387	−0.536973
$529$	44.3338	1.92756
$530$	10.0578	0.436884
$531$	−76.8759	−3.33613
$532$	−52.5665	−2.27905
$533$	9.02480	0.390908
$534$	90.8154	3.92997
$535$	2.92323	0.126382
$536$	0.110765	0.00478432
$537$	69.9825	3.01997
$538$	40.6347	1.75188
$539$	−2.23574	−0.0963003
$540$	25.5984	1.10158
$541$	36.1078	1.55240	0.776199	−	0.630488i	$-0.217145\pi$
$541$	36.1078	1.55240	0.776199	+	0.630488i	$0.217145\pi$
$542$	43.0417	1.84880
$543$	−23.3664	−1.00275
$544$	−20.7371	−0.889095
$545$	−12.7210	−0.544909
$546$	22.1783	0.949144
$547$	−38.8222	−1.65992	−0.829958	−	0.557826i	$-0.811636\pi$
$547$	−38.8222	−1.65992	−0.829958	+	0.557826i	$0.811636\pi$
$548$	−23.1011	−0.986829
$549$	−99.4725	−4.24538
$550$	2.01115	0.0857558
$551$	−37.8766	−1.61360
$552$	−2.33025	−0.0991822
$553$	−10.6362	−0.452297
$554$	25.3612	1.07750
$555$	−7.25884	−0.308121
$556$	20.7365	0.879423
$557$	−7.61234	−0.322545	−0.161273	−	0.986910i	$-0.551560\pi$
$557$	−7.61234	−0.322545	−0.161273	+	0.986910i	$0.551560\pi$
$558$	−18.0378	−0.763602
$559$	−3.01528	−0.127533
$560$	−11.8782	−0.501946
$561$	−8.14169	−0.343743
$562$	1.97397	0.0832667
$563$	−17.9461	−0.756338	−0.378169	−	0.925737i	$-0.623446\pi$
$563$	−17.9461	−0.756338	−0.378169	+	0.925737i	$0.623446\pi$
$564$	−55.3441	−2.33041
$565$	5.75958	0.242307
$566$	−20.5643	−0.864382
$567$	−56.5996	−2.37696
$568$	−1.32691	−0.0556760
$569$	−17.1967	−0.720922	−0.360461	−	0.932774i	$-0.617381\pi$
$569$	−17.1967	−0.720922	−0.360461	+	0.932774i	$0.617381\pi$
$570$	−53.7077	−2.24957
$571$	41.4435	1.73436	0.867179	−	0.497997i	$-0.165931\pi$
$571$	41.4435	1.73436	0.867179	+	0.497997i	$0.165931\pi$
$572$	2.35033	0.0982723
$573$	−84.6928	−3.53809
$574$	−47.9872	−2.00295
$575$	−8.20572	−0.342202
$576$	−58.1899	−2.42458
$577$	2.83794	0.118145	0.0590725	−	0.998254i	$-0.481186\pi$
$577$	2.83794	0.118145	0.0590725	+	0.998254i	$0.481186\pi$
$578$	20.8124	0.865681
$579$	−38.1505	−1.58548
$580$	9.15522	0.380150
$581$	−40.5635	−1.68286
$582$	18.7651	0.777838
$583$	−5.00103	−0.207121
$584$	0.0899564	0.00372242
$585$	8.00682	0.331041
$586$	4.24362	0.175302
$587$	−3.08894	−0.127494	−0.0637470	−	0.997966i	$-0.520305\pi$
$587$	−3.08894	−0.127494	−0.0637470	+	0.997966i	$0.520305\pi$
$588$	−14.4315	−0.595146
$589$	10.8921	0.448800
$590$	−22.1957	−0.913781
$591$	18.4938	0.760734
$592$	8.98726	0.369374
$593$	20.9776	0.861449	0.430724	−	0.902484i	$-0.358258\pi$
$593$	20.9776	0.861449	0.430724	+	0.902484i	$0.358258\pi$
$594$	−25.1781	−1.03307
$595$	−7.83783	−0.321320
$596$	35.6158	1.45888
$597$	13.0523	0.534196
$598$	−18.9694	−0.775718
$599$	20.9372	0.855470	0.427735	−	0.903904i	$-0.359312\pi$
$599$	20.9372	0.855470	0.427735	+	0.903904i	$0.359312\pi$
$600$	0.283979	0.0115934
$601$	−25.4041	−1.03625	−0.518127	−	0.855303i	$-0.673371\pi$
$601$	−25.4041	−1.03625	−0.518127	+	0.855303i	$0.673371\pi$
$602$	16.0330	0.653457
$603$	−8.57703	−0.349284
$604$	−12.8367	−0.522318
$605$	−1.00000	−0.0406558
$606$	−16.9198	−0.687321
$607$	15.4453	0.626904	0.313452	−	0.949604i	$-0.398514\pi$
$607$	15.4453	0.626904	0.313452	+	0.949604i	$0.398514\pi$
$608$	68.0182	2.75850
$609$	−42.9559	−1.74066
$610$	−28.7198	−1.16283
$611$	−9.85541	−0.398707
$612$	−36.7335	−1.48486
$613$	15.3486	0.619925	0.309962	−	0.950749i	$-0.399684\pi$
$613$	15.3486	0.619925	0.309962	+	0.950749i	$0.399684\pi$
$614$	−19.6464	−0.792866
$615$	−24.7856	−0.999451
$616$	−0.273381	−0.0110148
$617$	31.4577	1.26644	0.633219	−	0.773973i	$-0.281733\pi$
$617$	31.4577	1.26644	0.633219	+	0.773973i	$0.281733\pi$
$618$	60.6497	2.43969
$619$	−14.8598	−0.597267	−0.298633	−	0.954368i	$-0.596531\pi$
$619$	−14.8598	−0.597267	−0.298633	+	0.954368i	$0.596531\pi$
$620$	−2.63274	−0.105733
$621$	102.729	4.12239
$622$	22.2699	0.892942
$623$	−43.4707	−1.74162
$624$	−14.1828	−0.567767
$625$	1.00000	0.0400000
$626$	−12.3200	−0.492407
$627$	26.7050	1.06649
$628$	36.2621	1.44701
$629$	5.93025	0.236454
$630$	−42.5743	−1.69620
$631$	33.0325	1.31500	0.657502	−	0.753453i	$-0.271613\pi$
$631$	33.0325	1.31500	0.657502	+	0.753453i	$0.271613\pi$
$632$	−0.314835	−0.0125235
$633$	−50.7593	−2.01750
$634$	−51.8123	−2.05773
$635$	−11.7155	−0.464914
$636$	−32.2812	−1.28003
$637$	−2.56989	−0.101823
$638$	−9.00487	−0.356506
$639$	102.749	4.06468
$640$	−0.719471	−0.0284396
$641$	11.4189	0.451019	0.225509	−	0.974241i	$-0.427595\pi$
$641$	11.4189	0.451019	0.225509	+	0.974241i	$0.427595\pi$
$642$	−18.5593	−0.732479
$643$	−40.0896	−1.58098	−0.790489	−	0.612476i	$-0.790174\pi$
$643$	−40.0896	−1.58098	−0.790489	+	0.612476i	$0.790174\pi$
$644$	50.9904	2.00930
$645$	8.28112	0.326069
$646$	43.8776	1.72634
$647$	33.4755	1.31606	0.658029	−	0.752993i	$-0.271390\pi$
$647$	33.4755	1.31606	0.658029	+	0.752993i	$0.271390\pi$
$648$	−1.67537	−0.0658146
$649$	11.0363	0.433213
$650$	2.31174	0.0906737
$651$	12.3527	0.484142
$652$	18.5832	0.727773
$653$	−15.2964	−0.598596	−0.299298	−	0.954160i	$-0.596753\pi$
$653$	−15.2964	−0.598596	−0.299298	+	0.954160i	$0.596753\pi$
$654$	80.7646	3.15815
$655$	0.882785	0.0344933
$656$	30.6873	1.19814
$657$	−6.96573	−0.271759
$658$	52.4037	2.04291
$659$	−19.3409	−0.753413	−0.376707	−	0.926333i	$-0.622943\pi$
$659$	−19.3409	−0.753413	−0.376707	+	0.926333i	$0.622943\pi$
$660$	−6.45491	−0.251257
$661$	−20.4859	−0.796811	−0.398405	−	0.917209i	$-0.630436\pi$
$661$	−20.4859	−0.796811	−0.398405	+	0.917209i	$0.630436\pi$
$662$	−52.2715	−2.03159
$663$	−9.35854	−0.363456
$664$	−1.20069	−0.0465958
$665$	25.7083	0.996926
$666$	32.2125	1.24821
$667$	36.7409	1.42261
$668$	29.2490	1.13168
$669$	−14.7574	−0.570555
$670$	−2.47637	−0.0956704
$671$	14.2803	0.551283
$672$	77.1397	2.97573
$673$	−13.4844	−0.519784	−0.259892	−	0.965638i	$-0.583687\pi$
$673$	−13.4844	−0.519784	−0.259892	+	0.965638i	$0.583687\pi$
$674$	61.2033	2.35746
$675$	−12.5192	−0.481866
$676$	−23.8799	−0.918456
$677$	11.4209	0.438941	0.219470	−	0.975619i	$-0.429567\pi$
$677$	11.4209	0.438941	0.219470	+	0.975619i	$0.429567\pi$
$678$	−36.5671	−1.40435
$679$	−8.98229	−0.344709
$680$	−0.232002	−0.00889688
$681$	−62.0085	−2.37617
$682$	2.58951	0.0991574
$683$	23.5932	0.902770	0.451385	−	0.892329i	$-0.350930\pi$
$683$	23.5932	0.902770	0.451385	+	0.892329i	$0.350930\pi$
$684$	120.487	4.60693
$685$	11.2979	0.431669
$686$	−29.1190	−1.11177
$687$	−39.2573	−1.49776
$688$	−10.2530	−0.390890
$689$	−5.74848	−0.218999
$690$	52.0974	1.98331
$691$	0.785500	0.0298818	0.0149409	−	0.999888i	$-0.495244\pi$
$691$	0.785500	0.0298818	0.0149409	+	0.999888i	$0.495244\pi$
$692$	−27.9629	−1.06299
$693$	21.1691	0.804148
$694$	−5.35996	−0.203461
$695$	−10.1414	−0.384687
$696$	−1.27151	−0.0481964
$697$	20.2490	0.766987
$698$	50.3107	1.90429
$699$	4.48497	0.169637
$700$	−6.21401	−0.234867
$701$	30.7810	1.16258	0.581292	−	0.813695i	$-0.302547\pi$
$701$	30.7810	1.16258	0.581292	+	0.813695i	$0.302547\pi$
$702$	−28.9412	−1.09231
$703$	−19.4514	−0.733622
$704$	8.35374	0.314843
$705$	27.0667	1.01939
$706$	58.6754	2.20828
$707$	8.09902	0.304595
$708$	71.2383	2.67730
$709$	52.1336	1.95792	0.978959	−	0.204059i	$-0.0654134\pi$
$709$	52.1336	1.95792	0.978959	+	0.204059i	$0.0654134\pi$
$710$	29.6657	1.11333
$711$	24.3791	0.914287
$712$	−1.28675	−0.0482228
$713$	−10.5655	−0.395680
$714$	49.7617	1.86229
$715$	−1.14946	−0.0429873
$716$	−45.3284	−1.69400
$717$	32.6459	1.21918
$718$	48.4987	1.80995
$719$	−30.6759	−1.14402	−0.572009	−	0.820247i	$-0.693836\pi$
$719$	−30.6759	−1.14402	−0.572009	+	0.820247i	$0.693836\pi$
$720$	27.2258	1.01465
$721$	−29.0312	−1.08118
$722$	−105.708	−3.93403
$723$	−21.0082	−0.781302
$724$	15.1347	0.562476
$725$	−4.47747	−0.166289
$726$	6.34891	0.235630
$727$	−22.1727	−0.822339	−0.411170	−	0.911559i	$-0.634880\pi$
$727$	−22.1727	−0.822339	−0.411170	+	0.911559i	$0.634880\pi$
$728$	−0.314240	−0.0116465
$729$	11.1670	0.413593
$730$	−2.01115	−0.0744360
$731$	−6.76542	−0.250228
$732$	92.1778	3.40699
$733$	34.9801	1.29202	0.646009	−	0.763330i	$-0.276437\pi$
$733$	34.9801	1.29202	0.646009	+	0.763330i	$0.276437\pi$
$734$	51.8994	1.91564
$735$	7.05791	0.260335
$736$	−65.9787	−2.43201
$737$	1.23132	0.0453562
$738$	109.991	4.04881
$739$	−34.4149	−1.26597	−0.632987	−	0.774162i	$-0.718171\pi$
$739$	−34.4149	−1.26597	−0.632987	+	0.774162i	$0.718171\pi$
$740$	4.70163	0.172835
$741$	30.6963	1.12766
$742$	30.5661	1.12212
$743$	−47.2586	−1.73375	−0.866875	−	0.498525i	$-0.833875\pi$
$743$	−47.2586	−1.73375	−0.866875	+	0.498525i	$0.833875\pi$
$744$	0.365645	0.0134052
$745$	−17.4183	−0.638158
$746$	29.7330	1.08860
$747$	92.9749	3.40177
$748$	5.27346	0.192817
$749$	8.88381	0.324607
$750$	−6.34891	−0.231829
$751$	−6.86503	−0.250509	−0.125254	−	0.992125i	$-0.539975\pi$
$751$	−6.86503	−0.250509	−0.125254	+	0.992125i	$0.539975\pi$
$752$	−33.5117	−1.22204
$753$	52.7895	1.92376
$754$	−10.3507	−0.376951
$755$	6.27794	0.228478
$756$	77.7946	2.82936
$757$	23.8289	0.866074	0.433037	−	0.901376i	$-0.357442\pi$
$757$	23.8289	0.866074	0.433037	+	0.901376i	$0.357442\pi$
$758$	−20.8342	−0.756732
$759$	−25.9043	−0.940265
$760$	0.760974	0.0276034
$761$	−11.2327	−0.407184	−0.203592	−	0.979056i	$-0.565262\pi$
$761$	−11.2327	−0.407184	−0.203592	+	0.979056i	$0.565262\pi$
$762$	74.3805	2.69452
$763$	−38.6596	−1.39957
$764$	54.8564	1.98464
$765$	17.9650	0.649525
$766$	1.16159	0.0419699
$767$	12.6858	0.458057
$768$	−48.1752	−1.73837
$769$	2.40774	0.0868255	0.0434127	−	0.999057i	$-0.486177\pi$
$769$	2.40774	0.0868255	0.0434127	+	0.999057i	$0.486177\pi$
$770$	6.11196	0.220260
$771$	45.7939	1.64923
$772$	24.7105	0.889349
$773$	4.84251	0.174173	0.0870865	−	0.996201i	$-0.472244\pi$
$773$	4.84251	0.174173	0.0870865	+	0.996201i	$0.472244\pi$
$774$	−36.7490	−1.32092
$775$	1.28758	0.0462511
$776$	−0.265879	−0.00954448
$777$	−22.0599	−0.791394
$778$	−28.0848	−1.00689
$779$	−66.4174	−2.37965
$780$	−7.41965	−0.265666
$781$	−14.7506	−0.527818
$782$	−42.5619	−1.52201
$783$	56.0545	2.00322
$784$	−8.73849	−0.312089
$785$	−17.7344	−0.632969
$786$	−5.60472	−0.199914
$787$	−2.73990	−0.0976670	−0.0488335	−	0.998807i	$-0.515550\pi$
$787$	−2.73990	−0.0976670	−0.0488335	+	0.998807i	$0.515550\pi$
$788$	−11.9787	−0.426722
$789$	45.9180	1.63472
$790$	7.03875	0.250427
$791$	17.5036	0.622356
$792$	0.626612	0.0222657
$793$	16.4146	0.582899
$794$	−36.3416	−1.28971
$795$	15.7875	0.559926
$796$	−8.45413	−0.299649
$797$	−51.4516	−1.82251	−0.911255	−	0.411842i	$-0.864886\pi$
$797$	−51.4516	−1.82251	−0.911255	+	0.411842i	$0.864886\pi$
$798$	−163.220	−5.77792
$799$	−22.1127	−0.782290
$800$	8.04058	0.284277
$801$	99.6385	3.52055
$802$	−30.0023	−1.05942
$803$	1.00000	0.0352892
$804$	7.94805	0.280306
$805$	−24.9375	−0.878931
$806$	2.97653	0.104844
$807$	63.7832	2.24528
$808$	0.239733	0.00843379
$809$	−34.2357	−1.20366	−0.601832	−	0.798623i	$-0.705562\pi$
$809$	−34.2357	−1.20366	−0.601832	+	0.798623i	$0.705562\pi$
$810$	37.4561	1.31607
$811$	34.9492	1.22723	0.613617	−	0.789604i	$-0.289714\pi$
$811$	34.9492	1.22723	0.613617	+	0.789604i	$0.289714\pi$
$812$	27.8230	0.976397
$813$	67.5615	2.36949
$814$	−4.62442	−0.162086
$815$	−9.08833	−0.318350
$816$	−31.8221	−1.11400
$817$	22.1908	0.776356
$818$	42.1894	1.47512
$819$	24.3330	0.850264
$820$	16.0539	0.560626
$821$	37.7473	1.31739	0.658695	−	0.752410i	$-0.271109\pi$
$821$	37.7473	1.31739	0.658695	+	0.752410i	$0.271109\pi$
$822$	−71.7291	−2.50184
$823$	−23.0129	−0.802178	−0.401089	−	0.916039i	$-0.631368\pi$
$823$	−23.0129	−0.802178	−0.401089	+	0.916039i	$0.631368\pi$
$824$	−0.859333	−0.0299363
$825$	3.15685	0.109908
$826$	−67.4534	−2.34701
$827$	−2.58381	−0.0898479	−0.0449240	−	0.998990i	$-0.514305\pi$
$827$	−2.58381	−0.0898479	−0.0449240	+	0.998990i	$0.514305\pi$
$828$	−116.874	−4.06166
$829$	−45.9102	−1.59453	−0.797264	−	0.603630i	$-0.793720\pi$
$829$	−45.9102	−1.59453	−0.797264	+	0.603630i	$0.793720\pi$
$830$	26.8438	0.931762
$831$	39.8089	1.38096
$832$	9.60228	0.332899
$833$	−5.76610	−0.199783
$834$	64.3871	2.22954
$835$	−14.3046	−0.495030
$836$	−17.2971	−0.598233
$837$	−16.1195	−0.557170
$838$	40.2848	1.39162
$839$	−57.7530	−1.99385	−0.996927	−	0.0783328i	$-0.975040\pi$
$839$	−57.7530	−1.99385	−0.996927	+	0.0783328i	$0.975040\pi$
$840$	0.863023	0.0297771
$841$	−8.95225	−0.308698
$842$	−1.91164	−0.0658794
$843$	3.09849	0.106718
$844$	32.8773	1.13168
$845$	11.6787	0.401761
$846$	−120.114	−4.12959
$847$	−3.03904	−0.104423
$848$	−19.5467	−0.671237
$849$	−32.2793	−1.10782
$850$	5.18686	0.177908
$851$	18.8681	0.646792
$852$	−95.2139	−3.26197
$853$	14.5829	0.499308	0.249654	−	0.968335i	$-0.419683\pi$
$853$	14.5829	0.499308	0.249654	+	0.968335i	$0.419683\pi$
$854$	−87.2804	−2.98667
$855$	−58.9256	−2.01521
$856$	0.262963	0.00898790
$857$	46.5590	1.59043	0.795213	−	0.606330i	$-0.207359\pi$
$857$	46.5590	1.59043	0.795213	+	0.606330i	$0.207359\pi$
$858$	7.29781	0.249143
$859$	2.75708	0.0940703	0.0470351	−	0.998893i	$-0.485023\pi$
$859$	2.75708	0.0940703	0.0470351	+	0.998893i	$0.485023\pi$
$860$	−5.36377	−0.182903
$861$	−75.3243	−2.56704
$862$	−53.1903	−1.81167
$863$	12.5803	0.428239	0.214120	−	0.976807i	$-0.431312\pi$
$863$	12.5803	0.428239	0.214120	+	0.976807i	$0.431312\pi$
$864$	−100.662	−3.42459
$865$	13.6756	0.464984
$866$	10.4034	0.353522
$867$	32.6687	1.10949
$868$	−8.00100	−0.271572
$869$	−3.49986	−0.118725
$870$	28.4271	0.963768
$871$	1.41535	0.0479573
$872$	−1.14434	−0.0387522
$873$	20.5882	0.696804
$874$	139.604	4.72219
$875$	3.03904	0.102738
$876$	6.45491	0.218091
$877$	36.7864	1.24219	0.621094	−	0.783736i	$-0.286688\pi$
$877$	36.7864	1.24219	0.621094	+	0.783736i	$0.286688\pi$
$878$	−62.3789	−2.10518
$879$	6.66110	0.224673
$880$	−3.90854	−0.131757
$881$	4.69408	0.158148	0.0790738	−	0.996869i	$-0.474804\pi$
$881$	4.69408	0.158148	0.0790738	+	0.996869i	$0.474804\pi$
$882$	−31.3208	−1.05463
$883$	−43.0711	−1.44946	−0.724729	−	0.689034i	$-0.758035\pi$
$883$	−43.0711	−1.44946	−0.724729	+	0.689034i	$0.758035\pi$
$884$	6.06163	0.203875
$885$	−34.8400	−1.17113
$886$	22.8723	0.768409
$887$	27.2904	0.916323	0.458161	−	0.888869i	$-0.348508\pi$
$887$	27.2904	0.916323	0.458161	+	0.888869i	$0.348508\pi$
$888$	−0.652979	−0.0219125
$889$	−35.6037	−1.19411
$890$	28.7677	0.964295
$891$	−18.6242	−0.623934
$892$	9.55854	0.320044
$893$	72.5302	2.42713
$894$	110.587	3.69860
$895$	22.1684	0.741009
$896$	−2.18650	−0.0730458
$897$	−29.7759	−0.994188
$898$	73.4729	2.45182
$899$	−5.76508	−0.192276
$900$	14.2430	0.474768
$901$	−12.8979	−0.429692
$902$	−15.7903	−0.525758
$903$	25.1666	0.837493
$904$	0.518111	0.0172321
$905$	−7.40181	−0.246044
$906$	−39.8581	−1.32420
$907$	35.3861	1.17498	0.587488	−	0.809233i	$-0.300117\pi$
$907$	35.3861	1.17498	0.587488	+	0.809233i	$0.300117\pi$
$908$	40.1636	1.33288
$909$	−18.5636	−0.615717
$910$	7.02545	0.232891
$911$	−50.9984	−1.68965	−0.844827	−	0.535040i	$-0.820296\pi$
$911$	−50.9984	−1.68965	−0.844827	+	0.535040i	$0.820296\pi$
$912$	104.378	3.45628
$913$	−13.3475	−0.441737
$914$	−34.5812	−1.14385
$915$	−45.0807	−1.49032
$916$	25.4274	0.840144
$917$	2.68282	0.0885944
$918$	−64.9356	−2.14319
$919$	36.1544	1.19262	0.596312	−	0.802753i	$-0.296632\pi$
$919$	36.1544	1.19262	0.596312	+	0.802753i	$0.296632\pi$
$920$	−0.738157	−0.0243363
$921$	−30.8385	−1.01616
$922$	−18.7817	−0.618541
$923$	−16.9552	−0.558088
$924$	−19.6167	−0.645342
$925$	−2.29939	−0.0756035
$926$	18.0306	0.592523
$927$	66.5420	2.18553
$928$	−36.0015	−1.18181
$929$	−25.2454	−0.828275	−0.414137	−	0.910214i	$-0.635917\pi$
$929$	−25.2454	−0.828275	−0.414137	+	0.910214i	$0.635917\pi$
$930$	−8.17470	−0.268059
$931$	18.9130	0.619847
$932$	−2.90496	−0.0951552
$933$	34.9565	1.14443
$934$	77.6555	2.54097
$935$	−2.57905	−0.0843440
$936$	0.720265	0.0235426
$937$	9.08995	0.296956	0.148478	−	0.988916i	$-0.452563\pi$
$937$	9.08995	0.296956	0.148478	+	0.988916i	$0.452563\pi$
$938$	−7.52577	−0.245725
$939$	−19.3384	−0.631085
$940$	−17.5314	−0.571812
$941$	14.4522	0.471129	0.235565	−	0.971859i	$-0.424306\pi$
$941$	14.4522	0.471129	0.235565	+	0.971859i	$0.424306\pi$
$942$	112.594	3.66852
$943$	64.4260	2.09800
$944$	43.1358	1.40395
$945$	−38.0464	−1.23765
$946$	5.27569	0.171527
$947$	−7.50563	−0.243900	−0.121950	−	0.992536i	$-0.538915\pi$
$947$	−7.50563	−0.243900	−0.121950	+	0.992536i	$0.538915\pi$
$948$	−22.5913	−0.733731
$949$	1.14946	0.0373130
$950$	−17.0131	−0.551976
$951$	−81.3284	−2.63726
$952$	−0.705063	−0.0228512
$953$	58.0169	1.87935	0.939676	−	0.342065i	$-0.111126\pi$
$953$	58.0169	1.87935	0.939676	+	0.342065i	$0.111126\pi$
$954$	−70.0601	−2.26828
$955$	−26.8282	−0.868141
$956$	−21.1451	−0.683882
$957$	−14.1347	−0.456911
$958$	15.6555	0.505805
$959$	34.3346	1.10872
$960$	−26.3715	−0.851138
$961$	−29.3422	−0.946521
$962$	−5.31558	−0.171381
$963$	−20.3624	−0.656170
$964$	13.6072	0.438259
$965$	−12.0850	−0.389029
$966$	158.326	5.09405
$967$	0.955404	0.0307237	0.0153619	−	0.999882i	$-0.495110\pi$
$967$	0.955404	0.0307237	0.0153619	+	0.999882i	$0.495110\pi$
$968$	−0.0899564	−0.00289131
$969$	68.8735	2.21254
$970$	5.94423	0.190858
$971$	26.5310	0.851421	0.425711	−	0.904859i	$-0.360024\pi$
$971$	26.5310	0.851421	0.425711	+	0.904859i	$0.360024\pi$
$972$	−43.4223	−1.39277
$973$	−30.8202	−0.988050
$974$	48.4031	1.55093
$975$	3.62867	0.116211
$976$	55.8150	1.78659
$977$	−12.5764	−0.402355	−0.201178	−	0.979555i	$-0.564477\pi$
$977$	−12.5764	−0.402355	−0.201178	+	0.979555i	$0.564477\pi$
$978$	57.7010	1.84507
$979$	−14.3041	−0.457161
$980$	−4.57149	−0.146031
$981$	88.6112	2.82914
$982$	15.9530	0.509081
$983$	19.9658	0.636809	0.318405	−	0.947955i	$-0.396853\pi$
$983$	19.9658	0.636809	0.318405	+	0.947955i	$0.396853\pi$
$984$	−2.22962	−0.0710777
$985$	5.85831	0.186661
$986$	−23.2240	−0.739604
$987$	82.2568	2.61826
$988$	−19.8823	−0.632540
$989$	−21.5254	−0.684468
$990$	−14.0091	−0.445240
$991$	−18.5096	−0.587976	−0.293988	−	0.955809i	$-0.594983\pi$
$991$	−18.5096	−0.587976	−0.293988	+	0.955809i	$0.594983\pi$
$992$	10.3529	0.328703
$993$	−82.0493	−2.60376
$994$	90.1552	2.85955
$995$	4.13460	0.131076
$996$	−86.1568	−2.72998
$997$	−46.2112	−1.46352	−0.731761	−	0.681561i	$-0.761301\pi$
$997$	−46.2112	−1.46352	−0.731761	+	0.681561i	$0.761301\pi$
$998$	−52.3562	−1.65731
$999$	28.7866	0.910768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.7	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.01115 q^{2} -3.15685 q^{3} +2.04473 q^{4} -1.00000 q^{5} +6.34891 q^{6} -3.03904 q^{7} -0.0899564 q^{8} +6.96573 q^{9} +O(q^{10})\)	\(q-2.01115 q^{2} -3.15685 q^{3} +2.04473 q^{4} -1.00000 q^{5} +6.34891 q^{6} -3.03904 q^{7} -0.0899564 q^{8} +6.96573 q^{9} +2.01115 q^{10} -1.00000 q^{11} -6.45491 q^{12} -1.14946 q^{13} +6.11196 q^{14} +3.15685 q^{15} -3.90854 q^{16} -2.57905 q^{17} -14.0091 q^{18} +8.45936 q^{19} -2.04473 q^{20} +9.59380 q^{21} +2.01115 q^{22} -8.20572 q^{23} +0.283979 q^{24} +1.00000 q^{25} +2.31174 q^{26} -12.5192 q^{27} -6.21401 q^{28} -4.47747 q^{29} -6.34891 q^{30} +1.28758 q^{31} +8.04058 q^{32} +3.15685 q^{33} +5.18686 q^{34} +3.03904 q^{35} +14.2430 q^{36} -2.29939 q^{37} -17.0131 q^{38} +3.62867 q^{39} +0.0899564 q^{40} -7.85135 q^{41} -19.2946 q^{42} +2.62322 q^{43} -2.04473 q^{44} -6.96573 q^{45} +16.5029 q^{46} +8.57395 q^{47} +12.3387 q^{48} +2.23574 q^{49} -2.01115 q^{50} +8.14169 q^{51} -2.35033 q^{52} +5.00103 q^{53} +25.1781 q^{54} +1.00000 q^{55} +0.273381 q^{56} -26.7050 q^{57} +9.00487 q^{58} -11.0363 q^{59} +6.45491 q^{60} -14.2803 q^{61} -2.58951 q^{62} -21.1691 q^{63} -8.35374 q^{64} +1.14946 q^{65} -6.34891 q^{66} -1.23132 q^{67} -5.27346 q^{68} +25.9043 q^{69} -6.11196 q^{70} +14.7506 q^{71} -0.626612 q^{72} -1.00000 q^{73} +4.62442 q^{74} -3.15685 q^{75} +17.2971 q^{76} +3.03904 q^{77} -7.29781 q^{78} +3.49986 q^{79} +3.90854 q^{80} +18.6242 q^{81} +15.7903 q^{82} +13.3475 q^{83} +19.6167 q^{84} +2.57905 q^{85} -5.27569 q^{86} +14.1347 q^{87} +0.0899564 q^{88} +14.3041 q^{89} +14.0091 q^{90} +3.49325 q^{91} -16.7785 q^{92} -4.06469 q^{93} -17.2435 q^{94} -8.45936 q^{95} -25.3829 q^{96} +2.95564 q^{97} -4.49642 q^{98} -6.96573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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