LMFDB - Embedded newform 4015.2.a.h.1.19

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:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+0.132711 q^{2} +1.97030 q^{3} -1.98239 q^{4} +1.00000 q^{5} +0.261480 q^{6} +2.54454 q^{7} -0.528506 q^{8} +0.882080 q^{9} +O(q^{10})$	\(q+0.132711 q^{2} +1.97030 q^{3} -1.98239 q^{4} +1.00000 q^{5} +0.261480 q^{6} +2.54454 q^{7} -0.528506 q^{8} +0.882080 q^{9} +0.132711 q^{10} +1.00000 q^{11} -3.90590 q^{12} +3.82891 q^{13} +0.337688 q^{14} +1.97030 q^{15} +3.89464 q^{16} +3.23514 q^{17} +0.117062 q^{18} +3.88348 q^{19} -1.98239 q^{20} +5.01351 q^{21} +0.132711 q^{22} -0.671050 q^{23} -1.04132 q^{24} +1.00000 q^{25} +0.508138 q^{26} -4.17294 q^{27} -5.04427 q^{28} -4.15859 q^{29} +0.261480 q^{30} -1.65403 q^{31} +1.57387 q^{32} +1.97030 q^{33} +0.429338 q^{34} +2.54454 q^{35} -1.74862 q^{36} +11.2450 q^{37} +0.515380 q^{38} +7.54410 q^{39} -0.528506 q^{40} -5.91398 q^{41} +0.665347 q^{42} -8.13054 q^{43} -1.98239 q^{44} +0.882080 q^{45} -0.0890556 q^{46} -2.25578 q^{47} +7.67360 q^{48} -0.525313 q^{49} +0.132711 q^{50} +6.37420 q^{51} -7.59039 q^{52} +10.1295 q^{53} -0.553794 q^{54} +1.00000 q^{55} -1.34481 q^{56} +7.65162 q^{57} -0.551890 q^{58} +4.81921 q^{59} -3.90590 q^{60} +4.97900 q^{61} -0.219508 q^{62} +2.24449 q^{63} -7.58040 q^{64} +3.82891 q^{65} +0.261480 q^{66} -14.5608 q^{67} -6.41330 q^{68} -1.32217 q^{69} +0.337688 q^{70} +9.53201 q^{71} -0.466185 q^{72} +1.00000 q^{73} +1.49233 q^{74} +1.97030 q^{75} -7.69856 q^{76} +2.54454 q^{77} +1.00118 q^{78} -8.85321 q^{79} +3.89464 q^{80} -10.8682 q^{81} -0.784849 q^{82} -1.15591 q^{83} -9.93871 q^{84} +3.23514 q^{85} -1.07901 q^{86} -8.19367 q^{87} -0.528506 q^{88} -1.34094 q^{89} +0.117062 q^{90} +9.74282 q^{91} +1.33028 q^{92} -3.25894 q^{93} -0.299367 q^{94} +3.88348 q^{95} +3.10100 q^{96} +6.93229 q^{97} -0.0697148 q^{98} +0.882080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	0.132711	0.0938407	0.0469204	−	0.998899i	$-0.485059\pi$
$2$	0.132711	0.0938407	0.0469204	+	0.998899i	$0.485059\pi$
$3$	1.97030	1.13755	0.568776	−	0.822492i	$-0.307417\pi$
$3$	1.97030	1.13755	0.568776	+	0.822492i	$0.307417\pi$
$4$	−1.98239	−0.991194
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.261480	0.106749
$7$	2.54454	0.961746	0.480873	−	0.876790i	$-0.340320\pi$
$7$	2.54454	0.961746	0.480873	+	0.876790i	$0.340320\pi$
$8$	−0.528506	−0.186855
$9$	0.882080	0.294027
$10$	0.132711	0.0419669
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.90590	−1.12754
$13$	3.82891	1.06195	0.530974	−	0.847388i	$-0.321826\pi$
$13$	3.82891	1.06195	0.530974	+	0.847388i	$0.321826\pi$
$14$	0.337688	0.0902510
$15$	1.97030	0.508729
$16$	3.89464	0.973659
$17$	3.23514	0.784637	0.392318	−	0.919829i	$-0.371673\pi$
$17$	3.23514	0.784637	0.392318	+	0.919829i	$0.371673\pi$
$18$	0.117062	0.0275917
$19$	3.88348	0.890931	0.445466	−	0.895299i	$-0.353038\pi$
$19$	3.88348	0.890931	0.445466	+	0.895299i	$0.353038\pi$
$20$	−1.98239	−0.443275
$21$	5.01351	1.09404
$22$	0.132711	0.0282940
$23$	−0.671050	−0.139924	−0.0699618	−	0.997550i	$-0.522288\pi$
$23$	−0.671050	−0.139924	−0.0699618	+	0.997550i	$0.522288\pi$
$24$	−1.04132	−0.212558
$25$	1.00000	0.200000
$26$	0.508138	0.0996541
$27$	−4.17294	−0.803082
$28$	−5.04427	−0.953277
$29$	−4.15859	−0.772231	−0.386116	−	0.922450i	$-0.626183\pi$
$29$	−4.15859	−0.772231	−0.386116	+	0.922450i	$0.626183\pi$
$30$	0.261480	0.0477395
$31$	−1.65403	−0.297073	−0.148537	−	0.988907i	$-0.547456\pi$
$31$	−1.65403	−0.297073	−0.148537	+	0.988907i	$0.547456\pi$
$32$	1.57387	0.278224
$33$	1.97030	0.342985
$34$	0.429338	0.0736309
$35$	2.54454	0.430106
$36$	−1.74862	−0.291437
$37$	11.2450	1.84866	0.924332	−	0.381590i	$-0.124623\pi$
$37$	11.2450	1.84866	0.924332	+	0.381590i	$0.124623\pi$
$38$	0.515380	0.0836056
$39$	7.54410	1.20802
$40$	−0.528506	−0.0835642
$41$	−5.91398	−0.923608	−0.461804	−	0.886982i	$-0.652798\pi$
$41$	−5.91398	−0.923608	−0.461804	+	0.886982i	$0.652798\pi$
$42$	0.665347	0.102665
$43$	−8.13054	−1.23990	−0.619948	−	0.784643i	$-0.712846\pi$
$43$	−8.13054	−1.23990	−0.619948	+	0.784643i	$0.712846\pi$
$44$	−1.98239	−0.298856
$45$	0.882080	0.131493
$46$	−0.0890556	−0.0131305
$47$	−2.25578	−0.329040	−0.164520	−	0.986374i	$-0.552607\pi$
$47$	−2.25578	−0.329040	−0.164520	+	0.986374i	$0.552607\pi$
$48$	7.67360	1.10759
$49$	−0.525313	−0.0750448
$50$	0.132711	0.0187681
$51$	6.37420	0.892566
$52$	−7.59039	−1.05260
$53$	10.1295	1.39140	0.695698	−	0.718334i	$-0.255095\pi$
$53$	10.1295	1.39140	0.695698	+	0.718334i	$0.255095\pi$
$54$	−0.553794	−0.0753618
$55$	1.00000	0.134840
$56$	−1.34481	−0.179707
$57$	7.65162	1.01348
$58$	−0.551890	−0.0724668
$59$	4.81921	0.627407	0.313704	−	0.949521i	$-0.398430\pi$
$59$	4.81921	0.627407	0.313704	+	0.949521i	$0.398430\pi$
$60$	−3.90590	−0.504249
$61$	4.97900	0.637496	0.318748	−	0.947839i	$-0.396738\pi$
$61$	4.97900	0.637496	0.318748	+	0.947839i	$0.396738\pi$
$62$	−0.219508	−0.0278776
$63$	2.24449	0.282779
$64$	−7.58040	−0.947551
$65$	3.82891	0.474918
$66$	0.261480	0.0321860
$67$	−14.5608	−1.77889	−0.889445	−	0.457043i	$-0.848909\pi$
$67$	−14.5608	−1.77889	−0.889445	+	0.457043i	$0.848909\pi$
$68$	−6.41330	−0.777727
$69$	−1.32217	−0.159170
$70$	0.337688	0.0403615
$71$	9.53201	1.13124	0.565621	−	0.824665i	$-0.308637\pi$
$71$	9.53201	1.13124	0.565621	+	0.824665i	$0.308637\pi$
$72$	−0.466185	−0.0549404
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	1.49233	0.173480
$75$	1.97030	0.227511
$76$	−7.69856	−0.883085
$77$	2.54454	0.289977
$78$	1.00118	0.113362
$79$	−8.85321	−0.996064	−0.498032	−	0.867159i	$-0.665944\pi$
$79$	−8.85321	−0.996064	−0.498032	+	0.867159i	$0.665944\pi$
$80$	3.89464	0.435434
$81$	−10.8682	−1.20757
$82$	−0.784849	−0.0866721
$83$	−1.15591	−0.126878	−0.0634388	−	0.997986i	$-0.520207\pi$
$83$	−1.15591	−0.126878	−0.0634388	+	0.997986i	$0.520207\pi$
$84$	−9.93871	−1.08440
$85$	3.23514	0.350900
$86$	−1.07901	−0.116353
$87$	−8.19367	−0.878454
$88$	−0.528506	−0.0563389
$89$	−1.34094	−0.142140	−0.0710699	−	0.997471i	$-0.522641\pi$
$89$	−1.34094	−0.142140	−0.0710699	+	0.997471i	$0.522641\pi$
$90$	0.117062	0.0123394
$91$	9.74282	1.02132
$92$	1.33028	0.138691
$93$	−3.25894	−0.337936
$94$	−0.299367	−0.0308773
$95$	3.88348	0.398437
$96$	3.10100	0.316495
$97$	6.93229	0.703867	0.351933	−	0.936025i	$-0.385524\pi$
$97$	6.93229	0.703867	0.351933	+	0.936025i	$0.385524\pi$
$98$	−0.0697148	−0.00704226
$99$	0.882080	0.0886524
$100$	−1.98239	−0.198239
$101$	8.49613	0.845397	0.422698	−	0.906270i	$-0.361083\pi$
$101$	8.49613	0.845397	0.422698	+	0.906270i	$0.361083\pi$
$102$	0.845925	0.0837590
$103$	−0.217970	−0.0214772	−0.0107386	−	0.999942i	$-0.503418\pi$
$103$	−0.217970	−0.0214772	−0.0107386	+	0.999942i	$0.503418\pi$
$104$	−2.02360	−0.198431
$105$	5.01351	0.489268
$106$	1.34430	0.130570
$107$	3.99697	0.386401	0.193201	−	0.981159i	$-0.438113\pi$
$107$	3.99697	0.386401	0.193201	+	0.981159i	$0.438113\pi$
$108$	8.27238	0.796010
$109$	6.58915	0.631126	0.315563	−	0.948905i	$-0.397807\pi$
$109$	6.58915	0.631126	0.315563	+	0.948905i	$0.397807\pi$
$110$	0.132711	0.0126535
$111$	22.1560	2.10295
$112$	9.91006	0.936413
$113$	19.4398	1.82874	0.914372	−	0.404875i	$-0.132685\pi$
$113$	19.4398	1.82874	0.914372	+	0.404875i	$0.132685\pi$
$114$	1.01545	0.0951058
$115$	−0.671050	−0.0625757
$116$	8.24394	0.765431
$117$	3.37740	0.312241
$118$	0.639561	0.0588764
$119$	8.23195	0.754621
$120$	−1.04132	−0.0950586
$121$	1.00000	0.0909091
$122$	0.660768	0.0598231
$123$	−11.6523	−1.05065
$124$	3.27894	0.294457
$125$	1.00000	0.0894427
$126$	0.297868	0.0265362
$127$	9.38206	0.832523	0.416261	−	0.909245i	$-0.363340\pi$
$127$	9.38206	0.832523	0.416261	+	0.909245i	$0.363340\pi$
$128$	−4.15375	−0.367143
$129$	−16.0196	−1.41045
$130$	0.508138	0.0445666
$131$	8.55103	0.747107	0.373554	−	0.927609i	$-0.378139\pi$
$131$	8.55103	0.747107	0.373554	+	0.927609i	$0.378139\pi$
$132$	−3.90590	−0.339965
$133$	9.88167	0.856849
$134$	−1.93238	−0.166932
$135$	−4.17294	−0.359149
$136$	−1.70979	−0.146613
$137$	8.40839	0.718377	0.359189	−	0.933265i	$-0.383053\pi$
$137$	8.40839	0.718377	0.359189	+	0.933265i	$0.383053\pi$
$138$	−0.175466	−0.0149367
$139$	−16.1906	−1.37327	−0.686634	−	0.727004i	$-0.740912\pi$
$139$	−16.1906	−1.37327	−0.686634	+	0.727004i	$0.740912\pi$
$140$	−5.04427	−0.426318
$141$	−4.44457	−0.374300
$142$	1.26500	0.106157
$143$	3.82891	0.320190
$144$	3.43538	0.286282
$145$	−4.15859	−0.345352
$146$	0.132711	0.0109832
$147$	−1.03502	−0.0853674
$148$	−22.2919	−1.83238
$149$	−13.8410	−1.13390	−0.566951	−	0.823751i	$-0.691877\pi$
$149$	−13.8410	−1.13390	−0.566951	+	0.823751i	$0.691877\pi$
$150$	0.261480	0.0213498
$151$	10.6531	0.866939	0.433470	−	0.901168i	$-0.357289\pi$
$151$	10.6531	0.866939	0.433470	+	0.901168i	$0.357289\pi$
$152$	−2.05244	−0.166475
$153$	2.85365	0.230704
$154$	0.337688	0.0272117
$155$	−1.65403	−0.132855
$156$	−14.9553	−1.19738
$157$	1.34322	0.107201	0.0536005	−	0.998562i	$-0.482930\pi$
$157$	1.34322	0.107201	0.0536005	+	0.998562i	$0.482930\pi$
$158$	−1.17492	−0.0934714
$159$	19.9582	1.58279
$160$	1.57387	0.124426
$161$	−1.70751	−0.134571
$162$	−1.44232	−0.113320
$163$	11.7586	0.921003	0.460501	−	0.887659i	$-0.347670\pi$
$163$	11.7586	0.921003	0.460501	+	0.887659i	$0.347670\pi$
$164$	11.7238	0.915475
$165$	1.97030	0.153388
$166$	−0.153402	−0.0119063
$167$	8.00639	0.619553	0.309776	−	0.950809i	$-0.399746\pi$
$167$	8.00639	0.619553	0.309776	+	0.950809i	$0.399746\pi$
$168$	−2.64967	−0.204426
$169$	1.66055	0.127735
$170$	0.429338	0.0329287
$171$	3.42554	0.261957
$172$	16.1179	1.22898
$173$	17.1620	1.30481	0.652403	−	0.757872i	$-0.273761\pi$
$173$	17.1620	1.30481	0.652403	+	0.757872i	$0.273761\pi$
$174$	−1.08739	−0.0824348
$175$	2.54454	0.192349
$176$	3.89464	0.293569
$177$	9.49528	0.713709
$178$	−0.177958	−0.0133385
$179$	−22.4630	−1.67896	−0.839481	−	0.543389i	$-0.817141\pi$
$179$	−22.4630	−1.67896	−0.839481	+	0.543389i	$0.817141\pi$
$180$	−1.74862	−0.130335
$181$	5.63145	0.418583	0.209291	−	0.977853i	$-0.432884\pi$
$181$	5.63145	0.418583	0.209291	+	0.977853i	$0.432884\pi$
$182$	1.29298	0.0958419
$183$	9.81013	0.725186
$184$	0.354654	0.0261454
$185$	11.2450	0.826747
$186$	−0.432497	−0.0317122
$187$	3.23514	0.236577
$188$	4.47183	0.326142
$189$	−10.6182	−0.772361
$190$	0.515380	0.0373896
$191$	8.04571	0.582167	0.291084	−	0.956698i	$-0.405984\pi$
$191$	8.04571	0.582167	0.291084	+	0.956698i	$0.405984\pi$
$192$	−14.9357	−1.07789
$193$	−20.9449	−1.50764	−0.753822	−	0.657079i	$-0.771792\pi$
$193$	−20.9449	−1.50764	−0.753822	+	0.657079i	$0.771792\pi$
$194$	0.919989	0.0660514
$195$	7.54410	0.540244
$196$	1.04137	0.0743839
$197$	18.4399	1.31379	0.656894	−	0.753983i	$-0.271870\pi$
$197$	18.4399	1.31379	0.656894	+	0.753983i	$0.271870\pi$
$198$	0.117062	0.00831920
$199$	−9.26236	−0.656591	−0.328296	−	0.944575i	$-0.606474\pi$
$199$	−9.26236	−0.656591	−0.328296	+	0.944575i	$0.606474\pi$
$200$	−0.528506	−0.0373710
$201$	−28.6892	−2.02358
$202$	1.12753	0.0793327
$203$	−10.5817	−0.742690
$204$	−12.6361	−0.884706
$205$	−5.91398	−0.413050
$206$	−0.0289270	−0.00201544
$207$	−0.591919	−0.0411412
$208$	14.9122	1.03398
$209$	3.88348	0.268626
$210$	0.665347	0.0459133
$211$	−25.1125	−1.72881	−0.864407	−	0.502792i	$-0.832306\pi$
$211$	−25.1125	−1.72881	−0.864407	+	0.502792i	$0.832306\pi$
$212$	−20.0806	−1.37914
$213$	18.7809	1.28685
$214$	0.530441	0.0362602
$215$	−8.13054	−0.554498
$216$	2.20542	0.150060
$217$	−4.20876	−0.285709
$218$	0.874451	0.0592253
$219$	1.97030	0.133140
$220$	−1.98239	−0.133653
$221$	12.3871	0.833244
$222$	2.94034	0.197343
$223$	−13.7294	−0.919388	−0.459694	−	0.888077i	$-0.652041\pi$
$223$	−13.7294	−0.919388	−0.459694	+	0.888077i	$0.652041\pi$
$224$	4.00478	0.267581
$225$	0.882080	0.0588053
$226$	2.57988	0.171611
$227$	12.6613	0.840362	0.420181	−	0.907440i	$-0.361967\pi$
$227$	12.6613	0.840362	0.420181	+	0.907440i	$0.361967\pi$
$228$	−15.1685	−1.00456
$229$	4.59839	0.303870	0.151935	−	0.988390i	$-0.451450\pi$
$229$	4.59839	0.303870	0.151935	+	0.988390i	$0.451450\pi$
$230$	−0.0890556	−0.00587215
$231$	5.01351	0.329865
$232$	2.19784	0.144295
$233$	1.72131	0.112767	0.0563834	−	0.998409i	$-0.482043\pi$
$233$	1.72131	0.112767	0.0563834	+	0.998409i	$0.482043\pi$
$234$	0.448218	0.0293009
$235$	−2.25578	−0.147151
$236$	−9.55354	−0.621882
$237$	−17.4435	−1.13308
$238$	1.09247	0.0708142
$239$	−21.1154	−1.36584	−0.682922	−	0.730492i	$-0.739291\pi$
$239$	−21.1154	−1.36584	−0.682922	+	0.730492i	$0.739291\pi$
$240$	7.67360	0.495329
$241$	−3.67870	−0.236966	−0.118483	−	0.992956i	$-0.537803\pi$
$241$	−3.67870	−0.236966	−0.118483	+	0.992956i	$0.537803\pi$
$242$	0.132711	0.00853098
$243$	−8.89475	−0.570598
$244$	−9.87032	−0.631882
$245$	−0.525313	−0.0335610
$246$	−1.54639	−0.0985941
$247$	14.8695	0.946123
$248$	0.874167	0.0555096
$249$	−2.27749	−0.144330
$250$	0.132711	0.00839337
$251$	−6.09989	−0.385021	−0.192511	−	0.981295i	$-0.561663\pi$
$251$	−6.09989	−0.385021	−0.192511	+	0.981295i	$0.561663\pi$
$252$	−4.44945	−0.280289
$253$	−0.671050	−0.0421885
$254$	1.24510	0.0781246
$255$	6.37420	0.399168
$256$	14.6096	0.913098
$257$	−3.13747	−0.195710	−0.0978549	−	0.995201i	$-0.531198\pi$
$257$	−3.13747	−0.195710	−0.0978549	+	0.995201i	$0.531198\pi$
$258$	−2.12597	−0.132357
$259$	28.6133	1.77794
$260$	−7.59039	−0.470736
$261$	−3.66821	−0.227057
$262$	1.13481	0.0701091
$263$	−2.68651	−0.165657	−0.0828286	−	0.996564i	$-0.526395\pi$
$263$	−2.68651	−0.165657	−0.0828286	+	0.996564i	$0.526395\pi$
$264$	−1.04132	−0.0640885
$265$	10.1295	0.622252
$266$	1.31140	0.0804074
$267$	−2.64206	−0.161692
$268$	28.8652	1.76322
$269$	−10.5332	−0.642218	−0.321109	−	0.947042i	$-0.604056\pi$
$269$	−10.5332	−0.642218	−0.321109	+	0.947042i	$0.604056\pi$
$270$	−0.553794	−0.0337028
$271$	13.2890	0.807252	0.403626	−	0.914924i	$-0.367750\pi$
$271$	13.2890	0.807252	0.403626	+	0.914924i	$0.367750\pi$
$272$	12.5997	0.763969
$273$	19.1963	1.16181
$274$	1.11588	0.0674130
$275$	1.00000	0.0603023
$276$	2.62105	0.157769
$277$	−24.6994	−1.48404	−0.742022	−	0.670376i	$-0.766133\pi$
$277$	−24.6994	−1.48404	−0.742022	+	0.670376i	$0.766133\pi$
$278$	−2.14867	−0.128868
$279$	−1.45899	−0.0873474
$280$	−1.34481	−0.0803675
$281$	−25.3659	−1.51320	−0.756600	−	0.653878i	$-0.773141\pi$
$281$	−25.3659	−1.51320	−0.756600	+	0.653878i	$0.773141\pi$
$282$	−0.589842	−0.0351246
$283$	25.5812	1.52065	0.760323	−	0.649545i	$-0.225041\pi$
$283$	25.5812	1.52065	0.760323	+	0.649545i	$0.225041\pi$
$284$	−18.8961	−1.12128
$285$	7.65162	0.453243
$286$	0.508138	0.0300468
$287$	−15.0484	−0.888277
$288$	1.38828	0.0818053
$289$	−6.53387	−0.384345
$290$	−0.551890	−0.0324081
$291$	13.6587	0.800686
$292$	−1.98239	−0.116010
$293$	−4.53296	−0.264818	−0.132409	−	0.991195i	$-0.542271\pi$
$293$	−4.53296	−0.264818	−0.132409	+	0.991195i	$0.542271\pi$
$294$	−0.137359	−0.00801094
$295$	4.81921	0.280585
$296$	−5.94304	−0.345432
$297$	−4.17294	−0.242138
$298$	−1.83686	−0.106406
$299$	−2.56939	−0.148592
$300$	−3.90590	−0.225507
$301$	−20.6885	−1.19246
$302$	1.41379	0.0813542
$303$	16.7399	0.961684
$304$	15.1247	0.867463
$305$	4.97900	0.285097
$306$	0.378711	0.0216494
$307$	13.3064	0.759438	0.379719	−	0.925102i	$-0.376021\pi$
$307$	13.3064	0.759438	0.379719	+	0.925102i	$0.376021\pi$
$308$	−5.04427	−0.287424
$309$	−0.429466	−0.0244315
$310$	−0.219508	−0.0124672
$311$	−15.8864	−0.900836	−0.450418	−	0.892818i	$-0.648725\pi$
$311$	−15.8864	−0.900836	−0.450418	+	0.892818i	$0.648725\pi$
$312$	−3.98710	−0.225725
$313$	2.54881	0.144067	0.0720336	−	0.997402i	$-0.477051\pi$
$313$	2.54881	0.144067	0.0720336	+	0.997402i	$0.477051\pi$
$314$	0.178260	0.0100598
$315$	2.24449	0.126463
$316$	17.5505	0.987292
$317$	33.6871	1.89206	0.946028	−	0.324086i	$-0.105057\pi$
$317$	33.6871	1.89206	0.946028	+	0.324086i	$0.105057\pi$
$318$	2.64867	0.148530
$319$	−4.15859	−0.232837
$320$	−7.58040	−0.423757
$321$	7.87522	0.439552
$322$	−0.226606	−0.0126282
$323$	12.5636	0.699057
$324$	21.5449	1.19694
$325$	3.82891	0.212390
$326$	1.56049	0.0864276
$327$	12.9826	0.717939
$328$	3.12557	0.172581
$329$	−5.73993	−0.316452
$330$	0.261480	0.0143940
$331$	5.72012	0.314406	0.157203	−	0.987566i	$-0.449752\pi$
$331$	5.72012	0.314406	0.157203	+	0.987566i	$0.449752\pi$
$332$	2.29146	0.125760
$333$	9.91897	0.543556
$334$	1.06253	0.0581393
$335$	−14.5608	−0.795544
$336$	19.5258	1.06522
$337$	3.76158	0.204906	0.102453	−	0.994738i	$-0.467331\pi$
$337$	3.76158	0.204906	0.102453	+	0.994738i	$0.467331\pi$
$338$	0.220374	0.0119867
$339$	38.3023	2.08029
$340$	−6.41330	−0.347810
$341$	−1.65403	−0.0895709
$342$	0.454606	0.0245823
$343$	−19.1485	−1.03392
$344$	4.29704	0.231681
$345$	−1.32217	−0.0711832
$346$	2.27759	0.122444
$347$	−4.79279	−0.257290	−0.128645	−	0.991691i	$-0.541063\pi$
$347$	−4.79279	−0.257290	−0.128645	+	0.991691i	$0.541063\pi$
$348$	16.2430	0.870718
$349$	−30.9852	−1.65860	−0.829300	−	0.558804i	$-0.811261\pi$
$349$	−30.9852	−1.65860	−0.829300	+	0.558804i	$0.811261\pi$
$350$	0.337688	0.0180502
$351$	−15.9778	−0.852832
$352$	1.57387	0.0838877
$353$	21.3880	1.13837	0.569185	−	0.822210i	$-0.307259\pi$
$353$	21.3880	1.13837	0.569185	+	0.822210i	$0.307259\pi$
$354$	1.26013	0.0669750
$355$	9.53201	0.505907
$356$	2.65827	0.140888
$357$	16.2194	0.858422
$358$	−2.98108	−0.157555
$359$	6.98654	0.368736	0.184368	−	0.982857i	$-0.440976\pi$
$359$	6.98654	0.368736	0.184368	+	0.982857i	$0.440976\pi$
$360$	−0.466185	−0.0245701
$361$	−3.91859	−0.206242
$362$	0.747355	0.0392801
$363$	1.97030	0.103414
$364$	−19.3140	−1.01233
$365$	1.00000	0.0523424
$366$	1.30191	0.0680520
$367$	−13.3010	−0.694309	−0.347154	−	0.937808i	$-0.612852\pi$
$367$	−13.3010	−0.694309	−0.347154	+	0.937808i	$0.612852\pi$
$368$	−2.61350	−0.136238
$369$	−5.21660	−0.271565
$370$	1.49233	0.0775826
$371$	25.7750	1.33817
$372$	6.46049	0.334961
$373$	19.3542	1.00212	0.501060	−	0.865413i	$-0.332944\pi$
$373$	19.3542	1.00212	0.501060	+	0.865413i	$0.332944\pi$
$374$	0.429338	0.0222006
$375$	1.97030	0.101746
$376$	1.19219	0.0614827
$377$	−15.9229	−0.820070
$378$	−1.40915	−0.0724789
$379$	−7.41176	−0.380717	−0.190358	−	0.981715i	$-0.560965\pi$
$379$	−7.41176	−0.380717	−0.190358	+	0.981715i	$0.560965\pi$
$380$	−7.69856	−0.394928
$381$	18.4855	0.947039
$382$	1.06775	0.0546310
$383$	−22.8099	−1.16553	−0.582765	−	0.812641i	$-0.698029\pi$
$383$	−22.8099	−1.16553	−0.582765	+	0.812641i	$0.698029\pi$
$384$	−8.18413	−0.417644
$385$	2.54454	0.129682
$386$	−2.77961	−0.141478
$387$	−7.17178	−0.364562
$388$	−13.7425	−0.697669
$389$	−10.1628	−0.515275	−0.257638	−	0.966242i	$-0.582944\pi$
$389$	−10.1628	−0.515275	−0.257638	+	0.966242i	$0.582944\pi$
$390$	1.00118	0.0506969
$391$	−2.17094	−0.109789
$392$	0.277631	0.0140225
$393$	16.8481	0.849874
$394$	2.44717	0.123287
$395$	−8.85321	−0.445453
$396$	−1.74862	−0.0878717
$397$	−6.89456	−0.346028	−0.173014	−	0.984919i	$-0.555351\pi$
$397$	−6.89456	−0.346028	−0.173014	+	0.984919i	$0.555351\pi$
$398$	−1.22922	−0.0616150
$399$	19.4698	0.974711
$400$	3.89464	0.194732
$401$	20.0054	0.999022	0.499511	−	0.866308i	$-0.333513\pi$
$401$	20.0054	0.999022	0.499511	+	0.866308i	$0.333513\pi$
$402$	−3.80737	−0.189894
$403$	−6.33315	−0.315476
$404$	−16.8426	−0.837952
$405$	−10.8682	−0.540044
$406$	−1.40431	−0.0696946
$407$	11.2450	0.557393
$408$	−3.36880	−0.166780
$409$	1.48384	0.0733710	0.0366855	−	0.999327i	$-0.488320\pi$
$409$	1.48384	0.0733710	0.0366855	+	0.999327i	$0.488320\pi$
$410$	−0.784849	−0.0387609
$411$	16.5670	0.817192
$412$	0.432101	0.0212881
$413$	12.2627	0.603406
$414$	−0.0785541	−0.00386072
$415$	−1.15591	−0.0567414
$416$	6.02622	0.295460
$417$	−31.9003	−1.56216
$418$	0.515380	0.0252080
$419$	18.7532	0.916152	0.458076	−	0.888913i	$-0.348539\pi$
$419$	18.7532	0.916152	0.458076	+	0.888913i	$0.348539\pi$
$420$	−9.93871	−0.484960
$421$	−19.6952	−0.959887	−0.479944	−	0.877299i	$-0.659343\pi$
$421$	−19.6952	−0.959887	−0.479944	+	0.877299i	$0.659343\pi$
$422$	−3.33270	−0.162233
$423$	−1.98978	−0.0967464
$424$	−5.35351	−0.259990
$425$	3.23514	0.156927
$426$	2.49243	0.120759
$427$	12.6693	0.613109
$428$	−7.92354	−0.382999
$429$	7.54410	0.364233
$430$	−1.07901	−0.0520345
$431$	−14.4097	−0.694091	−0.347045	−	0.937848i	$-0.612815\pi$
$431$	−14.4097	−0.694091	−0.347045	+	0.937848i	$0.612815\pi$
$432$	−16.2521	−0.781928
$433$	−5.42227	−0.260578	−0.130289	−	0.991476i	$-0.541590\pi$
$433$	−5.42227	−0.260578	−0.130289	+	0.991476i	$0.541590\pi$
$434$	−0.558548	−0.0268111
$435$	−8.19367	−0.392857
$436$	−13.0622	−0.625568
$437$	−2.60601	−0.124662
$438$	0.261480	0.0124940
$439$	19.6784	0.939197	0.469599	−	0.882880i	$-0.344399\pi$
$439$	19.6784	0.939197	0.469599	+	0.882880i	$0.344399\pi$
$440$	−0.528506	−0.0251955
$441$	−0.463368	−0.0220652
$442$	1.64390	0.0781922
$443$	−19.5849	−0.930508	−0.465254	−	0.885177i	$-0.654037\pi$
$443$	−19.5849	−0.930508	−0.465254	+	0.885177i	$0.654037\pi$
$444$	−43.9217	−2.08443
$445$	−1.34094	−0.0635668
$446$	−1.82204	−0.0862761
$447$	−27.2710	−1.28987
$448$	−19.2886	−0.911303
$449$	−22.9616	−1.08362	−0.541812	−	0.840500i	$-0.682261\pi$
$449$	−22.9616	−1.08362	−0.541812	+	0.840500i	$0.682261\pi$
$450$	0.117062	0.00551834
$451$	−5.91398	−0.278478
$452$	−38.5373	−1.81264
$453$	20.9898	0.986189
$454$	1.68030	0.0788602
$455$	9.74282	0.456750
$456$	−4.04393	−0.189374
$457$	−6.57865	−0.307736	−0.153868	−	0.988091i	$-0.549173\pi$
$457$	−6.57865	−0.307736	−0.153868	+	0.988091i	$0.549173\pi$
$458$	0.610256	0.0285154
$459$	−13.5000	−0.630128
$460$	1.33028	0.0620247
$461$	28.2952	1.31784	0.658920	−	0.752213i	$-0.271013\pi$
$461$	28.2952	1.31784	0.658920	+	0.752213i	$0.271013\pi$
$462$	0.665347	0.0309547
$463$	−23.5149	−1.09283	−0.546415	−	0.837514i	$-0.684008\pi$
$463$	−23.5149	−1.09283	−0.546415	+	0.837514i	$0.684008\pi$
$464$	−16.1962	−0.751890
$465$	−3.25894	−0.151130
$466$	0.228437	0.0105821
$467$	−11.1027	−0.513774	−0.256887	−	0.966441i	$-0.582697\pi$
$467$	−11.1027	−0.513774	−0.256887	+	0.966441i	$0.582697\pi$
$468$	−6.69533	−0.309492
$469$	−37.0506	−1.71084
$470$	−0.299367	−0.0138088
$471$	2.64655	0.121947
$472$	−2.54698	−0.117234
$473$	−8.13054	−0.373843
$474$	−2.31494	−0.106329
$475$	3.88348	0.178186
$476$	−16.3189	−0.747976
$477$	8.93505	0.409108
$478$	−2.80225	−0.128172
$479$	−18.1299	−0.828375	−0.414188	−	0.910192i	$-0.635934\pi$
$479$	−18.1299	−0.828375	−0.414188	+	0.910192i	$0.635934\pi$
$480$	3.10100	0.141541
$481$	43.0560	1.96319
$482$	−0.488203	−0.0222371
$483$	−3.36431	−0.153082
$484$	−1.98239	−0.0901085
$485$	6.93229	0.314779
$486$	−1.18043	−0.0535454
$487$	−14.3673	−0.651045	−0.325522	−	0.945534i	$-0.605540\pi$
$487$	−14.3673	−0.651045	−0.325522	+	0.945534i	$0.605540\pi$
$488$	−2.63143	−0.119119
$489$	23.1679	1.04769
$490$	−0.0697148	−0.00314939
$491$	2.80368	0.126528	0.0632642	−	0.997997i	$-0.479849\pi$
$491$	2.80368	0.126528	0.0632642	+	0.997997i	$0.479849\pi$
$492$	23.0994	1.04140
$493$	−13.4536	−0.605921
$494$	1.97334	0.0887849
$495$	0.882080	0.0396465
$496$	−6.44186	−0.289248
$497$	24.2546	1.08797
$498$	−0.302248	−0.0135440
$499$	9.81848	0.439535	0.219768	−	0.975552i	$-0.429470\pi$
$499$	9.81848	0.439535	0.219768	+	0.975552i	$0.429470\pi$
$500$	−1.98239	−0.0886551
$501$	15.7750	0.704774
$502$	−0.809521	−0.0361307
$503$	4.01730	0.179123	0.0895613	−	0.995981i	$-0.471453\pi$
$503$	4.01730	0.179123	0.0895613	+	0.995981i	$0.471453\pi$
$504$	−1.18623	−0.0528387
$505$	8.49613	0.378073
$506$	−0.0890556	−0.00395900
$507$	3.27179	0.145305
$508$	−18.5989	−0.825192
$509$	−39.4244	−1.74746	−0.873728	−	0.486416i	$-0.838304\pi$
$509$	−39.4244	−1.74746	−0.873728	+	0.486416i	$0.838304\pi$
$510$	0.845925	0.0374582
$511$	2.54454	0.112564
$512$	10.2463	0.452829
$513$	−16.2055	−0.715491
$514$	−0.416376	−0.0183656
$515$	−0.217970	−0.00960490
$516$	31.7570	1.39803
$517$	−2.25578	−0.0992092
$518$	3.79730	0.166844
$519$	33.8144	1.48429
$520$	−2.02360	−0.0887408
$521$	−2.83163	−0.124056	−0.0620279	−	0.998074i	$-0.519757\pi$
$521$	−2.83163	−0.124056	−0.0620279	+	0.998074i	$0.519757\pi$
$522$	−0.486811	−0.0213072
$523$	6.86181	0.300046	0.150023	−	0.988683i	$-0.452065\pi$
$523$	6.86181	0.300046	0.150023	+	0.988683i	$0.452065\pi$
$524$	−16.9515	−0.740528
$525$	5.01351	0.218807
$526$	−0.356529	−0.0155454
$527$	−5.35103	−0.233095
$528$	7.67360	0.333951
$529$	−22.5497	−0.980421
$530$	1.34430	0.0583925
$531$	4.25093	0.184474
$532$	−19.5893	−0.849304
$533$	−22.6441	−0.980825
$534$	−0.350630	−0.0151733
$535$	3.99697	0.172804
$536$	7.69549	0.332395
$537$	−44.2588	−1.90991
$538$	−1.39786	−0.0602662
$539$	−0.525313	−0.0226269
$540$	8.27238	0.355987
$541$	8.15603	0.350655	0.175328	−	0.984510i	$-0.443902\pi$
$541$	8.15603	0.350655	0.175328	+	0.984510i	$0.443902\pi$
$542$	1.76360	0.0757531
$543$	11.0957	0.476160
$544$	5.09170	0.218305
$545$	6.58915	0.282248
$546$	2.54755	0.109025
$547$	38.8849	1.66260	0.831300	−	0.555824i	$-0.187597\pi$
$547$	38.8849	1.66260	0.831300	+	0.555824i	$0.187597\pi$
$548$	−16.6687	−0.712051
$549$	4.39188	0.187441
$550$	0.132711	0.00565881
$551$	−16.1498	−0.688005
$552$	0.698774	0.0297418
$553$	−22.5273	−0.957960
$554$	−3.27788	−0.139264
$555$	22.1560	0.940469
$556$	32.0960	1.36117
$557$	29.9230	1.26788	0.633939	−	0.773383i	$-0.281437\pi$
$557$	29.9230	1.26788	0.633939	+	0.773383i	$0.281437\pi$
$558$	−0.193624	−0.00819675
$559$	−31.1311	−1.31671
$560$	9.91006	0.418777
$561$	6.37420	0.269119
$562$	−3.36632	−0.142000
$563$	−25.1222	−1.05877	−0.529387	−	0.848380i	$-0.677578\pi$
$563$	−25.1222	−1.05877	−0.529387	+	0.848380i	$0.677578\pi$
$564$	8.81085	0.371004
$565$	19.4398	0.817839
$566$	3.39491	0.142699
$567$	−27.6545	−1.16138
$568$	−5.03773	−0.211378
$569$	29.3653	1.23106	0.615529	−	0.788114i	$-0.288942\pi$
$569$	29.3653	1.23106	0.615529	+	0.788114i	$0.288942\pi$
$570$	1.01545	0.0425326
$571$	14.4976	0.606705	0.303352	−	0.952878i	$-0.401894\pi$
$571$	14.4976	0.606705	0.303352	+	0.952878i	$0.401894\pi$
$572$	−7.59039	−0.317370
$573$	15.8525	0.662246
$574$	−1.99708	−0.0833565
$575$	−0.671050	−0.0279847
$576$	−6.68652	−0.278605
$577$	−4.09019	−0.170277	−0.0851384	−	0.996369i	$-0.527133\pi$
$577$	−4.09019	−0.170277	−0.0851384	+	0.996369i	$0.527133\pi$
$578$	−0.867115	−0.0360672
$579$	−41.2676	−1.71502
$580$	8.24394	0.342311
$581$	−2.94126	−0.122024
$582$	1.81265	0.0751370
$583$	10.1295	0.419522
$584$	−0.528506	−0.0218697
$585$	3.37740	0.139638
$586$	−0.601573	−0.0248507
$587$	−22.4572	−0.926907	−0.463453	−	0.886121i	$-0.653390\pi$
$587$	−22.4572	−0.926907	−0.463453	+	0.886121i	$0.653390\pi$
$588$	2.05182	0.0846156
$589$	−6.42340	−0.264672
$590$	0.639561	0.0263303
$591$	36.3321	1.49450
$592$	43.7951	1.79997
$593$	15.0724	0.618949	0.309474	−	0.950908i	$-0.399847\pi$
$593$	15.0724	0.618949	0.309474	+	0.950908i	$0.399847\pi$
$594$	−0.553794	−0.0227224
$595$	8.23195	0.337477
$596$	27.4383	1.12392
$597$	−18.2496	−0.746907
$598$	−0.340986	−0.0139439
$599$	16.6594	0.680687	0.340343	−	0.940301i	$-0.389457\pi$
$599$	16.6594	0.680687	0.340343	+	0.940301i	$0.389457\pi$
$600$	−1.04132	−0.0425115
$601$	−22.3272	−0.910744	−0.455372	−	0.890301i	$-0.650494\pi$
$601$	−22.3272	−0.910744	−0.455372	+	0.890301i	$0.650494\pi$
$602$	−2.74559	−0.111902
$603$	−12.8438	−0.523041
$604$	−21.1186	−0.859305
$605$	1.00000	0.0406558
$606$	2.22157	0.0902451
$607$	−20.7008	−0.840220	−0.420110	−	0.907473i	$-0.638008\pi$
$607$	−20.7008	−0.840220	−0.420110	+	0.907473i	$0.638008\pi$
$608$	6.11210	0.247878
$609$	−20.8491	−0.844850
$610$	0.660768	0.0267537
$611$	−8.63719	−0.349423
$612$	−5.65704	−0.228672
$613$	−5.03455	−0.203344	−0.101672	−	0.994818i	$-0.532419\pi$
$613$	−5.03455	−0.203344	−0.101672	+	0.994818i	$0.532419\pi$
$614$	1.76591	0.0712662
$615$	−11.6523	−0.469866
$616$	−1.34481	−0.0541837
$617$	−20.8441	−0.839154	−0.419577	−	0.907720i	$-0.637822\pi$
$617$	−20.8441	−0.839154	−0.419577	+	0.907720i	$0.637822\pi$
$618$	−0.0569948	−0.00229267
$619$	−21.1408	−0.849720	−0.424860	−	0.905259i	$-0.639677\pi$
$619$	−21.1408	−0.849720	−0.424860	+	0.905259i	$0.639677\pi$
$620$	3.27894	0.131685
$621$	2.80025	0.112370
$622$	−2.10830	−0.0845351
$623$	−3.41209	−0.136702
$624$	29.3815	1.17620
$625$	1.00000	0.0400000
$626$	0.338254	0.0135194
$627$	7.65162	0.305576
$628$	−2.66279	−0.106257
$629$	36.3791	1.45053
$630$	0.297868	0.0118673
$631$	16.5259	0.657887	0.328943	−	0.944350i	$-0.393307\pi$
$631$	16.5259	0.657887	0.328943	+	0.944350i	$0.393307\pi$
$632$	4.67897	0.186120
$633$	−49.4791	−1.96662
$634$	4.47064	0.177552
$635$	9.38206	0.372316
$636$	−39.5649	−1.56885
$637$	−2.01138	−0.0796937
$638$	−0.551890	−0.0218496
$639$	8.40800	0.332615
$640$	−4.15375	−0.164191
$641$	−4.49477	−0.177533	−0.0887663	−	0.996052i	$-0.528292\pi$
$641$	−4.49477	−0.177533	−0.0887663	+	0.996052i	$0.528292\pi$
$642$	1.04513	0.0412479
$643$	−33.2692	−1.31201	−0.656004	−	0.754757i	$-0.727755\pi$
$643$	−33.2692	−1.31201	−0.656004	+	0.754757i	$0.727755\pi$
$644$	3.38495	0.133386
$645$	−16.0196	−0.630771
$646$	1.66733	0.0656001
$647$	28.6260	1.12540	0.562702	−	0.826660i	$-0.309762\pi$
$647$	28.6260	1.12540	0.562702	+	0.826660i	$0.309762\pi$
$648$	5.74390	0.225642
$649$	4.81921	0.189170
$650$	0.508138	0.0199308
$651$	−8.29251	−0.325009
$652$	−23.3101	−0.912892
$653$	−26.8504	−1.05074	−0.525369	−	0.850874i	$-0.676073\pi$
$653$	−26.8504	−1.05074	−0.525369	+	0.850874i	$0.676073\pi$
$654$	1.72293	0.0673719
$655$	8.55103	0.334117
$656$	−23.0328	−0.899280
$657$	0.882080	0.0344132
$658$	−0.761751	−0.0296961
$659$	9.00813	0.350907	0.175453	−	0.984488i	$-0.443861\pi$
$659$	9.00813	0.350907	0.175453	+	0.984488i	$0.443861\pi$
$660$	−3.90590	−0.152037
$661$	−11.7105	−0.455487	−0.227743	−	0.973721i	$-0.573135\pi$
$661$	−11.7105	−0.455487	−0.227743	+	0.973721i	$0.573135\pi$
$662$	0.759123	0.0295041
$663$	24.4062	0.947859
$664$	0.610906	0.0237077
$665$	9.88167	0.383195
$666$	1.31636	0.0510077
$667$	2.79062	0.108053
$668$	−15.8718	−0.614097
$669$	−27.0510	−1.04585
$670$	−1.93238	−0.0746544
$671$	4.97900	0.192212
$672$	7.89062	0.304387
$673$	−31.9276	−1.23072	−0.615360	−	0.788246i	$-0.710989\pi$
$673$	−31.9276	−1.23072	−0.615360	+	0.788246i	$0.710989\pi$
$674$	0.499203	0.0192286
$675$	−4.17294	−0.160616
$676$	−3.29186	−0.126610
$677$	1.00170	0.0384983	0.0192492	−	0.999815i	$-0.493872\pi$
$677$	1.00170	0.0384983	0.0192492	+	0.999815i	$0.493872\pi$
$678$	5.08313	0.195216
$679$	17.6395	0.676941
$680$	−1.70979	−0.0655675
$681$	24.9466	0.955957
$682$	−0.219508	−0.00840540
$683$	35.6127	1.36268	0.681341	−	0.731967i	$-0.261397\pi$
$683$	35.6127	1.36268	0.681341	+	0.731967i	$0.261397\pi$
$684$	−6.79074	−0.259651
$685$	8.40839	0.321268
$686$	−2.54121	−0.0970238
$687$	9.06020	0.345668
$688$	−31.6655	−1.20724
$689$	38.7850	1.47759
$690$	−0.175466	−0.00667988
$691$	−49.8893	−1.89788	−0.948939	−	0.315460i	$-0.897841\pi$
$691$	−49.8893	−1.89788	−0.948939	+	0.315460i	$0.897841\pi$
$692$	−34.0218	−1.29332
$693$	2.24449	0.0852610
$694$	−0.636055	−0.0241443
$695$	−16.1906	−0.614144
$696$	4.33041	0.164144
$697$	−19.1326	−0.724697
$698$	−4.11207	−0.155644
$699$	3.39150	0.128278
$700$	−5.04427	−0.190655
$701$	−13.4608	−0.508408	−0.254204	−	0.967151i	$-0.581813\pi$
$701$	−13.4608	−0.508408	−0.254204	+	0.967151i	$0.581813\pi$
$702$	−2.12043	−0.0800304
$703$	43.6696	1.64703
$704$	−7.58040	−0.285697
$705$	−4.44457	−0.167392
$706$	2.83842	0.106825
$707$	21.6188	0.813057
$708$	−18.8233	−0.707424
$709$	−37.9966	−1.42699	−0.713497	−	0.700658i	$-0.752890\pi$
$709$	−37.9966	−1.42699	−0.713497	+	0.700658i	$0.752890\pi$
$710$	1.26500	0.0474747
$711$	−7.80924	−0.292869
$712$	0.708697	0.0265595
$713$	1.10994	0.0415675
$714$	2.15249	0.0805549
$715$	3.82891	0.143193
$716$	44.5303	1.66418
$717$	−41.6037	−1.55372
$718$	0.927190	0.0346024
$719$	−20.7668	−0.774469	−0.387235	−	0.921981i	$-0.626570\pi$
$719$	−20.7668	−0.774469	−0.387235	+	0.921981i	$0.626570\pi$
$720$	3.43538	0.128029
$721$	−0.554633	−0.0206556
$722$	−0.520040	−0.0193539
$723$	−7.24814	−0.269561
$724$	−11.1637	−0.414897
$725$	−4.15859	−0.154446
$726$	0.261480	0.00970444
$727$	45.1957	1.67621	0.838107	−	0.545506i	$-0.183662\pi$
$727$	45.1957	1.67621	0.838107	+	0.545506i	$0.183662\pi$
$728$	−5.14914	−0.190840
$729$	15.0792	0.558489
$730$	0.132711	0.00491185
$731$	−26.3034	−0.972867
$732$	−19.4475	−0.718800
$733$	51.7668	1.91205	0.956025	−	0.293287i	$-0.0947490\pi$
$733$	51.7668	1.91205	0.956025	+	0.293287i	$0.0947490\pi$
$734$	−1.76519	−0.0651545
$735$	−1.03502	−0.0381775
$736$	−1.05615	−0.0389301
$737$	−14.5608	−0.536355
$738$	−0.692300	−0.0254839
$739$	21.0525	0.774429	0.387214	−	0.921990i	$-0.373437\pi$
$739$	21.0525	0.774429	0.387214	+	0.921990i	$0.373437\pi$
$740$	−22.2919	−0.819467
$741$	29.2974	1.07627
$742$	3.42062	0.125575
$743$	−21.0814	−0.773401	−0.386700	−	0.922205i	$-0.626385\pi$
$743$	−21.0814	−0.773401	−0.386700	+	0.922205i	$0.626385\pi$
$744$	1.72237	0.0631452
$745$	−13.8410	−0.507097
$746$	2.56851	0.0940397
$747$	−1.01961	−0.0373054
$748$	−6.41330	−0.234494
$749$	10.1704	0.371620
$750$	0.261480	0.00954790
$751$	−20.2110	−0.737509	−0.368755	−	0.929527i	$-0.620216\pi$
$751$	−20.2110	−0.737509	−0.368755	+	0.929527i	$0.620216\pi$
$752$	−8.78545	−0.320372
$753$	−12.0186	−0.437982
$754$	−2.11314	−0.0769560
$755$	10.6531	0.387707
$756$	21.0494	0.765559
$757$	30.3677	1.10373	0.551866	−	0.833933i	$-0.313916\pi$
$757$	30.3677	1.10373	0.551866	+	0.833933i	$0.313916\pi$
$758$	−0.983621	−0.0357267
$759$	−1.32217	−0.0479917
$760$	−2.05244	−0.0744499
$761$	2.49497	0.0904426	0.0452213	−	0.998977i	$-0.485601\pi$
$761$	2.49497	0.0904426	0.0452213	+	0.998977i	$0.485601\pi$
$762$	2.45322	0.0888708
$763$	16.7663	0.606983
$764$	−15.9497	−0.577041
$765$	2.85365	0.103174
$766$	−3.02712	−0.109374
$767$	18.4523	0.666274
$768$	28.7852	1.03870
$769$	5.78286	0.208535	0.104268	−	0.994549i	$-0.466750\pi$
$769$	5.78286	0.208535	0.104268	+	0.994549i	$0.466750\pi$
$770$	0.337688	0.0121694
$771$	−6.18175	−0.222630
$772$	41.5208	1.49437
$773$	−12.9793	−0.466834	−0.233417	−	0.972377i	$-0.574991\pi$
$773$	−12.9793	−0.466834	−0.233417	+	0.972377i	$0.574991\pi$
$774$	−0.951773	−0.0342108
$775$	−1.65403	−0.0594146
$776$	−3.66375	−0.131521
$777$	56.3768	2.02251
$778$	−1.34872	−0.0483538
$779$	−22.9668	−0.822871
$780$	−14.9553	−0.535487
$781$	9.53201	0.341082
$782$	−0.288107	−0.0103027
$783$	17.3535	0.620165
$784$	−2.04591	−0.0730680
$785$	1.34322	0.0479417
$786$	2.23593	0.0797528
$787$	34.7102	1.23729	0.618643	−	0.785673i	$-0.287683\pi$
$787$	34.7102	1.23729	0.618643	+	0.785673i	$0.287683\pi$
$788$	−36.5550	−1.30222
$789$	−5.29323	−0.188444
$790$	−1.17492	−0.0418017
$791$	49.4654	1.75879
$792$	−0.466185	−0.0165651
$793$	19.0642	0.676988
$794$	−0.914982	−0.0324715
$795$	19.9582	0.707844
$796$	18.3616	0.650809
$797$	−24.9100	−0.882357	−0.441178	−	0.897419i	$-0.645439\pi$
$797$	−24.9100	−0.882357	−0.441178	+	0.897419i	$0.645439\pi$
$798$	2.58386	0.0914677
$799$	−7.29777	−0.258177
$800$	1.57387	0.0556448
$801$	−1.18282	−0.0417929
$802$	2.65493	0.0937490
$803$	1.00000	0.0352892
$804$	56.8731	2.00576
$805$	−1.70751	−0.0601819
$806$	−0.840477	−0.0296045
$807$	−20.7535	−0.730556
$808$	−4.49026	−0.157967
$809$	−25.9432	−0.912113	−0.456057	−	0.889951i	$-0.650739\pi$
$809$	−25.9432	−0.912113	−0.456057	+	0.889951i	$0.650739\pi$
$810$	−1.44232	−0.0506781
$811$	0.676194	0.0237444	0.0118722	−	0.999930i	$-0.496221\pi$
$811$	0.676194	0.0237444	0.0118722	+	0.999930i	$0.496221\pi$
$812$	20.9771	0.736150
$813$	26.1834	0.918292
$814$	1.49233	0.0523062
$815$	11.7586	0.411885
$816$	24.8252	0.869055
$817$	−31.5748	−1.10466
$818$	0.196921	0.00688519
$819$	8.59394	0.300297
$820$	11.7238	0.409413
$821$	46.4905	1.62253	0.811264	−	0.584680i	$-0.198780\pi$
$821$	46.4905	1.62253	0.811264	+	0.584680i	$0.198780\pi$
$822$	2.19863	0.0766859
$823$	40.0098	1.39465	0.697326	−	0.716754i	$-0.254373\pi$
$823$	40.0098	1.39465	0.697326	+	0.716754i	$0.254373\pi$
$824$	0.115198	0.00401313
$825$	1.97030	0.0685970
$826$	1.62739	0.0566241
$827$	−25.1725	−0.875333	−0.437667	−	0.899137i	$-0.644195\pi$
$827$	−25.1725	−0.875333	−0.437667	+	0.899137i	$0.644195\pi$
$828$	1.17341	0.0407789
$829$	37.1449	1.29009	0.645047	−	0.764143i	$-0.276838\pi$
$829$	37.1449	1.29009	0.645047	+	0.764143i	$0.276838\pi$
$830$	−0.153402	−0.00532466
$831$	−48.6652	−1.68818
$832$	−29.0247	−1.00625
$833$	−1.69946	−0.0588829
$834$	−4.23351	−0.146595
$835$	8.00639	0.277072
$836$	−7.69856	−0.266260
$837$	6.90218	0.238574
$838$	2.48875	0.0859724
$839$	6.15310	0.212429	0.106214	−	0.994343i	$-0.466127\pi$
$839$	6.15310	0.212429	0.106214	+	0.994343i	$0.466127\pi$
$840$	−2.64967	−0.0914223
$841$	−11.7061	−0.403659
$842$	−2.61377	−0.0900765
$843$	−49.9783	−1.72135
$844$	49.7827	1.71359
$845$	1.66055	0.0571248
$846$	−0.264065	−0.00907875
$847$	2.54454	0.0874314
$848$	39.4508	1.35475
$849$	50.4027	1.72982
$850$	0.429338	0.0147262
$851$	−7.54594	−0.258672
$852$	−37.2311	−1.27552
$853$	−38.4435	−1.31628	−0.658141	−	0.752895i	$-0.728657\pi$
$853$	−38.4435	−1.31628	−0.658141	+	0.752895i	$0.728657\pi$
$854$	1.68135	0.0575346
$855$	3.42554	0.117151
$856$	−2.11242	−0.0722011
$857$	−1.66089	−0.0567349	−0.0283675	−	0.999598i	$-0.509031\pi$
$857$	−1.66089	−0.0567349	−0.0283675	+	0.999598i	$0.509031\pi$
$858$	1.00118	0.0341799
$859$	−17.7609	−0.605995	−0.302998	−	0.952991i	$-0.597987\pi$
$859$	−17.7609	−0.605995	−0.302998	+	0.952991i	$0.597987\pi$
$860$	16.1179	0.549615
$861$	−29.6498	−1.01046
$862$	−1.91232	−0.0651340
$863$	−22.1899	−0.755354	−0.377677	−	0.925937i	$-0.623277\pi$
$863$	−22.1899	−0.755354	−0.377677	+	0.925937i	$0.623277\pi$
$864$	−6.56767	−0.223437
$865$	17.1620	0.583527
$866$	−0.719594	−0.0244528
$867$	−12.8737	−0.437213
$868$	8.34339	0.283193
$869$	−8.85321	−0.300324
$870$	−1.08739	−0.0368660
$871$	−55.7521	−1.88909
$872$	−3.48240	−0.117929
$873$	6.11483	0.206956
$874$	−0.345845	−0.0116984
$875$	2.54454	0.0860212
$876$	−3.90590	−0.131968
$877$	−35.5037	−1.19887	−0.599437	−	0.800422i	$-0.704609\pi$
$877$	−35.5037	−1.19887	−0.599437	+	0.800422i	$0.704609\pi$
$878$	2.61153	0.0881350
$879$	−8.93129	−0.301245
$880$	3.89464	0.131288
$881$	5.64538	0.190198	0.0950988	−	0.995468i	$-0.469683\pi$
$881$	5.64538	0.190198	0.0950988	+	0.995468i	$0.469683\pi$
$882$	−0.0614940	−0.00207061
$883$	9.39336	0.316112	0.158056	−	0.987430i	$-0.449477\pi$
$883$	9.39336	0.316112	0.158056	+	0.987430i	$0.449477\pi$
$884$	−24.5560	−0.825906
$885$	9.49528	0.319180
$886$	−2.59913	−0.0873196
$887$	−18.5335	−0.622296	−0.311148	−	0.950362i	$-0.600713\pi$
$887$	−18.5335	−0.622296	−0.311148	+	0.950362i	$0.600713\pi$
$888$	−11.7096	−0.392947
$889$	23.8730	0.800676
$890$	−0.177958	−0.00596516
$891$	−10.8682	−0.364098
$892$	27.2170	0.911292
$893$	−8.76028	−0.293152
$894$	−3.61916	−0.121043
$895$	−22.4630	−0.750854
$896$	−10.5694	−0.353098
$897$	−5.06247	−0.169031
$898$	−3.04725	−0.101688
$899$	6.87845	0.229409
$900$	−1.74862	−0.0582875
$901$	32.7704	1.09174
$902$	−0.784849	−0.0261326
$903$	−40.7625	−1.35649
$904$	−10.2741	−0.341710
$905$	5.63145	0.187196
$906$	2.78558	0.0925447
$907$	−41.0922	−1.36444	−0.682222	−	0.731145i	$-0.738986\pi$
$907$	−41.0922	−1.36444	−0.682222	+	0.731145i	$0.738986\pi$
$908$	−25.0997	−0.832962
$909$	7.49427	0.248569
$910$	1.29298	0.0428618
$911$	39.7424	1.31673	0.658363	−	0.752701i	$-0.271249\pi$
$911$	39.7424	1.31673	0.658363	+	0.752701i	$0.271249\pi$
$912$	29.8003	0.986785
$913$	−1.15591	−0.0382551
$914$	−0.873058	−0.0288782
$915$	9.81013	0.324313
$916$	−9.11579	−0.301194
$917$	21.7585	0.718527
$918$	−1.79160	−0.0591317
$919$	29.9968	0.989502	0.494751	−	0.869035i	$-0.335259\pi$
$919$	29.9968	0.989502	0.494751	+	0.869035i	$0.335259\pi$
$920$	0.354654	0.0116926
$921$	26.2176	0.863900
$922$	3.75509	0.123667
$923$	36.4972	1.20132
$924$	−9.93871	−0.326960
$925$	11.2450	0.369733
$926$	−3.12068	−0.102552
$927$	−0.192267	−0.00631487
$928$	−6.54510	−0.214853
$929$	−56.6461	−1.85850	−0.929249	−	0.369455i	$-0.879544\pi$
$929$	−56.6461	−1.85850	−0.929249	+	0.369455i	$0.879544\pi$
$930$	−0.432497	−0.0141821
$931$	−2.04004	−0.0668597
$932$	−3.41231	−0.111774
$933$	−31.3010	−1.02475
$934$	−1.47345	−0.0482129
$935$	3.23514	0.105800
$936$	−1.78498	−0.0583439
$937$	1.09346	0.0357219	0.0178610	−	0.999840i	$-0.494314\pi$
$937$	1.09346	0.0357219	0.0178610	+	0.999840i	$0.494314\pi$
$938$	−4.91702	−0.160546
$939$	5.02191	0.163884
$940$	4.47183	0.145855
$941$	7.32395	0.238754	0.119377	−	0.992849i	$-0.461910\pi$
$941$	7.32395	0.238754	0.119377	+	0.992849i	$0.461910\pi$
$942$	0.351226	0.0114436
$943$	3.96857	0.129235
$944$	18.7691	0.610881
$945$	−10.6182	−0.345410
$946$	−1.07901	−0.0350817
$947$	−5.17883	−0.168289	−0.0841446	−	0.996454i	$-0.526816\pi$
$947$	−5.17883	−0.168289	−0.0841446	+	0.996454i	$0.526816\pi$
$948$	34.5797	1.12310
$949$	3.82891	0.124292
$950$	0.515380	0.0167211
$951$	66.3736	2.15231
$952$	−4.35063	−0.141005
$953$	−33.6364	−1.08959	−0.544796	−	0.838569i	$-0.683393\pi$
$953$	−33.6364	−1.08959	−0.544796	+	0.838569i	$0.683393\pi$
$954$	1.18578	0.0383910
$955$	8.04571	0.260353
$956$	41.8590	1.35382
$957$	−8.19367	−0.264864
$958$	−2.40603	−0.0777354
$959$	21.3955	0.690896
$960$	−14.9357	−0.482047
$961$	−28.2642	−0.911748
$962$	5.71400	0.184227
$963$	3.52564	0.113612
$964$	7.29261	0.234879
$965$	−20.9449	−0.674239
$966$	−0.446481	−0.0143653
$967$	8.09327	0.260262	0.130131	−	0.991497i	$-0.458460\pi$
$967$	8.09327	0.260262	0.130131	+	0.991497i	$0.458460\pi$
$968$	−0.528506	−0.0169868
$969$	24.7541	0.795215
$970$	0.919989	0.0295391
$971$	−13.7786	−0.442177	−0.221088	−	0.975254i	$-0.570961\pi$
$971$	−13.7786	−0.442177	−0.221088	+	0.975254i	$0.570961\pi$
$972$	17.6328	0.565574
$973$	−41.1976	−1.32073
$974$	−1.90670	−0.0610945
$975$	7.54410	0.241605
$976$	19.3914	0.620704
$977$	−32.4506	−1.03819	−0.519093	−	0.854718i	$-0.673730\pi$
$977$	−32.4506	−1.03819	−0.519093	+	0.854718i	$0.673730\pi$
$978$	3.07463	0.0983160
$979$	−1.34094	−0.0428568
$980$	1.04137	0.0332655
$981$	5.81215	0.185568
$982$	0.372079	0.0118735
$983$	−46.2118	−1.47393	−0.736964	−	0.675932i	$-0.763741\pi$
$983$	−46.2118	−1.47393	−0.736964	+	0.675932i	$0.763741\pi$
$984$	6.15832	0.196320
$985$	18.4399	0.587544
$986$	−1.78544	−0.0568601
$987$	−11.3094	−0.359981
$988$	−29.4771	−0.937791
$989$	5.45599	0.173491
$990$	0.117062	0.00372046
$991$	−26.2698	−0.834487	−0.417243	−	0.908795i	$-0.637004\pi$
$991$	−26.2698	−0.834487	−0.417243	+	0.908795i	$0.637004\pi$
$992$	−2.60324	−0.0826529
$993$	11.2704	0.357654
$994$	3.21885	0.102096
$995$	−9.26236	−0.293637
$996$	4.51487	0.143059
$997$	−41.7385	−1.32187	−0.660936	−	0.750442i	$-0.729840\pi$
$997$	−41.7385	−1.32187	−0.660936	+	0.750442i	$0.729840\pi$
$998$	1.30302	0.0412463
$999$	−46.9246	−1.48463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.19	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.19	✓	37	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)

\(f(q)\)	\(=\)	\(q+0.132711 q^{2} +1.97030 q^{3} -1.98239 q^{4} +1.00000 q^{5} +0.261480 q^{6} +2.54454 q^{7} -0.528506 q^{8} +0.882080 q^{9} +O(q^{10})\)	\(q+0.132711 q^{2} +1.97030 q^{3} -1.98239 q^{4} +1.00000 q^{5} +0.261480 q^{6} +2.54454 q^{7} -0.528506 q^{8} +0.882080 q^{9} +0.132711 q^{10} +1.00000 q^{11} -3.90590 q^{12} +3.82891 q^{13} +0.337688 q^{14} +1.97030 q^{15} +3.89464 q^{16} +3.23514 q^{17} +0.117062 q^{18} +3.88348 q^{19} -1.98239 q^{20} +5.01351 q^{21} +0.132711 q^{22} -0.671050 q^{23} -1.04132 q^{24} +1.00000 q^{25} +0.508138 q^{26} -4.17294 q^{27} -5.04427 q^{28} -4.15859 q^{29} +0.261480 q^{30} -1.65403 q^{31} +1.57387 q^{32} +1.97030 q^{33} +0.429338 q^{34} +2.54454 q^{35} -1.74862 q^{36} +11.2450 q^{37} +0.515380 q^{38} +7.54410 q^{39} -0.528506 q^{40} -5.91398 q^{41} +0.665347 q^{42} -8.13054 q^{43} -1.98239 q^{44} +0.882080 q^{45} -0.0890556 q^{46} -2.25578 q^{47} +7.67360 q^{48} -0.525313 q^{49} +0.132711 q^{50} +6.37420 q^{51} -7.59039 q^{52} +10.1295 q^{53} -0.553794 q^{54} +1.00000 q^{55} -1.34481 q^{56} +7.65162 q^{57} -0.551890 q^{58} +4.81921 q^{59} -3.90590 q^{60} +4.97900 q^{61} -0.219508 q^{62} +2.24449 q^{63} -7.58040 q^{64} +3.82891 q^{65} +0.261480 q^{66} -14.5608 q^{67} -6.41330 q^{68} -1.32217 q^{69} +0.337688 q^{70} +9.53201 q^{71} -0.466185 q^{72} +1.00000 q^{73} +1.49233 q^{74} +1.97030 q^{75} -7.69856 q^{76} +2.54454 q^{77} +1.00118 q^{78} -8.85321 q^{79} +3.89464 q^{80} -10.8682 q^{81} -0.784849 q^{82} -1.15591 q^{83} -9.93871 q^{84} +3.23514 q^{85} -1.07901 q^{86} -8.19367 q^{87} -0.528506 q^{88} -1.34094 q^{89} +0.117062 q^{90} +9.74282 q^{91} +1.33028 q^{92} -3.25894 q^{93} -0.299367 q^{94} +3.88348 q^{95} +3.10100 q^{96} +6.93229 q^{97} -0.0697148 q^{98} +0.882080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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