LMFDB - Embedded newform 619.2.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.273610 q^{2} -2.79069 q^{3} -1.92514 q^{4} -0.828377 q^{5} -0.763560 q^{6} +5.25882 q^{7} -1.07396 q^{8} +4.78794 q^{9} +O(q^{10})$	\(q+0.273610 q^{2} -2.79069 q^{3} -1.92514 q^{4} -0.828377 q^{5} -0.763560 q^{6} +5.25882 q^{7} -1.07396 q^{8} +4.78794 q^{9} -0.226652 q^{10} -0.517602 q^{11} +5.37246 q^{12} -0.886062 q^{13} +1.43886 q^{14} +2.31174 q^{15} +3.55643 q^{16} +1.08930 q^{17} +1.31003 q^{18} -4.51791 q^{19} +1.59474 q^{20} -14.6757 q^{21} -0.141621 q^{22} -7.63401 q^{23} +2.99708 q^{24} -4.31379 q^{25} -0.242435 q^{26} -4.98959 q^{27} -10.1239 q^{28} -4.29152 q^{29} +0.632515 q^{30} +3.09141 q^{31} +3.12099 q^{32} +1.44447 q^{33} +0.298043 q^{34} -4.35628 q^{35} -9.21745 q^{36} -3.78889 q^{37} -1.23614 q^{38} +2.47272 q^{39} +0.889640 q^{40} +3.25938 q^{41} -4.01542 q^{42} +5.55274 q^{43} +0.996455 q^{44} -3.96622 q^{45} -2.08874 q^{46} -9.97044 q^{47} -9.92489 q^{48} +20.6551 q^{49} -1.18030 q^{50} -3.03990 q^{51} +1.70579 q^{52} -11.6390 q^{53} -1.36520 q^{54} +0.428769 q^{55} -5.64774 q^{56} +12.6081 q^{57} -1.17420 q^{58} -7.03787 q^{59} -4.45042 q^{60} -14.8645 q^{61} +0.845839 q^{62} +25.1789 q^{63} -6.25893 q^{64} +0.733993 q^{65} +0.395220 q^{66} +3.78987 q^{67} -2.09705 q^{68} +21.3041 q^{69} -1.19192 q^{70} -3.62598 q^{71} -5.14204 q^{72} -3.47800 q^{73} -1.03668 q^{74} +12.0384 q^{75} +8.69760 q^{76} -2.72197 q^{77} +0.676561 q^{78} +6.06325 q^{79} -2.94606 q^{80} -0.439442 q^{81} +0.891797 q^{82} +11.1403 q^{83} +28.2528 q^{84} -0.902352 q^{85} +1.51929 q^{86} +11.9763 q^{87} +0.555882 q^{88} +10.5859 q^{89} -1.08520 q^{90} -4.65964 q^{91} +14.6965 q^{92} -8.62715 q^{93} -2.72801 q^{94} +3.74253 q^{95} -8.70970 q^{96} -7.66913 q^{97} +5.65145 q^{98} -2.47825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) $ 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * 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 $

$2$	0.273610	0.193471	0.0967357	−	0.995310i	$-0.469160\pi$
$2$	0.273610	0.193471	0.0967357	+	0.995310i	$0.469160\pi$
$3$	−2.79069	−1.61120	−0.805602	−	0.592457i	$-0.798158\pi$
$3$	−2.79069	−1.61120	−0.805602	+	0.592457i	$0.798158\pi$
$4$	−1.92514	−0.962569
$5$	−0.828377	−0.370461	−0.185231	−	0.982695i	$-0.559303\pi$
$5$	−0.828377	−0.370461	−0.185231	+	0.982695i	$0.559303\pi$
$6$	−0.763560	−0.311722
$7$	5.25882	1.98765	0.993823	−	0.110978i	$-0.0353984\pi$
$7$	5.25882	1.98765	0.993823	+	0.110978i	$0.0353984\pi$
$8$	−1.07396	−0.379701
$9$	4.78794	1.59598
$10$	−0.226652	−0.0716736
$11$	−0.517602	−0.156063	−0.0780314	−	0.996951i	$-0.524863\pi$
$11$	−0.517602	−0.156063	−0.0780314	+	0.996951i	$0.524863\pi$
$12$	5.37246	1.55090
$13$	−0.886062	−0.245749	−0.122875	−	0.992422i	$-0.539211\pi$
$13$	−0.886062	−0.245749	−0.122875	+	0.992422i	$0.539211\pi$
$14$	1.43886	0.384552
$15$	2.31174	0.596889
$16$	3.55643	0.889108
$17$	1.08930	0.264194	0.132097	−	0.991237i	$-0.457829\pi$
$17$	1.08930	0.264194	0.132097	+	0.991237i	$0.457829\pi$
$18$	1.31003	0.308776
$19$	−4.51791	−1.03648	−0.518240	−	0.855235i	$-0.673413\pi$
$19$	−4.51791	−1.03648	−0.518240	+	0.855235i	$0.673413\pi$
$20$	1.59474	0.356595
$21$	−14.6757	−3.20250
$22$	−0.141621	−0.0301937
$23$	−7.63401	−1.59180	−0.795901	−	0.605427i	$-0.793002\pi$
$23$	−7.63401	−1.59180	−0.795901	+	0.605427i	$0.793002\pi$
$24$	2.99708	0.611776
$25$	−4.31379	−0.862758
$26$	−0.242435	−0.0475454
$27$	−4.98959	−0.960246
$28$	−10.1239	−1.91325
$29$	−4.29152	−0.796915	−0.398457	−	0.917187i	$-0.630454\pi$
$29$	−4.29152	−0.796915	−0.398457	+	0.917187i	$0.630454\pi$
$30$	0.632515	0.115481
$31$	3.09141	0.555233	0.277616	−	0.960692i	$-0.410456\pi$
$31$	3.09141	0.555233	0.277616	+	0.960692i	$0.410456\pi$
$32$	3.12099	0.551718
$33$	1.44447	0.251449
$34$	0.298043	0.0511140
$35$	−4.35628	−0.736346
$36$	−9.21745	−1.53624
$37$	−3.78889	−0.622890	−0.311445	−	0.950264i	$-0.600813\pi$
$37$	−3.78889	−0.622890	−0.311445	+	0.950264i	$0.600813\pi$
$38$	−1.23614	−0.200529
$39$	2.47272	0.395953
$40$	0.889640	0.140664
$41$	3.25938	0.509029	0.254515	−	0.967069i	$-0.418084\pi$
$41$	3.25938	0.509029	0.254515	+	0.967069i	$0.418084\pi$
$42$	−4.01542	−0.619593
$43$	5.55274	0.846786	0.423393	−	0.905946i	$-0.360839\pi$
$43$	5.55274	0.846786	0.423393	+	0.905946i	$0.360839\pi$
$44$	0.996455	0.150221
$45$	−3.96622	−0.591249
$46$	−2.08874	−0.307968
$47$	−9.97044	−1.45434	−0.727169	−	0.686458i	$-0.759164\pi$
$47$	−9.97044	−1.45434	−0.727169	+	0.686458i	$0.759164\pi$
$48$	−9.92489	−1.43253
$49$	20.6551	2.95074
$50$	−1.18030	−0.166919
$51$	−3.03990	−0.425671
$52$	1.70579	0.236551
$53$	−11.6390	−1.59874	−0.799370	−	0.600838i	$-0.794834\pi$
$53$	−11.6390	−1.59874	−0.799370	+	0.600838i	$0.794834\pi$
$54$	−1.36520	−0.185780
$55$	0.428769	0.0578152
$56$	−5.64774	−0.754711
$57$	12.6081	1.66998
$58$	−1.17420	−0.154180
$59$	−7.03787	−0.916252	−0.458126	−	0.888887i	$-0.651479\pi$
$59$	−7.03787	−0.916252	−0.458126	+	0.888887i	$0.651479\pi$
$60$	−4.45042	−0.574547
$61$	−14.8645	−1.90320	−0.951602	−	0.307332i	$-0.900564\pi$
$61$	−14.8645	−1.90320	−0.951602	+	0.307332i	$0.900564\pi$
$62$	0.845839	0.107422
$63$	25.1789	3.17224
$64$	−6.25893	−0.782366
$65$	0.733993	0.0910406
$66$	0.395220	0.0486482
$67$	3.78987	0.463006	0.231503	−	0.972834i	$-0.425636\pi$
$67$	3.78987	0.463006	0.231503	+	0.972834i	$0.425636\pi$
$68$	−2.09705	−0.254305
$69$	21.3041	2.56472
$70$	−1.19192	−0.142462
$71$	−3.62598	−0.430324	−0.215162	−	0.976578i	$-0.569028\pi$
$71$	−3.62598	−0.430324	−0.215162	+	0.976578i	$0.569028\pi$
$72$	−5.14204	−0.605995
$73$	−3.47800	−0.407069	−0.203535	−	0.979068i	$-0.565243\pi$
$73$	−3.47800	−0.407069	−0.203535	+	0.979068i	$0.565243\pi$
$74$	−1.03668	−0.120511
$75$	12.0384	1.39008
$76$	8.69760	0.997683
$77$	−2.72197	−0.310198
$78$	0.676561	0.0766054
$79$	6.06325	0.682168	0.341084	−	0.940033i	$-0.389206\pi$
$79$	6.06325	0.682168	0.341084	+	0.940033i	$0.389206\pi$
$80$	−2.94606	−0.329380
$81$	−0.439442	−0.0488269
$82$	0.891797	0.0984825
$83$	11.1403	1.22281	0.611403	−	0.791319i	$-0.290605\pi$
$83$	11.1403	1.22281	0.611403	+	0.791319i	$0.290605\pi$
$84$	28.2528	3.08263
$85$	−0.902352	−0.0978738
$86$	1.51929	0.163829
$87$	11.9763	1.28399
$88$	0.555882	0.0592572
$89$	10.5859	1.12210	0.561051	−	0.827781i	$-0.310397\pi$
$89$	10.5859	1.12210	0.561051	+	0.827781i	$0.310397\pi$
$90$	−1.08520	−0.114390
$91$	−4.65964	−0.488463
$92$	14.6965	1.53222
$93$	−8.62715	−0.894594
$94$	−2.72801	−0.281373
$95$	3.74253	0.383976
$96$	−8.70970	−0.888930
$97$	−7.66913	−0.778682	−0.389341	−	0.921094i	$-0.627297\pi$
$97$	−7.66913	−0.778682	−0.389341	+	0.921094i	$0.627297\pi$
$98$	5.65145	0.570883
$99$	−2.47825	−0.249073
$100$	8.30464	0.830464
$101$	−7.12974	−0.709436	−0.354718	−	0.934973i	$-0.615423\pi$
$101$	−7.12974	−0.709436	−0.354718	+	0.934973i	$0.615423\pi$
$102$	−0.831746	−0.0823552
$103$	−9.15450	−0.902019	−0.451010	−	0.892519i	$-0.648936\pi$
$103$	−9.15450	−0.902019	−0.451010	+	0.892519i	$0.648936\pi$
$104$	0.951591	0.0933112
$105$	12.1570	1.18640
$106$	−3.18455	−0.309311
$107$	−6.95126	−0.672004	−0.336002	−	0.941861i	$-0.609075\pi$
$107$	−6.95126	−0.672004	−0.336002	+	0.941861i	$0.609075\pi$
$108$	9.60564	0.924303
$109$	−12.7272	−1.21905	−0.609523	−	0.792768i	$-0.708639\pi$
$109$	−12.7272	−1.21905	−0.609523	+	0.792768i	$0.708639\pi$
$110$	0.117315	0.0111856
$111$	10.5736	1.00360
$112$	18.7026	1.76723
$113$	−14.9870	−1.40986	−0.704929	−	0.709278i	$-0.749021\pi$
$113$	−14.9870	−1.40986	−0.704929	+	0.709278i	$0.749021\pi$
$114$	3.44969	0.323093
$115$	6.32384	0.589701
$116$	8.26176	0.767086
$117$	−4.24241	−0.392211
$118$	−1.92563	−0.177269
$119$	5.72843	0.525125
$120$	−2.48271	−0.226639
$121$	−10.7321	−0.975644
$122$	−4.06707	−0.368215
$123$	−9.09591	−0.820150
$124$	−5.95138	−0.534450
$125$	7.71533	0.690080
$126$	6.88919	0.613738
$127$	7.55660	0.670539	0.335270	−	0.942122i	$-0.391173\pi$
$127$	7.55660	0.670539	0.335270	+	0.942122i	$0.391173\pi$
$128$	−7.95448	−0.703083
$129$	−15.4960	−1.36434
$130$	0.200828	0.0176137
$131$	8.65582	0.756262	0.378131	−	0.925752i	$-0.376567\pi$
$131$	8.65582	0.756262	0.378131	+	0.925752i	$0.376567\pi$
$132$	−2.78080	−0.242037
$133$	−23.7589	−2.06015
$134$	1.03694	0.0895783
$135$	4.13326	0.355734
$136$	−1.16986	−0.100315
$137$	8.84372	0.755570	0.377785	−	0.925893i	$-0.376686\pi$
$137$	8.84372	0.755570	0.377785	+	0.925893i	$0.376686\pi$
$138$	5.82902	0.496199
$139$	5.90751	0.501068	0.250534	−	0.968108i	$-0.419394\pi$
$139$	5.90751	0.501068	0.250534	+	0.968108i	$0.419394\pi$
$140$	8.38644	0.708784
$141$	27.8244	2.34324
$142$	−0.992103	−0.0832554
$143$	0.458627	0.0383523
$144$	17.0280	1.41900
$145$	3.55499	0.295226
$146$	−0.951615	−0.0787562
$147$	−57.6421	−4.75424
$148$	7.29414	0.599575
$149$	−11.0444	−0.904790	−0.452395	−	0.891818i	$-0.649430\pi$
$149$	−11.0444	−0.904790	−0.452395	+	0.891818i	$0.649430\pi$
$150$	3.29384	0.268941
$151$	−4.02776	−0.327774	−0.163887	−	0.986479i	$-0.552403\pi$
$151$	−4.02776	−0.327774	−0.163887	+	0.986479i	$0.552403\pi$
$152$	4.85204	0.393552
$153$	5.21551	0.421649
$154$	−0.744758	−0.0600143
$155$	−2.56085	−0.205692
$156$	−4.76033	−0.381132
$157$	15.2373	1.21607	0.608034	−	0.793911i	$-0.291959\pi$
$157$	15.2373	1.21607	0.608034	+	0.793911i	$0.291959\pi$
$158$	1.65896	0.131980
$159$	32.4808	2.57590
$160$	−2.58535	−0.204390
$161$	−40.1459	−3.16394
$162$	−0.120236	−0.00944660
$163$	24.8544	1.94675	0.973373	−	0.229225i	$-0.0736192\pi$
$163$	24.8544	1.94675	0.973373	+	0.229225i	$0.0736192\pi$
$164$	−6.27475	−0.489976
$165$	−1.19656	−0.0931522
$166$	3.04809	0.236578
$167$	12.7642	0.987726	0.493863	−	0.869540i	$-0.335584\pi$
$167$	12.7642	0.987726	0.493863	+	0.869540i	$0.335584\pi$
$168$	15.7611	1.21599
$169$	−12.2149	−0.939607
$170$	−0.246892	−0.0189358
$171$	−21.6315	−1.65420
$172$	−10.6898	−0.815089
$173$	−4.67384	−0.355345	−0.177673	−	0.984090i	$-0.556857\pi$
$173$	−4.67384	−0.355345	−0.177673	+	0.984090i	$0.556857\pi$
$174$	3.27683	0.248416
$175$	−22.6854	−1.71486
$176$	−1.84082	−0.138757
$177$	19.6405	1.47627
$178$	2.89640	0.217095
$179$	−15.5282	−1.16064	−0.580318	−	0.814390i	$-0.697072\pi$
$179$	−15.5282	−1.16064	−0.580318	+	0.814390i	$0.697072\pi$
$180$	7.63552	0.569118
$181$	0.625527	0.0464951	0.0232475	−	0.999730i	$-0.492599\pi$
$181$	0.625527	0.0464951	0.0232475	+	0.999730i	$0.492599\pi$
$182$	−1.27492	−0.0945035
$183$	41.4822	3.06645
$184$	8.19859	0.604408
$185$	3.13863	0.230757
$186$	−2.36047	−0.173078
$187$	−0.563824	−0.0412309
$188$	19.1945	1.39990
$189$	−26.2393	−1.90863
$190$	1.02399	0.0742883
$191$	−19.8658	−1.43744	−0.718718	−	0.695301i	$-0.755271\pi$
$191$	−19.8658	−1.43744	−0.718718	+	0.695301i	$0.755271\pi$
$192$	17.4667	1.26055
$193$	−8.03470	−0.578350	−0.289175	−	0.957276i	$-0.593381\pi$
$193$	−8.03470	−0.578350	−0.289175	+	0.957276i	$0.593381\pi$
$194$	−2.09835	−0.150653
$195$	−2.04835	−0.146685
$196$	−39.7640	−2.84029
$197$	1.01060	0.0720021	0.0360010	−	0.999352i	$-0.488538\pi$
$197$	1.01060	0.0720021	0.0360010	+	0.999352i	$0.488538\pi$
$198$	−0.678073	−0.0481885
$199$	7.72201	0.547399	0.273699	−	0.961815i	$-0.411753\pi$
$199$	7.72201	0.547399	0.273699	+	0.961815i	$0.411753\pi$
$200$	4.63282	0.327590
$201$	−10.5763	−0.745997
$202$	−1.95077	−0.137256
$203$	−22.5683	−1.58398
$204$	5.85223	0.409738
$205$	−2.69999	−0.188576
$206$	−2.50476	−0.174515
$207$	−36.5512	−2.54048
$208$	−3.15122	−0.218498
$209$	2.33848	0.161756
$210$	3.32628	0.229535
$211$	17.8498	1.22883	0.614414	−	0.788984i	$-0.289393\pi$
$211$	17.8498	1.22883	0.614414	+	0.788984i	$0.289393\pi$
$212$	22.4067	1.53890
$213$	10.1190	0.693341
$214$	−1.90193	−0.130013
$215$	−4.59976	−0.313701
$216$	5.35860	0.364606
$217$	16.2571	1.10361
$218$	−3.48229	−0.235851
$219$	9.70602	0.655872
$220$	−0.825440	−0.0556512
$221$	−0.965188	−0.0649256
$222$	2.89305	0.194168
$223$	10.1268	0.678139	0.339070	−	0.940761i	$-0.389888\pi$
$223$	10.1268	0.678139	0.339070	+	0.940761i	$0.389888\pi$
$224$	16.4127	1.09662
$225$	−20.6542	−1.37695
$226$	−4.10059	−0.272767
$227$	−5.28053	−0.350481	−0.175240	−	0.984526i	$-0.556070\pi$
$227$	−5.28053	−0.350481	−0.175240	+	0.984526i	$0.556070\pi$
$228$	−24.2723	−1.60747
$229$	2.37546	0.156975	0.0784874	−	0.996915i	$-0.474991\pi$
$229$	2.37546	0.156975	0.0784874	+	0.996915i	$0.474991\pi$
$230$	1.73026	0.114090
$231$	7.59618	0.499792
$232$	4.60890	0.302589
$233$	25.5917	1.67657	0.838284	−	0.545234i	$-0.183559\pi$
$233$	25.5917	1.67657	0.838284	+	0.545234i	$0.183559\pi$
$234$	−1.16077	−0.0758816
$235$	8.25928	0.538776
$236$	13.5489	0.881956
$237$	−16.9206	−1.09911
$238$	1.56736	0.101597
$239$	7.27106	0.470326	0.235163	−	0.971956i	$-0.424438\pi$
$239$	7.27106	0.470326	0.235163	+	0.971956i	$0.424438\pi$
$240$	8.22155	0.530699
$241$	−10.2297	−0.658954	−0.329477	−	0.944164i	$-0.606872\pi$
$241$	−10.2297	−0.658954	−0.329477	+	0.944164i	$0.606872\pi$
$242$	−2.93640	−0.188759
$243$	16.1951	1.03892
$244$	28.6162	1.83197
$245$	−17.1102	−1.09313
$246$	−2.48873	−0.158676
$247$	4.00315	0.254714
$248$	−3.32003	−0.210822
$249$	−31.0891	−1.97019
$250$	2.11099	0.133511
$251$	12.1482	0.766789	0.383394	−	0.923585i	$-0.374755\pi$
$251$	12.1482	0.766789	0.383394	+	0.923585i	$0.374755\pi$
$252$	−48.4729	−3.05350
$253$	3.95138	0.248421
$254$	2.06756	0.129730
$255$	2.51818	0.157695
$256$	10.3414	0.646340
$257$	15.1139	0.942780	0.471390	−	0.881925i	$-0.343752\pi$
$257$	15.1139	0.942780	0.471390	+	0.881925i	$0.343752\pi$
$258$	−4.23985	−0.263962
$259$	−19.9251	−1.23808
$260$	−1.41304	−0.0876329
$261$	−20.5475	−1.27186
$262$	2.36832	0.146315
$263$	−29.6782	−1.83003	−0.915017	−	0.403416i	$-0.867823\pi$
$263$	−29.6782	−1.83003	−0.915017	+	0.403416i	$0.867823\pi$
$264$	−1.55129	−0.0954754
$265$	9.64148	0.592272
$266$	−6.50066	−0.398581
$267$	−29.5419	−1.80794
$268$	−7.29601	−0.445675
$269$	−19.2810	−1.17558	−0.587792	−	0.809012i	$-0.700003\pi$
$269$	−19.2810	−1.17558	−0.587792	+	0.809012i	$0.700003\pi$
$270$	1.13090	0.0688244
$271$	5.15546	0.313172	0.156586	−	0.987664i	$-0.449951\pi$
$271$	5.15546	0.313172	0.156586	+	0.987664i	$0.449951\pi$
$272$	3.87402	0.234897
$273$	13.0036	0.787013
$274$	2.41973	0.146181
$275$	2.23283	0.134645
$276$	−41.0134	−2.46872
$277$	3.98815	0.239625	0.119812	−	0.992797i	$-0.461771\pi$
$277$	3.98815	0.239625	0.119812	+	0.992797i	$0.461771\pi$
$278$	1.61635	0.0969424
$279$	14.8015	0.886141
$280$	4.67845	0.279591
$281$	−11.8454	−0.706638	−0.353319	−	0.935503i	$-0.614947\pi$
$281$	−11.8454	−0.706638	−0.353319	+	0.935503i	$0.614947\pi$
$282$	7.61302	0.453349
$283$	−1.23633	−0.0734923	−0.0367462	−	0.999325i	$-0.511699\pi$
$283$	−1.23633	−0.0734923	−0.0367462	+	0.999325i	$0.511699\pi$
$284$	6.98051	0.414217
$285$	−10.4442	−0.618663
$286$	0.125485	0.00742008
$287$	17.1405	1.01177
$288$	14.9431	0.880530
$289$	−15.8134	−0.930201
$290$	0.972681	0.0571178
$291$	21.4022	1.25462
$292$	6.69563	0.391832
$293$	−3.19894	−0.186884	−0.0934421	−	0.995625i	$-0.529787\pi$
$293$	−3.19894	−0.186884	−0.0934421	+	0.995625i	$0.529787\pi$
$294$	−15.7714	−0.919809
$295$	5.83000	0.339436
$296$	4.06910	0.236512
$297$	2.58262	0.149859
$298$	−3.02185	−0.175051
$299$	6.76421	0.391184
$300$	−23.1757	−1.33805
$301$	29.2009	1.68311
$302$	−1.10203	−0.0634149
$303$	19.8969	1.14305
$304$	−16.0676	−0.921542
$305$	12.3134	0.705064
$306$	1.42701	0.0815770
$307$	26.4074	1.50715	0.753575	−	0.657362i	$-0.228328\pi$
$307$	26.4074	1.50715	0.753575	+	0.657362i	$0.228328\pi$
$308$	5.24017	0.298587
$309$	25.5473	1.45334
$310$	−0.700673	−0.0397956
$311$	26.6861	1.51323	0.756616	−	0.653860i	$-0.226851\pi$
$311$	26.6861	1.51323	0.756616	+	0.653860i	$0.226851\pi$
$312$	−2.65560	−0.150343
$313$	26.0013	1.46968	0.734841	−	0.678239i	$-0.237257\pi$
$313$	26.0013	1.46968	0.734841	+	0.678239i	$0.237257\pi$
$314$	4.16907	0.235274
$315$	−20.8576	−1.17519
$316$	−11.6726	−0.656634
$317$	−20.6168	−1.15796	−0.578978	−	0.815343i	$-0.696548\pi$
$317$	−20.6168	−1.15796	−0.578978	+	0.815343i	$0.696548\pi$
$318$	8.88708	0.498363
$319$	2.22130	0.124369
$320$	5.18475	0.289836
$321$	19.3988	1.08274
$322$	−10.9843	−0.612131
$323$	−4.92137	−0.273832
$324$	0.845986	0.0469992
$325$	3.82229	0.212022
$326$	6.80041	0.376640
$327$	35.5177	1.96413
$328$	−3.50043	−0.193279
$329$	−52.4327	−2.89071
$330$	−0.327391	−0.0180223
$331$	−16.5841	−0.911542	−0.455771	−	0.890097i	$-0.650636\pi$
$331$	−16.5841	−0.911542	−0.455771	+	0.890097i	$0.650636\pi$
$332$	−21.4466	−1.17704
$333$	−18.1410	−0.994121
$334$	3.49242	0.191097
$335$	−3.13944	−0.171526
$336$	−52.1932	−2.84737
$337$	−4.15284	−0.226220	−0.113110	−	0.993582i	$-0.536081\pi$
$337$	−4.15284	−0.226220	−0.113110	+	0.993582i	$0.536081\pi$
$338$	−3.34211	−0.181787
$339$	41.8240	2.27157
$340$	1.73715	0.0942103
$341$	−1.60012	−0.0866512
$342$	−5.91859	−0.320041
$343$	71.8099	3.87737
$344$	−5.96340	−0.321525
$345$	−17.6479	−0.950129
$346$	−1.27881	−0.0687491
$347$	−22.6161	−1.21409	−0.607047	−	0.794666i	$-0.707646\pi$
$347$	−22.6161	−1.21409	−0.607047	+	0.794666i	$0.707646\pi$
$348$	−23.0560	−1.23593
$349$	−13.3867	−0.716573	−0.358286	−	0.933612i	$-0.616639\pi$
$349$	−13.3867	−0.716573	−0.358286	+	0.933612i	$0.616639\pi$
$350$	−6.20696	−0.331776
$351$	4.42108	0.235980
$352$	−1.61543	−0.0861026
$353$	17.0515	0.907561	0.453781	−	0.891113i	$-0.350075\pi$
$353$	17.0515	0.907561	0.453781	+	0.891113i	$0.350075\pi$
$354$	5.37383	0.285616
$355$	3.00368	0.159419
$356$	−20.3793	−1.08010
$357$	−15.9863	−0.846083
$358$	−4.24868	−0.224550
$359$	−37.3204	−1.96970	−0.984849	−	0.173416i	$-0.944520\pi$
$359$	−37.3204	−1.96970	−0.984849	+	0.173416i	$0.944520\pi$
$360$	4.25954	0.224498
$361$	1.41152	0.0742903
$362$	0.171150	0.00899546
$363$	29.9499	1.57196
$364$	8.97044	0.470179
$365$	2.88109	0.150803
$366$	11.3499	0.593270
$367$	−11.1278	−0.580865	−0.290432	−	0.956896i	$-0.593799\pi$
$367$	−11.1278	−0.580865	−0.290432	+	0.956896i	$0.593799\pi$
$368$	−27.1498	−1.41528
$369$	15.6057	0.812401
$370$	0.858760	0.0446448
$371$	−61.2074	−3.17773
$372$	16.6085	0.861108
$373$	29.2724	1.51567	0.757834	−	0.652447i	$-0.226257\pi$
$373$	29.2724	1.51567	0.757834	+	0.652447i	$0.226257\pi$
$374$	−0.154268	−0.00797700
$375$	−21.5311	−1.11186
$376$	10.7078	0.552213
$377$	3.80255	0.195841
$378$	−7.17933	−0.369265
$379$	23.2660	1.19509	0.597547	−	0.801834i	$-0.296142\pi$
$379$	23.2660	1.19509	0.597547	+	0.801834i	$0.296142\pi$
$380$	−7.20489	−0.369603
$381$	−21.0881	−1.08038
$382$	−5.43547	−0.278103
$383$	19.4203	0.992332	0.496166	−	0.868228i	$-0.334741\pi$
$383$	19.4203	0.992332	0.496166	+	0.868228i	$0.334741\pi$
$384$	22.1985	1.13281
$385$	2.25482	0.114916
$386$	−2.19837	−0.111894
$387$	26.5862	1.35145
$388$	14.7641	0.749535
$389$	12.6086	0.639281	0.319640	−	0.947539i	$-0.396438\pi$
$389$	12.6086	0.639281	0.319640	+	0.947539i	$0.396438\pi$
$390$	−0.560447	−0.0283794
$391$	−8.31574	−0.420545
$392$	−22.1827	−1.12040
$393$	−24.1557	−1.21849
$394$	0.276509	0.0139303
$395$	−5.02265	−0.252717
$396$	4.77097	0.239750
$397$	−11.9357	−0.599036	−0.299518	−	0.954091i	$-0.596826\pi$
$397$	−11.9357	−0.599036	−0.299518	+	0.954091i	$0.596826\pi$
$398$	2.11282	0.105906
$399$	66.3036	3.31933
$400$	−15.3417	−0.767085
$401$	22.6746	1.13232	0.566158	−	0.824296i	$-0.308429\pi$
$401$	22.6746	1.13232	0.566158	+	0.824296i	$0.308429\pi$
$402$	−2.89379	−0.144329
$403$	−2.73918	−0.136448
$404$	13.7257	0.682881
$405$	0.364023	0.0180885
$406$	−6.17491	−0.306456
$407$	1.96114	0.0972100
$408$	3.26472	0.161628
$409$	−1.80073	−0.0890402	−0.0445201	−	0.999008i	$-0.514176\pi$
$409$	−1.80073	−0.0890402	−0.0445201	+	0.999008i	$0.514176\pi$
$410$	−0.738744	−0.0364840
$411$	−24.6801	−1.21738
$412$	17.6237	0.868256
$413$	−37.0108	−1.82118
$414$	−10.0008	−0.491511
$415$	−9.22836	−0.453003
$416$	−2.76539	−0.135584
$417$	−16.4860	−0.807324
$418$	0.639831	0.0312951
$419$	−9.36699	−0.457607	−0.228804	−	0.973473i	$-0.573481\pi$
$419$	−9.36699	−0.457607	−0.228804	+	0.973473i	$0.573481\pi$
$420$	−23.4039	−1.14200
$421$	−3.27077	−0.159408	−0.0797039	−	0.996819i	$-0.525397\pi$
$421$	−3.27077	−0.159408	−0.0797039	+	0.996819i	$0.525397\pi$
$422$	4.88387	0.237743
$423$	−47.7379	−2.32110
$424$	12.4998	0.607043
$425$	−4.69902	−0.227936
$426$	2.76865	0.134142
$427$	−78.1697	−3.78290
$428$	13.3821	0.646850
$429$	−1.27989	−0.0617935
$430$	−1.25854	−0.0606922
$431$	36.2702	1.74708	0.873538	−	0.486756i	$-0.161820\pi$
$431$	36.2702	1.74708	0.873538	+	0.486756i	$0.161820\pi$
$432$	−17.7451	−0.853762
$433$	−21.3741	−1.02717	−0.513587	−	0.858037i	$-0.671684\pi$
$433$	−21.3741	−1.02717	−0.513587	+	0.858037i	$0.671684\pi$
$434$	4.44811	0.213516
$435$	−9.92088	−0.475670
$436$	24.5017	1.17342
$437$	34.4898	1.64987
$438$	2.65566	0.126892
$439$	−24.2905	−1.15932	−0.579661	−	0.814857i	$-0.696815\pi$
$439$	−24.2905	−1.15932	−0.579661	+	0.814857i	$0.696815\pi$
$440$	−0.460479	−0.0219525
$441$	98.8956	4.70932
$442$	−0.264085	−0.0125612
$443$	−12.0962	−0.574707	−0.287353	−	0.957825i	$-0.592775\pi$
$443$	−12.0962	−0.574707	−0.287353	+	0.957825i	$0.592775\pi$
$444$	−20.3557	−0.966038
$445$	−8.76911	−0.415696
$446$	2.77079	0.131200
$447$	30.8214	1.45780
$448$	−32.9146	−1.55507
$449$	−36.8733	−1.74016	−0.870079	−	0.492912i	$-0.835933\pi$
$449$	−36.8733	−1.74016	−0.870079	+	0.492912i	$0.835933\pi$
$450$	−5.65119	−0.266399
$451$	−1.68706	−0.0794405
$452$	28.8520	1.35709
$453$	11.2402	0.528111
$454$	−1.44480	−0.0678080
$455$	3.85993	0.180957
$456$	−13.5405	−0.634093
$457$	8.52938	0.398987	0.199494	−	0.979899i	$-0.436070\pi$
$457$	8.52938	0.398987	0.199494	+	0.979899i	$0.436070\pi$
$458$	0.649949	0.0303701
$459$	−5.43516	−0.253692
$460$	−12.1743	−0.567628
$461$	−12.9579	−0.603512	−0.301756	−	0.953385i	$-0.597573\pi$
$461$	−12.9579	−0.603512	−0.301756	+	0.953385i	$0.597573\pi$
$462$	2.07839	0.0966954
$463$	20.4673	0.951197	0.475599	−	0.879662i	$-0.342231\pi$
$463$	20.4673	0.951197	0.475599	+	0.879662i	$0.342231\pi$
$464$	−15.2625	−0.708543
$465$	7.14653	0.331412
$466$	7.00214	0.324368
$467$	−34.9333	−1.61652	−0.808261	−	0.588824i	$-0.799591\pi$
$467$	−34.9333	−1.61652	−0.808261	+	0.588824i	$0.799591\pi$
$468$	8.16723	0.377530
$469$	19.9302	0.920291
$470$	2.25982	0.104238
$471$	−42.5225	−1.95933
$472$	7.55836	0.347902
$473$	−2.87411	−0.132152
$474$	−4.62965	−0.212647
$475$	19.4893	0.894232
$476$	−11.0280	−0.505469
$477$	−55.7269	−2.55156
$478$	1.98943	0.0909946
$479$	27.7462	1.26776	0.633878	−	0.773433i	$-0.281462\pi$
$479$	27.7462	1.26776	0.633878	+	0.773433i	$0.281462\pi$
$480$	7.21491	0.329314
$481$	3.35719	0.153075
$482$	−2.79895	−0.127489
$483$	112.035	5.09775
$484$	20.6607	0.939125
$485$	6.35293	0.288472
$486$	4.43114	0.201001
$487$	1.05782	0.0479344	0.0239672	−	0.999713i	$-0.492370\pi$
$487$	1.05782	0.0479344	0.0239672	+	0.999713i	$0.492370\pi$
$488$	15.9638	0.722648
$489$	−69.3609	−3.13661
$490$	−4.68153	−0.211490
$491$	4.10462	0.185239	0.0926195	−	0.995702i	$-0.470476\pi$
$491$	4.10462	0.185239	0.0926195	+	0.995702i	$0.470476\pi$
$492$	17.5109	0.789451
$493$	−4.67476	−0.210540
$494$	1.09530	0.0492799
$495$	2.05292	0.0922720
$496$	10.9944	0.493662
$497$	−19.0684	−0.855332
$498$	−8.50628	−0.381176
$499$	−2.70166	−0.120943	−0.0604715	−	0.998170i	$-0.519260\pi$
$499$	−2.70166	−0.120943	−0.0604715	+	0.998170i	$0.519260\pi$
$500$	−14.8531	−0.664249
$501$	−35.6210	−1.59143
$502$	3.32387	0.148352
$503$	−6.13508	−0.273550	−0.136775	−	0.990602i	$-0.543674\pi$
$503$	−6.13508	−0.273550	−0.136775	+	0.990602i	$0.543674\pi$
$504$	−27.0410	−1.20450
$505$	5.90611	0.262819
$506$	1.08114	0.0480623
$507$	34.0880	1.51390
$508$	−14.5475	−0.645440
$509$	−21.5476	−0.955079	−0.477539	−	0.878610i	$-0.658471\pi$
$509$	−21.5476	−0.955079	−0.477539	+	0.878610i	$0.658471\pi$
$510$	0.688999	0.0305094
$511$	−18.2902	−0.809109
$512$	18.7385	0.828131
$513$	22.5425	0.995276
$514$	4.13531	0.182401
$515$	7.58337	0.334163
$516$	29.8319	1.31328
$517$	5.16072	0.226968
$518$	−5.45170	−0.239534
$519$	13.0432	0.572534
$520$	−0.788276	−0.0345682
$521$	−8.97998	−0.393420	−0.196710	−	0.980462i	$-0.563026\pi$
$521$	−8.97998	−0.393420	−0.196710	+	0.980462i	$0.563026\pi$
$522$	−5.62201	−0.246069
$523$	30.4357	1.33086	0.665429	−	0.746461i	$-0.268248\pi$
$523$	30.4357	1.33086	0.665429	+	0.746461i	$0.268248\pi$
$524$	−16.6636	−0.727954
$525$	63.3080	2.76299
$526$	−8.12023	−0.354059
$527$	3.36747	0.146689
$528$	5.13714	0.223565
$529$	35.2781	1.53383
$530$	2.63800	0.114588
$531$	−33.6969	−1.46232
$532$	45.7391	1.98304
$533$	−2.88801	−0.125094
$534$	−8.08296	−0.349784
$535$	5.75826	0.248951
$536$	−4.07015	−0.175804
$537$	43.3345	1.87002
$538$	−5.27547	−0.227442
$539$	−10.6911	−0.460500
$540$	−7.95709	−0.342419
$541$	−33.8402	−1.45490	−0.727452	−	0.686159i	$-0.759296\pi$
$541$	−33.8402	−1.45490	−0.727452	+	0.686159i	$0.759296\pi$
$542$	1.41058	0.0605898
$543$	−1.74565	−0.0749131
$544$	3.39969	0.145761
$545$	10.5429	0.451610
$546$	3.55791	0.152264
$547$	31.3485	1.34036	0.670182	−	0.742196i	$-0.266216\pi$
$547$	31.3485	1.34036	0.670182	+	0.742196i	$0.266216\pi$
$548$	−17.0254	−0.727288
$549$	−71.1704	−3.03748
$550$	0.610923	0.0260499
$551$	19.3887	0.825986
$552$	−22.8797	−0.973825
$553$	31.8855	1.35591
$554$	1.09120	0.0463605
$555$	−8.75894	−0.371796
$556$	−11.3728	−0.482313
$557$	24.8399	1.05250	0.526251	−	0.850329i	$-0.323597\pi$
$557$	24.8399	1.05250	0.526251	+	0.850329i	$0.323597\pi$
$558$	4.04983	0.171443
$559$	−4.92008	−0.208097
$560$	−15.4928	−0.654691
$561$	1.57346	0.0664314
$562$	−3.24102	−0.136714
$563$	−34.7868	−1.46609	−0.733045	−	0.680180i	$-0.761901\pi$
$563$	−34.7868	−1.46609	−0.733045	+	0.680180i	$0.761901\pi$
$564$	−53.5658	−2.25553
$565$	12.4149	0.522298
$566$	−0.338273	−0.0142187
$567$	−2.31094	−0.0970505
$568$	3.89414	0.163394
$569$	38.7142	1.62298	0.811492	−	0.584364i	$-0.198656\pi$
$569$	38.7142	1.62298	0.811492	+	0.584364i	$0.198656\pi$
$570$	−2.85765	−0.119694
$571$	25.6468	1.07329	0.536643	−	0.843809i	$-0.319692\pi$
$571$	25.6468	1.07329	0.536643	+	0.843809i	$0.319692\pi$
$572$	−0.882921	−0.0369168
$573$	55.4392	2.31600
$574$	4.68980	0.195748
$575$	32.9315	1.37334
$576$	−29.9674	−1.24864
$577$	−29.9811	−1.24813	−0.624064	−	0.781373i	$-0.714520\pi$
$577$	−29.9811	−1.24813	−0.624064	+	0.781373i	$0.714520\pi$
$578$	−4.32671	−0.179967
$579$	22.4223	0.931841
$580$	−6.84385	−0.284176
$581$	58.5848	2.43051
$582$	5.85584	0.242732
$583$	6.02437	0.249504
$584$	3.73522	0.154565
$585$	3.51432	0.145299
$586$	−0.875262	−0.0361567
$587$	24.9277	1.02888	0.514438	−	0.857528i	$-0.328001\pi$
$587$	24.9277	1.02888	0.514438	+	0.857528i	$0.328001\pi$
$588$	110.969	4.57628
$589$	−13.9667	−0.575488
$590$	1.59515	0.0656711
$591$	−2.82026	−0.116010
$592$	−13.4749	−0.553816
$593$	−28.9192	−1.18757	−0.593786	−	0.804623i	$-0.702367\pi$
$593$	−28.9192	−1.18757	−0.593786	+	0.804623i	$0.702367\pi$
$594$	0.706630	0.0289934
$595$	−4.74530	−0.194538
$596$	21.2619	0.870922
$597$	−21.5497	−0.881971
$598$	1.85075	0.0756829
$599$	−23.4306	−0.957349	−0.478674	−	0.877993i	$-0.658883\pi$
$599$	−23.4306	−0.957349	−0.478674	+	0.877993i	$0.658883\pi$
$600$	−12.9288	−0.527815
$601$	0.404809	0.0165125	0.00825625	−	0.999966i	$-0.497372\pi$
$601$	0.404809	0.0165125	0.00825625	+	0.999966i	$0.497372\pi$
$602$	7.98964	0.325633
$603$	18.1457	0.738948
$604$	7.75399	0.315505
$605$	8.89021	0.361438
$606$	5.44398	0.221147
$607$	−10.6841	−0.433655	−0.216828	−	0.976210i	$-0.569571\pi$
$607$	−10.6841	−0.433655	−0.216828	+	0.976210i	$0.569571\pi$
$608$	−14.1003	−0.571844
$609$	62.9811	2.55212
$610$	3.36907	0.136410
$611$	8.83443	0.357403
$612$	−10.0406	−0.405866
$613$	44.6025	1.80148	0.900739	−	0.434360i	$-0.143026\pi$
$613$	44.6025	1.80148	0.900739	+	0.434360i	$0.143026\pi$
$614$	7.22532	0.291590
$615$	7.53484	0.303834
$616$	2.92328	0.117782
$617$	−25.8319	−1.03995	−0.519977	−	0.854181i	$-0.674059\pi$
$617$	−25.8319	−1.03995	−0.519977	+	0.854181i	$0.674059\pi$
$618$	6.99000	0.281179
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	4.92999	0.197993
$621$	38.0906	1.52852
$622$	7.30158	0.292767
$623$	55.6693	2.23034
$624$	8.79407	0.352044
$625$	15.1778	0.607111
$626$	7.11422	0.284341
$627$	−6.52597	−0.260622
$628$	−29.3339	−1.17055
$629$	−4.12725	−0.164564
$630$	−5.70685	−0.227366
$631$	−25.5449	−1.01693	−0.508464	−	0.861083i	$-0.669787\pi$
$631$	−25.5449	−1.01693	−0.508464	+	0.861083i	$0.669787\pi$
$632$	−6.51166	−0.259020
$633$	−49.8131	−1.97989
$634$	−5.64096	−0.224031
$635$	−6.25971	−0.248409
$636$	−62.5301	−2.47948
$637$	−18.3017	−0.725141
$638$	0.607769	0.0240618
$639$	−17.3610	−0.686789
$640$	6.58930	0.260465
$641$	28.4247	1.12271	0.561354	−	0.827575i	$-0.310280\pi$
$641$	28.4247	1.12271	0.561354	+	0.827575i	$0.310280\pi$
$642$	5.30770	0.209478
$643$	21.1113	0.832548	0.416274	−	0.909239i	$-0.363336\pi$
$643$	21.1113	0.832548	0.416274	+	0.909239i	$0.363336\pi$
$644$	77.2863	3.04551
$645$	12.8365	0.505437
$646$	−1.34653	−0.0529787
$647$	35.4992	1.39562	0.697809	−	0.716284i	$-0.254159\pi$
$647$	35.4992	1.39562	0.697809	+	0.716284i	$0.254159\pi$
$648$	0.471941	0.0185396
$649$	3.64281	0.142993
$650$	1.04581	0.0410202
$651$	−45.3686	−1.77814
$652$	−47.8481	−1.87388
$653$	24.8111	0.970932	0.485466	−	0.874255i	$-0.338650\pi$
$653$	24.8111	0.970932	0.485466	+	0.874255i	$0.338650\pi$
$654$	9.71799	0.380004
$655$	−7.17028	−0.280166
$656$	11.5917	0.452582
$657$	−16.6525	−0.649675
$658$	−14.3461	−0.559269
$659$	−33.1089	−1.28974	−0.644870	−	0.764292i	$-0.723088\pi$
$659$	−33.1089	−1.28974	−0.644870	+	0.764292i	$0.723088\pi$
$660$	2.30355	0.0896654
$661$	−20.6127	−0.801741	−0.400871	−	0.916135i	$-0.631292\pi$
$661$	−20.6127	−0.801741	−0.400871	+	0.916135i	$0.631292\pi$
$662$	−4.53756	−0.176357
$663$	2.69354	0.104608
$664$	−11.9642	−0.464301
$665$	19.6813	0.763208
$666$	−4.96355	−0.192334
$667$	32.7615	1.26853
$668$	−24.5729	−0.950754
$669$	−28.2607	−1.09262
$670$	−0.858980	−0.0331853
$671$	7.69389	0.297019
$672$	−45.8027	−1.76688
$673$	−5.98440	−0.230682	−0.115341	−	0.993326i	$-0.536796\pi$
$673$	−5.98440	−0.230682	−0.115341	+	0.993326i	$0.536796\pi$
$674$	−1.13626	−0.0437670
$675$	21.5240	0.828461
$676$	23.5154	0.904437
$677$	12.1342	0.466353	0.233177	−	0.972434i	$-0.425088\pi$
$677$	12.1342	0.466353	0.233177	+	0.972434i	$0.425088\pi$
$678$	11.4435	0.439484
$679$	−40.3305	−1.54774
$680$	0.969086	0.0371627
$681$	14.7363	0.564696
$682$	−0.437808	−0.0167645
$683$	−1.18963	−0.0455199	−0.0227599	−	0.999741i	$-0.507245\pi$
$683$	−1.18963	−0.0455199	−0.0227599	+	0.999741i	$0.507245\pi$
$684$	41.6436	1.59228
$685$	−7.32593	−0.279909
$686$	19.6479	0.750160
$687$	−6.62916	−0.252918
$688$	19.7480	0.752884
$689$	10.3129	0.392890
$690$	−4.82863	−0.183823
$691$	−30.8157	−1.17229	−0.586143	−	0.810208i	$-0.699354\pi$
$691$	−30.8157	−1.17229	−0.586143	+	0.810208i	$0.699354\pi$
$692$	8.99778	0.342044
$693$	−13.0326	−0.495069
$694$	−6.18798	−0.234892
$695$	−4.89364	−0.185626
$696$	−12.8620	−0.487533
$697$	3.55044	0.134483
$698$	−3.66273	−0.138636
$699$	−71.4184	−2.70129
$700$	43.6726	1.65067
$701$	28.8960	1.09139	0.545693	−	0.837985i	$-0.316267\pi$
$701$	28.8960	1.09139	0.545693	+	0.837985i	$0.316267\pi$
$702$	1.20965	0.0456553
$703$	17.1179	0.645613
$704$	3.23963	0.122098
$705$	−23.0491	−0.868078
$706$	4.66546	0.175587
$707$	−37.4940	−1.41011
$708$	−37.8107	−1.42101
$709$	4.48734	0.168526	0.0842628	−	0.996444i	$-0.473146\pi$
$709$	4.48734	0.168526	0.0842628	+	0.996444i	$0.473146\pi$
$710$	0.821835	0.0308429
$711$	29.0305	1.08873
$712$	−11.3688	−0.426063
$713$	−23.5998	−0.883821
$714$	−4.37400	−0.163693
$715$	−0.379916	−0.0142081
$716$	29.8940	1.11719
$717$	−20.2913	−0.757791
$718$	−10.2112	−0.381080
$719$	37.9566	1.41554	0.707771	−	0.706442i	$-0.249701\pi$
$719$	37.9566	1.41554	0.707771	+	0.706442i	$0.249701\pi$
$720$	−14.1056	−0.525684
$721$	−48.1418	−1.79289
$722$	0.386204	0.0143730
$723$	28.5480	1.06171
$724$	−1.20423	−0.0447547
$725$	18.5127	0.687545
$726$	8.19459	0.304130
$727$	13.4736	0.499707	0.249853	−	0.968284i	$-0.419618\pi$
$727$	13.4736	0.499707	0.249853	+	0.968284i	$0.419618\pi$
$728$	5.00424	0.185470
$729$	−43.8772	−1.62508
$730$	0.788296	0.0291761
$731$	6.04861	0.223716
$732$	−79.8589	−2.95167
$733$	34.3813	1.26990	0.634952	−	0.772552i	$-0.281020\pi$
$733$	34.3813	1.26990	0.634952	+	0.772552i	$0.281020\pi$
$734$	−3.04466	−0.112381
$735$	47.7494	1.76126
$736$	−23.8256	−0.878225
$737$	−1.96164	−0.0722580
$738$	4.26987	0.157176
$739$	0.391433	0.0143991	0.00719955	−	0.999974i	$-0.497708\pi$
$739$	0.391433	0.0143991	0.00719955	+	0.999974i	$0.497708\pi$
$740$	−6.04230	−0.222119
$741$	−11.1715	−0.410397
$742$	−16.7469	−0.614800
$743$	−46.9736	−1.72329	−0.861647	−	0.507508i	$-0.830567\pi$
$743$	−46.9736	−1.72329	−0.861647	+	0.507508i	$0.830567\pi$
$744$	9.26518	0.339678
$745$	9.14890	0.335190
$746$	8.00922	0.293238
$747$	53.3391	1.95158
$748$	1.08544	0.0396876
$749$	−36.5554	−1.33571
$750$	−5.89111	−0.215113
$751$	−51.3361	−1.87328	−0.936640	−	0.350292i	$-0.886082\pi$
$751$	−51.3361	−1.87328	−0.936640	+	0.350292i	$0.886082\pi$
$752$	−35.4592	−1.29306
$753$	−33.9019	−1.23545
$754$	1.04042	0.0378897
$755$	3.33650	0.121428
$756$	50.5143	1.83719
$757$	10.3206	0.375107	0.187554	−	0.982254i	$-0.439944\pi$
$757$	10.3206	0.375107	0.187554	+	0.982254i	$0.439944\pi$
$758$	6.36580	0.231216
$759$	−11.0271	−0.400257
$760$	−4.01931	−0.145796
$761$	42.2896	1.53300	0.766498	−	0.642246i	$-0.221997\pi$
$761$	42.2896	1.53300	0.766498	+	0.642246i	$0.221997\pi$
$762$	−5.76991	−0.209022
$763$	−66.9301	−2.42303
$764$	38.2443	1.38363
$765$	−4.32041	−0.156205
$766$	5.31359	0.191988
$767$	6.23599	0.225168
$768$	−28.8597	−1.04139
$769$	25.6137	0.923654	0.461827	−	0.886970i	$-0.347194\pi$
$769$	25.6137	0.923654	0.461827	+	0.886970i	$0.347194\pi$
$770$	0.616940	0.0222330
$771$	−42.1782	−1.51901
$772$	15.4679	0.556702
$773$	22.7498	0.818255	0.409127	−	0.912477i	$-0.365833\pi$
$773$	22.7498	0.818255	0.409127	+	0.912477i	$0.365833\pi$
$774$	7.27425	0.261467
$775$	−13.3357	−0.479032
$776$	8.23631	0.295666
$777$	55.6047	1.99481
$778$	3.44983	0.123682
$779$	−14.7256	−0.527598
$780$	3.94335	0.141194
$781$	1.87681	0.0671576
$782$	−2.27527	−0.0813634
$783$	21.4129	0.765235
$784$	73.4586	2.62352
$785$	−12.6222	−0.450506
$786$	−6.60923	−0.235743
$787$	15.6086	0.556385	0.278192	−	0.960525i	$-0.410265\pi$
$787$	15.6086	0.556385	0.278192	+	0.960525i	$0.410265\pi$
$788$	−1.94554	−0.0693070
$789$	82.8225	2.94856
$790$	−1.37425	−0.0488935
$791$	−78.8138	−2.80230
$792$	2.66153	0.0945733
$793$	13.1709	0.467711
$794$	−3.26573	−0.115896
$795$	−26.9064	−0.954271
$796$	−14.8659	−0.526909
$797$	47.9585	1.69878	0.849388	−	0.527769i	$-0.176971\pi$
$797$	47.9585	1.69878	0.849388	+	0.527769i	$0.176971\pi$
$798$	18.1413	0.642195
$799$	−10.8608	−0.384228
$800$	−13.4633	−0.475999
$801$	50.6847	1.79085
$802$	6.20400	0.219071
$803$	1.80022	0.0635284
$804$	20.3609	0.718073
$805$	33.2559	1.17212
$806$	−0.749466	−0.0263988
$807$	53.8073	1.89411
$808$	7.65703	0.269373
$809$	−21.3474	−0.750535	−0.375268	−	0.926916i	$-0.622449\pi$
$809$	−21.3474	−0.750535	−0.375268	+	0.926916i	$0.622449\pi$
$810$	0.0996003	0.00349960
$811$	−5.61499	−0.197169	−0.0985845	−	0.995129i	$-0.531431\pi$
$811$	−5.61499	−0.197169	−0.0985845	+	0.995129i	$0.531431\pi$
$812$	43.4471	1.52469
$813$	−14.3873	−0.504584
$814$	0.536587	0.0188073
$815$	−20.5888	−0.721194
$816$	−10.8112	−0.378467
$817$	−25.0868	−0.877676
$818$	−0.492696	−0.0172267
$819$	−22.3101	−0.779577
$820$	5.19786	0.181517
$821$	1.94104	0.0677428	0.0338714	−	0.999426i	$-0.489216\pi$
$821$	1.94104	0.0677428	0.0338714	+	0.999426i	$0.489216\pi$
$822$	−6.75270	−0.235528
$823$	−50.0586	−1.74493	−0.872466	−	0.488675i	$-0.837480\pi$
$823$	−50.0586	−1.74493	−0.872466	+	0.488675i	$0.837480\pi$
$824$	9.83153	0.342497
$825$	−6.23112	−0.216940
$826$	−10.1265	−0.352347
$827$	−33.3432	−1.15946	−0.579729	−	0.814809i	$-0.696842\pi$
$827$	−33.3432	−1.15946	−0.579729	+	0.814809i	$0.696842\pi$
$828$	70.3661	2.44539
$829$	−36.7502	−1.27639	−0.638194	−	0.769875i	$-0.720318\pi$
$829$	−36.7502	−1.27639	−0.638194	+	0.769875i	$0.720318\pi$
$830$	−2.52497	−0.0876430
$831$	−11.1297	−0.386085
$832$	5.54580	0.192266
$833$	22.4997	0.779568
$834$	−4.51073	−0.156194
$835$	−10.5736	−0.365914
$836$	−4.50189	−0.155701
$837$	−15.4248	−0.533160
$838$	−2.56290	−0.0885339
$839$	−32.9859	−1.13880	−0.569400	−	0.822061i	$-0.692824\pi$
$839$	−32.9859	−1.13880	−0.569400	+	0.822061i	$0.692824\pi$
$840$	−13.0561	−0.450478
$841$	−10.5829	−0.364927
$842$	−0.894916	−0.0308408
$843$	33.0568	1.13854
$844$	−34.3632	−1.18283
$845$	10.1185	0.348088
$846$	−13.0616	−0.449065
$847$	−56.4381	−1.93924
$848$	−41.3933	−1.42145
$849$	3.45022	0.118411
$850$	−1.28570	−0.0440991
$851$	28.9245	0.991518
$852$	−19.4804	−0.667388
$853$	5.90927	0.202329	0.101165	−	0.994870i	$-0.467743\pi$
$853$	5.90927	0.202329	0.101165	+	0.994870i	$0.467743\pi$
$854$	−21.3880	−0.731882
$855$	17.9190	0.612818
$856$	7.46535	0.255160
$857$	−21.7500	−0.742967	−0.371484	−	0.928440i	$-0.621151\pi$
$857$	−21.7500	−0.742967	−0.371484	+	0.928440i	$0.621151\pi$
$858$	−0.350189	−0.0119553
$859$	−37.4777	−1.27872	−0.639362	−	0.768906i	$-0.720801\pi$
$859$	−37.4777	−1.27872	−0.639362	+	0.768906i	$0.720801\pi$
$860$	8.85518	0.301959
$861$	−47.8337	−1.63017
$862$	9.92389	0.338009
$863$	−19.6375	−0.668467	−0.334234	−	0.942490i	$-0.608477\pi$
$863$	−19.6375	−0.668467	−0.334234	+	0.942490i	$0.608477\pi$
$864$	−15.5724	−0.529785
$865$	3.87170	0.131642
$866$	−5.84817	−0.198729
$867$	44.1303	1.49874
$868$	−31.2972	−1.06230
$869$	−3.13835	−0.106461
$870$	−2.71445	−0.0920284
$871$	−3.35806	−0.113783
$872$	13.6685	0.462873
$873$	−36.7193	−1.24276
$874$	9.43674	0.319202
$875$	40.5735	1.37163
$876$	−18.6854	−0.631322
$877$	23.3371	0.788039	0.394019	−	0.919102i	$-0.371084\pi$
$877$	23.3371	0.788039	0.394019	+	0.919102i	$0.371084\pi$
$878$	−6.64612	−0.224296
$879$	8.92725	0.301109
$880$	1.52489	0.0514040
$881$	−2.61301	−0.0880346	−0.0440173	−	0.999031i	$-0.514016\pi$
$881$	−2.61301	−0.0880346	−0.0440173	+	0.999031i	$0.514016\pi$
$882$	27.0588	0.911117
$883$	−13.9390	−0.469085	−0.234542	−	0.972106i	$-0.575359\pi$
$883$	−13.9390	−0.469085	−0.234542	+	0.972106i	$0.575359\pi$
$884$	1.85812	0.0624954
$885$	−16.2697	−0.546901
$886$	−3.30963	−0.111189
$887$	51.3120	1.72289	0.861444	−	0.507853i	$-0.169561\pi$
$887$	51.3120	1.72289	0.861444	+	0.507853i	$0.169561\pi$
$888$	−11.3556	−0.381069
$889$	39.7387	1.33279
$890$	−2.39931	−0.0804252
$891$	0.227456	0.00762006
$892$	−19.4954	−0.652756
$893$	45.0456	1.50739
$894$	8.43303	0.282043
$895$	12.8632	0.429970
$896$	−41.8311	−1.39748
$897$	−18.8768	−0.630278
$898$	−10.0889	−0.336671
$899$	−13.2668	−0.442473
$900$	39.7621	1.32540
$901$	−12.6784	−0.422378
$902$	−0.461596	−0.0153695
$903$	−81.4905	−2.71183
$904$	16.0954	0.535324
$905$	−0.518172	−0.0172246
$906$	3.07543	0.102174
$907$	−40.9581	−1.35999	−0.679995	−	0.733216i	$-0.738018\pi$
$907$	−40.9581	−1.35999	−0.679995	+	0.733216i	$0.738018\pi$
$908$	10.1657	0.337362
$909$	−34.1368	−1.13225
$910$	1.05612	0.0350099
$911$	−7.46181	−0.247221	−0.123610	−	0.992331i	$-0.539447\pi$
$911$	−7.46181	−0.247221	−0.123610	+	0.992331i	$0.539447\pi$
$912$	44.8398	1.48479
$913$	−5.76624	−0.190835
$914$	2.33372	0.0771926
$915$	−34.3629	−1.13600
$916$	−4.57309	−0.151099
$917$	45.5193	1.50318
$918$	−1.48711	−0.0490821
$919$	−23.1702	−0.764313	−0.382157	−	0.924098i	$-0.624819\pi$
$919$	−23.1702	−0.764313	−0.382157	+	0.924098i	$0.624819\pi$
$920$	−6.79152	−0.223910
$921$	−73.6948	−2.42833
$922$	−3.54542	−0.116762
$923$	3.21284	0.105752
$924$	−14.6237	−0.481084
$925$	16.3445	0.537404
$926$	5.60006	0.184029
$927$	−43.8312	−1.43961
$928$	−13.3938	−0.439672
$929$	−5.82082	−0.190975	−0.0954874	−	0.995431i	$-0.530441\pi$
$929$	−5.82082	−0.190975	−0.0954874	+	0.995431i	$0.530441\pi$
$930$	1.95536	0.0641188
$931$	−93.3181	−3.05838
$932$	−49.2675	−1.61381
$933$	−74.4727	−2.43813
$934$	−9.55810	−0.312751
$935$	0.467059	0.0152745
$936$	4.55616	0.148923
$937$	−1.19620	−0.0390781	−0.0195390	−	0.999809i	$-0.506220\pi$
$937$	−1.19620	−0.0390781	−0.0195390	+	0.999809i	$0.506220\pi$
$938$	5.45310	0.178050
$939$	−72.5616	−2.36796
$940$	−15.9003	−0.518609
$941$	−13.6021	−0.443417	−0.221709	−	0.975113i	$-0.571163\pi$
$941$	−13.6021	−0.443417	−0.221709	+	0.975113i	$0.571163\pi$
$942$	−11.6346	−0.379075
$943$	−24.8821	−0.810273
$944$	−25.0297	−0.814647
$945$	21.7360	0.707073
$946$	−0.786385	−0.0255676
$947$	−20.3941	−0.662719	−0.331360	−	0.943505i	$-0.607507\pi$
$947$	−20.3941	−0.662719	−0.331360	+	0.943505i	$0.607507\pi$
$948$	32.5745	1.05797
$949$	3.08172	0.100037
$950$	5.33247	0.173008
$951$	57.5351	1.86570
$952$	−6.15209	−0.199390
$953$	−21.3575	−0.691838	−0.345919	−	0.938264i	$-0.612433\pi$
$953$	−21.3575	−0.691838	−0.345919	+	0.938264i	$0.612433\pi$
$954$	−15.2474	−0.493654
$955$	16.4563	0.532515
$956$	−13.9978	−0.452721
$957$	−6.19895	−0.200384
$958$	7.59162	0.245274
$959$	46.5075	1.50180
$960$	−14.4690	−0.466986
$961$	−21.4432	−0.691716
$962$	0.918561	0.0296156
$963$	−33.2822	−1.07250
$964$	19.6936	0.634289
$965$	6.65576	0.214256
$966$	30.6538	0.986268
$967$	54.6648	1.75790	0.878951	−	0.476913i	$-0.158244\pi$
$967$	54.6648	1.75790	0.878951	+	0.476913i	$0.158244\pi$
$968$	11.5258	0.370453
$969$	13.7340	0.441200
$970$	1.73822	0.0558110
$971$	58.8857	1.88973	0.944866	−	0.327458i	$-0.106192\pi$
$971$	58.8857	1.88973	0.944866	+	0.327458i	$0.106192\pi$
$972$	−31.1778	−1.00003
$973$	31.0665	0.995946
$974$	0.289430	0.00927394
$975$	−10.6668	−0.341611
$976$	−52.8646	−1.69215
$977$	18.7796	0.600812	0.300406	−	0.953811i	$-0.402878\pi$
$977$	18.7796	0.600812	0.300406	+	0.953811i	$0.402878\pi$
$978$	−18.9778	−0.606844
$979$	−5.47928	−0.175119
$980$	32.9396	1.05222
$981$	−60.9372	−1.94557
$982$	1.12306	0.0358384
$983$	−21.4780	−0.685040	−0.342520	−	0.939510i	$-0.611281\pi$
$983$	−21.4780	−0.685040	−0.342520	+	0.939510i	$0.611281\pi$
$984$	9.76860	0.311412
$985$	−0.837155	−0.0266740
$986$	−1.27906	−0.0407335
$987$	146.323	4.65752
$988$	−7.70661	−0.245180
$989$	−42.3897	−1.34791
$990$	0.561700	0.0178520
$991$	−31.6503	−1.00541	−0.502703	−	0.864459i	$-0.667661\pi$
$991$	−31.6503	−1.00541	−0.502703	+	0.864459i	$0.667661\pi$
$992$	9.64823	0.306332
$993$	46.2809	1.46868
$994$	−5.21729	−0.165482
$995$	−6.39673	−0.202790
$996$	59.8508	1.89645
$997$	37.4488	1.18602	0.593008	−	0.805197i	$-0.297940\pi$
$997$	37.4488	1.18602	0.593008	+	0.805197i	$0.297940\pi$
$998$	−0.739201	−0.0233990
$999$	18.9050	0.598128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.a.1.14	✓	21
3.2	odd	2		5571.2.a.e.1.8		21
4.3	odd	2		9904.2.a.j.1.20		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.a.1.14	✓	21	1.1	even	1	trivial
5571.2.a.e.1.8		21	3.2	odd	2
9904.2.a.j.1.20		21	4.3	odd	2

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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q+0.273610 q^{2} -2.79069 q^{3} -1.92514 q^{4} -0.828377 q^{5} -0.763560 q^{6} +5.25882 q^{7} -1.07396 q^{8} +4.78794 q^{9} +O(q^{10})\)	\(q+0.273610 q^{2} -2.79069 q^{3} -1.92514 q^{4} -0.828377 q^{5} -0.763560 q^{6} +5.25882 q^{7} -1.07396 q^{8} +4.78794 q^{9} -0.226652 q^{10} -0.517602 q^{11} +5.37246 q^{12} -0.886062 q^{13} +1.43886 q^{14} +2.31174 q^{15} +3.55643 q^{16} +1.08930 q^{17} +1.31003 q^{18} -4.51791 q^{19} +1.59474 q^{20} -14.6757 q^{21} -0.141621 q^{22} -7.63401 q^{23} +2.99708 q^{24} -4.31379 q^{25} -0.242435 q^{26} -4.98959 q^{27} -10.1239 q^{28} -4.29152 q^{29} +0.632515 q^{30} +3.09141 q^{31} +3.12099 q^{32} +1.44447 q^{33} +0.298043 q^{34} -4.35628 q^{35} -9.21745 q^{36} -3.78889 q^{37} -1.23614 q^{38} +2.47272 q^{39} +0.889640 q^{40} +3.25938 q^{41} -4.01542 q^{42} +5.55274 q^{43} +0.996455 q^{44} -3.96622 q^{45} -2.08874 q^{46} -9.97044 q^{47} -9.92489 q^{48} +20.6551 q^{49} -1.18030 q^{50} -3.03990 q^{51} +1.70579 q^{52} -11.6390 q^{53} -1.36520 q^{54} +0.428769 q^{55} -5.64774 q^{56} +12.6081 q^{57} -1.17420 q^{58} -7.03787 q^{59} -4.45042 q^{60} -14.8645 q^{61} +0.845839 q^{62} +25.1789 q^{63} -6.25893 q^{64} +0.733993 q^{65} +0.395220 q^{66} +3.78987 q^{67} -2.09705 q^{68} +21.3041 q^{69} -1.19192 q^{70} -3.62598 q^{71} -5.14204 q^{72} -3.47800 q^{73} -1.03668 q^{74} +12.0384 q^{75} +8.69760 q^{76} -2.72197 q^{77} +0.676561 q^{78} +6.06325 q^{79} -2.94606 q^{80} -0.439442 q^{81} +0.891797 q^{82} +11.1403 q^{83} +28.2528 q^{84} -0.902352 q^{85} +1.51929 q^{86} +11.9763 q^{87} +0.555882 q^{88} +10.5859 q^{89} -1.08520 q^{90} -4.65964 q^{91} +14.6965 q^{92} -8.62715 q^{93} -2.72801 q^{94} +3.74253 q^{95} -8.70970 q^{96} -7.66913 q^{97} +5.65145 q^{98} -2.47825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * q^99

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