LMFDB - Embedded newform 4015.2.a.h.1.13

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			1.13
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)

$f(q)$	$=$	$q-0.745458 q^{2} +3.05905 q^{3} -1.44429 q^{4} +1.00000 q^{5} -2.28039 q^{6} -3.66055 q^{7} +2.56757 q^{8} +6.35779 q^{9} +O(q^{10})$	\(q-0.745458 q^{2} +3.05905 q^{3} -1.44429 q^{4} +1.00000 q^{5} -2.28039 q^{6} -3.66055 q^{7} +2.56757 q^{8} +6.35779 q^{9} -0.745458 q^{10} +1.00000 q^{11} -4.41817 q^{12} +1.02611 q^{13} +2.72879 q^{14} +3.05905 q^{15} +0.974567 q^{16} +7.92938 q^{17} -4.73947 q^{18} -1.53458 q^{19} -1.44429 q^{20} -11.1978 q^{21} -0.745458 q^{22} -9.02592 q^{23} +7.85434 q^{24} +1.00000 q^{25} -0.764924 q^{26} +10.2717 q^{27} +5.28691 q^{28} +3.19396 q^{29} -2.28039 q^{30} -7.54361 q^{31} -5.86165 q^{32} +3.05905 q^{33} -5.91102 q^{34} -3.66055 q^{35} -9.18251 q^{36} +6.07994 q^{37} +1.14397 q^{38} +3.13893 q^{39} +2.56757 q^{40} +7.65235 q^{41} +8.34749 q^{42} +8.29774 q^{43} -1.44429 q^{44} +6.35779 q^{45} +6.72844 q^{46} +9.63324 q^{47} +2.98125 q^{48} +6.39962 q^{49} -0.745458 q^{50} +24.2564 q^{51} -1.48201 q^{52} -3.09231 q^{53} -7.65709 q^{54} +1.00000 q^{55} -9.39873 q^{56} -4.69437 q^{57} -2.38096 q^{58} +8.32297 q^{59} -4.41817 q^{60} -7.95140 q^{61} +5.62344 q^{62} -23.2730 q^{63} +2.42048 q^{64} +1.02611 q^{65} -2.28039 q^{66} -2.85577 q^{67} -11.4523 q^{68} -27.6108 q^{69} +2.72879 q^{70} -3.17918 q^{71} +16.3241 q^{72} +1.00000 q^{73} -4.53234 q^{74} +3.05905 q^{75} +2.21639 q^{76} -3.66055 q^{77} -2.33994 q^{78} +16.2070 q^{79} +0.974567 q^{80} +12.3481 q^{81} -5.70450 q^{82} -1.77293 q^{83} +16.1729 q^{84} +7.92938 q^{85} -6.18561 q^{86} +9.77049 q^{87} +2.56757 q^{88} +0.725334 q^{89} -4.73947 q^{90} -3.75614 q^{91} +13.0361 q^{92} -23.0763 q^{93} -7.18117 q^{94} -1.53458 q^{95} -17.9311 q^{96} +18.9489 q^{97} -4.77065 q^{98} +6.35779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.745458	−0.527118	−0.263559	−	0.964643i	$-0.584896\pi$
$2$	−0.745458	−0.527118	−0.263559	+	0.964643i	$0.584896\pi$
$3$	3.05905	1.76614	0.883072	−	0.469238i	$-0.155471\pi$
$3$	3.05905	1.76614	0.883072	+	0.469238i	$0.155471\pi$
$4$	−1.44429	−0.722146
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.28039	−0.930967
$7$	−3.66055	−1.38356	−0.691779	−	0.722109i	$-0.743173\pi$
$7$	−3.66055	−1.38356	−0.691779	+	0.722109i	$0.743173\pi$
$8$	2.56757	0.907775
$9$	6.35779	2.11926
$10$	−0.745458	−0.235734
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.41817	−1.27541
$13$	1.02611	0.284593	0.142296	−	0.989824i	$-0.454551\pi$
$13$	1.02611	0.284593	0.142296	+	0.989824i	$0.454551\pi$
$14$	2.72879	0.729298
$15$	3.05905	0.789844
$16$	0.974567	0.243642
$17$	7.92938	1.92316	0.961579	−	0.274529i	$-0.0885219\pi$
$17$	7.92938	1.92316	0.961579	+	0.274529i	$0.0885219\pi$
$18$	−4.73947	−1.11710
$19$	−1.53458	−0.352057	−0.176029	−	0.984385i	$-0.556325\pi$
$19$	−1.53458	−0.352057	−0.176029	+	0.984385i	$0.556325\pi$
$20$	−1.44429	−0.322954
$21$	−11.1978	−2.44356
$22$	−0.745458	−0.158932
$23$	−9.02592	−1.88203	−0.941017	−	0.338358i	$-0.890129\pi$
$23$	−9.02592	−1.88203	−0.941017	+	0.338358i	$0.890129\pi$
$24$	7.85434	1.60326
$25$	1.00000	0.200000
$26$	−0.764924	−0.150014
$27$	10.2717	1.97678
$28$	5.28691	0.999131
$29$	3.19396	0.593104	0.296552	−	0.955017i	$-0.404163\pi$
$29$	3.19396	0.593104	0.296552	+	0.955017i	$0.404163\pi$
$30$	−2.28039	−0.416341
$31$	−7.54361	−1.35487	−0.677436	−	0.735582i	$-0.736909\pi$
$31$	−7.54361	−1.35487	−0.677436	+	0.735582i	$0.736909\pi$
$32$	−5.86165	−1.03620
$33$	3.05905	0.532512
$34$	−5.91102	−1.01373
$35$	−3.66055	−0.618746
$36$	−9.18251	−1.53042
$37$	6.07994	0.999535	0.499768	−	0.866159i	$-0.333419\pi$
$37$	6.07994	0.999535	0.499768	+	0.866159i	$0.333419\pi$
$38$	1.14397	0.185576
$39$	3.13893	0.502631
$40$	2.56757	0.405969
$41$	7.65235	1.19510	0.597548	−	0.801833i	$-0.296142\pi$
$41$	7.65235	1.19510	0.597548	+	0.801833i	$0.296142\pi$
$42$	8.34749	1.28805
$43$	8.29774	1.26539	0.632696	−	0.774400i	$-0.281948\pi$
$43$	8.29774	1.26539	0.632696	+	0.774400i	$0.281948\pi$
$44$	−1.44429	−0.217735
$45$	6.35779	0.947764
$46$	6.72844	0.992055
$47$	9.63324	1.40515	0.702576	−	0.711609i	$-0.252033\pi$
$47$	9.63324	1.40515	0.702576	+	0.711609i	$0.252033\pi$
$48$	2.98125	0.430307
$49$	6.39962	0.914232
$50$	−0.745458	−0.105424
$51$	24.2564	3.39657
$52$	−1.48201	−0.205518
$53$	−3.09231	−0.424762	−0.212381	−	0.977187i	$-0.568122\pi$
$53$	−3.09231	−0.424762	−0.212381	+	0.977187i	$0.568122\pi$
$54$	−7.65709	−1.04200
$55$	1.00000	0.134840
$56$	−9.39873	−1.25596
$57$	−4.69437	−0.621784
$58$	−2.38096	−0.312636
$59$	8.32297	1.08356	0.541779	−	0.840521i	$-0.317751\pi$
$59$	8.32297	1.08356	0.541779	+	0.840521i	$0.317751\pi$
$60$	−4.41817	−0.570383
$61$	−7.95140	−1.01807	−0.509036	−	0.860745i	$-0.669998\pi$
$61$	−7.95140	−1.01807	−0.509036	+	0.860745i	$0.669998\pi$
$62$	5.62344	0.714178
$63$	−23.2730	−2.93212
$64$	2.42048	0.302560
$65$	1.02611	0.127274
$66$	−2.28039	−0.280697
$67$	−2.85577	−0.348888	−0.174444	−	0.984667i	$-0.555813\pi$
$67$	−2.85577	−0.348888	−0.174444	+	0.984667i	$0.555813\pi$
$68$	−11.4523	−1.38880
$69$	−27.6108	−3.32394
$70$	2.72879	0.326152
$71$	−3.17918	−0.377300	−0.188650	−	0.982044i	$-0.560411\pi$
$71$	−3.17918	−0.377300	−0.188650	+	0.982044i	$0.560411\pi$
$72$	16.3241	1.92381
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−4.53234	−0.526873
$75$	3.05905	0.353229
$76$	2.21639	0.254237
$77$	−3.66055	−0.417158
$78$	−2.33994	−0.264946
$79$	16.2070	1.82343	0.911717	−	0.410820i	$-0.134757\pi$
$79$	16.2070	1.82343	0.911717	+	0.410820i	$0.134757\pi$
$80$	0.974567	0.108960
$81$	12.3481	1.37202
$82$	−5.70450	−0.629957
$83$	−1.77293	−0.194604	−0.0973021	−	0.995255i	$-0.531021\pi$
$83$	−1.77293	−0.194604	−0.0973021	+	0.995255i	$0.531021\pi$
$84$	16.1729	1.76461
$85$	7.92938	0.860062
$86$	−6.18561	−0.667012
$87$	9.77049	1.04751
$88$	2.56757	0.273704
$89$	0.725334	0.0768852	0.0384426	−	0.999261i	$-0.487760\pi$
$89$	0.725334	0.0768852	0.0384426	+	0.999261i	$0.487760\pi$
$90$	−4.73947	−0.499584
$91$	−3.75614	−0.393750
$92$	13.0361	1.35910
$93$	−23.0763	−2.39290
$94$	−7.18117	−0.740681
$95$	−1.53458	−0.157445
$96$	−17.9311	−1.83008
$97$	18.9489	1.92397	0.961983	−	0.273110i	$-0.0880524\pi$
$97$	18.9489	1.92397	0.961983	+	0.273110i	$0.0880524\pi$
$98$	−4.77065	−0.481908
$99$	6.35779	0.638982
$100$	−1.44429	−0.144429
$101$	2.13994	0.212932	0.106466	−	0.994316i	$-0.466046\pi$
$101$	2.13994	0.212932	0.106466	+	0.994316i	$0.466046\pi$
$102$	−18.0821	−1.79040
$103$	−5.76145	−0.567693	−0.283846	−	0.958870i	$-0.591611\pi$
$103$	−5.76145	−0.567693	−0.283846	+	0.958870i	$0.591611\pi$
$104$	2.63462	0.258346
$105$	−11.1978	−1.09279
$106$	2.30519	0.223900
$107$	−17.7209	−1.71314	−0.856571	−	0.516029i	$-0.827410\pi$
$107$	−17.7209	−1.71314	−0.856571	+	0.516029i	$0.827410\pi$
$108$	−14.8353	−1.42753
$109$	10.8333	1.03764	0.518821	−	0.854883i	$-0.326371\pi$
$109$	10.8333	1.03764	0.518821	+	0.854883i	$0.326371\pi$
$110$	−0.745458	−0.0710766
$111$	18.5988	1.76532
$112$	−3.56745	−0.337093
$113$	−12.3929	−1.16583	−0.582914	−	0.812534i	$-0.698087\pi$
$113$	−12.3929	−1.16583	−0.582914	+	0.812534i	$0.698087\pi$
$114$	3.49945	0.327754
$115$	−9.02592	−0.841672
$116$	−4.61302	−0.428308
$117$	6.52381	0.603127
$118$	−6.20442	−0.571164
$119$	−29.0259	−2.66080
$120$	7.85434	0.717000
$121$	1.00000	0.0909091
$122$	5.92744	0.536645
$123$	23.4089	2.11071
$124$	10.8952	0.978416
$125$	1.00000	0.0894427
$126$	17.3490	1.54558
$127$	16.4683	1.46133	0.730664	−	0.682737i	$-0.239210\pi$
$127$	16.4683	1.46133	0.730664	+	0.682737i	$0.239210\pi$
$128$	9.91893	0.876718
$129$	25.3832	2.23487
$130$	−0.764924	−0.0670883
$131$	−0.222835	−0.0194692	−0.00973461	−	0.999953i	$-0.503099\pi$
$131$	−0.222835	−0.0194692	−0.00973461	+	0.999953i	$0.503099\pi$
$132$	−4.41817	−0.384552
$133$	5.61742	0.487092
$134$	2.12886	0.183905
$135$	10.2717	0.884044
$136$	20.3593	1.74579
$137$	0.277250	0.0236871	0.0118435	−	0.999930i	$-0.496230\pi$
$137$	0.277250	0.0236871	0.0118435	+	0.999930i	$0.496230\pi$
$138$	20.5827	1.75211
$139$	7.00548	0.594197	0.297098	−	0.954847i	$-0.403981\pi$
$139$	7.00548	0.594197	0.297098	+	0.954847i	$0.403981\pi$
$140$	5.28691	0.446825
$141$	29.4686	2.48170
$142$	2.36995	0.198882
$143$	1.02611	0.0858079
$144$	6.19610	0.516341
$145$	3.19396	0.265244
$146$	−0.745458	−0.0616945
$147$	19.5768	1.61467
$148$	−8.78121	−0.721811
$149$	−0.618196	−0.0506446	−0.0253223	−	0.999679i	$-0.508061\pi$
$149$	−0.618196	−0.0506446	−0.0253223	+	0.999679i	$0.508061\pi$
$150$	−2.28039	−0.186193
$151$	−8.77873	−0.714403	−0.357201	−	0.934027i	$-0.616269\pi$
$151$	−8.77873	−0.714403	−0.357201	+	0.934027i	$0.616269\pi$
$152$	−3.94016	−0.319589
$153$	50.4134	4.07568
$154$	2.72879	0.219892
$155$	−7.54361	−0.605917
$156$	−4.53354	−0.362974
$157$	5.14023	0.410235	0.205118	−	0.978737i	$-0.434242\pi$
$157$	5.14023	0.410235	0.205118	+	0.978737i	$0.434242\pi$
$158$	−12.0817	−0.961165
$159$	−9.45954	−0.750190
$160$	−5.86165	−0.463404
$161$	33.0398	2.60390
$162$	−9.20502	−0.723215
$163$	−10.5410	−0.825637	−0.412818	−	0.910813i	$-0.635456\pi$
$163$	−10.5410	−0.825637	−0.412818	+	0.910813i	$0.635456\pi$
$164$	−11.0522	−0.863035
$165$	3.05905	0.238147
$166$	1.32164	0.102579
$167$	0.991594	0.0767319	0.0383659	−	0.999264i	$-0.487785\pi$
$167$	0.991594	0.0767319	0.0383659	+	0.999264i	$0.487785\pi$
$168$	−28.7512	−2.21820
$169$	−11.9471	−0.919007
$170$	−5.91102	−0.453354
$171$	−9.75656	−0.746103
$172$	−11.9844	−0.913799
$173$	−4.27659	−0.325143	−0.162572	−	0.986697i	$-0.551979\pi$
$173$	−4.27659	−0.325143	−0.162572	+	0.986697i	$0.551979\pi$
$174$	−7.28349	−0.552160
$175$	−3.66055	−0.276712
$176$	0.974567	0.0734608
$177$	25.4604	1.91372
$178$	−0.540706	−0.0405276
$179$	2.49969	0.186836	0.0934179	−	0.995627i	$-0.470221\pi$
$179$	2.49969	0.186836	0.0934179	+	0.995627i	$0.470221\pi$
$180$	−9.18251	−0.684424
$181$	3.30917	0.245969	0.122984	−	0.992409i	$-0.460753\pi$
$181$	3.30917	0.245969	0.122984	+	0.992409i	$0.460753\pi$
$182$	2.80004	0.207553
$183$	−24.3237	−1.79806
$184$	−23.1747	−1.70846
$185$	6.07994	0.447006
$186$	17.2024	1.26134
$187$	7.92938	0.579854
$188$	−13.9132	−1.01473
$189$	−37.5999	−2.73499
$190$	1.14397	0.0829920
$191$	23.7192	1.71626	0.858132	−	0.513429i	$-0.171625\pi$
$191$	23.7192	1.71626	0.858132	+	0.513429i	$0.171625\pi$
$192$	7.40436	0.534364
$193$	9.56799	0.688719	0.344359	−	0.938838i	$-0.388096\pi$
$193$	9.56799	0.688719	0.344359	+	0.938838i	$0.388096\pi$
$194$	−14.1256	−1.01416
$195$	3.13893	0.224784
$196$	−9.24293	−0.660209
$197$	13.1006	0.933380	0.466690	−	0.884421i	$-0.345446\pi$
$197$	13.1006	0.933380	0.466690	+	0.884421i	$0.345446\pi$
$198$	−4.73947	−0.336819
$199$	−12.6096	−0.893870	−0.446935	−	0.894566i	$-0.647485\pi$
$199$	−12.6096	−0.893870	−0.446935	+	0.894566i	$0.647485\pi$
$200$	2.56757	0.181555
$201$	−8.73595	−0.616187
$202$	−1.59524	−0.112241
$203$	−11.6917	−0.820593
$204$	−35.0333	−2.45282
$205$	7.65235	0.534463
$206$	4.29492	0.299241
$207$	−57.3849	−3.98853
$208$	1.00002	0.0693387
$209$	−1.53458	−0.106149
$210$	8.34749	0.576032
$211$	13.6724	0.941245	0.470622	−	0.882335i	$-0.344029\pi$
$211$	13.6724	0.941245	0.470622	+	0.882335i	$0.344029\pi$
$212$	4.46620	0.306740
$213$	−9.72529	−0.666366
$214$	13.2102	0.903029
$215$	8.29774	0.565901
$216$	26.3733	1.79447
$217$	27.6137	1.87454
$218$	−8.07577	−0.546960
$219$	3.05905	0.206712
$220$	−1.44429	−0.0973742
$221$	8.13644	0.547316
$222$	−13.8646	−0.930534
$223$	17.2192	1.15308	0.576541	−	0.817068i	$-0.304402\pi$
$223$	17.2192	1.15308	0.576541	+	0.817068i	$0.304402\pi$
$224$	21.4569	1.43365
$225$	6.35779	0.423853
$226$	9.23839	0.614529
$227$	19.9155	1.32184	0.660918	−	0.750458i	$-0.270167\pi$
$227$	19.9155	1.32184	0.660918	+	0.750458i	$0.270167\pi$
$228$	6.78004	0.449019
$229$	2.12024	0.140109	0.0700547	−	0.997543i	$-0.477683\pi$
$229$	2.12024	0.140109	0.0700547	+	0.997543i	$0.477683\pi$
$230$	6.72844	0.443660
$231$	−11.1978	−0.736762
$232$	8.20073	0.538405
$233$	19.4593	1.27482	0.637410	−	0.770525i	$-0.280006\pi$
$233$	19.4593	1.27482	0.637410	+	0.770525i	$0.280006\pi$
$234$	−4.86323	−0.317919
$235$	9.63324	0.628403
$236$	−12.0208	−0.782488
$237$	49.5781	3.22045
$238$	21.6376	1.40256
$239$	1.35119	0.0874013	0.0437006	−	0.999045i	$-0.486085\pi$
$239$	1.35119	0.0874013	0.0437006	+	0.999045i	$0.486085\pi$
$240$	2.98125	0.192439
$241$	19.4434	1.25246	0.626228	−	0.779640i	$-0.284598\pi$
$241$	19.4434	1.25246	0.626228	+	0.779640i	$0.284598\pi$
$242$	−0.745458	−0.0479198
$243$	6.95864	0.446397
$244$	11.4842	0.735198
$245$	6.39962	0.408857
$246$	−17.4504	−1.11259
$247$	−1.57466	−0.100193
$248$	−19.3688	−1.22992
$249$	−5.42348	−0.343699
$250$	−0.745458	−0.0471469
$251$	4.96317	0.313273	0.156636	−	0.987656i	$-0.449935\pi$
$251$	4.96317	0.313273	0.156636	+	0.987656i	$0.449935\pi$
$252$	33.6130	2.11742
$253$	−9.02592	−0.567455
$254$	−12.2765	−0.770293
$255$	24.2564	1.51899
$256$	−12.2351	−0.764694
$257$	6.95937	0.434113	0.217057	−	0.976159i	$-0.430354\pi$
$257$	6.95937	0.434113	0.217057	+	0.976159i	$0.430354\pi$
$258$	−18.9221	−1.17804
$259$	−22.2559	−1.38292
$260$	−1.48201	−0.0919102
$261$	20.3065	1.25694
$262$	0.166114	0.0102626
$263$	−21.5934	−1.33150	−0.665752	−	0.746173i	$-0.731889\pi$
$263$	−21.5934	−1.33150	−0.665752	+	0.746173i	$0.731889\pi$
$264$	7.85434	0.483401
$265$	−3.09231	−0.189959
$266$	−4.18755	−0.256755
$267$	2.21883	0.135790
$268$	4.12457	0.251948
$269$	−25.2542	−1.53977	−0.769887	−	0.638180i	$-0.779688\pi$
$269$	−25.2542	−1.53977	−0.769887	+	0.638180i	$0.779688\pi$
$270$	−7.65709	−0.465995
$271$	−0.0873812	−0.00530803	−0.00265402	−	0.999996i	$-0.500845\pi$
$271$	−0.0873812	−0.00530803	−0.00265402	+	0.999996i	$0.500845\pi$
$272$	7.72772	0.468562
$273$	−11.4902	−0.695420
$274$	−0.206678	−0.0124859
$275$	1.00000	0.0603023
$276$	39.8780	2.40037
$277$	−15.5840	−0.936350	−0.468175	−	0.883636i	$-0.655088\pi$
$277$	−15.5840	−0.936350	−0.468175	+	0.883636i	$0.655088\pi$
$278$	−5.22229	−0.313212
$279$	−47.9607	−2.87133
$280$	−9.39873	−0.561682
$281$	−23.2266	−1.38558	−0.692791	−	0.721138i	$-0.743619\pi$
$281$	−23.2266	−1.38558	−0.692791	+	0.721138i	$0.743619\pi$
$282$	−21.9676	−1.30815
$283$	−2.22884	−0.132491	−0.0662453	−	0.997803i	$-0.521102\pi$
$283$	−2.22884	−0.132491	−0.0662453	+	0.997803i	$0.521102\pi$
$284$	4.59167	0.272466
$285$	−4.69437	−0.278070
$286$	−0.764924	−0.0452309
$287$	−28.0118	−1.65348
$288$	−37.2671	−2.19599
$289$	45.8751	2.69854
$290$	−2.38096	−0.139815
$291$	57.9655	3.39800
$292$	−1.44429	−0.0845208
$293$	−0.867891	−0.0507027	−0.0253514	−	0.999679i	$-0.508070\pi$
$293$	−0.867891	−0.0507027	−0.0253514	+	0.999679i	$0.508070\pi$
$294$	−14.5937	−0.851119
$295$	8.32297	0.484582
$296$	15.6107	0.907353
$297$	10.2717	0.596022
$298$	0.460839	0.0266957
$299$	−9.26162	−0.535613
$300$	−4.41817	−0.255083
$301$	−30.3743	−1.75074
$302$	6.54417	0.376575
$303$	6.54620	0.376069
$304$	−1.49555	−0.0857759
$305$	−7.95140	−0.455296
$306$	−37.5810	−2.14836
$307$	21.7728	1.24264	0.621319	−	0.783558i	$-0.286597\pi$
$307$	21.7728	1.24264	0.621319	+	0.783558i	$0.286597\pi$
$308$	5.28691	0.301249
$309$	−17.6246	−1.00263
$310$	5.62344	0.319390
$311$	−23.3048	−1.32149	−0.660747	−	0.750609i	$-0.729760\pi$
$311$	−23.3048	−1.32149	−0.660747	+	0.750609i	$0.729760\pi$
$312$	8.05944	0.456276
$313$	21.1142	1.19344	0.596722	−	0.802448i	$-0.296469\pi$
$313$	21.1142	1.19344	0.596722	+	0.802448i	$0.296469\pi$
$314$	−3.83183	−0.216242
$315$	−23.2730	−1.31129
$316$	−23.4077	−1.31679
$317$	−0.318916	−0.0179121	−0.00895605	−	0.999960i	$-0.502851\pi$
$317$	−0.318916	−0.0179121	−0.00895605	+	0.999960i	$0.502851\pi$
$318$	7.05169	0.395439
$319$	3.19396	0.178827
$320$	2.42048	0.135309
$321$	−54.2091	−3.02566
$322$	−24.6298	−1.37257
$323$	−12.1683	−0.677062
$324$	−17.8343	−0.990797
$325$	1.02611	0.0569185
$326$	7.85789	0.435208
$327$	33.1396	1.83263
$328$	19.6480	1.08488
$329$	−35.2629	−1.94411
$330$	−2.28039	−0.125532
$331$	−27.0626	−1.48749	−0.743747	−	0.668462i	$-0.766953\pi$
$331$	−27.0626	−1.48749	−0.743747	+	0.668462i	$0.766953\pi$
$332$	2.56063	0.140533
$333$	38.6550	2.11828
$334$	−0.739192	−0.0404468
$335$	−2.85577	−0.156028
$336$	−10.9130	−0.595354
$337$	11.4837	0.625555	0.312778	−	0.949826i	$-0.398741\pi$
$337$	11.4837	0.625555	0.312778	+	0.949826i	$0.398741\pi$
$338$	8.90605	0.484425
$339$	−37.9106	−2.05902
$340$	−11.4523	−0.621091
$341$	−7.54361	−0.408509
$342$	7.27310	0.393284
$343$	2.19770	0.118665
$344$	21.3051	1.14869
$345$	−27.6108	−1.48651
$346$	3.18802	0.171389
$347$	−13.5714	−0.728550	−0.364275	−	0.931291i	$-0.618683\pi$
$347$	−13.5714	−0.728550	−0.364275	+	0.931291i	$0.618683\pi$
$348$	−14.1114	−0.756453
$349$	18.2877	0.978917	0.489459	−	0.872026i	$-0.337194\pi$
$349$	18.2877	0.978917	0.489459	+	0.872026i	$0.337194\pi$
$350$	2.72879	0.145860
$351$	10.5399	0.562577
$352$	−5.86165	−0.312427
$353$	−25.7020	−1.36798	−0.683989	−	0.729492i	$-0.739757\pi$
$353$	−25.7020	−1.36798	−0.683989	+	0.729492i	$0.739757\pi$
$354$	−18.9797	−1.00876
$355$	−3.17918	−0.168734
$356$	−1.04759	−0.0555224
$357$	−88.7917	−4.69936
$358$	−1.86342	−0.0984846
$359$	−5.27668	−0.278493	−0.139246	−	0.990258i	$-0.544468\pi$
$359$	−5.27668	−0.278493	−0.139246	+	0.990258i	$0.544468\pi$
$360$	16.3241	0.860356
$361$	−16.6451	−0.876056
$362$	−2.46685	−0.129655
$363$	3.05905	0.160559
$364$	5.42496	0.284345
$365$	1.00000	0.0523424
$366$	18.1323	0.947792
$367$	−21.0497	−1.09879	−0.549393	−	0.835564i	$-0.685141\pi$
$367$	−21.0497	−1.09879	−0.549393	+	0.835564i	$0.685141\pi$
$368$	−8.79637	−0.458542
$369$	48.6521	2.53273
$370$	−4.53234	−0.235625
$371$	11.3196	0.587682
$372$	33.3289	1.72802
$373$	27.2340	1.41012	0.705062	−	0.709146i	$-0.250919\pi$
$373$	27.2340	1.41012	0.705062	+	0.709146i	$0.250919\pi$
$374$	−5.91102	−0.305652
$375$	3.05905	0.157969
$376$	24.7341	1.27556
$377$	3.27737	0.168793
$378$	28.0291	1.44166
$379$	−3.29864	−0.169440	−0.0847200	−	0.996405i	$-0.527000\pi$
$379$	−3.29864	−0.169440	−0.0847200	+	0.996405i	$0.527000\pi$
$380$	2.21639	0.113698
$381$	50.3775	2.58092
$382$	−17.6817	−0.904674
$383$	−5.14155	−0.262721	−0.131361	−	0.991335i	$-0.541935\pi$
$383$	−5.14155	−0.262721	−0.131361	+	0.991335i	$0.541935\pi$
$384$	30.3425	1.54841
$385$	−3.66055	−0.186559
$386$	−7.13253	−0.363036
$387$	52.7553	2.68170
$388$	−27.3677	−1.38938
$389$	−5.42794	−0.275207	−0.137604	−	0.990487i	$-0.543940\pi$
$389$	−5.42794	−0.275207	−0.137604	+	0.990487i	$0.543940\pi$
$390$	−2.33994	−0.118488
$391$	−71.5700	−3.61945
$392$	16.4315	0.829917
$393$	−0.681665	−0.0343854
$394$	−9.76595	−0.492002
$395$	16.2070	0.815464
$396$	−9.18251	−0.461439
$397$	−32.9788	−1.65516	−0.827580	−	0.561348i	$-0.810283\pi$
$397$	−32.9788	−1.65516	−0.827580	+	0.561348i	$0.810283\pi$
$398$	9.39992	0.471175
$399$	17.1840	0.860274
$400$	0.974567	0.0487284
$401$	16.3960	0.818775	0.409388	−	0.912361i	$-0.365742\pi$
$401$	16.3960	0.818775	0.409388	+	0.912361i	$0.365742\pi$
$402$	6.51228	0.324803
$403$	−7.74060	−0.385587
$404$	−3.09071	−0.153768
$405$	12.3481	0.613584
$406$	8.71563	0.432550
$407$	6.07994	0.301371
$408$	62.2801	3.08332
$409$	−28.6106	−1.41470	−0.707351	−	0.706863i	$-0.750110\pi$
$409$	−28.6106	−1.41470	−0.707351	+	0.706863i	$0.750110\pi$
$410$	−5.70450	−0.281725
$411$	0.848122	0.0418348
$412$	8.32123	0.409957
$413$	−30.4667	−1.49917
$414$	42.7780	2.10243
$415$	−1.77293	−0.0870297
$416$	−6.01471	−0.294896
$417$	21.4301	1.04944
$418$	1.14397	0.0559532
$419$	−30.1719	−1.47400	−0.736998	−	0.675895i	$-0.763757\pi$
$419$	−30.1719	−1.47400	−0.736998	+	0.675895i	$0.763757\pi$
$420$	16.1729	0.789157
$421$	−15.5634	−0.758512	−0.379256	−	0.925292i	$-0.623820\pi$
$421$	−15.5634	−0.758512	−0.379256	+	0.925292i	$0.623820\pi$
$422$	−10.1922	−0.496147
$423$	61.2461	2.97789
$424$	−7.93974	−0.385588
$425$	7.92938	0.384632
$426$	7.24979	0.351254
$427$	29.1065	1.40856
$428$	25.5941	1.23714
$429$	3.13893	0.151549
$430$	−6.18561	−0.298297
$431$	−30.5031	−1.46928	−0.734641	−	0.678456i	$-0.762649\pi$
$431$	−30.5031	−1.46928	−0.734641	+	0.678456i	$0.762649\pi$
$432$	10.0104	0.481627
$433$	−28.0526	−1.34812	−0.674061	−	0.738676i	$-0.735451\pi$
$433$	−28.0526	−1.34812	−0.674061	+	0.738676i	$0.735451\pi$
$434$	−20.5849	−0.988106
$435$	9.77049	0.468459
$436$	−15.6465	−0.749330
$437$	13.8510	0.662584
$438$	−2.28039	−0.108961
$439$	−6.29430	−0.300411	−0.150205	−	0.988655i	$-0.547993\pi$
$439$	−6.29430	−0.300411	−0.150205	+	0.988655i	$0.547993\pi$
$440$	2.56757	0.122404
$441$	40.6875	1.93750
$442$	−6.06537	−0.288500
$443$	−26.4873	−1.25845	−0.629225	−	0.777223i	$-0.716627\pi$
$443$	−26.4873	−1.25845	−0.629225	+	0.777223i	$0.716627\pi$
$444$	−26.8622	−1.27482
$445$	0.725334	0.0343841
$446$	−12.8362	−0.607810
$447$	−1.89109	−0.0894457
$448$	−8.86027	−0.418609
$449$	29.1325	1.37485	0.687423	−	0.726257i	$-0.258742\pi$
$449$	29.1325	1.37485	0.687423	+	0.726257i	$0.258742\pi$
$450$	−4.73947	−0.223421
$451$	7.65235	0.360335
$452$	17.8990	0.841898
$453$	−26.8546	−1.26174
$454$	−14.8461	−0.696764
$455$	−3.75614	−0.176090
$456$	−12.0531	−0.564440
$457$	21.4931	1.00541	0.502703	−	0.864459i	$-0.332339\pi$
$457$	21.4931	1.00541	0.502703	+	0.864459i	$0.332339\pi$
$458$	−1.58055	−0.0738542
$459$	81.4479	3.80166
$460$	13.0361	0.607810
$461$	−7.98018	−0.371674	−0.185837	−	0.982581i	$-0.559500\pi$
$461$	−7.98018	−0.371674	−0.185837	+	0.982581i	$0.559500\pi$
$462$	8.34749	0.388360
$463$	16.0042	0.743779	0.371889	−	0.928277i	$-0.378710\pi$
$463$	16.0042	0.743779	0.371889	+	0.928277i	$0.378710\pi$
$464$	3.11273	0.144505
$465$	−23.0763	−1.07014
$466$	−14.5061	−0.671980
$467$	−32.8843	−1.52170	−0.760851	−	0.648926i	$-0.775218\pi$
$467$	−32.8843	−1.52170	−0.760851	+	0.648926i	$0.775218\pi$
$468$	−9.42230	−0.435546
$469$	10.4537	0.482707
$470$	−7.18117	−0.331243
$471$	15.7242	0.724534
$472$	21.3699	0.983627
$473$	8.29774	0.381530
$474$	−36.9584	−1.69756
$475$	−1.53458	−0.0704115
$476$	41.9219	1.92149
$477$	−19.6603	−0.900182
$478$	−1.00726	−0.0460708
$479$	26.6751	1.21882	0.609408	−	0.792857i	$-0.291407\pi$
$479$	26.6751	1.21882	0.609408	+	0.792857i	$0.291407\pi$
$480$	−17.9311	−0.818438
$481$	6.23870	0.284460
$482$	−14.4942	−0.660193
$483$	101.071	4.59887
$484$	−1.44429	−0.0656497
$485$	18.9489	0.860423
$486$	−5.18737	−0.235304
$487$	−27.0336	−1.22501	−0.612504	−	0.790467i	$-0.709838\pi$
$487$	−27.0336	−1.22501	−0.612504	+	0.790467i	$0.709838\pi$
$488$	−20.4158	−0.924181
$489$	−32.2455	−1.45819
$490$	−4.77065	−0.215516
$491$	32.6940	1.47546	0.737731	−	0.675095i	$-0.235898\pi$
$491$	32.6940	1.47546	0.737731	+	0.675095i	$0.235898\pi$
$492$	−33.8094	−1.52424
$493$	25.3261	1.14063
$494$	1.17384	0.0528135
$495$	6.35779	0.285762
$496$	−7.35175	−0.330103
$497$	11.6376	0.522016
$498$	4.04298	0.181170
$499$	6.50850	0.291361	0.145680	−	0.989332i	$-0.453463\pi$
$499$	6.50850	0.291361	0.145680	+	0.989332i	$0.453463\pi$
$500$	−1.44429	−0.0645907
$501$	3.03334	0.135520
$502$	−3.69984	−0.165132
$503$	34.5960	1.54256	0.771280	−	0.636495i	$-0.219617\pi$
$503$	34.5960	1.54256	0.771280	+	0.636495i	$0.219617\pi$
$504$	−59.7552	−2.66171
$505$	2.13994	0.0952263
$506$	6.72844	0.299116
$507$	−36.5468	−1.62310
$508$	−23.7851	−1.05529
$509$	24.2189	1.07348	0.536741	−	0.843747i	$-0.319655\pi$
$509$	24.2189	1.07348	0.536741	+	0.843747i	$0.319655\pi$
$510$	−18.0821	−0.800689
$511$	−3.66055	−0.161933
$512$	−10.7171	−0.473634
$513$	−15.7627	−0.695941
$514$	−5.18791	−0.228829
$515$	−5.76145	−0.253880
$516$	−36.6608	−1.61390
$517$	9.63324	0.423669
$518$	16.5908	0.728960
$519$	−13.0823	−0.574250
$520$	2.63462	0.115536
$521$	24.2739	1.06346	0.531730	−	0.846914i	$-0.321542\pi$
$521$	24.2739	1.06346	0.531730	+	0.846914i	$0.321542\pi$
$522$	−15.1377	−0.662558
$523$	−35.7848	−1.56476	−0.782380	−	0.622802i	$-0.785994\pi$
$523$	−35.7848	−1.56476	−0.782380	+	0.622802i	$0.785994\pi$
$524$	0.321840	0.0140596
$525$	−11.1978	−0.488712
$526$	16.0969	0.701860
$527$	−59.8161	−2.60563
$528$	2.98125	0.129742
$529$	58.4673	2.54206
$530$	2.30519	0.100131
$531$	52.9157	2.29635
$532$	−8.11319	−0.351752
$533$	7.85218	0.340116
$534$	−1.65405	−0.0715776
$535$	−17.7209	−0.766141
$536$	−7.33241	−0.316712
$537$	7.64669	0.329979
$538$	18.8259	0.811643
$539$	6.39962	0.275651
$540$	−14.8353	−0.638409
$541$	−4.42411	−0.190207	−0.0951037	−	0.995467i	$-0.530318\pi$
$541$	−4.42411	−0.190207	−0.0951037	+	0.995467i	$0.530318\pi$
$542$	0.0651390	0.00279796
$543$	10.1229	0.434416
$544$	−46.4792	−1.99278
$545$	10.8333	0.464048
$546$	8.56547	0.366568
$547$	−8.59061	−0.367308	−0.183654	−	0.982991i	$-0.558793\pi$
$547$	−8.59061	−0.367308	−0.183654	+	0.982991i	$0.558793\pi$
$548$	−0.400430	−0.0171055
$549$	−50.5534	−2.15757
$550$	−0.745458	−0.0317864
$551$	−4.90140	−0.208807
$552$	−70.8927	−3.01739
$553$	−59.3266	−2.52283
$554$	11.6172	0.493567
$555$	18.5988	0.789477
$556$	−10.1180	−0.429097
$557$	−18.6859	−0.791745	−0.395873	−	0.918305i	$-0.629558\pi$
$557$	−18.6859	−0.791745	−0.395873	+	0.918305i	$0.629558\pi$
$558$	35.7527	1.51353
$559$	8.51442	0.360121
$560$	−3.56745	−0.150752
$561$	24.2564	1.02411
$562$	17.3144	0.730366
$563$	−8.39664	−0.353876	−0.176938	−	0.984222i	$-0.556619\pi$
$563$	−8.39664	−0.353876	−0.176938	+	0.984222i	$0.556619\pi$
$564$	−42.5612	−1.79215
$565$	−12.3929	−0.521374
$566$	1.66150	0.0698382
$567$	−45.2010	−1.89826
$568$	−8.16279	−0.342503
$569$	32.4465	1.36023	0.680113	−	0.733107i	$-0.261931\pi$
$569$	32.4465	1.36023	0.680113	+	0.733107i	$0.261931\pi$
$570$	3.49945	0.146576
$571$	10.5141	0.440000	0.220000	−	0.975500i	$-0.429394\pi$
$571$	10.5141	0.440000	0.220000	+	0.975500i	$0.429394\pi$
$572$	−1.48201	−0.0619659
$573$	72.5584	3.03117
$574$	20.8816	0.871582
$575$	−9.02592	−0.376407
$576$	15.3889	0.641204
$577$	−11.6334	−0.484304	−0.242152	−	0.970238i	$-0.577853\pi$
$577$	−11.6334	−0.484304	−0.242152	+	0.970238i	$0.577853\pi$
$578$	−34.1980	−1.42245
$579$	29.2690	1.21638
$580$	−4.61302	−0.191545
$581$	6.48990	0.269246
$582$	−43.2109	−1.79115
$583$	−3.09231	−0.128070
$584$	2.56757	0.106247
$585$	6.52381	0.269727
$586$	0.646976	0.0267263
$587$	0.883663	0.0364727	0.0182363	−	0.999834i	$-0.494195\pi$
$587$	0.883663	0.0364727	0.0182363	+	0.999834i	$0.494195\pi$
$588$	−28.2746	−1.16602
$589$	11.5763	0.476993
$590$	−6.20442	−0.255432
$591$	40.0754	1.64848
$592$	5.92531	0.243529
$593$	2.67385	0.109802	0.0549008	−	0.998492i	$-0.482516\pi$
$593$	2.67385	0.109802	0.0549008	+	0.998492i	$0.482516\pi$
$594$	−7.65709	−0.314174
$595$	−29.0259	−1.18995
$596$	0.892856	0.0365728
$597$	−38.5734	−1.57870
$598$	6.90414	0.282331
$599$	−4.46895	−0.182596	−0.0912982	−	0.995824i	$-0.529102\pi$
$599$	−4.46895	−0.182596	−0.0912982	+	0.995824i	$0.529102\pi$
$600$	7.85434	0.320652
$601$	−25.3077	−1.03232	−0.516162	−	0.856491i	$-0.672640\pi$
$601$	−25.3077	−1.03232	−0.516162	+	0.856491i	$0.672640\pi$
$602$	22.6427	0.922849
$603$	−18.1564	−0.739386
$604$	12.6791	0.515903
$605$	1.00000	0.0406558
$606$	−4.87992	−0.198233
$607$	−26.9252	−1.09286	−0.546431	−	0.837504i	$-0.684014\pi$
$607$	−26.9252	−1.09286	−0.546431	+	0.837504i	$0.684014\pi$
$608$	8.99518	0.364803
$609$	−35.7654	−1.44929
$610$	5.92744	0.239995
$611$	9.88479	0.399896
$612$	−72.8117	−2.94324
$613$	5.84970	0.236267	0.118133	−	0.992998i	$-0.462309\pi$
$613$	5.84970	0.236267	0.118133	+	0.992998i	$0.462309\pi$
$614$	−16.2307	−0.655017
$615$	23.4089	0.943939
$616$	−9.39873	−0.378686
$617$	25.6742	1.03360	0.516802	−	0.856105i	$-0.327122\pi$
$617$	25.6742	1.03360	0.516802	+	0.856105i	$0.327122\pi$
$618$	13.1384	0.528503
$619$	28.5604	1.14794	0.573969	−	0.818877i	$-0.305403\pi$
$619$	28.5604	1.14794	0.573969	+	0.818877i	$0.305403\pi$
$620$	10.8952	0.437561
$621$	−92.7112	−3.72037
$622$	17.3727	0.696583
$623$	−2.65512	−0.106375
$624$	3.05910	0.122462
$625$	1.00000	0.0400000
$626$	−15.7397	−0.629086
$627$	−4.69437	−0.187475
$628$	−7.42400	−0.296250
$629$	48.2101	1.92226
$630$	17.3490	0.691203
$631$	−13.7548	−0.547570	−0.273785	−	0.961791i	$-0.588276\pi$
$631$	−13.7548	−0.547570	−0.273785	+	0.961791i	$0.588276\pi$
$632$	41.6128	1.65527
$633$	41.8245	1.66237
$634$	0.237738	0.00944179
$635$	16.4683	0.653526
$636$	13.6623	0.541747
$637$	6.56674	0.260184
$638$	−2.38096	−0.0942632
$639$	−20.2126	−0.799598
$640$	9.91893	0.392080
$641$	−37.3178	−1.47396	−0.736982	−	0.675912i	$-0.763750\pi$
$641$	−37.3178	−1.47396	−0.736982	+	0.675912i	$0.763750\pi$
$642$	40.4106	1.59488
$643$	−30.2238	−1.19191	−0.595956	−	0.803017i	$-0.703227\pi$
$643$	−30.2238	−1.19191	−0.595956	+	0.803017i	$0.703227\pi$
$644$	−47.7192	−1.88040
$645$	25.3832	0.999462
$646$	9.07095	0.356892
$647$	0.269979	0.0106140	0.00530699	−	0.999986i	$-0.498311\pi$
$647$	0.269979	0.0106140	0.00530699	+	0.999986i	$0.498311\pi$
$648$	31.7048	1.24548
$649$	8.32297	0.326705
$650$	−0.764924	−0.0300028
$651$	84.4719	3.31071
$652$	15.2243	0.596231
$653$	−36.8015	−1.44016	−0.720078	−	0.693893i	$-0.755894\pi$
$653$	−36.8015	−1.44016	−0.720078	+	0.693893i	$0.755894\pi$
$654$	−24.7042	−0.966010
$655$	−0.222835	−0.00870690
$656$	7.45773	0.291175
$657$	6.35779	0.248041
$658$	26.2870	1.02478
$659$	−11.7704	−0.458510	−0.229255	−	0.973366i	$-0.573629\pi$
$659$	−11.7704	−0.458510	−0.229255	+	0.973366i	$0.573629\pi$
$660$	−4.41817	−0.171977
$661$	−26.0057	−1.01151	−0.505753	−	0.862679i	$-0.668785\pi$
$661$	−26.0057	−1.01151	−0.505753	+	0.862679i	$0.668785\pi$
$662$	20.1740	0.784085
$663$	24.8898	0.966640
$664$	−4.55213	−0.176657
$665$	5.61742	0.217834
$666$	−28.8157	−1.11658
$667$	−28.8284	−1.11624
$668$	−1.43215	−0.0554117
$669$	52.6743	2.03651
$670$	2.12886	0.0822449
$671$	−7.95140	−0.306961
$672$	65.6376	2.53203
$673$	−44.5215	−1.71618	−0.858088	−	0.513503i	$-0.828348\pi$
$673$	−44.5215	−1.71618	−0.858088	+	0.513503i	$0.828348\pi$
$674$	−8.56059	−0.329742
$675$	10.2717	0.395356
$676$	17.2551	0.663658
$677$	−38.7167	−1.48801	−0.744003	−	0.668177i	$-0.767075\pi$
$677$	−38.7167	−1.48801	−0.744003	+	0.668177i	$0.767075\pi$
$678$	28.2607	1.08535
$679$	−69.3632	−2.66192
$680$	20.3593	0.780743
$681$	60.9224	2.33455
$682$	5.62344	0.215333
$683$	32.4364	1.24114	0.620572	−	0.784149i	$-0.286900\pi$
$683$	32.4364	1.24114	0.620572	+	0.784149i	$0.286900\pi$
$684$	14.0913	0.538795
$685$	0.277250	0.0105932
$686$	−1.63830	−0.0625504
$687$	6.48592	0.247453
$688$	8.08670	0.308303
$689$	−3.17306	−0.120884
$690$	20.5827	0.783568
$691$	9.99291	0.380148	0.190074	−	0.981770i	$-0.439127\pi$
$691$	9.99291	0.380148	0.190074	+	0.981770i	$0.439127\pi$
$692$	6.17665	0.234801
$693$	−23.2730	−0.884069
$694$	10.1169	0.384032
$695$	7.00548	0.265733
$696$	25.0865	0.950900
$697$	60.6784	2.29836
$698$	−13.6327	−0.516005
$699$	59.5269	2.25151
$700$	5.28691	0.199826
$701$	−23.9841	−0.905867	−0.452934	−	0.891544i	$-0.649623\pi$
$701$	−23.9841	−0.905867	−0.452934	+	0.891544i	$0.649623\pi$
$702$	−7.85704	−0.296545
$703$	−9.33017	−0.351894
$704$	2.42048	0.0912251
$705$	29.4686	1.10985
$706$	19.1597	0.721087
$707$	−7.83337	−0.294604
$708$	−36.7723	−1.38199
$709$	17.0050	0.638637	0.319319	−	0.947647i	$-0.396546\pi$
$709$	17.0050	0.638637	0.319319	+	0.947647i	$0.396546\pi$
$710$	2.36995	0.0889426
$711$	103.041	3.86434
$712$	1.86235	0.0697945
$713$	68.0880	2.54992
$714$	66.1905	2.47712
$715$	1.02611	0.0383745
$716$	−3.61029	−0.134923
$717$	4.13336	0.154363
$718$	3.93354	0.146799
$719$	2.46818	0.0920478	0.0460239	−	0.998940i	$-0.485345\pi$
$719$	2.46818	0.0920478	0.0460239	+	0.998940i	$0.485345\pi$
$720$	6.19610	0.230915
$721$	21.0901	0.785436
$722$	12.4082	0.461785
$723$	59.4782	2.21202
$724$	−4.77941	−0.177625
$725$	3.19396	0.118621
$726$	−2.28039	−0.0846333
$727$	−18.8451	−0.698924	−0.349462	−	0.936950i	$-0.613636\pi$
$727$	−18.8451	−0.698924	−0.349462	+	0.936950i	$0.613636\pi$
$728$	−9.64417	−0.357437
$729$	−15.7576	−0.583615
$730$	−0.745458	−0.0275906
$731$	65.7959	2.43355
$732$	35.1306	1.29846
$733$	8.26369	0.305226	0.152613	−	0.988286i	$-0.451231\pi$
$733$	8.26369	0.305226	0.152613	+	0.988286i	$0.451231\pi$
$734$	15.6917	0.579191
$735$	19.5768	0.722100
$736$	52.9068	1.95017
$737$	−2.85577	−0.105194
$738$	−36.2681	−1.33505
$739$	−38.7957	−1.42712	−0.713562	−	0.700592i	$-0.752919\pi$
$739$	−38.7957	−1.42712	−0.713562	+	0.700592i	$0.752919\pi$
$740$	−8.78121	−0.322804
$741$	−4.81695	−0.176955
$742$	−8.43826	−0.309778
$743$	−12.6764	−0.465052	−0.232526	−	0.972590i	$-0.574699\pi$
$743$	−12.6764	−0.465052	−0.232526	+	0.972590i	$0.574699\pi$
$744$	−59.2501	−2.17221
$745$	−0.618196	−0.0226490
$746$	−20.3018	−0.743302
$747$	−11.2719	−0.412418
$748$	−11.4523	−0.418739
$749$	64.8682	2.37023
$750$	−2.28039	−0.0832682
$751$	−29.8876	−1.09061	−0.545307	−	0.838236i	$-0.683587\pi$
$751$	−29.8876	−1.09061	−0.545307	+	0.838236i	$0.683587\pi$
$752$	9.38824	0.342354
$753$	15.1826	0.553285
$754$	−2.44314	−0.0889738
$755$	−8.77873	−0.319491
$756$	54.3053	1.97506
$757$	−19.8595	−0.721807	−0.360903	−	0.932603i	$-0.617532\pi$
$757$	−19.8595	−0.721807	−0.360903	+	0.932603i	$0.617532\pi$
$758$	2.45900	0.0893149
$759$	−27.6108	−1.00221
$760$	−3.94016	−0.142924
$761$	−22.5344	−0.816870	−0.408435	−	0.912787i	$-0.633925\pi$
$761$	−22.5344	−0.816870	−0.408435	+	0.912787i	$0.633925\pi$
$762$	−37.5543	−1.36045
$763$	−39.6558	−1.43564
$764$	−34.2575	−1.23939
$765$	50.4134	1.82270
$766$	3.83281	0.138485
$767$	8.54031	0.308373
$768$	−37.4278	−1.35056
$769$	−33.6335	−1.21286	−0.606428	−	0.795139i	$-0.707398\pi$
$769$	−33.6335	−1.21286	−0.606428	+	0.795139i	$0.707398\pi$
$770$	2.72879	0.0983386
$771$	21.2891	0.766707
$772$	−13.8190	−0.497356
$773$	−3.81775	−0.137315	−0.0686575	−	0.997640i	$-0.521872\pi$
$773$	−3.81775	−0.137315	−0.0686575	+	0.997640i	$0.521872\pi$
$774$	−39.3268	−1.41357
$775$	−7.54361	−0.270974
$776$	48.6526	1.74653
$777$	−68.0820	−2.44243
$778$	4.04630	0.145067
$779$	−11.7432	−0.420743
$780$	−4.53354	−0.162327
$781$	−3.17918	−0.113760
$782$	53.3524	1.90788
$783$	32.8073	1.17244
$784$	6.23686	0.222745
$785$	5.14023	0.183463
$786$	0.508152	0.0181252
$787$	−16.4419	−0.586089	−0.293045	−	0.956099i	$-0.594668\pi$
$787$	−16.4419	−0.586089	−0.293045	+	0.956099i	$0.594668\pi$
$788$	−18.9211	−0.674037
$789$	−66.0552	−2.35163
$790$	−12.0817	−0.429846
$791$	45.3649	1.61299
$792$	16.3241	0.580052
$793$	−8.15904	−0.289736
$794$	24.5843	0.872465
$795$	−9.45954	−0.335495
$796$	18.2119	0.645505
$797$	38.6822	1.37020	0.685098	−	0.728451i	$-0.259760\pi$
$797$	38.6822	1.37020	0.685098	+	0.728451i	$0.259760\pi$
$798$	−12.8099	−0.453466
$799$	76.3856	2.70233
$800$	−5.86165	−0.207241
$801$	4.61152	0.162940
$802$	−12.2225	−0.431591
$803$	1.00000	0.0352892
$804$	12.6173	0.444977
$805$	33.0398	1.16450
$806$	5.77029	0.203250
$807$	−77.2538	−2.71946
$808$	5.49447	0.193295
$809$	28.5008	1.00203	0.501017	−	0.865438i	$-0.332960\pi$
$809$	28.5008	1.00203	0.501017	+	0.865438i	$0.332960\pi$
$810$	−9.20502	−0.323432
$811$	−13.3390	−0.468396	−0.234198	−	0.972189i	$-0.575246\pi$
$811$	−13.3390	−0.468396	−0.234198	+	0.972189i	$0.575246\pi$
$812$	16.8862	0.592588
$813$	−0.267304	−0.00937475
$814$	−4.53234	−0.158858
$815$	−10.5410	−0.369236
$816$	23.6395	0.827547
$817$	−12.7336	−0.445491
$818$	21.3280	0.745715
$819$	−23.8807	−0.834461
$820$	−11.0522	−0.385961
$821$	22.4293	0.782787	0.391393	−	0.920223i	$-0.371993\pi$
$821$	22.4293	0.782787	0.391393	+	0.920223i	$0.371993\pi$
$822$	−0.632239	−0.0220519
$823$	−7.55118	−0.263218	−0.131609	−	0.991302i	$-0.542014\pi$
$823$	−7.55118	−0.263218	−0.131609	+	0.991302i	$0.542014\pi$
$824$	−14.7930	−0.515337
$825$	3.05905	0.106502
$826$	22.7116	0.790238
$827$	−0.858475	−0.0298521	−0.0149260	−	0.999889i	$-0.504751\pi$
$827$	−0.858475	−0.0298521	−0.0149260	+	0.999889i	$0.504751\pi$
$828$	82.8807	2.88030
$829$	46.3599	1.61015	0.805073	−	0.593175i	$-0.202126\pi$
$829$	46.3599	1.61015	0.805073	+	0.593175i	$0.202126\pi$
$830$	1.32164	0.0458749
$831$	−47.6721	−1.65373
$832$	2.48368	0.0861062
$833$	50.7451	1.75821
$834$	−15.9752	−0.553178
$835$	0.991594	0.0343155
$836$	2.21639	0.0766553
$837$	−77.4854	−2.67829
$838$	22.4919	0.776970
$839$	1.05196	0.0363178	0.0181589	−	0.999835i	$-0.494220\pi$
$839$	1.05196	0.0363178	0.0181589	+	0.999835i	$0.494220\pi$
$840$	−28.7512	−0.992011
$841$	−18.7986	−0.648228
$842$	11.6018	0.399825
$843$	−71.0513	−2.44714
$844$	−19.7469	−0.679717
$845$	−11.9471	−0.410992
$846$	−45.6564	−1.56970
$847$	−3.66055	−0.125778
$848$	−3.01367	−0.103490
$849$	−6.81813	−0.233998
$850$	−5.91102	−0.202746
$851$	−54.8770	−1.88116
$852$	14.0462	0.481214
$853$	−23.3445	−0.799300	−0.399650	−	0.916668i	$-0.630868\pi$
$853$	−23.3445	−0.799300	−0.399650	+	0.916668i	$0.630868\pi$
$854$	−21.6977	−0.742479
$855$	−9.75656	−0.333667
$856$	−45.4997	−1.55515
$857$	−8.85205	−0.302380	−0.151190	−	0.988505i	$-0.548311\pi$
$857$	−8.85205	−0.302380	−0.151190	+	0.988505i	$0.548311\pi$
$858$	−2.33994	−0.0798843
$859$	−15.5623	−0.530977	−0.265489	−	0.964114i	$-0.585533\pi$
$859$	−15.5623	−0.530977	−0.265489	+	0.964114i	$0.585533\pi$
$860$	−11.9844	−0.408663
$861$	−85.6896	−2.92029
$862$	22.7388	0.774485
$863$	28.5694	0.972515	0.486258	−	0.873816i	$-0.338362\pi$
$863$	28.5694	0.972515	0.486258	+	0.873816i	$0.338362\pi$
$864$	−60.2088	−2.04835
$865$	−4.27659	−0.145409
$866$	20.9120	0.710619
$867$	140.334	4.76600
$868$	−39.8823	−1.35369
$869$	16.2070	0.549786
$870$	−7.28349	−0.246933
$871$	−2.93035	−0.0992910
$872$	27.8153	0.941946
$873$	120.473	4.07739
$874$	−10.3254	−0.349260
$875$	−3.66055	−0.123749
$876$	−4.41817	−0.149276
$877$	−51.3452	−1.73380	−0.866902	−	0.498479i	$-0.833892\pi$
$877$	−51.3452	−1.73380	−0.866902	+	0.498479i	$0.833892\pi$
$878$	4.69214	0.158352
$879$	−2.65492	−0.0895483
$880$	0.974567	0.0328527
$881$	−31.6055	−1.06482	−0.532408	−	0.846488i	$-0.678713\pi$
$881$	−31.6055	−1.06482	−0.532408	+	0.846488i	$0.678713\pi$
$882$	−30.3308	−1.02129
$883$	−53.5711	−1.80281	−0.901405	−	0.432977i	$-0.857463\pi$
$883$	−53.5711	−1.80281	−0.901405	+	0.432977i	$0.857463\pi$
$884$	−11.7514	−0.395243
$885$	25.4604	0.855842
$886$	19.7452	0.663352
$887$	−20.1353	−0.676077	−0.338038	−	0.941132i	$-0.609763\pi$
$887$	−20.1353	−0.676077	−0.338038	+	0.941132i	$0.609763\pi$
$888$	47.7539	1.60252
$889$	−60.2832	−2.02183
$890$	−0.540706	−0.0181245
$891$	12.3481	0.413679
$892$	−24.8695	−0.832693
$893$	−14.7830	−0.494694
$894$	1.40973	0.0471484
$895$	2.49969	0.0835555
$896$	−36.3087	−1.21299
$897$	−28.3318	−0.945970
$898$	−21.7170	−0.724707
$899$	−24.0940	−0.803580
$900$	−9.18251	−0.306084
$901$	−24.5201	−0.816884
$902$	−5.70450	−0.189939
$903$	−92.9164	−3.09207
$904$	−31.8197	−1.05831
$905$	3.30917	0.110001
$906$	20.0189	0.665085
$907$	48.1956	1.60031	0.800154	−	0.599794i	$-0.204751\pi$
$907$	48.1956	1.60031	0.800154	+	0.599794i	$0.204751\pi$
$908$	−28.7638	−0.954559
$909$	13.6053	0.451260
$910$	2.80004	0.0928205
$911$	2.65861	0.0880838	0.0440419	−	0.999030i	$-0.485976\pi$
$911$	2.65861	0.0880838	0.0440419	+	0.999030i	$0.485976\pi$
$912$	−4.57498	−0.151493
$913$	−1.77293	−0.0586754
$914$	−16.0222	−0.529967
$915$	−24.3237	−0.804118
$916$	−3.06225	−0.101179
$917$	0.815700	0.0269368
$918$	−60.7160	−2.00393
$919$	34.0241	1.12235	0.561176	−	0.827696i	$-0.310349\pi$
$919$	34.0241	1.12235	0.561176	+	0.827696i	$0.310349\pi$
$920$	−23.1747	−0.764048
$921$	66.6040	2.19468
$922$	5.94889	0.195916
$923$	−3.26220	−0.107377
$924$	16.1729	0.532050
$925$	6.07994	0.199907
$926$	−11.9305	−0.392059
$927$	−36.6301	−1.20309
$928$	−18.7219	−0.614576
$929$	45.1410	1.48103	0.740514	−	0.672041i	$-0.234582\pi$
$929$	45.1410	1.48103	0.740514	+	0.672041i	$0.234582\pi$
$930$	17.2024	0.564089
$931$	−9.82075	−0.321862
$932$	−28.1049	−0.920606
$933$	−71.2906	−2.33395
$934$	24.5138	0.802117
$935$	7.92938	0.259319
$936$	16.7504	0.547503
$937$	23.6534	0.772721	0.386361	−	0.922348i	$-0.373732\pi$
$937$	23.6534	0.772721	0.386361	+	0.922348i	$0.373732\pi$
$938$	−7.79279	−0.254444
$939$	64.5894	2.10780
$940$	−13.9132	−0.453799
$941$	−35.5296	−1.15823	−0.579116	−	0.815245i	$-0.696602\pi$
$941$	−35.5296	−1.15823	−0.579116	+	0.815245i	$0.696602\pi$
$942$	−11.7218	−0.381915
$943$	−69.0695	−2.24921
$944$	8.11130	0.264000
$945$	−37.5999	−1.22313
$946$	−6.18561	−0.201112
$947$	11.0303	0.358437	0.179219	−	0.983809i	$-0.442643\pi$
$947$	11.0303	0.358437	0.179219	+	0.983809i	$0.442643\pi$
$948$	−71.6053	−2.32563
$949$	1.02611	0.0333090
$950$	1.14397	0.0371152
$951$	−0.975580	−0.0316353
$952$	−74.5262	−2.41541
$953$	−39.0570	−1.26518	−0.632590	−	0.774487i	$-0.718008\pi$
$953$	−39.0570	−1.26518	−0.632590	+	0.774487i	$0.718008\pi$
$954$	14.6559	0.474503
$955$	23.7192	0.767537
$956$	−1.95151	−0.0631165
$957$	9.77049	0.315835
$958$	−19.8851	−0.642460
$959$	−1.01489	−0.0327724
$960$	7.40436	0.238975
$961$	25.9060	0.835678
$962$	−4.65069	−0.149944
$963$	−112.666	−3.63060
$964$	−28.0819	−0.904457
$965$	9.56799	0.308004
$966$	−75.3438	−2.42415
$967$	−43.6286	−1.40300	−0.701500	−	0.712669i	$-0.747486\pi$
$967$	−43.6286	−1.40300	−0.701500	+	0.712669i	$0.747486\pi$
$968$	2.56757	0.0825250
$969$	−37.2234	−1.19579
$970$	−14.1256	−0.453545
$971$	−29.7850	−0.955847	−0.477924	−	0.878401i	$-0.658610\pi$
$971$	−29.7850	−0.955847	−0.477924	+	0.878401i	$0.658610\pi$
$972$	−10.0503	−0.322364
$973$	−25.6439	−0.822106
$974$	20.1524	0.645724
$975$	3.13893	0.100526
$976$	−7.74918	−0.248045
$977$	−42.9978	−1.37562	−0.687810	−	0.725890i	$-0.741428\pi$
$977$	−42.9978	−1.37562	−0.687810	+	0.725890i	$0.741428\pi$
$978$	24.0377	0.768640
$979$	0.725334	0.0231818
$980$	−9.24293	−0.295255
$981$	68.8759	2.19904
$982$	−24.3720	−0.777742
$983$	49.6405	1.58329	0.791643	−	0.610984i	$-0.209226\pi$
$983$	49.6405	1.58329	0.791643	+	0.610984i	$0.209226\pi$
$984$	60.1042	1.91605
$985$	13.1006	0.417420
$986$	−18.8796	−0.601248
$987$	−107.871	−3.43358
$988$	2.27426	0.0723540
$989$	−74.8947	−2.38151
$990$	−4.73947	−0.150630
$991$	48.0861	1.52751	0.763753	−	0.645509i	$-0.223355\pi$
$991$	48.0861	1.52751	0.763753	+	0.645509i	$0.223355\pi$
$992$	44.2180	1.40392
$993$	−82.7858	−2.62713
$994$	−8.67531	−0.275164
$995$	−12.6096	−0.399751
$996$	7.83310	0.248201
$997$	−37.4483	−1.18600	−0.592999	−	0.805203i	$-0.702056\pi$
$997$	−37.4483	−1.18600	−0.592999	+	0.805203i	$0.702056\pi$
$998$	−4.85181	−0.153581
$999$	62.4510	1.97586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.13	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-0.745458 q^{2} +3.05905 q^{3} -1.44429 q^{4} +1.00000 q^{5} -2.28039 q^{6} -3.66055 q^{7} +2.56757 q^{8} +6.35779 q^{9} +O(q^{10})\)	\(q-0.745458 q^{2} +3.05905 q^{3} -1.44429 q^{4} +1.00000 q^{5} -2.28039 q^{6} -3.66055 q^{7} +2.56757 q^{8} +6.35779 q^{9} -0.745458 q^{10} +1.00000 q^{11} -4.41817 q^{12} +1.02611 q^{13} +2.72879 q^{14} +3.05905 q^{15} +0.974567 q^{16} +7.92938 q^{17} -4.73947 q^{18} -1.53458 q^{19} -1.44429 q^{20} -11.1978 q^{21} -0.745458 q^{22} -9.02592 q^{23} +7.85434 q^{24} +1.00000 q^{25} -0.764924 q^{26} +10.2717 q^{27} +5.28691 q^{28} +3.19396 q^{29} -2.28039 q^{30} -7.54361 q^{31} -5.86165 q^{32} +3.05905 q^{33} -5.91102 q^{34} -3.66055 q^{35} -9.18251 q^{36} +6.07994 q^{37} +1.14397 q^{38} +3.13893 q^{39} +2.56757 q^{40} +7.65235 q^{41} +8.34749 q^{42} +8.29774 q^{43} -1.44429 q^{44} +6.35779 q^{45} +6.72844 q^{46} +9.63324 q^{47} +2.98125 q^{48} +6.39962 q^{49} -0.745458 q^{50} +24.2564 q^{51} -1.48201 q^{52} -3.09231 q^{53} -7.65709 q^{54} +1.00000 q^{55} -9.39873 q^{56} -4.69437 q^{57} -2.38096 q^{58} +8.32297 q^{59} -4.41817 q^{60} -7.95140 q^{61} +5.62344 q^{62} -23.2730 q^{63} +2.42048 q^{64} +1.02611 q^{65} -2.28039 q^{66} -2.85577 q^{67} -11.4523 q^{68} -27.6108 q^{69} +2.72879 q^{70} -3.17918 q^{71} +16.3241 q^{72} +1.00000 q^{73} -4.53234 q^{74} +3.05905 q^{75} +2.21639 q^{76} -3.66055 q^{77} -2.33994 q^{78} +16.2070 q^{79} +0.974567 q^{80} +12.3481 q^{81} -5.70450 q^{82} -1.77293 q^{83} +16.1729 q^{84} +7.92938 q^{85} -6.18561 q^{86} +9.77049 q^{87} +2.56757 q^{88} +0.725334 q^{89} -4.73947 q^{90} -3.75614 q^{91} +13.0361 q^{92} -23.0763 q^{93} -7.18117 q^{94} -1.53458 q^{95} -17.9311 q^{96} +18.9489 q^{97} -4.77065 q^{98} +6.35779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 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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