LMFDB - Embedded newform 4015.2.a.b.1.15

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:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+0.430868 q^{2} -1.25921 q^{3} -1.81435 q^{4} +1.00000 q^{5} -0.542554 q^{6} +4.34543 q^{7} -1.64348 q^{8} -1.41438 q^{9} +O(q^{10})$	\(q+0.430868 q^{2} -1.25921 q^{3} -1.81435 q^{4} +1.00000 q^{5} -0.542554 q^{6} +4.34543 q^{7} -1.64348 q^{8} -1.41438 q^{9} +0.430868 q^{10} +1.00000 q^{11} +2.28466 q^{12} +2.04719 q^{13} +1.87231 q^{14} -1.25921 q^{15} +2.92058 q^{16} -4.46141 q^{17} -0.609413 q^{18} -0.805772 q^{19} -1.81435 q^{20} -5.47182 q^{21} +0.430868 q^{22} -4.40182 q^{23} +2.06949 q^{24} +1.00000 q^{25} +0.882068 q^{26} +5.55865 q^{27} -7.88415 q^{28} -8.69912 q^{29} -0.542554 q^{30} -8.06884 q^{31} +4.54535 q^{32} -1.25921 q^{33} -1.92228 q^{34} +4.34543 q^{35} +2.56619 q^{36} -4.32966 q^{37} -0.347181 q^{38} -2.57785 q^{39} -1.64348 q^{40} +11.0196 q^{41} -2.35763 q^{42} -2.09677 q^{43} -1.81435 q^{44} -1.41438 q^{45} -1.89660 q^{46} +1.21889 q^{47} -3.67763 q^{48} +11.8828 q^{49} +0.430868 q^{50} +5.61787 q^{51} -3.71433 q^{52} +3.55096 q^{53} +2.39504 q^{54} +1.00000 q^{55} -7.14164 q^{56} +1.01464 q^{57} -3.74817 q^{58} +7.54910 q^{59} +2.28466 q^{60} -4.89718 q^{61} -3.47660 q^{62} -6.14612 q^{63} -3.88273 q^{64} +2.04719 q^{65} -0.542554 q^{66} -0.726723 q^{67} +8.09458 q^{68} +5.54282 q^{69} +1.87231 q^{70} -1.00506 q^{71} +2.32451 q^{72} -1.00000 q^{73} -1.86551 q^{74} -1.25921 q^{75} +1.46196 q^{76} +4.34543 q^{77} -1.11071 q^{78} +3.36242 q^{79} +2.92058 q^{80} -2.75636 q^{81} +4.74800 q^{82} -13.4190 q^{83} +9.92782 q^{84} -4.46141 q^{85} -0.903432 q^{86} +10.9540 q^{87} -1.64348 q^{88} -0.909073 q^{89} -0.609413 q^{90} +8.89593 q^{91} +7.98645 q^{92} +10.1604 q^{93} +0.525182 q^{94} -0.805772 q^{95} -5.72356 q^{96} +12.5213 q^{97} +5.11991 q^{98} -1.41438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * 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 $

$2$	0.430868	0.304669	0.152335	−	0.988329i	$-0.451321\pi$
$2$	0.430868	0.304669	0.152335	+	0.988329i	$0.451321\pi$
$3$	−1.25921	−0.727006	−0.363503	−	0.931593i	$-0.618419\pi$
$3$	−1.25921	−0.727006	−0.363503	+	0.931593i	$0.618419\pi$
$4$	−1.81435	−0.907177
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.542554	−0.221497
$7$	4.34543	1.64242	0.821210	−	0.570626i	$-0.193300\pi$
$7$	4.34543	1.64242	0.821210	+	0.570626i	$0.193300\pi$
$8$	−1.64348	−0.581058
$9$	−1.41438	−0.471462
$10$	0.430868	0.136252
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.28466	0.659523
$13$	2.04719	0.567789	0.283894	−	0.958856i	$-0.408374\pi$
$13$	2.04719	0.567789	0.283894	+	0.958856i	$0.408374\pi$
$14$	1.87231	0.500395
$15$	−1.25921	−0.325127
$16$	2.92058	0.730146
$17$	−4.46141	−1.08205	−0.541026	−	0.841006i	$-0.681964\pi$
$17$	−4.46141	−1.08205	−0.541026	+	0.841006i	$0.681964\pi$
$18$	−0.609413	−0.143640
$19$	−0.805772	−0.184857	−0.0924284	−	0.995719i	$-0.529463\pi$
$19$	−0.805772	−0.184857	−0.0924284	+	0.995719i	$0.529463\pi$
$20$	−1.81435	−0.405702
$21$	−5.47182	−1.19405
$22$	0.430868	0.0918613
$23$	−4.40182	−0.917842	−0.458921	−	0.888477i	$-0.651764\pi$
$23$	−4.40182	−0.917842	−0.458921	+	0.888477i	$0.651764\pi$
$24$	2.06949	0.422433
$25$	1.00000	0.200000
$26$	0.882068	0.172988
$27$	5.55865	1.06976
$28$	−7.88415	−1.48996
$29$	−8.69912	−1.61539	−0.807693	−	0.589603i	$-0.799284\pi$
$29$	−8.69912	−1.61539	−0.807693	+	0.589603i	$0.799284\pi$
$30$	−0.542554	−0.0990563
$31$	−8.06884	−1.44921	−0.724603	−	0.689166i	$-0.757977\pi$
$31$	−8.06884	−1.44921	−0.724603	+	0.689166i	$0.757977\pi$
$32$	4.54535	0.803511
$33$	−1.25921	−0.219201
$34$	−1.92228	−0.329668
$35$	4.34543	0.734512
$36$	2.56619	0.427699
$37$	−4.32966	−0.711791	−0.355896	−	0.934526i	$-0.615824\pi$
$37$	−4.32966	−0.711791	−0.355896	+	0.934526i	$0.615824\pi$
$38$	−0.347181	−0.0563202
$39$	−2.57785	−0.412786
$40$	−1.64348	−0.259857
$41$	11.0196	1.72098	0.860488	−	0.509470i	$-0.170159\pi$
$41$	11.0196	1.72098	0.860488	+	0.509470i	$0.170159\pi$
$42$	−2.35763	−0.363790
$43$	−2.09677	−0.319755	−0.159877	−	0.987137i	$-0.551110\pi$
$43$	−2.09677	−0.319755	−0.159877	+	0.987137i	$0.551110\pi$
$44$	−1.81435	−0.273524
$45$	−1.41438	−0.210844
$46$	−1.89660	−0.279638
$47$	1.21889	0.177794	0.0888969	−	0.996041i	$-0.471666\pi$
$47$	1.21889	0.177794	0.0888969	+	0.996041i	$0.471666\pi$
$48$	−3.67763	−0.530821
$49$	11.8828	1.69754
$50$	0.430868	0.0609339
$51$	5.61787	0.786659
$52$	−3.71433	−0.515085
$53$	3.55096	0.487761	0.243881	−	0.969805i	$-0.421579\pi$
$53$	3.55096	0.487761	0.243881	+	0.969805i	$0.421579\pi$
$54$	2.39504	0.325924
$55$	1.00000	0.134840
$56$	−7.14164	−0.954341
$57$	1.01464	0.134392
$58$	−3.74817	−0.492159
$59$	7.54910	0.982809	0.491404	−	0.870932i	$-0.336484\pi$
$59$	7.54910	0.982809	0.491404	+	0.870932i	$0.336484\pi$
$60$	2.28466	0.294948
$61$	−4.89718	−0.627020	−0.313510	−	0.949585i	$-0.601505\pi$
$61$	−4.89718	−0.627020	−0.313510	+	0.949585i	$0.601505\pi$
$62$	−3.47660	−0.441529
$63$	−6.14612	−0.774338
$64$	−3.88273	−0.485341
$65$	2.04719	0.253923
$66$	−0.542554	−0.0667837
$67$	−0.726723	−0.0887833	−0.0443916	−	0.999014i	$-0.514135\pi$
$67$	−0.726723	−0.0887833	−0.0443916	+	0.999014i	$0.514135\pi$
$68$	8.09458	0.981612
$69$	5.54282	0.667277
$70$	1.87231	0.223783
$71$	−1.00506	−0.119278	−0.0596391	−	0.998220i	$-0.518995\pi$
$71$	−1.00506	−0.119278	−0.0596391	+	0.998220i	$0.518995\pi$
$72$	2.32451	0.273947
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−1.86551	−0.216861
$75$	−1.25921	−0.145401
$76$	1.46196	0.167698
$77$	4.34543	0.495208
$78$	−1.11071	−0.125763
$79$	3.36242	0.378302	0.189151	−	0.981948i	$-0.439427\pi$
$79$	3.36242	0.378302	0.189151	+	0.981948i	$0.439427\pi$
$80$	2.92058	0.326531
$81$	−2.75636	−0.306262
$82$	4.74800	0.524329
$83$	−13.4190	−1.47293	−0.736464	−	0.676476i	$-0.763506\pi$
$83$	−13.4190	−1.47293	−0.736464	+	0.676476i	$0.763506\pi$
$84$	9.92782	1.08321
$85$	−4.46141	−0.483908
$86$	−0.903432	−0.0974195
$87$	10.9540	1.17440
$88$	−1.64348	−0.175196
$89$	−0.909073	−0.0963616	−0.0481808	−	0.998839i	$-0.515342\pi$
$89$	−0.909073	−0.0963616	−0.0481808	+	0.998839i	$0.515342\pi$
$90$	−0.609413	−0.0642377
$91$	8.89593	0.932547
$92$	7.98645	0.832645
$93$	10.1604	1.05358
$94$	0.525182	0.0541683
$95$	−0.805772	−0.0826705
$96$	−5.72356	−0.584158
$97$	12.5213	1.27134	0.635671	−	0.771960i	$-0.280724\pi$
$97$	12.5213	1.27134	0.635671	+	0.771960i	$0.280724\pi$
$98$	5.11991	0.517189
$99$	−1.41438	−0.142151
$100$	−1.81435	−0.181435
$101$	1.90006	0.189063	0.0945313	−	0.995522i	$-0.469865\pi$
$101$	1.90006	0.189063	0.0945313	+	0.995522i	$0.469865\pi$
$102$	2.42056	0.239671
$103$	−11.0610	−1.08988	−0.544938	−	0.838476i	$-0.683447\pi$
$103$	−11.0610	−1.08988	−0.544938	+	0.838476i	$0.683447\pi$
$104$	−3.36452	−0.329918
$105$	−5.47182	−0.533995
$106$	1.52999	0.148606
$107$	−8.52547	−0.824188	−0.412094	−	0.911141i	$-0.635202\pi$
$107$	−8.52547	−0.824188	−0.412094	+	0.911141i	$0.635202\pi$
$108$	−10.0853	−0.970463
$109$	−1.49132	−0.142842	−0.0714212	−	0.997446i	$-0.522753\pi$
$109$	−1.49132	−0.142842	−0.0714212	+	0.997446i	$0.522753\pi$
$110$	0.430868	0.0410816
$111$	5.45196	0.517477
$112$	12.6912	1.19921
$113$	−19.9472	−1.87648	−0.938238	−	0.345992i	$-0.887542\pi$
$113$	−19.9472	−1.87648	−0.938238	+	0.345992i	$0.887542\pi$
$114$	0.437175	0.0409451
$115$	−4.40182	−0.410472
$116$	15.7833	1.46544
$117$	−2.89552	−0.267691
$118$	3.25266	0.299432
$119$	−19.3868	−1.77718
$120$	2.06949	0.188918
$121$	1.00000	0.0909091
$122$	−2.11004	−0.191034
$123$	−13.8760	−1.25116
$124$	14.6397	1.31469
$125$	1.00000	0.0894427
$126$	−2.64816	−0.235917
$127$	−1.03375	−0.0917304	−0.0458652	−	0.998948i	$-0.514604\pi$
$127$	−1.03375	−0.0917304	−0.0458652	+	0.998948i	$0.514604\pi$
$128$	−10.7636	−0.951380
$129$	2.64028	0.232464
$130$	0.882068	0.0773625
$131$	−12.9303	−1.12972	−0.564861	−	0.825186i	$-0.691070\pi$
$131$	−12.9303	−1.12972	−0.564861	+	0.825186i	$0.691070\pi$
$132$	2.28466	0.198854
$133$	−3.50143	−0.303612
$134$	−0.313121	−0.0270495
$135$	5.55865	0.478412
$136$	7.33225	0.628735
$137$	−16.5969	−1.41797	−0.708986	−	0.705222i	$-0.750847\pi$
$137$	−16.5969	−1.41797	−0.708986	+	0.705222i	$0.750847\pi$
$138$	2.38822	0.203299
$139$	3.98807	0.338263	0.169132	−	0.985593i	$-0.445904\pi$
$139$	3.98807	0.338263	0.169132	+	0.985593i	$0.445904\pi$
$140$	−7.88415	−0.666332
$141$	−1.53485	−0.129257
$142$	−0.433046	−0.0363404
$143$	2.04719	0.171195
$144$	−4.13083	−0.344236
$145$	−8.69912	−0.722423
$146$	−0.430868	−0.0356588
$147$	−14.9630	−1.23412
$148$	7.85553	0.645720
$149$	−7.89587	−0.646855	−0.323427	−	0.946253i	$-0.604835\pi$
$149$	−7.89587	−0.646855	−0.323427	+	0.946253i	$0.604835\pi$
$150$	−0.542554	−0.0442993
$151$	−4.73288	−0.385156	−0.192578	−	0.981282i	$-0.561685\pi$
$151$	−4.73288	−0.385156	−0.192578	+	0.981282i	$0.561685\pi$
$152$	1.32427	0.107413
$153$	6.31016	0.510146
$154$	1.87231	0.150875
$155$	−8.06884	−0.648105
$156$	4.67713	0.374470
$157$	0.699194	0.0558018	0.0279009	−	0.999611i	$-0.491118\pi$
$157$	0.699194	0.0558018	0.0279009	+	0.999611i	$0.491118\pi$
$158$	1.44876	0.115257
$159$	−4.47141	−0.354606
$160$	4.54535	0.359341
$161$	−19.1278	−1.50748
$162$	−1.18763	−0.0933087
$163$	5.52700	0.432908	0.216454	−	0.976293i	$-0.430551\pi$
$163$	5.52700	0.432908	0.216454	+	0.976293i	$0.430551\pi$
$164$	−19.9935	−1.56123
$165$	−1.25921	−0.0980295
$166$	−5.78182	−0.448756
$167$	−9.89897	−0.766005	−0.383003	−	0.923747i	$-0.625110\pi$
$167$	−9.89897	−0.766005	−0.383003	+	0.923747i	$0.625110\pi$
$168$	8.99284	0.693812
$169$	−8.80901	−0.677616
$170$	−1.92228	−0.147432
$171$	1.13967	0.0871529
$172$	3.80429	0.290074
$173$	−5.10157	−0.387865	−0.193933	−	0.981015i	$-0.562124\pi$
$173$	−5.10157	−0.387865	−0.193933	+	0.981015i	$0.562124\pi$
$174$	4.71974	0.357802
$175$	4.34543	0.328484
$176$	2.92058	0.220147
$177$	−9.50592	−0.714508
$178$	−0.391690	−0.0293584
$179$	−6.22042	−0.464936	−0.232468	−	0.972604i	$-0.574680\pi$
$179$	−6.22042	−0.464936	−0.232468	+	0.972604i	$0.574680\pi$
$180$	2.56619	0.191273
$181$	5.78660	0.430115	0.215057	−	0.976601i	$-0.431006\pi$
$181$	5.78660	0.430115	0.215057	+	0.976601i	$0.431006\pi$
$182$	3.83297	0.284119
$183$	6.16659	0.455847
$184$	7.23430	0.533320
$185$	−4.32966	−0.318323
$186$	4.37778	0.320994
$187$	−4.46141	−0.326251
$188$	−2.21150	−0.161290
$189$	24.1547	1.75700
$190$	−0.347181	−0.0251872
$191$	6.71778	0.486081	0.243041	−	0.970016i	$-0.421855\pi$
$191$	6.71778	0.486081	0.243041	+	0.970016i	$0.421855\pi$
$192$	4.88917	0.352846
$193$	−4.31146	−0.310346	−0.155173	−	0.987887i	$-0.549593\pi$
$193$	−4.31146	−0.310346	−0.155173	+	0.987887i	$0.549593\pi$
$194$	5.39500	0.387339
$195$	−2.57785	−0.184604
$196$	−21.5596	−1.53997
$197$	12.4166	0.884648	0.442324	−	0.896855i	$-0.354154\pi$
$197$	12.4166	0.884648	0.442324	+	0.896855i	$0.354154\pi$
$198$	−0.609413	−0.0433091
$199$	1.99287	0.141271	0.0706353	−	0.997502i	$-0.477497\pi$
$199$	1.99287	0.141271	0.0706353	+	0.997502i	$0.477497\pi$
$200$	−1.64348	−0.116212
$201$	0.915098	0.0645460
$202$	0.818673	0.0576016
$203$	−37.8015	−2.65314
$204$	−10.1928	−0.713638
$205$	11.0196	0.769644
$206$	−4.76584	−0.332052
$207$	6.22586	0.432727
$208$	5.97899	0.414569
$209$	−0.805772	−0.0557364
$210$	−2.35763	−0.162692
$211$	−18.2961	−1.25955	−0.629777	−	0.776776i	$-0.716854\pi$
$211$	−18.2961	−1.25955	−0.629777	+	0.776776i	$0.716854\pi$
$212$	−6.44269	−0.442486
$213$	1.26558	0.0867159
$214$	−3.67335	−0.251105
$215$	−2.09677	−0.142999
$216$	−9.13553	−0.621594
$217$	−35.0626	−2.38020
$218$	−0.642561	−0.0435197
$219$	1.25921	0.0850897
$220$	−1.81435	−0.122324
$221$	−9.13337	−0.614377
$222$	2.34907	0.157659
$223$	6.19512	0.414856	0.207428	−	0.978250i	$-0.433491\pi$
$223$	6.19512	0.414856	0.207428	+	0.978250i	$0.433491\pi$
$224$	19.7515	1.31970
$225$	−1.41438	−0.0942923
$226$	−8.59460	−0.571704
$227$	23.2020	1.53997	0.769986	−	0.638060i	$-0.220263\pi$
$227$	23.2020	1.53997	0.769986	+	0.638060i	$0.220263\pi$
$228$	−1.84091	−0.121917
$229$	−6.11617	−0.404168	−0.202084	−	0.979368i	$-0.564771\pi$
$229$	−6.11617	−0.404168	−0.202084	+	0.979368i	$0.564771\pi$
$230$	−1.89660	−0.125058
$231$	−5.47182	−0.360020
$232$	14.2968	0.938633
$233$	2.24109	0.146819	0.0734094	−	0.997302i	$-0.476612\pi$
$233$	2.24109	0.146819	0.0734094	+	0.997302i	$0.476612\pi$
$234$	−1.24758	−0.0815571
$235$	1.21889	0.0795118
$236$	−13.6967	−0.891581
$237$	−4.23400	−0.275028
$238$	−8.35313	−0.541453
$239$	−28.5404	−1.84613	−0.923064	−	0.384647i	$-0.874323\pi$
$239$	−28.5404	−1.84613	−0.923064	+	0.384647i	$0.874323\pi$
$240$	−3.67763	−0.237390
$241$	−7.64404	−0.492396	−0.246198	−	0.969220i	$-0.579181\pi$
$241$	−7.64404	−0.492396	−0.246198	+	0.969220i	$0.579181\pi$
$242$	0.430868	0.0276972
$243$	−13.2051	−0.847107
$244$	8.88521	0.568818
$245$	11.8828	0.759164
$246$	−5.97874	−0.381190
$247$	−1.64957	−0.104960
$248$	13.2610	0.842073
$249$	16.8974	1.07083
$250$	0.430868	0.0272505
$251$	−9.79917	−0.618518	−0.309259	−	0.950978i	$-0.600081\pi$
$251$	−9.79917	−0.618518	−0.309259	+	0.950978i	$0.600081\pi$
$252$	11.1512	0.702461
$253$	−4.40182	−0.276740
$254$	−0.445409	−0.0279474
$255$	5.61787	0.351804
$256$	3.12775	0.195484
$257$	15.9565	0.995336	0.497668	−	0.867367i	$-0.334190\pi$
$257$	15.9565	0.995336	0.497668	+	0.867367i	$0.334190\pi$
$258$	1.13761	0.0708246
$259$	−18.8142	−1.16906
$260$	−3.71433	−0.230353
$261$	12.3039	0.761593
$262$	−5.57123	−0.344191
$263$	−20.3638	−1.25568	−0.627842	−	0.778341i	$-0.716062\pi$
$263$	−20.3638	−1.25568	−0.627842	+	0.778341i	$0.716062\pi$
$264$	2.06949	0.127368
$265$	3.55096	0.218133
$266$	−1.50865	−0.0925014
$267$	1.14472	0.0700555
$268$	1.31853	0.0805421
$269$	−5.18249	−0.315982	−0.157991	−	0.987441i	$-0.550502\pi$
$269$	−5.18249	−0.315982	−0.157991	+	0.987441i	$0.550502\pi$
$270$	2.39504	0.145758
$271$	19.5862	1.18977	0.594887	−	0.803809i	$-0.297197\pi$
$271$	19.5862	1.18977	0.594887	+	0.803809i	$0.297197\pi$
$272$	−13.0299	−0.790056
$273$	−11.2019	−0.677968
$274$	−7.15109	−0.432013
$275$	1.00000	0.0603023
$276$	−10.0566	−0.605338
$277$	10.4023	0.625016	0.312508	−	0.949915i	$-0.398831\pi$
$277$	10.4023	0.625016	0.312508	+	0.949915i	$0.398831\pi$
$278$	1.71833	0.103059
$279$	11.4124	0.683245
$280$	−7.14164	−0.426794
$281$	17.0429	1.01670	0.508348	−	0.861152i	$-0.330256\pi$
$281$	17.0429	1.01670	0.508348	+	0.861152i	$0.330256\pi$
$282$	−0.661315	−0.0393807
$283$	−25.5569	−1.51920	−0.759599	−	0.650392i	$-0.774605\pi$
$283$	−25.5569	−1.51920	−0.759599	+	0.650392i	$0.774605\pi$
$284$	1.82353	0.108206
$285$	1.01464	0.0601020
$286$	0.882068	0.0521578
$287$	47.8851	2.82657
$288$	−6.42887	−0.378825
$289$	2.90422	0.170836
$290$	−3.74817	−0.220100
$291$	−15.7669	−0.924273
$292$	1.81435	0.106177
$293$	−2.16131	−0.126265	−0.0631327	−	0.998005i	$-0.520109\pi$
$293$	−2.16131	−0.126265	−0.0631327	+	0.998005i	$0.520109\pi$
$294$	−6.44705	−0.376000
$295$	7.54910	0.439525
$296$	7.11571	0.413592
$297$	5.55865	0.322545
$298$	−3.40207	−0.197077
$299$	−9.01136	−0.521140
$300$	2.28466	0.131905
$301$	−9.11139	−0.525172
$302$	−2.03924	−0.117345
$303$	−2.39257	−0.137450
$304$	−2.35332	−0.134972
$305$	−4.89718	−0.280412
$306$	2.71884	0.155426
$307$	13.6472	0.778889	0.389444	−	0.921050i	$-0.372667\pi$
$307$	13.6472	0.778889	0.389444	+	0.921050i	$0.372667\pi$
$308$	−7.88415	−0.449241
$309$	13.9282	0.792347
$310$	−3.47660	−0.197458
$311$	−26.6900	−1.51345	−0.756727	−	0.653732i	$-0.773203\pi$
$311$	−26.6900	−1.51345	−0.756727	+	0.653732i	$0.773203\pi$
$312$	4.23664	0.239853
$313$	−21.9797	−1.24236	−0.621182	−	0.783666i	$-0.713347\pi$
$313$	−21.9797	−1.24236	−0.621182	+	0.783666i	$0.713347\pi$
$314$	0.301260	0.0170011
$315$	−6.14612	−0.346294
$316$	−6.10061	−0.343186
$317$	−24.3964	−1.37024	−0.685119	−	0.728431i	$-0.740250\pi$
$317$	−24.3964	−1.37024	−0.685119	+	0.728431i	$0.740250\pi$
$318$	−1.92658	−0.108037
$319$	−8.69912	−0.487057
$320$	−3.88273	−0.217051
$321$	10.7354	0.599190
$322$	−8.24155	−0.459284
$323$	3.59488	0.200025
$324$	5.00101	0.277834
$325$	2.04719	0.113558
$326$	2.38141	0.131894
$327$	1.87789	0.103847
$328$	−18.1105	−0.999988
$329$	5.29662	0.292012
$330$	−0.542554	−0.0298666
$331$	31.0541	1.70689	0.853444	−	0.521184i	$-0.174509\pi$
$331$	31.0541	1.70689	0.853444	+	0.521184i	$0.174509\pi$
$332$	24.3468	1.33621
$333$	6.12380	0.335582
$334$	−4.26514	−0.233378
$335$	−0.726723	−0.0397051
$336$	−15.9809	−0.871831
$337$	10.6811	0.581838	0.290919	−	0.956748i	$-0.406039\pi$
$337$	10.6811	0.581838	0.290919	+	0.956748i	$0.406039\pi$
$338$	−3.79552	−0.206449
$339$	25.1178	1.36421
$340$	8.09458	0.438990
$341$	−8.06884	−0.436952
$342$	0.491048	0.0265528
$343$	21.2179	1.14566
$344$	3.44601	0.185796
$345$	5.54282	0.298416
$346$	−2.19810	−0.118171
$347$	−15.4006	−0.826748	−0.413374	−	0.910561i	$-0.635650\pi$
$347$	−15.4006	−0.826748	−0.413374	+	0.910561i	$0.635650\pi$
$348$	−19.8745	−1.06538
$349$	19.2351	1.02963	0.514817	−	0.857300i	$-0.327860\pi$
$349$	19.2351	1.02963	0.514817	+	0.857300i	$0.327860\pi$
$350$	1.87231	0.100079
$351$	11.3796	0.607399
$352$	4.54535	0.242268
$353$	−27.2644	−1.45114	−0.725570	−	0.688148i	$-0.758424\pi$
$353$	−27.2644	−1.45114	−0.725570	+	0.688148i	$0.758424\pi$
$354$	−4.09579	−0.217689
$355$	−1.00506	−0.0533428
$356$	1.64938	0.0874169
$357$	24.4121	1.29202
$358$	−2.68018	−0.141652
$359$	29.0045	1.53080	0.765401	−	0.643554i	$-0.222541\pi$
$359$	29.0045	1.53080	0.765401	+	0.643554i	$0.222541\pi$
$360$	2.32451	0.122513
$361$	−18.3507	−0.965828
$362$	2.49326	0.131043
$363$	−1.25921	−0.0660915
$364$	−16.1404	−0.845985
$365$	−1.00000	−0.0523424
$366$	2.65698	0.138883
$367$	7.99474	0.417322	0.208661	−	0.977988i	$-0.433090\pi$
$367$	7.99474	0.417322	0.208661	+	0.977988i	$0.433090\pi$
$368$	−12.8559	−0.670159
$369$	−15.5860	−0.811374
$370$	−1.86551	−0.0969832
$371$	15.4304	0.801109
$372$	−18.4345	−0.955785
$373$	−1.50510	−0.0779314	−0.0389657	−	0.999241i	$-0.512406\pi$
$373$	−1.50510	−0.0779314	−0.0389657	+	0.999241i	$0.512406\pi$
$374$	−1.92228	−0.0993987
$375$	−1.25921	−0.0650254
$376$	−2.00323	−0.103309
$377$	−17.8088	−0.917198
$378$	10.4075	0.535303
$379$	−32.7874	−1.68418	−0.842088	−	0.539340i	$-0.818674\pi$
$379$	−32.7874	−1.68418	−0.842088	+	0.539340i	$0.818674\pi$
$380$	1.46196	0.0749967
$381$	1.30171	0.0666886
$382$	2.89447	0.148094
$383$	17.6754	0.903173	0.451586	−	0.892227i	$-0.350858\pi$
$383$	17.6754	0.903173	0.451586	+	0.892227i	$0.350858\pi$
$384$	13.5537	0.691659
$385$	4.34543	0.221464
$386$	−1.85767	−0.0945528
$387$	2.96564	0.150752
$388$	−22.7180	−1.15333
$389$	16.1827	0.820496	0.410248	−	0.911974i	$-0.365442\pi$
$389$	16.1827	0.820496	0.410248	+	0.911974i	$0.365442\pi$
$390$	−1.11071	−0.0562430
$391$	19.6383	0.993153
$392$	−19.5291	−0.986371
$393$	16.2819	0.821315
$394$	5.34992	0.269525
$395$	3.36242	0.169182
$396$	2.56619	0.128956
$397$	−36.1889	−1.81627	−0.908135	−	0.418678i	$-0.862494\pi$
$397$	−36.1889	−1.81627	−0.908135	+	0.418678i	$0.862494\pi$
$398$	0.858662	0.0430408
$399$	4.40904	0.220728
$400$	2.92058	0.146029
$401$	−26.3890	−1.31780	−0.658901	−	0.752230i	$-0.728978\pi$
$401$	−26.3890	−1.31780	−0.658901	+	0.752230i	$0.728978\pi$
$402$	0.394286	0.0196652
$403$	−16.5185	−0.822843
$404$	−3.44737	−0.171513
$405$	−2.75636	−0.136965
$406$	−16.2874	−0.808331
$407$	−4.32966	−0.214613
$408$	−9.23286	−0.457095
$409$	12.6022	0.623141	0.311570	−	0.950223i	$-0.399145\pi$
$409$	12.6022	0.623141	0.311570	+	0.950223i	$0.399145\pi$
$410$	4.74800	0.234487
$411$	20.8991	1.03088
$412$	20.0686	0.988710
$413$	32.8041	1.61418
$414$	2.68252	0.131839
$415$	−13.4190	−0.658714
$416$	9.30519	0.456225
$417$	−5.02182	−0.245920
$418$	−0.347181	−0.0169812
$419$	8.85156	0.432427	0.216213	−	0.976346i	$-0.430629\pi$
$419$	8.85156	0.432427	0.216213	+	0.976346i	$0.430629\pi$
$420$	9.92782	0.484428
$421$	12.5035	0.609384	0.304692	−	0.952451i	$-0.401447\pi$
$421$	12.5035	0.609384	0.304692	+	0.952451i	$0.401447\pi$
$422$	−7.88318	−0.383747
$423$	−1.72398	−0.0838230
$424$	−5.83593	−0.283418
$425$	−4.46141	−0.216410
$426$	0.545296	0.0264197
$427$	−21.2804	−1.02983
$428$	15.4682	0.747684
$429$	−2.57785	−0.124460
$430$	−0.903432	−0.0435673
$431$	−28.1126	−1.35413	−0.677067	−	0.735921i	$-0.736749\pi$
$431$	−28.1126	−1.35413	−0.677067	+	0.735921i	$0.736749\pi$
$432$	16.2345	0.781082
$433$	5.70434	0.274133	0.137066	−	0.990562i	$-0.456233\pi$
$433$	5.70434	0.274133	0.137066	+	0.990562i	$0.456233\pi$
$434$	−15.1073	−0.725175
$435$	10.9540	0.525206
$436$	2.70578	0.129583
$437$	3.54686	0.169669
$438$	0.542554	0.0259242
$439$	−3.72556	−0.177811	−0.0889057	−	0.996040i	$-0.528337\pi$
$439$	−3.72556	−0.177811	−0.0889057	+	0.996040i	$0.528337\pi$
$440$	−1.64348	−0.0783499
$441$	−16.8068	−0.800326
$442$	−3.93527	−0.187182
$443$	22.9016	1.08809	0.544043	−	0.839057i	$-0.316893\pi$
$443$	22.9016	1.08809	0.544043	+	0.839057i	$0.316893\pi$
$444$	−9.89178	−0.469443
$445$	−0.909073	−0.0430942
$446$	2.66927	0.126394
$447$	9.94257	0.470268
$448$	−16.8721	−0.797133
$449$	−30.0335	−1.41737	−0.708683	−	0.705527i	$-0.750710\pi$
$449$	−30.0335	−1.41737	−0.708683	+	0.705527i	$0.750710\pi$
$450$	−0.609413	−0.0287280
$451$	11.0196	0.518894
$452$	36.1913	1.70229
$453$	5.95970	0.280011
$454$	9.99700	0.469182
$455$	8.89593	0.417048
$456$	−1.66754	−0.0780896
$457$	4.08131	0.190915	0.0954577	−	0.995433i	$-0.469569\pi$
$457$	4.08131	0.190915	0.0954577	+	0.995433i	$0.469569\pi$
$458$	−2.63526	−0.123137
$459$	−24.7994	−1.15754
$460$	7.98645	0.372370
$461$	−17.8285	−0.830358	−0.415179	−	0.909740i	$-0.636281\pi$
$461$	−17.8285	−0.830358	−0.415179	+	0.909740i	$0.636281\pi$
$462$	−2.35763	−0.109687
$463$	−27.9533	−1.29910	−0.649549	−	0.760319i	$-0.725042\pi$
$463$	−27.9533	−1.29910	−0.649549	+	0.760319i	$0.725042\pi$
$464$	−25.4065	−1.17947
$465$	10.1604	0.471176
$466$	0.965614	0.0447312
$467$	−20.5254	−0.949801	−0.474900	−	0.880040i	$-0.657516\pi$
$467$	−20.5254	−0.949801	−0.474900	+	0.880040i	$0.657516\pi$
$468$	5.25349	0.242843
$469$	−3.15792	−0.145819
$470$	0.525182	0.0242248
$471$	−0.880434	−0.0405683
$472$	−12.4068	−0.571069
$473$	−2.09677	−0.0964097
$474$	−1.82429	−0.0837925
$475$	−0.805772	−0.0369714
$476$	35.1745	1.61222
$477$	−5.02242	−0.229961
$478$	−12.2971	−0.562458
$479$	−4.72042	−0.215682	−0.107841	−	0.994168i	$-0.534394\pi$
$479$	−4.72042	−0.215682	−0.107841	+	0.994168i	$0.534394\pi$
$480$	−5.72356	−0.261243
$481$	−8.86364	−0.404147
$482$	−3.29357	−0.150018
$483$	24.0860	1.09595
$484$	−1.81435	−0.0824706
$485$	12.5213	0.568561
$486$	−5.68965	−0.258088
$487$	−11.4788	−0.520153	−0.260077	−	0.965588i	$-0.583748\pi$
$487$	−11.4788	−0.520153	−0.260077	+	0.965588i	$0.583748\pi$
$488$	8.04842	0.364335
$489$	−6.95967	−0.314727
$490$	5.11991	0.231294
$491$	15.2939	0.690202	0.345101	−	0.938565i	$-0.387845\pi$
$491$	15.2939	0.690202	0.345101	+	0.938565i	$0.387845\pi$
$492$	25.1760	1.13502
$493$	38.8104	1.74793
$494$	−0.710746	−0.0319780
$495$	−1.41438	−0.0635719
$496$	−23.5657	−1.05813
$497$	−4.36740	−0.195905
$498$	7.28054	0.326249
$499$	2.54834	0.114079	0.0570397	−	0.998372i	$-0.481834\pi$
$499$	2.54834	0.114079	0.0570397	+	0.998372i	$0.481834\pi$
$500$	−1.81435	−0.0811403
$501$	12.4649	0.556891
$502$	−4.22214	−0.188443
$503$	35.7406	1.59360	0.796798	−	0.604246i	$-0.206526\pi$
$503$	35.7406	1.59360	0.796798	+	0.604246i	$0.206526\pi$
$504$	10.1010	0.449935
$505$	1.90006	0.0845514
$506$	−1.89660	−0.0843142
$507$	11.0924	0.492631
$508$	1.87559	0.0832157
$509$	−27.0875	−1.20063	−0.600317	−	0.799762i	$-0.704959\pi$
$509$	−27.0875	−1.20063	−0.600317	+	0.799762i	$0.704959\pi$
$510$	2.42056	0.107184
$511$	−4.34543	−0.192231
$512$	22.8749	1.01094
$513$	−4.47900	−0.197753
$514$	6.87512	0.303248
$515$	−11.0610	−0.487407
$516$	−4.79040	−0.210886
$517$	1.21889	0.0536069
$518$	−8.10644	−0.356177
$519$	6.42396	0.281981
$520$	−3.36452	−0.147544
$521$	−9.02646	−0.395456	−0.197728	−	0.980257i	$-0.563356\pi$
$521$	−9.02646	−0.395456	−0.197728	+	0.980257i	$0.563356\pi$
$522$	5.30135	0.232034
$523$	20.5686	0.899400	0.449700	−	0.893180i	$-0.351531\pi$
$523$	20.5686	0.899400	0.449700	+	0.893180i	$0.351531\pi$
$524$	23.4600	1.02486
$525$	−5.47182	−0.238810
$526$	−8.77409	−0.382568
$527$	35.9984	1.56812
$528$	−3.67763	−0.160048
$529$	−3.62400	−0.157565
$530$	1.52999	0.0664586
$531$	−10.6773	−0.463357
$532$	6.35283	0.275430
$533$	22.5593	0.977151
$534$	0.493221	0.0213438
$535$	−8.52547	−0.368588
$536$	1.19435	0.0515883
$537$	7.83283	0.338011
$538$	−2.23297	−0.0962701
$539$	11.8828	0.511828
$540$	−10.0853	−0.434004
$541$	−8.27814	−0.355905	−0.177952	−	0.984039i	$-0.556947\pi$
$541$	−8.27814	−0.355905	−0.177952	+	0.984039i	$0.556947\pi$
$542$	8.43904	0.362488
$543$	−7.28656	−0.312696
$544$	−20.2787	−0.869441
$545$	−1.49132	−0.0638811
$546$	−4.82652	−0.206556
$547$	14.6034	0.624396	0.312198	−	0.950017i	$-0.398935\pi$
$547$	14.6034	0.624396	0.312198	+	0.950017i	$0.398935\pi$
$548$	30.1127	1.28635
$549$	6.92650	0.295616
$550$	0.430868	0.0183723
$551$	7.00951	0.298615
$552$	−9.10952	−0.387727
$553$	14.6112	0.621330
$554$	4.48203	0.190423
$555$	5.45196	0.231423
$556$	−7.23576	−0.306865
$557$	36.8507	1.56141	0.780706	−	0.624898i	$-0.214860\pi$
$557$	36.8507	1.56141	0.780706	+	0.624898i	$0.214860\pi$
$558$	4.91725	0.208164
$559$	−4.29250	−0.181553
$560$	12.6912	0.536301
$561$	5.61787	0.237187
$562$	7.34324	0.309756
$563$	−10.9807	−0.462781	−0.231390	−	0.972861i	$-0.574327\pi$
$563$	−10.9807	−0.462781	−0.231390	+	0.972861i	$0.574327\pi$
$564$	2.78475	0.117259
$565$	−19.9472	−0.839185
$566$	−11.0116	−0.462853
$567$	−11.9776	−0.503011
$568$	1.65179	0.0693075
$569$	−23.1135	−0.968969	−0.484485	−	0.874800i	$-0.660993\pi$
$569$	−23.1135	−0.968969	−0.484485	+	0.874800i	$0.660993\pi$
$570$	0.437175	0.0183112
$571$	−6.56724	−0.274830	−0.137415	−	0.990514i	$-0.543879\pi$
$571$	−6.56724	−0.274830	−0.137415	+	0.990514i	$0.543879\pi$
$572$	−3.71433	−0.155304
$573$	−8.45911	−0.353384
$574$	20.6321	0.861168
$575$	−4.40182	−0.183568
$576$	5.49167	0.228820
$577$	16.0528	0.668286	0.334143	−	0.942522i	$-0.391553\pi$
$577$	16.0528	0.668286	0.334143	+	0.942522i	$0.391553\pi$
$578$	1.25133	0.0520486
$579$	5.42904	0.225623
$580$	15.7833	0.655365
$581$	−58.3115	−2.41917
$582$	−6.79345	−0.281598
$583$	3.55096	0.147066
$584$	1.64348	0.0680077
$585$	−2.89552	−0.119715
$586$	−0.931240	−0.0384692
$587$	8.57689	0.354006	0.177003	−	0.984210i	$-0.443360\pi$
$587$	8.57689	0.354006	0.177003	+	0.984210i	$0.443360\pi$
$588$	27.1481	1.11957
$589$	6.50164	0.267896
$590$	3.25266	0.133910
$591$	−15.6352	−0.643145
$592$	−12.6451	−0.519712
$593$	39.2349	1.61118	0.805592	−	0.592470i	$-0.201847\pi$
$593$	39.2349	1.61118	0.805592	+	0.592470i	$0.201847\pi$
$594$	2.39504	0.0982697
$595$	−19.3868	−0.794780
$596$	14.3259	0.586811
$597$	−2.50944	−0.102705
$598$	−3.88270	−0.158776
$599$	17.0298	0.695819	0.347909	−	0.937528i	$-0.386892\pi$
$599$	17.0298	0.695819	0.347909	+	0.937528i	$0.386892\pi$
$600$	2.06949	0.0844866
$601$	17.2844	0.705045	0.352522	−	0.935803i	$-0.385324\pi$
$601$	17.2844	0.705045	0.352522	+	0.935803i	$0.385324\pi$
$602$	−3.92580	−0.160004
$603$	1.02787	0.0418579
$604$	8.58712	0.349405
$605$	1.00000	0.0406558
$606$	−1.03088	−0.0418767
$607$	−0.321159	−0.0130355	−0.00651773	−	0.999979i	$-0.502075\pi$
$607$	−0.321159	−0.0130355	−0.00651773	+	0.999979i	$0.502075\pi$
$608$	−3.66251	−0.148535
$609$	47.6000	1.92885
$610$	−2.11004	−0.0854328
$611$	2.49531	0.100949
$612$	−11.4489	−0.462792
$613$	42.7273	1.72574	0.862869	−	0.505427i	$-0.168665\pi$
$613$	42.7273	1.72574	0.862869	+	0.505427i	$0.168665\pi$
$614$	5.88015	0.237303
$615$	−13.8760	−0.559536
$616$	−7.14164	−0.287745
$617$	−36.9849	−1.48896	−0.744479	−	0.667646i	$-0.767302\pi$
$617$	−36.9849	−1.48896	−0.744479	+	0.667646i	$0.767302\pi$
$618$	6.00120	0.241404
$619$	−6.85858	−0.275669	−0.137835	−	0.990455i	$-0.544014\pi$
$619$	−6.85858	−0.275669	−0.137835	+	0.990455i	$0.544014\pi$
$620$	14.6397	0.587945
$621$	−24.4681	−0.981873
$622$	−11.4999	−0.461103
$623$	−3.95032	−0.158266
$624$	−7.52882	−0.301394
$625$	1.00000	0.0400000
$626$	−9.47032	−0.378510
$627$	1.01464	0.0405207
$628$	−1.26859	−0.0506221
$629$	19.3164	0.770195
$630$	−2.64816	−0.105505
$631$	18.5947	0.740241	0.370121	−	0.928984i	$-0.379316\pi$
$631$	18.5947	0.740241	0.370121	+	0.928984i	$0.379316\pi$
$632$	−5.52607	−0.219815
$633$	23.0386	0.915704
$634$	−10.5116	−0.417469
$635$	−1.03375	−0.0410231
$636$	8.11271	0.321690
$637$	24.3264	0.963845
$638$	−3.74817	−0.148391
$639$	1.42153	0.0562350
$640$	−10.7636	−0.425470
$641$	11.3088	0.446669	0.223335	−	0.974742i	$-0.428306\pi$
$641$	11.3088	0.446669	0.223335	+	0.974742i	$0.428306\pi$
$642$	4.62552	0.182555
$643$	28.0470	1.10607	0.553033	−	0.833160i	$-0.313471\pi$
$643$	28.0470	1.10607	0.553033	+	0.833160i	$0.313471\pi$
$644$	34.7046	1.36755
$645$	2.64028	0.103961
$646$	1.54892	0.0609414
$647$	43.7577	1.72029	0.860147	−	0.510047i	$-0.170372\pi$
$647$	43.7577	1.72029	0.860147	+	0.510047i	$0.170372\pi$
$648$	4.53003	0.177956
$649$	7.54910	0.296328
$650$	0.882068	0.0345976
$651$	44.1513	1.73042
$652$	−10.0279	−0.392724
$653$	31.8679	1.24709	0.623543	−	0.781789i	$-0.285693\pi$
$653$	31.8679	1.24709	0.623543	+	0.781789i	$0.285693\pi$
$654$	0.809121	0.0316391
$655$	−12.9303	−0.505227
$656$	32.1837	1.25656
$657$	1.41438	0.0551804
$658$	2.28214	0.0889671
$659$	9.23671	0.359811	0.179906	−	0.983684i	$-0.442421\pi$
$659$	9.23671	0.359811	0.179906	+	0.983684i	$0.442421\pi$
$660$	2.28466	0.0889301
$661$	−3.99120	−0.155240	−0.0776199	−	0.996983i	$-0.524732\pi$
$661$	−3.99120	−0.155240	−0.0776199	+	0.996983i	$0.524732\pi$
$662$	13.3802	0.520037
$663$	11.5008	0.446656
$664$	22.0539	0.855857
$665$	−3.50143	−0.135780
$666$	2.63855	0.102242
$667$	38.2919	1.48267
$668$	17.9602	0.694902
$669$	−7.80097	−0.301603
$670$	−0.313121	−0.0120969
$671$	−4.89718	−0.189054
$672$	−24.8713	−0.959432
$673$	49.0666	1.89138	0.945689	−	0.325073i	$-0.105389\pi$
$673$	49.0666	1.89138	0.945689	+	0.325073i	$0.105389\pi$
$674$	4.60215	0.177268
$675$	5.55865	0.213952
$676$	15.9827	0.614717
$677$	16.5529	0.636178	0.318089	−	0.948061i	$-0.396959\pi$
$677$	16.5529	0.636178	0.318089	+	0.948061i	$0.396959\pi$
$678$	10.8224	0.415633
$679$	54.4103	2.08808
$680$	7.33225	0.281179
$681$	−29.2163	−1.11957
$682$	−3.47660	−0.133126
$683$	−12.8711	−0.492498	−0.246249	−	0.969207i	$-0.579198\pi$
$683$	−12.8711	−0.492498	−0.246249	+	0.969207i	$0.579198\pi$
$684$	−2.06777	−0.0790631
$685$	−16.5969	−0.634137
$686$	9.14209	0.349047
$687$	7.70155	0.293832
$688$	−6.12380	−0.233468
$689$	7.26948	0.276945
$690$	2.38822	0.0909181
$691$	43.3719	1.64995	0.824973	−	0.565172i	$-0.191190\pi$
$691$	43.3719	1.64995	0.824973	+	0.565172i	$0.191190\pi$
$692$	9.25605	0.351862
$693$	−6.14612	−0.233472
$694$	−6.63562	−0.251885
$695$	3.98807	0.151276
$696$	−18.0028	−0.682393
$697$	−49.1631	−1.86219
$698$	8.28780	0.313698
$699$	−2.82201	−0.106738
$700$	−7.88415	−0.297993
$701$	−46.7221	−1.76467	−0.882335	−	0.470622i	$-0.844030\pi$
$701$	−46.7221	−1.76467	−0.882335	+	0.470622i	$0.844030\pi$
$702$	4.90311	0.185056
$703$	3.48872	0.131579
$704$	−3.88273	−0.146336
$705$	−1.53485	−0.0578056
$706$	−11.7474	−0.442118
$707$	8.25657	0.310520
$708$	17.2471	0.648185
$709$	−22.6462	−0.850497	−0.425248	−	0.905077i	$-0.639813\pi$
$709$	−22.6462	−0.850497	−0.425248	+	0.905077i	$0.639813\pi$
$710$	−0.433046	−0.0162519
$711$	−4.75575	−0.178355
$712$	1.49404	0.0559917
$713$	35.5176	1.33014
$714$	10.5184	0.393640
$715$	2.04719	0.0765606
$716$	11.2860	0.421779
$717$	35.9385	1.34215
$718$	12.4971	0.466388
$719$	3.93514	0.146756	0.0733780	−	0.997304i	$-0.476622\pi$
$719$	3.93514	0.146756	0.0733780	+	0.997304i	$0.476622\pi$
$720$	−4.13083	−0.153947
$721$	−48.0650	−1.79003
$722$	−7.90673	−0.294258
$723$	9.62546	0.357975
$724$	−10.4989	−0.390190
$725$	−8.69912	−0.323077
$726$	−0.542554	−0.0201361
$727$	25.5489	0.947555	0.473777	−	0.880645i	$-0.342890\pi$
$727$	25.5489	0.947555	0.473777	+	0.880645i	$0.342890\pi$
$728$	−14.6203	−0.541864
$729$	24.8971	0.922115
$730$	−0.430868	−0.0159471
$731$	9.35457	0.345991
$732$	−11.1884	−0.413534
$733$	33.9532	1.25409	0.627045	−	0.778983i	$-0.284264\pi$
$733$	33.9532	1.25409	0.627045	+	0.778983i	$0.284264\pi$
$734$	3.44467	0.127145
$735$	−14.9630	−0.551917
$736$	−20.0078	−0.737497
$737$	−0.726723	−0.0267692
$738$	−6.71550	−0.247201
$739$	−8.98910	−0.330669	−0.165335	−	0.986238i	$-0.552870\pi$
$739$	−8.98910	−0.330669	−0.165335	+	0.986238i	$0.552870\pi$
$740$	7.85553	0.288775
$741$	2.07716	0.0763063
$742$	6.64848	0.244073
$743$	50.8018	1.86374	0.931869	−	0.362796i	$-0.118178\pi$
$743$	50.8018	1.86374	0.931869	+	0.362796i	$0.118178\pi$
$744$	−16.6984	−0.612193
$745$	−7.89587	−0.289282
$746$	−0.648501	−0.0237433
$747$	18.9797	0.694429
$748$	8.09458	0.295967
$749$	−37.0468	−1.35366
$750$	−0.542554	−0.0198113
$751$	41.7214	1.52244	0.761219	−	0.648495i	$-0.224601\pi$
$751$	41.7214	1.52244	0.761219	+	0.648495i	$0.224601\pi$
$752$	3.55988	0.129815
$753$	12.3392	0.449667
$754$	−7.67322	−0.279442
$755$	−4.73288	−0.172247
$756$	−43.8252	−1.59391
$757$	−41.5063	−1.50857	−0.754287	−	0.656545i	$-0.772017\pi$
$757$	−41.5063	−1.50857	−0.754287	+	0.656545i	$0.772017\pi$
$758$	−14.1270	−0.513117
$759$	5.54282	0.201192
$760$	1.32427	0.0480364
$761$	−25.0358	−0.907547	−0.453773	−	0.891117i	$-0.649922\pi$
$761$	−25.0358	−0.907547	−0.453773	+	0.891117i	$0.649922\pi$
$762$	0.560864	0.0203180
$763$	−6.48043	−0.234607
$764$	−12.1884	−0.440962
$765$	6.31016	0.228144
$766$	7.61577	0.275169
$767$	15.4544	0.558028
$768$	−3.93850	−0.142118
$769$	41.7111	1.50414	0.752070	−	0.659084i	$-0.229056\pi$
$769$	41.7111	1.50414	0.752070	+	0.659084i	$0.229056\pi$
$770$	1.87231	0.0674732
$771$	−20.0926	−0.723616
$772$	7.82251	0.281538
$773$	−13.1852	−0.474238	−0.237119	−	0.971481i	$-0.576203\pi$
$773$	−13.1852	−0.474238	−0.237119	+	0.971481i	$0.576203\pi$
$774$	1.27780	0.0459296
$775$	−8.06884	−0.289841
$776$	−20.5785	−0.738723
$777$	23.6911	0.849914
$778$	6.97260	0.249980
$779$	−8.87931	−0.318134
$780$	4.67713	0.167468
$781$	−1.00506	−0.0359637
$782$	8.46152	0.302583
$783$	−48.3553	−1.72808
$784$	34.7047	1.23945
$785$	0.699194	0.0249553
$786$	7.01535	0.250229
$787$	−27.7638	−0.989671	−0.494835	−	0.868987i	$-0.664772\pi$
$787$	−27.7638	−0.989671	−0.494835	+	0.868987i	$0.664772\pi$
$788$	−22.5281	−0.802532
$789$	25.6423	0.912890
$790$	1.44876	0.0515445
$791$	−86.6793	−3.08196
$792$	2.32451	0.0825980
$793$	−10.0255	−0.356015
$794$	−15.5926	−0.553362
$795$	−4.47141	−0.158584
$796$	−3.61576	−0.128157
$797$	28.7975	1.02006	0.510030	−	0.860156i	$-0.329634\pi$
$797$	28.7975	1.02006	0.510030	+	0.860156i	$0.329634\pi$
$798$	1.89971	0.0672491
$799$	−5.43799	−0.192382
$800$	4.54535	0.160702
$801$	1.28578	0.0454308
$802$	−11.3701	−0.401494
$803$	−1.00000	−0.0352892
$804$	−1.66031	−0.0585546
$805$	−19.1278	−0.674167
$806$	−7.11726	−0.250695
$807$	6.52586	0.229721
$808$	−3.12271	−0.109856
$809$	−37.6461	−1.32357	−0.661784	−	0.749695i	$-0.730200\pi$
$809$	−37.6461	−1.32357	−0.661784	+	0.749695i	$0.730200\pi$
$810$	−1.18763	−0.0417289
$811$	−7.77411	−0.272986	−0.136493	−	0.990641i	$-0.543583\pi$
$811$	−7.77411	−0.272986	−0.136493	+	0.990641i	$0.543583\pi$
$812$	68.5852	2.40687
$813$	−24.6631	−0.864974
$814$	−1.86551	−0.0653860
$815$	5.52700	0.193602
$816$	16.4075	0.574376
$817$	1.68952	0.0591089
$818$	5.42990	0.189852
$819$	−12.5823	−0.439660
$820$	−19.9935	−0.698203
$821$	−54.6845	−1.90850	−0.954251	−	0.299006i	$-0.903345\pi$
$821$	−54.6845	−1.90850	−0.954251	+	0.299006i	$0.903345\pi$
$822$	9.00473	0.314076
$823$	−6.45285	−0.224932	−0.112466	−	0.993656i	$-0.535875\pi$
$823$	−6.45285	−0.224932	−0.112466	+	0.993656i	$0.535875\pi$
$824$	18.1786	0.633281
$825$	−1.25921	−0.0438401
$826$	14.1342	0.491793
$827$	12.8480	0.446768	0.223384	−	0.974731i	$-0.428290\pi$
$827$	12.8480	0.446768	0.223384	+	0.974731i	$0.428290\pi$
$828$	−11.2959	−0.392560
$829$	−44.4989	−1.54551	−0.772755	−	0.634704i	$-0.781122\pi$
$829$	−44.4989	−1.54551	−0.772755	+	0.634704i	$0.781122\pi$
$830$	−5.78182	−0.200690
$831$	−13.0988	−0.454391
$832$	−7.94868	−0.275571
$833$	−53.0141	−1.83683
$834$	−2.16374	−0.0749242
$835$	−9.89897	−0.342568
$836$	1.46196	0.0505628
$837$	−44.8518	−1.55031
$838$	3.81385	0.131747
$839$	−40.5784	−1.40092	−0.700460	−	0.713691i	$-0.747022\pi$
$839$	−40.5784	−1.40092	−0.700460	+	0.713691i	$0.747022\pi$
$840$	8.99284	0.310282
$841$	46.6747	1.60947
$842$	5.38735	0.185661
$843$	−21.4607	−0.739144
$844$	33.1955	1.14264
$845$	−8.80901	−0.303039
$846$	−0.742809	−0.0255383
$847$	4.34543	0.149311
$848$	10.3709	0.356137
$849$	32.1815	1.10447
$850$	−1.92228	−0.0659336
$851$	19.0584	0.653312
$852$	−2.29620	−0.0786667
$853$	16.4998	0.564942	0.282471	−	0.959276i	$-0.408846\pi$
$853$	16.4998	0.564942	0.282471	+	0.959276i	$0.408846\pi$
$854$	−9.16902	−0.313757
$855$	1.13967	0.0389760
$856$	14.0114	0.478901
$857$	−34.8201	−1.18943	−0.594716	−	0.803936i	$-0.702735\pi$
$857$	−34.8201	−1.18943	−0.594716	+	0.803936i	$0.702735\pi$
$858$	−1.11071	−0.0379190
$859$	8.31306	0.283638	0.141819	−	0.989893i	$-0.454705\pi$
$859$	8.31306	0.283638	0.141819	+	0.989893i	$0.454705\pi$
$860$	3.80429	0.129725
$861$	−60.2974	−2.05493
$862$	−12.1128	−0.412563
$863$	25.0399	0.852369	0.426184	−	0.904636i	$-0.359858\pi$
$863$	25.0399	0.852369	0.426184	+	0.904636i	$0.359858\pi$
$864$	25.2660	0.859566
$865$	−5.10157	−0.173459
$866$	2.45781	0.0835199
$867$	−3.65702	−0.124199
$868$	63.6159	2.15927
$869$	3.36242	0.114062
$870$	4.71974	0.160014
$871$	−1.48774	−0.0504101
$872$	2.45095	0.0829998
$873$	−17.7099	−0.599389
$874$	1.52823	0.0516931
$875$	4.34543	0.146902
$876$	−2.28466	−0.0771914
$877$	−13.4174	−0.453073	−0.226536	−	0.974003i	$-0.572740\pi$
$877$	−13.4174	−0.453073	−0.226536	+	0.974003i	$0.572740\pi$
$878$	−1.60522	−0.0541737
$879$	2.72155	0.0917957
$880$	2.92058	0.0984529
$881$	10.2501	0.345336	0.172668	−	0.984980i	$-0.444761\pi$
$881$	10.2501	0.345336	0.172668	+	0.984980i	$0.444761\pi$
$882$	−7.24152	−0.243835
$883$	54.8704	1.84654	0.923268	−	0.384156i	$-0.125508\pi$
$883$	54.8704	1.84654	0.923268	+	0.384156i	$0.125508\pi$
$884$	16.5712	0.557348
$885$	−9.50592	−0.319538
$886$	9.86754	0.331506
$887$	39.9923	1.34281	0.671405	−	0.741091i	$-0.265691\pi$
$887$	39.9923	1.34281	0.671405	+	0.741091i	$0.265691\pi$
$888$	−8.96019	−0.300684
$889$	−4.49209	−0.150660
$890$	−0.391690	−0.0131295
$891$	−2.75636	−0.0923416
$892$	−11.2401	−0.376347
$893$	−0.982150	−0.0328664
$894$	4.28393	0.143276
$895$	−6.22042	−0.207926
$896$	−46.7727	−1.56256
$897$	11.3472	0.378872
$898$	−12.9404	−0.431828
$899$	70.1918	2.34103
$900$	2.56619	0.0855398
$901$	−15.8423	−0.527783
$902$	4.74800	0.158091
$903$	11.4732	0.381803
$904$	32.7828	1.09034
$905$	5.78660	0.192353
$906$	2.56784	0.0853108
$907$	−38.7925	−1.28808	−0.644041	−	0.764991i	$-0.722743\pi$
$907$	−38.7925	−1.28808	−0.644041	+	0.764991i	$0.722743\pi$
$908$	−42.0967	−1.39703
$909$	−2.68741	−0.0891358
$910$	3.83297	0.127062
$911$	30.2986	1.00384	0.501918	−	0.864915i	$-0.332628\pi$
$911$	30.2986	1.00384	0.501918	+	0.864915i	$0.332628\pi$
$912$	2.96334	0.0981258
$913$	−13.4190	−0.444105
$914$	1.75850	0.0581661
$915$	6.16659	0.203861
$916$	11.0969	0.366651
$917$	−56.1876	−1.85548
$918$	−10.6853	−0.352666
$919$	−55.8493	−1.84230	−0.921149	−	0.389210i	$-0.872748\pi$
$919$	−55.8493	−1.84230	−0.921149	+	0.389210i	$0.872748\pi$
$920$	7.23430	0.238508
$921$	−17.1848	−0.566257
$922$	−7.68174	−0.252985
$923$	−2.05754	−0.0677247
$924$	9.92782	0.326601
$925$	−4.32966	−0.142358
$926$	−12.0442	−0.395796
$927$	15.6446	0.513835
$928$	−39.5405	−1.29798
$929$	41.5645	1.36369	0.681843	−	0.731499i	$-0.261179\pi$
$929$	41.5645	1.36369	0.681843	+	0.731499i	$0.261179\pi$
$930$	4.37778	0.143553
$931$	−9.57482	−0.313802
$932$	−4.06613	−0.133191
$933$	33.6084	1.10029
$934$	−8.84372	−0.289375
$935$	−4.46141	−0.145904
$936$	4.75873	0.155544
$937$	−3.94257	−0.128798	−0.0643991	−	0.997924i	$-0.520513\pi$
$937$	−3.94257	−0.128798	−0.0643991	+	0.997924i	$0.520513\pi$
$938$	−1.36065	−0.0444267
$939$	27.6771	0.903207
$940$	−2.21150	−0.0721313
$941$	−43.8101	−1.42817	−0.714084	−	0.700060i	$-0.753157\pi$
$941$	−43.8101	−1.42817	−0.714084	+	0.700060i	$0.753157\pi$
$942$	−0.379350	−0.0123599
$943$	−48.5064	−1.57959
$944$	22.0478	0.717594
$945$	24.1547	0.785753
$946$	−0.903432	−0.0293731
$947$	−34.4895	−1.12076	−0.560379	−	0.828236i	$-0.689345\pi$
$947$	−34.4895	−1.12076	−0.560379	+	0.828236i	$0.689345\pi$
$948$	7.68197	0.249499
$949$	−2.04719	−0.0664546
$950$	−0.347181	−0.0112640
$951$	30.7202	0.996172
$952$	31.8618	1.03265
$953$	−41.1940	−1.33440	−0.667202	−	0.744877i	$-0.732508\pi$
$953$	−41.1940	−1.33440	−0.667202	+	0.744877i	$0.732508\pi$
$954$	−2.16400	−0.0700620
$955$	6.71778	0.217382
$956$	51.7824	1.67476
$957$	10.9540	0.354094
$958$	−2.03388	−0.0657116
$959$	−72.1209	−2.32891
$960$	4.88917	0.157797
$961$	34.1061	1.10020
$962$	−3.81905	−0.123131
$963$	12.0583	0.388573
$964$	13.8690	0.446690
$965$	−4.31146	−0.138791
$966$	10.3779	0.333902
$967$	−30.2740	−0.973546	−0.486773	−	0.873528i	$-0.661826\pi$
$967$	−30.2740	−0.973546	−0.486773	+	0.873528i	$0.661826\pi$
$968$	−1.64348	−0.0528235
$969$	−4.52672	−0.145419
$970$	5.39500	0.173223
$971$	−32.6100	−1.04650	−0.523252	−	0.852178i	$-0.675281\pi$
$971$	−32.6100	−1.04650	−0.523252	+	0.852178i	$0.675281\pi$
$972$	23.9587	0.768476
$973$	17.3299	0.555571
$974$	−4.94584	−0.158475
$975$	−2.57785	−0.0825572
$976$	−14.3026	−0.457816
$977$	39.3613	1.25928	0.629639	−	0.776888i	$-0.283203\pi$
$977$	39.3613	1.25928	0.629639	+	0.776888i	$0.283203\pi$
$978$	−2.99870	−0.0958877
$979$	−0.909073	−0.0290541
$980$	−21.5596	−0.688696
$981$	2.10930	0.0673448
$982$	6.58963	0.210284
$983$	3.03888	0.0969252	0.0484626	−	0.998825i	$-0.484568\pi$
$983$	3.03888	0.0969252	0.0484626	+	0.998825i	$0.484568\pi$
$984$	22.8050	0.726997
$985$	12.4166	0.395626
$986$	16.7221	0.532541
$987$	−6.66957	−0.212295
$988$	2.99290	0.0952169
$989$	9.22961	0.293485
$990$	−0.609413	−0.0193684
$991$	39.9971	1.27055	0.635275	−	0.772286i	$-0.280887\pi$
$991$	39.9971	1.27055	0.635275	+	0.772286i	$0.280887\pi$
$992$	−36.6757	−1.16445
$993$	−39.1037	−1.24092
$994$	−1.88177	−0.0596862
$995$	1.99287	0.0631781
$996$	−30.6578	−0.971431
$997$	23.1955	0.734608	0.367304	−	0.930101i	$-0.380281\pi$
$997$	23.1955	0.734608	0.367304	+	0.930101i	$0.380281\pi$
$998$	1.09800	0.0347565
$999$	−24.0670	−0.761447

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.b.1.15	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.b.1.15	✓	23	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)

\(f(q)\)	\(=\)	\(q+0.430868 q^{2} -1.25921 q^{3} -1.81435 q^{4} +1.00000 q^{5} -0.542554 q^{6} +4.34543 q^{7} -1.64348 q^{8} -1.41438 q^{9} +O(q^{10})\)	\(q+0.430868 q^{2} -1.25921 q^{3} -1.81435 q^{4} +1.00000 q^{5} -0.542554 q^{6} +4.34543 q^{7} -1.64348 q^{8} -1.41438 q^{9} +0.430868 q^{10} +1.00000 q^{11} +2.28466 q^{12} +2.04719 q^{13} +1.87231 q^{14} -1.25921 q^{15} +2.92058 q^{16} -4.46141 q^{17} -0.609413 q^{18} -0.805772 q^{19} -1.81435 q^{20} -5.47182 q^{21} +0.430868 q^{22} -4.40182 q^{23} +2.06949 q^{24} +1.00000 q^{25} +0.882068 q^{26} +5.55865 q^{27} -7.88415 q^{28} -8.69912 q^{29} -0.542554 q^{30} -8.06884 q^{31} +4.54535 q^{32} -1.25921 q^{33} -1.92228 q^{34} +4.34543 q^{35} +2.56619 q^{36} -4.32966 q^{37} -0.347181 q^{38} -2.57785 q^{39} -1.64348 q^{40} +11.0196 q^{41} -2.35763 q^{42} -2.09677 q^{43} -1.81435 q^{44} -1.41438 q^{45} -1.89660 q^{46} +1.21889 q^{47} -3.67763 q^{48} +11.8828 q^{49} +0.430868 q^{50} +5.61787 q^{51} -3.71433 q^{52} +3.55096 q^{53} +2.39504 q^{54} +1.00000 q^{55} -7.14164 q^{56} +1.01464 q^{57} -3.74817 q^{58} +7.54910 q^{59} +2.28466 q^{60} -4.89718 q^{61} -3.47660 q^{62} -6.14612 q^{63} -3.88273 q^{64} +2.04719 q^{65} -0.542554 q^{66} -0.726723 q^{67} +8.09458 q^{68} +5.54282 q^{69} +1.87231 q^{70} -1.00506 q^{71} +2.32451 q^{72} -1.00000 q^{73} -1.86551 q^{74} -1.25921 q^{75} +1.46196 q^{76} +4.34543 q^{77} -1.11071 q^{78} +3.36242 q^{79} +2.92058 q^{80} -2.75636 q^{81} +4.74800 q^{82} -13.4190 q^{83} +9.92782 q^{84} -4.46141 q^{85} -0.903432 q^{86} +10.9540 q^{87} -1.64348 q^{88} -0.909073 q^{89} -0.609413 q^{90} +8.89593 q^{91} +7.98645 q^{92} +10.1604 q^{93} +0.525182 q^{94} -0.805772 q^{95} -5.72356 q^{96} +12.5213 q^{97} +5.11991 q^{98} -1.41438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * q^99

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