LMFDB - Embedded newform 6035.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61440 q^{2} +2.49037 q^{3} +4.83510 q^{4} +1.00000 q^{5} -6.51084 q^{6} +2.00109 q^{7} -7.41211 q^{8} +3.20197 q^{9} +O(q^{10})$	\(q-2.61440 q^{2} +2.49037 q^{3} +4.83510 q^{4} +1.00000 q^{5} -6.51084 q^{6} +2.00109 q^{7} -7.41211 q^{8} +3.20197 q^{9} -2.61440 q^{10} -2.86712 q^{11} +12.0412 q^{12} -2.84461 q^{13} -5.23167 q^{14} +2.49037 q^{15} +9.70803 q^{16} +1.00000 q^{17} -8.37123 q^{18} -2.39792 q^{19} +4.83510 q^{20} +4.98348 q^{21} +7.49581 q^{22} -0.448199 q^{23} -18.4589 q^{24} +1.00000 q^{25} +7.43696 q^{26} +0.502971 q^{27} +9.67550 q^{28} -2.83337 q^{29} -6.51084 q^{30} -7.70787 q^{31} -10.5565 q^{32} -7.14020 q^{33} -2.61440 q^{34} +2.00109 q^{35} +15.4818 q^{36} -3.27577 q^{37} +6.26914 q^{38} -7.08414 q^{39} -7.41211 q^{40} +7.74396 q^{41} -13.0288 q^{42} -9.45879 q^{43} -13.8628 q^{44} +3.20197 q^{45} +1.17177 q^{46} -6.83108 q^{47} +24.1766 q^{48} -2.99562 q^{49} -2.61440 q^{50} +2.49037 q^{51} -13.7540 q^{52} +2.90826 q^{53} -1.31497 q^{54} -2.86712 q^{55} -14.8323 q^{56} -5.97173 q^{57} +7.40757 q^{58} +9.63215 q^{59} +12.0412 q^{60} -1.94075 q^{61} +20.1515 q^{62} +6.40744 q^{63} +8.18285 q^{64} -2.84461 q^{65} +18.6674 q^{66} -11.3025 q^{67} +4.83510 q^{68} -1.11618 q^{69} -5.23167 q^{70} -1.00000 q^{71} -23.7333 q^{72} +6.12763 q^{73} +8.56418 q^{74} +2.49037 q^{75} -11.5942 q^{76} -5.73738 q^{77} +18.5208 q^{78} -0.904474 q^{79} +9.70803 q^{80} -8.35331 q^{81} -20.2458 q^{82} +11.1731 q^{83} +24.0956 q^{84} +1.00000 q^{85} +24.7291 q^{86} -7.05616 q^{87} +21.2514 q^{88} +4.28985 q^{89} -8.37123 q^{90} -5.69233 q^{91} -2.16709 q^{92} -19.1955 q^{93} +17.8592 q^{94} -2.39792 q^{95} -26.2896 q^{96} -7.73520 q^{97} +7.83176 q^{98} -9.18042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.61440	−1.84866	−0.924331	−	0.381591i	$-0.875376\pi$
$2$	−2.61440	−1.84866	−0.924331	+	0.381591i	$0.875376\pi$
$3$	2.49037	1.43782	0.718909	−	0.695104i	$-0.244642\pi$
$3$	2.49037	1.43782	0.718909	+	0.695104i	$0.244642\pi$
$4$	4.83510	2.41755
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.51084	−2.65804
$7$	2.00109	0.756343	0.378171	−	0.925736i	$-0.376553\pi$
$7$	2.00109	0.756343	0.378171	+	0.925736i	$0.376553\pi$
$8$	−7.41211	−2.62058
$9$	3.20197	1.06732
$10$	−2.61440	−0.826747
$11$	−2.86712	−0.864469	−0.432234	−	0.901761i	$-0.642275\pi$
$11$	−2.86712	−0.864469	−0.432234	+	0.901761i	$0.642275\pi$
$12$	12.0412	3.47600
$13$	−2.84461	−0.788953	−0.394476	−	0.918906i	$-0.629074\pi$
$13$	−2.84461	−0.788953	−0.394476	+	0.918906i	$0.629074\pi$
$14$	−5.23167	−1.39822
$15$	2.49037	0.643012
$16$	9.70803	2.42701
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−8.37123	−1.97312
$19$	−2.39792	−0.550121	−0.275061	−	0.961427i	$-0.588698\pi$
$19$	−2.39792	−0.550121	−0.275061	+	0.961427i	$0.588698\pi$
$20$	4.83510	1.08116
$21$	4.98348	1.08748
$22$	7.49581	1.59811
$23$	−0.448199	−0.0934559	−0.0467280	−	0.998908i	$-0.514879\pi$
$23$	−0.448199	−0.0934559	−0.0467280	+	0.998908i	$0.514879\pi$
$24$	−18.4589	−3.76791
$25$	1.00000	0.200000
$26$	7.43696	1.45851
$27$	0.502971	0.0967969
$28$	9.67550	1.82850
$29$	−2.83337	−0.526144	−0.263072	−	0.964776i	$-0.584736\pi$
$29$	−2.83337	−0.526144	−0.263072	+	0.964776i	$0.584736\pi$
$30$	−6.51084	−1.18871
$31$	−7.70787	−1.38437	−0.692187	−	0.721718i	$-0.743353\pi$
$31$	−7.70787	−1.38437	−0.692187	+	0.721718i	$0.743353\pi$
$32$	−10.5565	−1.86614
$33$	−7.14020	−1.24295
$34$	−2.61440	−0.448366
$35$	2.00109	0.338247
$36$	15.4818	2.58031
$37$	−3.27577	−0.538533	−0.269267	−	0.963066i	$-0.586781\pi$
$37$	−3.27577	−0.538533	−0.269267	+	0.963066i	$0.586781\pi$
$38$	6.26914	1.01699
$39$	−7.08414	−1.13437
$40$	−7.41211	−1.17196
$41$	7.74396	1.20940	0.604702	−	0.796452i	$-0.293292\pi$
$41$	7.74396	1.20940	0.604702	+	0.796452i	$0.293292\pi$
$42$	−13.0288	−2.01039
$43$	−9.45879	−1.44245	−0.721226	−	0.692700i	$-0.756421\pi$
$43$	−9.45879	−1.44245	−0.721226	+	0.692700i	$0.756421\pi$
$44$	−13.8628	−2.08990
$45$	3.20197	0.477321
$46$	1.17177	0.172768
$47$	−6.83108	−0.996416	−0.498208	−	0.867058i	$-0.666008\pi$
$47$	−6.83108	−0.996416	−0.498208	+	0.867058i	$0.666008\pi$
$48$	24.1766	3.48959
$49$	−2.99562	−0.427946
$50$	−2.61440	−0.369732
$51$	2.49037	0.348722
$52$	−13.7540	−1.90733
$53$	2.90826	0.399481	0.199740	−	0.979849i	$-0.435990\pi$
$53$	2.90826	0.399481	0.199740	+	0.979849i	$0.435990\pi$
$54$	−1.31497	−0.178945
$55$	−2.86712	−0.386602
$56$	−14.8323	−1.98205
$57$	−5.97173	−0.790975
$58$	7.40757	0.972662
$59$	9.63215	1.25400	0.627000	−	0.779020i	$-0.284283\pi$
$59$	9.63215	1.25400	0.627000	+	0.779020i	$0.284283\pi$
$60$	12.0412	1.55452
$61$	−1.94075	−0.248487	−0.124244	−	0.992252i	$-0.539650\pi$
$61$	−1.94075	−0.248487	−0.124244	+	0.992252i	$0.539650\pi$
$62$	20.1515	2.55924
$63$	6.40744	0.807261
$64$	8.18285	1.02286
$65$	−2.84461	−0.352830
$66$	18.6674	2.29779
$67$	−11.3025	−1.38082	−0.690411	−	0.723418i	$-0.742570\pi$
$67$	−11.3025	−1.38082	−0.690411	+	0.723418i	$0.742570\pi$
$68$	4.83510	0.586343
$69$	−1.11618	−0.134373
$70$	−5.23167	−0.625304
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−23.7333	−2.79700
$73$	6.12763	0.717185	0.358593	−	0.933494i	$-0.383257\pi$
$73$	6.12763	0.717185	0.358593	+	0.933494i	$0.383257\pi$
$74$	8.56418	0.995566
$75$	2.49037	0.287564
$76$	−11.5942	−1.32995
$77$	−5.73738	−0.653835
$78$	18.5208	2.09707
$79$	−0.904474	−0.101761	−0.0508807	−	0.998705i	$-0.516203\pi$
$79$	−0.904474	−0.101761	−0.0508807	+	0.998705i	$0.516203\pi$
$80$	9.70803	1.08539
$81$	−8.35331	−0.928146
$82$	−20.2458	−2.23578
$83$	11.1731	1.22641	0.613205	−	0.789924i	$-0.289880\pi$
$83$	11.1731	1.22641	0.613205	+	0.789924i	$0.289880\pi$
$84$	24.0956	2.62905
$85$	1.00000	0.108465
$86$	24.7291	2.66661
$87$	−7.05616	−0.756499
$88$	21.2514	2.26541
$89$	4.28985	0.454723	0.227361	−	0.973810i	$-0.426990\pi$
$89$	4.28985	0.454723	0.227361	+	0.973810i	$0.426990\pi$
$90$	−8.37123	−0.882405
$91$	−5.69233	−0.596719
$92$	−2.16709	−0.225935
$93$	−19.1955	−1.99048
$94$	17.8592	1.84204
$95$	−2.39792	−0.246022
$96$	−26.2896	−2.68317
$97$	−7.73520	−0.785391	−0.392695	−	0.919669i	$-0.628457\pi$
$97$	−7.73520	−0.785391	−0.392695	+	0.919669i	$0.628457\pi$
$98$	7.83176	0.791127
$99$	−9.18042	−0.922667
$100$	4.83510	0.483510
$101$	−15.0373	−1.49627	−0.748133	−	0.663548i	$-0.769050\pi$
$101$	−15.0373	−1.49627	−0.748133	+	0.663548i	$0.769050\pi$
$102$	−6.51084	−0.644670
$103$	−4.97593	−0.490293	−0.245147	−	0.969486i	$-0.578836\pi$
$103$	−4.97593	−0.490293	−0.245147	+	0.969486i	$0.578836\pi$
$104$	21.0845	2.06751
$105$	4.98348	0.486337
$106$	−7.60337	−0.738505
$107$	−4.14083	−0.400309	−0.200155	−	0.979764i	$-0.564144\pi$
$107$	−4.14083	−0.400309	−0.200155	+	0.979764i	$0.564144\pi$
$108$	2.43192	0.234012
$109$	−0.898682	−0.0860781	−0.0430391	−	0.999073i	$-0.513704\pi$
$109$	−0.898682	−0.0860781	−0.0430391	+	0.999073i	$0.513704\pi$
$110$	7.49581	0.714697
$111$	−8.15789	−0.774313
$112$	19.4267	1.83565
$113$	13.6324	1.28243	0.641214	−	0.767362i	$-0.278431\pi$
$113$	13.6324	1.28243	0.641214	+	0.767362i	$0.278431\pi$
$114$	15.6125	1.46224
$115$	−0.448199	−0.0417948
$116$	−13.6996	−1.27198
$117$	−9.10834	−0.842067
$118$	−25.1823	−2.31822
$119$	2.00109	0.183440
$120$	−18.4589	−1.68506
$121$	−2.77963	−0.252694
$122$	5.07389	0.459369
$123$	19.2854	1.73890
$124$	−37.2684	−3.34680
$125$	1.00000	0.0894427
$126$	−16.7516	−1.49235
$127$	6.48939	0.575841	0.287920	−	0.957654i	$-0.407036\pi$
$127$	6.48939	0.575841	0.287920	+	0.957654i	$0.407036\pi$
$128$	−0.280301	−0.0247754
$129$	−23.5559	−2.07398
$130$	7.43696	0.652264
$131$	15.7546	1.37648	0.688241	−	0.725482i	$-0.258383\pi$
$131$	15.7546	1.37648	0.688241	+	0.725482i	$0.258383\pi$
$132$	−34.5236	−3.00489
$133$	−4.79847	−0.416080
$134$	29.5493	2.55267
$135$	0.502971	0.0432889
$136$	−7.41211	−0.635583
$137$	−8.90136	−0.760495	−0.380247	−	0.924885i	$-0.624161\pi$
$137$	−8.90136	−0.760495	−0.380247	+	0.924885i	$0.624161\pi$
$138$	2.91815	0.248410
$139$	−9.22806	−0.782714	−0.391357	−	0.920239i	$-0.627994\pi$
$139$	−9.22806	−0.782714	−0.391357	+	0.920239i	$0.627994\pi$
$140$	9.67550	0.817729
$141$	−17.0120	−1.43267
$142$	2.61440	0.219396
$143$	8.15583	0.682025
$144$	31.0848	2.59040
$145$	−2.83337	−0.235299
$146$	−16.0201	−1.32583
$147$	−7.46022	−0.615308
$148$	−15.8387	−1.30193
$149$	−21.6938	−1.77722	−0.888612	−	0.458661i	$-0.848329\pi$
$149$	−21.6938	−1.77722	−0.888612	+	0.458661i	$0.848329\pi$
$150$	−6.51084	−0.531608
$151$	18.6306	1.51614	0.758069	−	0.652174i	$-0.226143\pi$
$151$	18.6306	1.51614	0.758069	+	0.652174i	$0.226143\pi$
$152$	17.7737	1.44163
$153$	3.20197	0.258864
$154$	14.9998	1.20872
$155$	−7.70787	−0.619111
$156$	−34.2526	−2.74240
$157$	−8.25827	−0.659082	−0.329541	−	0.944141i	$-0.606894\pi$
$157$	−8.25827	−0.659082	−0.329541	+	0.944141i	$0.606894\pi$
$158$	2.36466	0.188122
$159$	7.24266	0.574381
$160$	−10.5565	−0.834563
$161$	−0.896888	−0.0706847
$162$	21.8389	1.71583
$163$	−0.100251	−0.00785225	−0.00392612	−	0.999992i	$-0.501250\pi$
$163$	−0.100251	−0.00785225	−0.00392612	+	0.999992i	$0.501250\pi$
$164$	37.4429	2.92380
$165$	−7.14020	−0.555864
$166$	−29.2110	−2.26722
$167$	12.4033	0.959793	0.479896	−	0.877325i	$-0.340674\pi$
$167$	12.4033	0.959793	0.479896	+	0.877325i	$0.340674\pi$
$168$	−36.9380	−2.84983
$169$	−4.90820	−0.377554
$170$	−2.61440	−0.200516
$171$	−7.67807	−0.587157
$172$	−45.7342	−3.48720
$173$	−4.75093	−0.361206	−0.180603	−	0.983556i	$-0.557805\pi$
$173$	−4.75093	−0.361206	−0.180603	+	0.983556i	$0.557805\pi$
$174$	18.4476	1.39851
$175$	2.00109	0.151269
$176$	−27.8341	−2.09807
$177$	23.9877	1.80302
$178$	−11.2154	−0.840629
$179$	−12.0009	−0.896992	−0.448496	−	0.893785i	$-0.648040\pi$
$179$	−12.0009	−0.896992	−0.448496	+	0.893785i	$0.648040\pi$
$180$	15.4818	1.15395
$181$	−18.9394	−1.40775	−0.703877	−	0.710322i	$-0.748549\pi$
$181$	−18.9394	−1.40775	−0.703877	+	0.710322i	$0.748549\pi$
$182$	14.8821	1.10313
$183$	−4.83319	−0.357279
$184$	3.32210	0.244908
$185$	−3.27577	−0.240839
$186$	50.1848	3.67973
$187$	−2.86712	−0.209665
$188$	−33.0290	−2.40889
$189$	1.00649	0.0732116
$190$	6.26914	0.454811
$191$	−21.7515	−1.57388	−0.786941	−	0.617028i	$-0.788337\pi$
$191$	−21.7515	−1.57388	−0.786941	+	0.617028i	$0.788337\pi$
$192$	20.3784	1.47068
$193$	8.42325	0.606319	0.303160	−	0.952940i	$-0.401958\pi$
$193$	8.42325	0.606319	0.303160	+	0.952940i	$0.401958\pi$
$194$	20.2229	1.45192
$195$	−7.08414	−0.507306
$196$	−14.4841	−1.03458
$197$	8.09535	0.576770	0.288385	−	0.957515i	$-0.406882\pi$
$197$	8.09535	0.576770	0.288385	+	0.957515i	$0.406882\pi$
$198$	24.0013	1.70570
$199$	1.10791	0.0785377	0.0392688	−	0.999229i	$-0.487497\pi$
$199$	1.10791	0.0785377	0.0392688	+	0.999229i	$0.487497\pi$
$200$	−7.41211	−0.524115
$201$	−28.1475	−1.98537
$202$	39.3136	2.76609
$203$	−5.66984	−0.397945
$204$	12.0412	0.843054
$205$	7.74396	0.540862
$206$	13.0091	0.906386
$207$	−1.43512	−0.0997476
$208$	−27.6155	−1.91479
$209$	6.87513	0.475563
$210$	−13.0288	−0.899074
$211$	−1.58370	−0.109026	−0.0545131	−	0.998513i	$-0.517361\pi$
$211$	−1.58370	−0.109026	−0.0545131	+	0.998513i	$0.517361\pi$
$212$	14.0618	0.965765
$213$	−2.49037	−0.170638
$214$	10.8258	0.740037
$215$	−9.45879	−0.645084
$216$	−3.72808	−0.253664
$217$	−15.4242	−1.04706
$218$	2.34952	0.159129
$219$	15.2601	1.03118
$220$	−13.8628	−0.934631
$221$	−2.84461	−0.191349
$222$	21.3280	1.43144
$223$	−17.0892	−1.14438	−0.572189	−	0.820122i	$-0.693906\pi$
$223$	−17.0892	−1.14438	−0.572189	+	0.820122i	$0.693906\pi$
$224$	−21.1245	−1.41144
$225$	3.20197	0.213464
$226$	−35.6406	−2.37078
$227$	9.09393	0.603585	0.301793	−	0.953374i	$-0.402415\pi$
$227$	9.09393	0.603585	0.301793	+	0.953374i	$0.402415\pi$
$228$	−28.8739	−1.91222
$229$	−16.7654	−1.10789	−0.553945	−	0.832553i	$-0.686878\pi$
$229$	−16.7654	−1.10789	−0.553945	+	0.832553i	$0.686878\pi$
$230$	1.17177	0.0772644
$231$	−14.2882	−0.940096
$232$	21.0012	1.37880
$233$	6.82505	0.447124	0.223562	−	0.974690i	$-0.428231\pi$
$233$	6.82505	0.447124	0.223562	+	0.974690i	$0.428231\pi$
$234$	23.8129	1.55670
$235$	−6.83108	−0.445611
$236$	46.5724	3.03161
$237$	−2.25248	−0.146314
$238$	−5.23167	−0.339119
$239$	−12.3743	−0.800426	−0.400213	−	0.916422i	$-0.631064\pi$
$239$	−12.3743	−0.800426	−0.400213	+	0.916422i	$0.631064\pi$
$240$	24.1766	1.56059
$241$	−10.9353	−0.704404	−0.352202	−	0.935924i	$-0.614567\pi$
$241$	−10.9353	−0.704404	−0.352202	+	0.935924i	$0.614567\pi$
$242$	7.26707	0.467145
$243$	−22.3118	−1.43130
$244$	−9.38371	−0.600731
$245$	−2.99562	−0.191383
$246$	−50.4197	−3.21464
$247$	6.82116	0.434020
$248$	57.1316	3.62786
$249$	27.8253	1.76335
$250$	−2.61440	−0.165349
$251$	−8.34158	−0.526516	−0.263258	−	0.964725i	$-0.584797\pi$
$251$	−8.34158	−0.526516	−0.263258	+	0.964725i	$0.584797\pi$
$252$	30.9806	1.95160
$253$	1.28504	0.0807897
$254$	−16.9659	−1.06453
$255$	2.49037	0.155953
$256$	−15.6329	−0.977055
$257$	−7.75926	−0.484009	−0.242005	−	0.970275i	$-0.577805\pi$
$257$	−7.75926	−0.484009	−0.242005	+	0.970275i	$0.577805\pi$
$258$	61.5847	3.83409
$259$	−6.55512	−0.407316
$260$	−13.7540	−0.852986
$261$	−9.07236	−0.561565
$262$	−41.1888	−2.54465
$263$	5.88584	0.362936	0.181468	−	0.983397i	$-0.441915\pi$
$263$	5.88584	0.362936	0.181468	+	0.983397i	$0.441915\pi$
$264$	52.9239	3.25724
$265$	2.90826	0.178653
$266$	12.5451	0.769192
$267$	10.6833	0.653809
$268$	−54.6488	−3.33821
$269$	−13.4819	−0.822006	−0.411003	−	0.911634i	$-0.634821\pi$
$269$	−13.4819	−0.822006	−0.411003	+	0.911634i	$0.634821\pi$
$270$	−1.31497	−0.0800265
$271$	23.0193	1.39832	0.699161	−	0.714964i	$-0.253557\pi$
$271$	23.0193	1.39832	0.699161	+	0.714964i	$0.253557\pi$
$272$	9.70803	0.588635
$273$	−14.1760	−0.857973
$274$	23.2717	1.40590
$275$	−2.86712	−0.172894
$276$	−5.39686	−0.324853
$277$	27.1226	1.62964	0.814818	−	0.579717i	$-0.196837\pi$
$277$	27.1226	1.62964	0.814818	+	0.579717i	$0.196837\pi$
$278$	24.1259	1.44697
$279$	−24.6803	−1.47757
$280$	−14.8323	−0.886401
$281$	−2.90669	−0.173398	−0.0866992	−	0.996235i	$-0.527632\pi$
$281$	−2.90669	−0.173398	−0.0866992	+	0.996235i	$0.527632\pi$
$282$	44.4761	2.64851
$283$	7.87502	0.468121	0.234061	−	0.972222i	$-0.424799\pi$
$283$	7.87502	0.468121	0.234061	+	0.972222i	$0.424799\pi$
$284$	−4.83510	−0.286911
$285$	−5.97173	−0.353735
$286$	−21.3226	−1.26083
$287$	15.4964	0.914723
$288$	−33.8015	−1.99177
$289$	1.00000	0.0588235
$290$	7.40757	0.434988
$291$	−19.2636	−1.12925
$292$	29.6277	1.73383
$293$	−12.3019	−0.718685	−0.359343	−	0.933206i	$-0.616999\pi$
$293$	−12.3019	−0.718685	−0.359343	+	0.933206i	$0.616999\pi$
$294$	19.5040	1.13750
$295$	9.63215	0.560805
$296$	24.2803	1.41127
$297$	−1.44208	−0.0836779
$298$	56.7163	3.28549
$299$	1.27495	0.0737323
$300$	12.0412	0.695200
$301$	−18.9279	−1.09099
$302$	−48.7080	−2.80283
$303$	−37.4485	−2.15136
$304$	−23.2791	−1.33515
$305$	−1.94075	−0.111127
$306$	−8.37123	−0.478551
$307$	4.44616	0.253756	0.126878	−	0.991918i	$-0.459504\pi$
$307$	4.44616	0.253756	0.126878	+	0.991918i	$0.459504\pi$
$308$	−27.7408	−1.58068
$309$	−12.3919	−0.704952
$310$	20.1515	1.14453
$311$	2.00831	0.113881	0.0569403	−	0.998378i	$-0.481866\pi$
$311$	2.00831	0.113881	0.0569403	+	0.998378i	$0.481866\pi$
$312$	52.5084	2.97270
$313$	−17.3207	−0.979025	−0.489512	−	0.871996i	$-0.662825\pi$
$313$	−17.3207	−0.979025	−0.489512	+	0.871996i	$0.662825\pi$
$314$	21.5905	1.21842
$315$	6.40744	0.361018
$316$	−4.37323	−0.246013
$317$	−9.38102	−0.526891	−0.263445	−	0.964674i	$-0.584859\pi$
$317$	−9.38102	−0.526891	−0.263445	+	0.964674i	$0.584859\pi$
$318$	−18.9352	−1.06184
$319$	8.12361	0.454835
$320$	8.18285	0.457435
$321$	−10.3122	−0.575572
$322$	2.34483	0.130672
$323$	−2.39792	−0.133424
$324$	−40.3891	−2.24384
$325$	−2.84461	−0.157791
$326$	0.262096	0.0145162
$327$	−2.23805	−0.123765
$328$	−57.3990	−3.16933
$329$	−13.6696	−0.753632
$330$	18.6674	1.02760
$331$	26.0404	1.43131	0.715655	−	0.698454i	$-0.246128\pi$
$331$	26.0404	1.43131	0.715655	+	0.698454i	$0.246128\pi$
$332$	54.0232	2.96491
$333$	−10.4889	−0.574788
$334$	−32.4271	−1.77433
$335$	−11.3025	−0.617522
$336$	48.3797	2.63933
$337$	−9.30227	−0.506727	−0.253363	−	0.967371i	$-0.581537\pi$
$337$	−9.30227	−0.506727	−0.253363	+	0.967371i	$0.581537\pi$
$338$	12.8320	0.697969
$339$	33.9498	1.84390
$340$	4.83510	0.262220
$341$	22.0994	1.19675
$342$	20.0736	1.08545
$343$	−20.0022	−1.08002
$344$	70.1095	3.78005
$345$	−1.11618	−0.0600933
$346$	12.4208	0.667748
$347$	8.81037	0.472965	0.236483	−	0.971636i	$-0.424005\pi$
$347$	8.81037	0.472965	0.236483	+	0.971636i	$0.424005\pi$
$348$	−34.1172	−1.82888
$349$	17.7142	0.948218	0.474109	−	0.880466i	$-0.342770\pi$
$349$	17.7142	0.948218	0.474109	+	0.880466i	$0.342770\pi$
$350$	−5.23167	−0.279644
$351$	−1.43076	−0.0763682
$352$	30.2667	1.61322
$353$	17.1061	0.910467	0.455234	−	0.890372i	$-0.349556\pi$
$353$	17.1061	0.910467	0.455234	+	0.890372i	$0.349556\pi$
$354$	−62.7134	−3.33318
$355$	−1.00000	−0.0530745
$356$	20.7418	1.09932
$357$	4.98348	0.263753
$358$	31.3753	1.65824
$359$	22.1741	1.17031	0.585153	−	0.810923i	$-0.301035\pi$
$359$	22.1741	1.17031	0.585153	+	0.810923i	$0.301035\pi$
$360$	−23.7333	−1.25086
$361$	−13.2500	−0.697367
$362$	49.5152	2.60246
$363$	−6.92232	−0.363327
$364$	−27.5230	−1.44260
$365$	6.12763	0.320735
$366$	12.6359	0.660489
$367$	23.7190	1.23812	0.619060	−	0.785343i	$-0.287514\pi$
$367$	23.7190	1.23812	0.619060	+	0.785343i	$0.287514\pi$
$368$	−4.35113	−0.226818
$369$	24.7959	1.29082
$370$	8.56418	0.445231
$371$	5.81971	0.302144
$372$	−92.8122	−4.81209
$373$	16.2381	0.840775	0.420387	−	0.907345i	$-0.361894\pi$
$373$	16.2381	0.840775	0.420387	+	0.907345i	$0.361894\pi$
$374$	7.49581	0.387599
$375$	2.49037	0.128602
$376$	50.6327	2.61118
$377$	8.05983	0.415103
$378$	−2.63138	−0.135344
$379$	−7.63050	−0.391952	−0.195976	−	0.980609i	$-0.562788\pi$
$379$	−7.63050	−0.391952	−0.195976	+	0.980609i	$0.562788\pi$
$380$	−11.5942	−0.594770
$381$	16.1610	0.827954
$382$	56.8672	2.90958
$383$	−4.24028	−0.216668	−0.108334	−	0.994115i	$-0.534552\pi$
$383$	−4.24028	−0.216668	−0.108334	+	0.994115i	$0.534552\pi$
$384$	−0.698055	−0.0356225
$385$	−5.73738	−0.292404
$386$	−22.0218	−1.12088
$387$	−30.2867	−1.53956
$388$	−37.4005	−1.89872
$389$	17.1822	0.871173	0.435586	−	0.900147i	$-0.356541\pi$
$389$	17.1822	0.871173	0.435586	+	0.900147i	$0.356541\pi$
$390$	18.5208	0.937838
$391$	−0.448199	−0.0226664
$392$	22.2039	1.12146
$393$	39.2347	1.97913
$394$	−21.1645	−1.06625
$395$	−0.904474	−0.0455090
$396$	−44.3883	−2.23059
$397$	31.5406	1.58298	0.791488	−	0.611185i	$-0.209307\pi$
$397$	31.5406	1.58298	0.791488	+	0.611185i	$0.209307\pi$
$398$	−2.89652	−0.145190
$399$	−11.9500	−0.598248
$400$	9.70803	0.485401
$401$	21.7746	1.08737	0.543687	−	0.839288i	$-0.317028\pi$
$401$	21.7746	1.08737	0.543687	+	0.839288i	$0.317028\pi$
$402$	73.5889	3.67028
$403$	21.9259	1.09221
$404$	−72.7069	−3.61730
$405$	−8.35331	−0.415079
$406$	14.8233	0.735666
$407$	9.39202	0.465545
$408$	−18.4589	−0.913853
$409$	28.4020	1.40439	0.702195	−	0.711985i	$-0.252204\pi$
$409$	28.4020	1.40439	0.702195	+	0.711985i	$0.252204\pi$
$410$	−20.2458	−0.999870
$411$	−22.1677	−1.09345
$412$	−24.0591	−1.18531
$413$	19.2748	0.948453
$414$	3.75198	0.184400
$415$	11.1731	0.548467
$416$	30.0291	1.47230
$417$	−22.9813	−1.12540
$418$	−17.9744	−0.879155
$419$	23.1258	1.12977	0.564884	−	0.825170i	$-0.308921\pi$
$419$	23.1258	1.12977	0.564884	+	0.825170i	$0.308921\pi$
$420$	24.0956	1.17575
$421$	−24.2458	−1.18167	−0.590833	−	0.806794i	$-0.701201\pi$
$421$	−24.2458	−1.18167	−0.590833	+	0.806794i	$0.701201\pi$
$422$	4.14042	0.201553
$423$	−21.8729	−1.06350
$424$	−21.5563	−1.04687
$425$	1.00000	0.0485071
$426$	6.51084	0.315451
$427$	−3.88362	−0.187941
$428$	−20.0214	−0.967768
$429$	20.3111	0.980628
$430$	24.7291	1.19254
$431$	−33.4677	−1.61208	−0.806041	−	0.591859i	$-0.798394\pi$
$431$	−33.4677	−1.61208	−0.806041	+	0.591859i	$0.798394\pi$
$432$	4.88286	0.234927
$433$	6.03277	0.289916	0.144958	−	0.989438i	$-0.453695\pi$
$433$	6.03277	0.289916	0.144958	+	0.989438i	$0.453695\pi$
$434$	40.3250	1.93566
$435$	−7.05616	−0.338317
$436$	−4.34522	−0.208098
$437$	1.07475	0.0514121
$438$	−39.8961	−1.90631
$439$	18.5059	0.883240	0.441620	−	0.897202i	$-0.354404\pi$
$439$	18.5059	0.883240	0.441620	+	0.897202i	$0.354404\pi$
$440$	21.2514	1.01312
$441$	−9.59188	−0.456756
$442$	7.43696	0.353740
$443$	−11.1054	−0.527634	−0.263817	−	0.964573i	$-0.584982\pi$
$443$	−11.1054	−0.527634	−0.263817	+	0.964573i	$0.584982\pi$
$444$	−39.4443	−1.87194
$445$	4.28985	0.203358
$446$	44.6781	2.11557
$447$	−54.0256	−2.55532
$448$	16.3747	0.773630
$449$	−29.2276	−1.37933	−0.689667	−	0.724126i	$-0.742243\pi$
$449$	−29.2276	−1.37933	−0.689667	+	0.724126i	$0.742243\pi$
$450$	−8.37123	−0.394624
$451$	−22.2029	−1.04549
$452$	65.9140	3.10034
$453$	46.3972	2.17993
$454$	−23.7752	−1.11583
$455$	−5.69233	−0.266861
$456$	44.2631	2.07281
$457$	−4.50535	−0.210751	−0.105376	−	0.994432i	$-0.533605\pi$
$457$	−4.50535	−0.210751	−0.105376	+	0.994432i	$0.533605\pi$
$458$	43.8315	2.04811
$459$	0.502971	0.0234767
$460$	−2.16709	−0.101041
$461$	14.1209	0.657676	0.328838	−	0.944386i	$-0.393343\pi$
$461$	14.1209	0.657676	0.328838	+	0.944386i	$0.393343\pi$
$462$	37.3552	1.73792
$463$	−10.6184	−0.493479	−0.246739	−	0.969082i	$-0.579359\pi$
$463$	−10.6184	−0.493479	−0.246739	+	0.969082i	$0.579359\pi$
$464$	−27.5064	−1.27695
$465$	−19.1955	−0.890170
$466$	−17.8434	−0.826581
$467$	27.5228	1.27360	0.636802	−	0.771027i	$-0.280257\pi$
$467$	27.5228	1.27360	0.636802	+	0.771027i	$0.280257\pi$
$468$	−44.0398	−2.03574
$469$	−22.6174	−1.04437
$470$	17.8592	0.823784
$471$	−20.5662	−0.947640
$472$	−71.3945	−3.28620
$473$	27.1195	1.24695
$474$	5.88889	0.270486
$475$	−2.39792	−0.110024
$476$	9.67550	0.443476
$477$	9.31216	0.426374
$478$	32.3514	1.47972
$479$	−9.06750	−0.414305	−0.207152	−	0.978309i	$-0.566420\pi$
$479$	−9.06750	−0.414305	−0.207152	+	0.978309i	$0.566420\pi$
$480$	−26.2896	−1.19995
$481$	9.31828	0.424877
$482$	28.5892	1.30220
$483$	−2.23359	−0.101632
$484$	−13.4398	−0.610900
$485$	−7.73520	−0.351237
$486$	58.3320	2.64599
$487$	29.3789	1.33128	0.665641	−	0.746272i	$-0.268158\pi$
$487$	29.3789	1.33128	0.665641	+	0.746272i	$0.268158\pi$
$488$	14.3850	0.651179
$489$	−0.249662	−0.0112901
$490$	7.83176	0.353803
$491$	−27.9762	−1.26255	−0.631275	−	0.775559i	$-0.717468\pi$
$491$	−27.9762	−1.26255	−0.631275	+	0.775559i	$0.717468\pi$
$492$	93.2467	4.20389
$493$	−2.83337	−0.127609
$494$	−17.8333	−0.802356
$495$	−9.18042	−0.412629
$496$	−74.8282	−3.35989
$497$	−2.00109	−0.0897614
$498$	−72.7464	−3.25985
$499$	42.4681	1.90113	0.950566	−	0.310521i	$-0.100504\pi$
$499$	42.4681	1.90113	0.950566	+	0.310521i	$0.100504\pi$
$500$	4.83510	0.216232
$501$	30.8887	1.38001
$502$	21.8083	0.973350
$503$	−11.3612	−0.506569	−0.253284	−	0.967392i	$-0.581511\pi$
$503$	−11.3612	−0.506569	−0.253284	+	0.967392i	$0.581511\pi$
$504$	−47.4926	−2.11549
$505$	−15.0373	−0.669151
$506$	−3.35961	−0.149353
$507$	−12.2232	−0.542853
$508$	31.3769	1.39212
$509$	0.360200	0.0159656	0.00798280	−	0.999968i	$-0.497459\pi$
$509$	0.360200	0.0159656	0.00798280	+	0.999968i	$0.497459\pi$
$510$	−6.51084	−0.288305
$511$	12.2620	0.542438
$512$	41.4312	1.83102
$513$	−1.20609	−0.0532500
$514$	20.2858	0.894770
$515$	−4.97593	−0.219266
$516$	−113.895	−5.01396
$517$	19.5855	0.861370
$518$	17.1377	0.752989
$519$	−11.8316	−0.519349
$520$	21.0845	0.924619
$521$	2.91642	0.127771	0.0638854	−	0.997957i	$-0.479651\pi$
$521$	2.91642	0.127771	0.0638854	+	0.997957i	$0.479651\pi$
$522$	23.7188	1.03814
$523$	−21.2438	−0.928926	−0.464463	−	0.885593i	$-0.653753\pi$
$523$	−21.2438	−0.928926	−0.464463	+	0.885593i	$0.653753\pi$
$524$	76.1749	3.32772
$525$	4.98348	0.217497
$526$	−15.3880	−0.670947
$527$	−7.70787	−0.335760
$528$	−69.3172	−3.01665
$529$	−22.7991	−0.991266
$530$	−7.60337	−0.330269
$531$	30.8418	1.33842
$532$	−23.2011	−1.00590
$533$	−22.0285	−0.954162
$534$	−27.9305	−1.20867
$535$	−4.14083	−0.179024
$536$	83.7754	3.61855
$537$	−29.8868	−1.28971
$538$	35.2471	1.51961
$539$	8.58880	0.369946
$540$	2.43192	0.104653
$541$	1.50494	0.0647022	0.0323511	−	0.999477i	$-0.489701\pi$
$541$	1.50494	0.0647022	0.0323511	+	0.999477i	$0.489701\pi$
$542$	−60.1817	−2.58503
$543$	−47.1662	−2.02409
$544$	−10.5565	−0.452605
$545$	−0.898682	−0.0384953
$546$	37.0619	1.58610
$547$	2.28100	0.0975285	0.0487642	−	0.998810i	$-0.484472\pi$
$547$	2.28100	0.0975285	0.0487642	+	0.998810i	$0.484472\pi$
$548$	−43.0390	−1.83854
$549$	−6.21420	−0.265216
$550$	7.49581	0.319622
$551$	6.79421	0.289443
$552$	8.27327	0.352134
$553$	−1.80994	−0.0769664
$554$	−70.9093	−3.01265
$555$	−8.15789	−0.346283
$556$	−44.6186	−1.89225
$557$	25.8151	1.09382	0.546910	−	0.837191i	$-0.315804\pi$
$557$	25.8151	1.09382	0.546910	+	0.837191i	$0.315804\pi$
$558$	64.5244	2.73154
$559$	26.9066	1.13803
$560$	19.4267	0.820927
$561$	−7.14020	−0.301459
$562$	7.59925	0.320555
$563$	−15.1584	−0.638852	−0.319426	−	0.947611i	$-0.603490\pi$
$563$	−15.1584	−0.638852	−0.319426	+	0.947611i	$0.603490\pi$
$564$	−82.2546	−3.46354
$565$	13.6324	0.573519
$566$	−20.5885	−0.865398
$567$	−16.7158	−0.701996
$568$	7.41211	0.311005
$569$	−39.1747	−1.64229	−0.821143	−	0.570722i	$-0.806663\pi$
$569$	−39.1747	−1.64229	−0.821143	+	0.570722i	$0.806663\pi$
$570$	15.6125	0.653936
$571$	−37.4474	−1.56712	−0.783562	−	0.621313i	$-0.786599\pi$
$571$	−37.4474	−1.56712	−0.783562	+	0.621313i	$0.786599\pi$
$572$	39.4343	1.64883
$573$	−54.1694	−2.26296
$574$	−40.5138	−1.69101
$575$	−0.448199	−0.0186912
$576$	26.2012	1.09172
$577$	40.9409	1.70439	0.852196	−	0.523222i	$-0.175270\pi$
$577$	40.9409	1.70439	0.852196	+	0.523222i	$0.175270\pi$
$578$	−2.61440	−0.108745
$579$	20.9771	0.871777
$580$	−13.6996	−0.568847
$581$	22.3585	0.927586
$582$	50.3627	2.08760
$583$	−8.33833	−0.345339
$584$	−45.4187	−1.87944
$585$	−9.10834	−0.376584
$586$	32.1621	1.32861
$587$	36.1493	1.49204	0.746020	−	0.665924i	$-0.231962\pi$
$587$	36.1493	1.49204	0.746020	+	0.665924i	$0.231962\pi$
$588$	−36.0709	−1.48754
$589$	18.4829	0.761574
$590$	−25.1823	−1.03674
$591$	20.1604	0.829290
$592$	−31.8012	−1.30702
$593$	7.68674	0.315657	0.157828	−	0.987467i	$-0.449551\pi$
$593$	7.68674	0.315657	0.157828	+	0.987467i	$0.449551\pi$
$594$	3.77018	0.154692
$595$	2.00109	0.0820369
$596$	−104.892	−4.29653
$597$	2.75911	0.112923
$598$	−3.33324	−0.136306
$599$	5.93819	0.242628	0.121314	−	0.992614i	$-0.461289\pi$
$599$	5.93819	0.242628	0.121314	+	0.992614i	$0.461289\pi$
$600$	−18.4589	−0.753582
$601$	−13.8776	−0.566081	−0.283040	−	0.959108i	$-0.591343\pi$
$601$	−13.8776	−0.566081	−0.283040	+	0.959108i	$0.591343\pi$
$602$	49.4852	2.01687
$603$	−36.1903	−1.47378
$604$	90.0810	3.66534
$605$	−2.77963	−0.113008
$606$	97.9055	3.97714
$607$	31.1274	1.26342	0.631711	−	0.775204i	$-0.282353\pi$
$607$	31.1274	1.26342	0.631711	+	0.775204i	$0.282353\pi$
$608$	25.3136	1.02660
$609$	−14.1200	−0.572173
$610$	5.07389	0.205436
$611$	19.4318	0.786125
$612$	15.4818	0.625816
$613$	−44.0812	−1.78042	−0.890211	−	0.455547i	$-0.849444\pi$
$613$	−44.0812	−1.78042	−0.890211	+	0.455547i	$0.849444\pi$
$614$	−11.6241	−0.469109
$615$	19.2854	0.777661
$616$	42.5260	1.71342
$617$	13.0400	0.524969	0.262484	−	0.964936i	$-0.415458\pi$
$617$	13.0400	0.524969	0.262484	+	0.964936i	$0.415458\pi$
$618$	32.3975	1.30322
$619$	−26.2925	−1.05678	−0.528392	−	0.849001i	$-0.677205\pi$
$619$	−26.2925	−1.05678	−0.528392	+	0.849001i	$0.677205\pi$
$620$	−37.2684	−1.49673
$621$	−0.225431	−0.00904624
$622$	−5.25052	−0.210527
$623$	8.58439	0.343926
$624$	−68.7730	−2.75313
$625$	1.00000	0.0400000
$626$	45.2833	1.80989
$627$	17.1217	0.683773
$628$	−39.9296	−1.59336
$629$	−3.27577	−0.130613
$630$	−16.7516	−0.667401
$631$	−9.13813	−0.363783	−0.181892	−	0.983319i	$-0.558222\pi$
$631$	−9.13813	−0.363783	−0.181892	+	0.983319i	$0.558222\pi$
$632$	6.70406	0.266673
$633$	−3.94400	−0.156760
$634$	24.5258	0.974043
$635$	6.48939	0.257524
$636$	35.0190	1.38859
$637$	8.52137	0.337629
$638$	−21.2384	−0.840836
$639$	−3.20197	−0.126668
$640$	−0.280301	−0.0110799
$641$	−18.3571	−0.725062	−0.362531	−	0.931972i	$-0.618087\pi$
$641$	−18.3571	−0.725062	−0.362531	+	0.931972i	$0.618087\pi$
$642$	26.9603	1.06404
$643$	38.3650	1.51297	0.756485	−	0.654011i	$-0.226915\pi$
$643$	38.3650	1.51297	0.756485	+	0.654011i	$0.226915\pi$
$644$	−4.33655	−0.170884
$645$	−23.5559	−0.927514
$646$	6.26914	0.246656
$647$	−7.39643	−0.290784	−0.145392	−	0.989374i	$-0.546444\pi$
$647$	−7.39643	−0.290784	−0.145392	+	0.989374i	$0.546444\pi$
$648$	61.9156	2.43228
$649$	−27.6165	−1.08404
$650$	7.43696	0.291701
$651$	−38.4120	−1.50548
$652$	−0.484723	−0.0189832
$653$	19.3277	0.756351	0.378176	−	0.925734i	$-0.376552\pi$
$653$	19.3277	0.756351	0.378176	+	0.925734i	$0.376552\pi$
$654$	5.85118	0.228799
$655$	15.7546	0.615581
$656$	75.1786	2.93523
$657$	19.6205	0.765467
$658$	35.7380	1.39321
$659$	−27.1591	−1.05797	−0.528985	−	0.848631i	$-0.677427\pi$
$659$	−27.1591	−1.05797	−0.528985	+	0.848631i	$0.677427\pi$
$660$	−34.5236	−1.34383
$661$	−39.9757	−1.55488	−0.777438	−	0.628960i	$-0.783481\pi$
$661$	−39.9757	−1.55488	−0.777438	+	0.628960i	$0.783481\pi$
$662$	−68.0801	−2.64601
$663$	−7.08414	−0.275125
$664$	−82.8163	−3.21390
$665$	−4.79847	−0.186077
$666$	27.4222	1.06259
$667$	1.26991	0.0491713
$668$	59.9710	2.32035
$669$	−42.5585	−1.64541
$670$	29.5493	1.14159
$671$	5.56435	0.214809
$672$	−52.6080	−2.02940
$673$	3.30322	0.127330	0.0636648	−	0.997971i	$-0.479721\pi$
$673$	3.30322	0.127330	0.0636648	+	0.997971i	$0.479721\pi$
$674$	24.3199	0.936767
$675$	0.502971	0.0193594
$676$	−23.7316	−0.912755
$677$	−9.99159	−0.384008	−0.192004	−	0.981394i	$-0.561499\pi$
$677$	−9.99159	−0.384008	−0.192004	+	0.981394i	$0.561499\pi$
$678$	−88.7584	−3.40874
$679$	−15.4789	−0.594025
$680$	−7.41211	−0.284241
$681$	22.6473	0.867846
$682$	−57.7767	−2.21238
$683$	11.4745	0.439061	0.219531	−	0.975606i	$-0.429547\pi$
$683$	11.4745	0.439061	0.219531	+	0.975606i	$0.429547\pi$
$684$	−37.1243	−1.41948
$685$	−8.90136	−0.340104
$686$	52.2938	1.99659
$687$	−41.7522	−1.59294
$688$	−91.8261	−3.50084
$689$	−8.27287	−0.315171
$690$	2.91815	0.111092
$691$	18.0754	0.687620	0.343810	−	0.939039i	$-0.388282\pi$
$691$	18.0754	0.687620	0.343810	+	0.939039i	$0.388282\pi$
$692$	−22.9712	−0.873235
$693$	−18.3709	−0.697852
$694$	−23.0339	−0.874353
$695$	−9.22806	−0.350040
$696$	52.3010	1.98246
$697$	7.74396	0.293323
$698$	−46.3120	−1.75294
$699$	16.9969	0.642883
$700$	9.67550	0.365700
$701$	−25.4467	−0.961109	−0.480555	−	0.876965i	$-0.659565\pi$
$701$	−25.4467	−0.961109	−0.480555	+	0.876965i	$0.659565\pi$
$702$	3.74058	0.141179
$703$	7.85504	0.296259
$704$	−23.4612	−0.884227
$705$	−17.0120	−0.640707
$706$	−44.7223	−1.68315
$707$	−30.0911	−1.13169
$708$	115.983	4.35890
$709$	−11.1781	−0.419804	−0.209902	−	0.977722i	$-0.567315\pi$
$709$	−11.1781	−0.419804	−0.209902	+	0.977722i	$0.567315\pi$
$710$	2.61440	0.0981168
$711$	−2.89610	−0.108612
$712$	−31.7968	−1.19163
$713$	3.45466	0.129378
$714$	−13.0288	−0.487591
$715$	8.15583	0.305011
$716$	−58.0258	−2.16852
$717$	−30.8166	−1.15087
$718$	−57.9721	−2.16350
$719$	24.3260	0.907206	0.453603	−	0.891204i	$-0.350138\pi$
$719$	24.3260	0.907206	0.453603	+	0.891204i	$0.350138\pi$
$720$	31.0848	1.15846
$721$	−9.95731	−0.370830
$722$	34.6408	1.28920
$723$	−27.2330	−1.01280
$724$	−91.5739	−3.40332
$725$	−2.83337	−0.105229
$726$	18.0977	0.671670
$727$	−2.36442	−0.0876915	−0.0438457	−	0.999038i	$-0.513961\pi$
$727$	−2.36442	−0.0876915	−0.0438457	+	0.999038i	$0.513961\pi$
$728$	42.1922	1.56375
$729$	−30.5048	−1.12981
$730$	−16.0201	−0.592930
$731$	−9.45879	−0.349846
$732$	−23.3690	−0.863742
$733$	1.64332	0.0606975	0.0303487	−	0.999539i	$-0.490338\pi$
$733$	1.64332	0.0606975	0.0303487	+	0.999539i	$0.490338\pi$
$734$	−62.0110	−2.28887
$735$	−7.46022	−0.275174
$736$	4.73140	0.174402
$737$	32.4056	1.19368
$738$	−64.8265	−2.38630
$739$	5.86399	0.215710	0.107855	−	0.994167i	$-0.465602\pi$
$739$	5.86399	0.215710	0.107855	+	0.994167i	$0.465602\pi$
$740$	−15.8387	−0.582242
$741$	16.9872	0.624042
$742$	−15.2151	−0.558563
$743$	−6.38901	−0.234390	−0.117195	−	0.993109i	$-0.537390\pi$
$743$	−6.38901	−0.234390	−0.117195	+	0.993109i	$0.537390\pi$
$744$	142.279	5.21620
$745$	−21.6938	−0.794798
$746$	−42.4528	−1.55431
$747$	35.7760	1.30897
$748$	−13.8628	−0.506875
$749$	−8.28619	−0.302771
$750$	−6.51084	−0.237742
$751$	−12.1488	−0.443315	−0.221657	−	0.975125i	$-0.571147\pi$
$751$	−12.1488	−0.443315	−0.221657	+	0.975125i	$0.571147\pi$
$752$	−66.3163	−2.41831
$753$	−20.7737	−0.757034
$754$	−21.0717	−0.767385
$755$	18.6306	0.678038
$756$	4.86650	0.176993
$757$	−30.3018	−1.10134	−0.550668	−	0.834724i	$-0.685627\pi$
$757$	−30.3018	−1.10134	−0.550668	+	0.834724i	$0.685627\pi$
$758$	19.9492	0.724587
$759$	3.20023	0.116161
$760$	17.7737	0.644718
$761$	6.98464	0.253193	0.126596	−	0.991954i	$-0.459595\pi$
$761$	6.98464	0.253193	0.126596	+	0.991954i	$0.459595\pi$
$762$	−42.2514	−1.53061
$763$	−1.79835	−0.0651046
$764$	−105.171	−3.80494
$765$	3.20197	0.115767
$766$	11.0858	0.400546
$767$	−27.3997	−0.989346
$768$	−38.9317	−1.40483
$769$	−19.1884	−0.691950	−0.345975	−	0.938244i	$-0.612452\pi$
$769$	−19.1884	−0.691950	−0.345975	+	0.938244i	$0.612452\pi$
$770$	14.9998	0.540556
$771$	−19.3235	−0.695917
$772$	40.7273	1.46581
$773$	5.17203	0.186025	0.0930124	−	0.995665i	$-0.470350\pi$
$773$	5.17203	0.186025	0.0930124	+	0.995665i	$0.470350\pi$
$774$	79.1817	2.84613
$775$	−7.70787	−0.276875
$776$	57.3341	2.05818
$777$	−16.3247	−0.585646
$778$	−44.9212	−1.61050
$779$	−18.5694	−0.665318
$780$	−34.2526	−1.22644
$781$	2.86712	0.102594
$782$	1.17177	0.0419025
$783$	−1.42510	−0.0509291
$784$	−29.0816	−1.03863
$785$	−8.25827	−0.294750
$786$	−102.575	−3.65874
$787$	−49.9699	−1.78123	−0.890617	−	0.454754i	$-0.849727\pi$
$787$	−49.9699	−1.78123	−0.890617	+	0.454754i	$0.849727\pi$
$788$	39.1418	1.39437
$789$	14.6579	0.521837
$790$	2.36466	0.0841308
$791$	27.2797	0.969955
$792$	68.0462	2.41792
$793$	5.52067	0.196045
$794$	−82.4598	−2.92639
$795$	7.24266	0.256871
$796$	5.35686	0.189869
$797$	−28.8466	−1.02180	−0.510900	−	0.859640i	$-0.670688\pi$
$797$	−28.8466	−1.02180	−0.510900	+	0.859640i	$0.670688\pi$
$798$	31.2421	1.10596
$799$	−6.83108	−0.241666
$800$	−10.5565	−0.373228
$801$	13.7359	0.485336
$802$	−56.9277	−2.01019
$803$	−17.5686	−0.619984
$804$	−136.096	−4.79974
$805$	−0.896888	−0.0316112
$806$	−57.3231	−2.01912
$807$	−33.5750	−1.18190
$808$	111.458	3.92108
$809$	52.5391	1.84718	0.923588	−	0.383387i	$-0.125242\pi$
$809$	52.5391	1.84718	0.923588	+	0.383387i	$0.125242\pi$
$810$	21.8389	0.767342
$811$	11.4880	0.403398	0.201699	−	0.979448i	$-0.435354\pi$
$811$	11.4880	0.403398	0.201699	+	0.979448i	$0.435354\pi$
$812$	−27.4143	−0.962053
$813$	57.3266	2.01053
$814$	−24.5545	−0.860636
$815$	−0.100251	−0.00351163
$816$	24.1766	0.846351
$817$	22.6814	0.793523
$818$	−74.2543	−2.59624
$819$	−18.2267	−0.636891
$820$	37.4429	1.30756
$821$	−21.9348	−0.765531	−0.382766	−	0.923845i	$-0.625028\pi$
$821$	−21.9348	−0.765531	−0.382766	+	0.923845i	$0.625028\pi$
$822$	57.9554	2.02143
$823$	−23.2058	−0.808904	−0.404452	−	0.914559i	$-0.632538\pi$
$823$	−23.2058	−0.808904	−0.404452	+	0.914559i	$0.632538\pi$
$824$	36.8821	1.28485
$825$	−7.14020	−0.248590
$826$	−50.3922	−1.75337
$827$	−40.8623	−1.42092	−0.710460	−	0.703737i	$-0.751513\pi$
$827$	−40.8623	−1.42092	−0.710460	+	0.703737i	$0.751513\pi$
$828$	−6.93894	−0.241145
$829$	32.4641	1.12753	0.563763	−	0.825937i	$-0.309353\pi$
$829$	32.4641	1.12753	0.563763	+	0.825937i	$0.309353\pi$
$830$	−29.2110	−1.01393
$831$	67.5453	2.34312
$832$	−23.2770	−0.806985
$833$	−2.99562	−0.103792
$834$	60.0825	2.08049
$835$	12.4033	0.429232
$836$	33.2420	1.14970
$837$	−3.87684	−0.134003
$838$	−60.4601	−2.08856
$839$	27.3066	0.942727	0.471363	−	0.881939i	$-0.343762\pi$
$839$	27.3066	0.942727	0.471363	+	0.881939i	$0.343762\pi$
$840$	−36.9380	−1.27448
$841$	−20.9720	−0.723173
$842$	63.3882	2.18450
$843$	−7.23874	−0.249315
$844$	−7.65734	−0.263576
$845$	−4.90820	−0.168847
$846$	57.1846	1.96605
$847$	−5.56230	−0.191123
$848$	28.2335	0.969542
$849$	19.6117	0.673073
$850$	−2.61440	−0.0896733
$851$	1.46820	0.0503291
$852$	−12.0412	−0.412525
$853$	48.8901	1.67396	0.836982	−	0.547230i	$-0.184318\pi$
$853$	48.8901	1.67396	0.836982	+	0.547230i	$0.184318\pi$
$854$	10.1533	0.347440
$855$	−7.67807	−0.262584
$856$	30.6923	1.04904
$857$	−38.4348	−1.31291	−0.656455	−	0.754366i	$-0.727945\pi$
$857$	−38.4348	−1.31291	−0.656455	+	0.754366i	$0.727945\pi$
$858$	−53.1014	−1.81285
$859$	−30.5685	−1.04299	−0.521493	−	0.853256i	$-0.674625\pi$
$859$	−30.5685	−1.04299	−0.521493	+	0.853256i	$0.674625\pi$
$860$	−45.7342	−1.55952
$861$	38.5918	1.31521
$862$	87.4981	2.98020
$863$	32.7735	1.11562	0.557812	−	0.829967i	$-0.311641\pi$
$863$	32.7735	1.11562	0.557812	+	0.829967i	$0.311641\pi$
$864$	−5.30961	−0.180637
$865$	−4.75093	−0.161536
$866$	−15.7721	−0.535957
$867$	2.49037	0.0845776
$868$	−74.5775	−2.53133
$869$	2.59324	0.0879695
$870$	18.4476	0.625433
$871$	32.1512	1.08940
$872$	6.66113	0.225574
$873$	−24.7679	−0.838265
$874$	−2.80982	−0.0950436
$875$	2.00109	0.0676493
$876$	73.7842	2.49294
$877$	−1.18863	−0.0401371	−0.0200685	−	0.999799i	$-0.506388\pi$
$877$	−1.18863	−0.0401371	−0.0200685	+	0.999799i	$0.506388\pi$
$878$	−48.3820	−1.63281
$879$	−30.6364	−1.03334
$880$	−27.8341	−0.938286
$881$	13.7354	0.462756	0.231378	−	0.972864i	$-0.425677\pi$
$881$	13.7354	0.462756	0.231378	+	0.972864i	$0.425677\pi$
$882$	25.0770	0.844388
$883$	6.63265	0.223206	0.111603	−	0.993753i	$-0.464401\pi$
$883$	6.63265	0.223206	0.111603	+	0.993753i	$0.464401\pi$
$884$	−13.7540	−0.462597
$885$	23.9877	0.806336
$886$	29.0340	0.975418
$887$	19.6033	0.658214	0.329107	−	0.944293i	$-0.393252\pi$
$887$	19.6033	0.658214	0.329107	+	0.944293i	$0.393252\pi$
$888$	60.4672	2.02914
$889$	12.9859	0.435533
$890$	−11.2154	−0.375941
$891$	23.9499	0.802353
$892$	−82.6281	−2.76659
$893$	16.3804	0.548150
$894$	141.245	4.72393
$895$	−12.0009	−0.401147
$896$	−0.560909	−0.0187387
$897$	3.17511	0.106014
$898$	76.4127	2.54992
$899$	21.8393	0.728380
$900$	15.4818	0.516061
$901$	2.90826	0.0968883
$902$	58.0472	1.93276
$903$	−47.1376	−1.56864
$904$	−101.045	−3.36070
$905$	−18.9394	−0.629566
$906$	−121.301	−4.02996
$907$	−6.15912	−0.204510	−0.102255	−	0.994758i	$-0.532606\pi$
$907$	−6.15912	−0.204510	−0.102255	+	0.994758i	$0.532606\pi$
$908$	43.9701	1.45920
$909$	−48.1489	−1.59700
$910$	14.8821	0.493335
$911$	−16.7842	−0.556085	−0.278043	−	0.960569i	$-0.589686\pi$
$911$	−16.7842	−0.556085	−0.278043	+	0.960569i	$0.589686\pi$
$912$	−57.9737	−1.91970
$913$	−32.0347	−1.06019
$914$	11.7788	0.389608
$915$	−4.83319	−0.159780
$916$	−81.0625	−2.67838
$917$	31.5264	1.04109
$918$	−1.31497	−0.0434005
$919$	21.0669	0.694933	0.347467	−	0.937692i	$-0.387042\pi$
$919$	21.0669	0.694933	0.347467	+	0.937692i	$0.387042\pi$
$920$	3.32210	0.109526
$921$	11.0726	0.364855
$922$	−36.9177	−1.21582
$923$	2.84461	0.0936315
$924$	−69.0850	−2.27273
$925$	−3.27577	−0.107707
$926$	27.7608	0.912275
$927$	−15.9328	−0.523301
$928$	29.9104	0.981858
$929$	10.5593	0.346440	0.173220	−	0.984883i	$-0.444583\pi$
$929$	10.5593	0.346440	0.173220	+	0.984883i	$0.444583\pi$
$930$	50.1848	1.64562
$931$	7.18327	0.235422
$932$	32.9998	1.08095
$933$	5.00144	0.163740
$934$	−71.9557	−2.35446
$935$	−2.86712	−0.0937648
$936$	67.5120	2.20670
$937$	24.8792	0.812768	0.406384	−	0.913702i	$-0.366790\pi$
$937$	24.8792	0.812768	0.406384	+	0.913702i	$0.366790\pi$
$938$	59.1310	1.93069
$939$	−43.1351	−1.40766
$940$	−33.0290	−1.07729
$941$	−45.6606	−1.48849	−0.744246	−	0.667905i	$-0.767191\pi$
$941$	−45.6606	−1.48849	−0.744246	+	0.667905i	$0.767191\pi$
$942$	53.7683	1.75187
$943$	−3.47083	−0.113026
$944$	93.5092	3.04346
$945$	1.00649	0.0327412
$946$	−70.9012	−2.30520
$947$	−30.4536	−0.989608	−0.494804	−	0.869004i	$-0.664760\pi$
$947$	−30.4536	−0.989608	−0.494804	+	0.869004i	$0.664760\pi$
$948$	−10.8910	−0.353722
$949$	−17.4307	−0.565825
$950$	6.26914	0.203398
$951$	−23.3623	−0.757573
$952$	−14.8323	−0.480718
$953$	36.9292	1.19625	0.598127	−	0.801401i	$-0.295912\pi$
$953$	36.9292	1.19625	0.598127	+	0.801401i	$0.295912\pi$
$954$	−24.3457	−0.788222
$955$	−21.7515	−0.703862
$956$	−59.8310	−1.93507
$957$	20.2308	0.653970
$958$	23.7061	0.765910
$959$	−17.8125	−0.575195
$960$	20.3784	0.657709
$961$	28.4113	0.916494
$962$	−24.3618	−0.785454
$963$	−13.2588	−0.427259
$964$	−52.8732	−1.70293
$965$	8.42325	0.271154
$966$	5.83950	0.187883
$967$	−15.3302	−0.492985	−0.246492	−	0.969145i	$-0.579278\pi$
$967$	−15.3302	−0.492985	−0.246492	+	0.969145i	$0.579278\pi$
$968$	20.6029	0.662202
$969$	−5.97173	−0.191840
$970$	20.2229	0.649320
$971$	4.88889	0.156892	0.0784459	−	0.996918i	$-0.475004\pi$
$971$	4.88889	0.156892	0.0784459	+	0.996918i	$0.475004\pi$
$972$	−107.880	−3.46025
$973$	−18.4662	−0.592000
$974$	−76.8082	−2.46109
$975$	−7.08414	−0.226874
$976$	−18.8408	−0.603080
$977$	5.32403	0.170331	0.0851654	−	0.996367i	$-0.472858\pi$
$977$	5.32403	0.170331	0.0851654	+	0.996367i	$0.472858\pi$
$978$	0.652717	0.0208716
$979$	−12.2995	−0.393094
$980$	−14.4841	−0.462679
$981$	−2.87755	−0.0918731
$982$	73.1412	2.33403
$983$	−41.1878	−1.31369	−0.656843	−	0.754027i	$-0.728109\pi$
$983$	−41.1878	−1.31369	−0.656843	+	0.754027i	$0.728109\pi$
$984$	−142.945	−4.55692
$985$	8.09535	0.257939
$986$	7.40757	0.235905
$987$	−34.0425	−1.08359
$988$	32.9810	1.04927
$989$	4.23942	0.134806
$990$	24.0013	0.762812
$991$	1.84039	0.0584619	0.0292310	−	0.999573i	$-0.490694\pi$
$991$	1.84039	0.0584619	0.0292310	+	0.999573i	$0.490694\pi$
$992$	81.3680	2.58344
$993$	64.8504	2.05796
$994$	5.23167	0.165938
$995$	1.10791	0.0351231
$996$	134.538	4.26300
$997$	−21.4131	−0.678159	−0.339080	−	0.940758i	$-0.610116\pi$
$997$	−21.4131	−0.678159	−0.339080	+	0.940758i	$0.610116\pi$
$998$	−111.029	−3.51455
$999$	−1.64762	−0.0521283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.2	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61440 q^{2} +2.49037 q^{3} +4.83510 q^{4} +1.00000 q^{5} -6.51084 q^{6} +2.00109 q^{7} -7.41211 q^{8} +3.20197 q^{9} +O(q^{10})\)	\(q-2.61440 q^{2} +2.49037 q^{3} +4.83510 q^{4} +1.00000 q^{5} -6.51084 q^{6} +2.00109 q^{7} -7.41211 q^{8} +3.20197 q^{9} -2.61440 q^{10} -2.86712 q^{11} +12.0412 q^{12} -2.84461 q^{13} -5.23167 q^{14} +2.49037 q^{15} +9.70803 q^{16} +1.00000 q^{17} -8.37123 q^{18} -2.39792 q^{19} +4.83510 q^{20} +4.98348 q^{21} +7.49581 q^{22} -0.448199 q^{23} -18.4589 q^{24} +1.00000 q^{25} +7.43696 q^{26} +0.502971 q^{27} +9.67550 q^{28} -2.83337 q^{29} -6.51084 q^{30} -7.70787 q^{31} -10.5565 q^{32} -7.14020 q^{33} -2.61440 q^{34} +2.00109 q^{35} +15.4818 q^{36} -3.27577 q^{37} +6.26914 q^{38} -7.08414 q^{39} -7.41211 q^{40} +7.74396 q^{41} -13.0288 q^{42} -9.45879 q^{43} -13.8628 q^{44} +3.20197 q^{45} +1.17177 q^{46} -6.83108 q^{47} +24.1766 q^{48} -2.99562 q^{49} -2.61440 q^{50} +2.49037 q^{51} -13.7540 q^{52} +2.90826 q^{53} -1.31497 q^{54} -2.86712 q^{55} -14.8323 q^{56} -5.97173 q^{57} +7.40757 q^{58} +9.63215 q^{59} +12.0412 q^{60} -1.94075 q^{61} +20.1515 q^{62} +6.40744 q^{63} +8.18285 q^{64} -2.84461 q^{65} +18.6674 q^{66} -11.3025 q^{67} +4.83510 q^{68} -1.11618 q^{69} -5.23167 q^{70} -1.00000 q^{71} -23.7333 q^{72} +6.12763 q^{73} +8.56418 q^{74} +2.49037 q^{75} -11.5942 q^{76} -5.73738 q^{77} +18.5208 q^{78} -0.904474 q^{79} +9.70803 q^{80} -8.35331 q^{81} -20.2458 q^{82} +11.1731 q^{83} +24.0956 q^{84} +1.00000 q^{85} +24.7291 q^{86} -7.05616 q^{87} +21.2514 q^{88} +4.28985 q^{89} -8.37123 q^{90} -5.69233 q^{91} -2.16709 q^{92} -19.1955 q^{93} +17.8592 q^{94} -2.39792 q^{95} -26.2896 q^{96} -7.73520 q^{97} +7.83176 q^{98} -9.18042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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