LMFDB - Embedded newform 6037.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, 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("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71870 q^{2} +0.776703 q^{3} +5.39133 q^{4} +1.67497 q^{5} -2.11162 q^{6} +0.286183 q^{7} -9.22001 q^{8} -2.39673 q^{9} +O(q^{10})$	\(q-2.71870 q^{2} +0.776703 q^{3} +5.39133 q^{4} +1.67497 q^{5} -2.11162 q^{6} +0.286183 q^{7} -9.22001 q^{8} -2.39673 q^{9} -4.55375 q^{10} -5.88809 q^{11} +4.18746 q^{12} +2.73763 q^{13} -0.778045 q^{14} +1.30096 q^{15} +14.2838 q^{16} +1.59192 q^{17} +6.51600 q^{18} -1.02964 q^{19} +9.03033 q^{20} +0.222279 q^{21} +16.0079 q^{22} +4.22846 q^{23} -7.16121 q^{24} -2.19447 q^{25} -7.44279 q^{26} -4.19166 q^{27} +1.54291 q^{28} +6.29312 q^{29} -3.53691 q^{30} -10.0645 q^{31} -20.3933 q^{32} -4.57330 q^{33} -4.32795 q^{34} +0.479348 q^{35} -12.9216 q^{36} +7.64888 q^{37} +2.79928 q^{38} +2.12633 q^{39} -15.4433 q^{40} -9.64721 q^{41} -0.604310 q^{42} +0.886321 q^{43} -31.7446 q^{44} -4.01446 q^{45} -11.4959 q^{46} +11.4726 q^{47} +11.0943 q^{48} -6.91810 q^{49} +5.96611 q^{50} +1.23645 q^{51} +14.7595 q^{52} +7.67727 q^{53} +11.3959 q^{54} -9.86238 q^{55} -2.63861 q^{56} -0.799723 q^{57} -17.1091 q^{58} -1.79305 q^{59} +7.01388 q^{60} +11.1902 q^{61} +27.3623 q^{62} -0.685903 q^{63} +26.8757 q^{64} +4.58545 q^{65} +12.4334 q^{66} +11.9139 q^{67} +8.58256 q^{68} +3.28426 q^{69} -1.30320 q^{70} -10.0144 q^{71} +22.0979 q^{72} +6.68326 q^{73} -20.7950 q^{74} -1.70445 q^{75} -5.55112 q^{76} -1.68507 q^{77} -5.78084 q^{78} +12.5463 q^{79} +23.9249 q^{80} +3.93452 q^{81} +26.2279 q^{82} -10.3837 q^{83} +1.19838 q^{84} +2.66642 q^{85} -2.40964 q^{86} +4.88788 q^{87} +54.2882 q^{88} -4.50334 q^{89} +10.9141 q^{90} +0.783462 q^{91} +22.7970 q^{92} -7.81710 q^{93} -31.1905 q^{94} -1.72461 q^{95} -15.8395 q^{96} -5.79710 q^{97} +18.8082 q^{98} +14.1122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.71870	−1.92241	−0.961206	−	0.275833i	$-0.911046\pi$
$2$	−2.71870	−1.92241	−0.961206	+	0.275833i	$0.911046\pi$
$3$	0.776703	0.448430	0.224215	−	0.974540i	$-0.428018\pi$
$3$	0.776703	0.448430	0.224215	+	0.974540i	$0.428018\pi$
$4$	5.39133	2.69567
$5$	1.67497	0.749070	0.374535	−	0.927213i	$-0.377802\pi$
$5$	1.67497	0.749070	0.374535	+	0.927213i	$0.377802\pi$
$6$	−2.11162	−0.862067
$7$	0.286183	0.108167	0.0540835	−	0.998536i	$-0.482776\pi$
$7$	0.286183	0.108167	0.0540835	+	0.998536i	$0.482776\pi$
$8$	−9.22001	−3.25977
$9$	−2.39673	−0.798911
$10$	−4.55375	−1.44002
$11$	−5.88809	−1.77532	−0.887662	−	0.460495i	$-0.847672\pi$
$11$	−5.88809	−1.77532	−0.887662	+	0.460495i	$0.847672\pi$
$12$	4.18746	1.20882
$13$	2.73763	0.759282	0.379641	−	0.925134i	$-0.376048\pi$
$13$	2.73763	0.759282	0.379641	+	0.925134i	$0.376048\pi$
$14$	−0.778045	−0.207941
$15$	1.30096	0.335905
$16$	14.2838	3.57095
$17$	1.59192	0.386097	0.193048	−	0.981189i	$-0.438163\pi$
$17$	1.59192	0.386097	0.193048	+	0.981189i	$0.438163\pi$
$18$	6.51600	1.53583
$19$	−1.02964	−0.236215	−0.118108	−	0.993001i	$-0.537683\pi$
$19$	−1.02964	−0.236215	−0.118108	+	0.993001i	$0.537683\pi$
$20$	9.03033	2.01924
$21$	0.222279	0.0485053
$22$	16.0079	3.41290
$23$	4.22846	0.881694	0.440847	−	0.897582i	$-0.354678\pi$
$23$	4.22846	0.881694	0.440847	+	0.897582i	$0.354678\pi$
$24$	−7.16121	−1.46178
$25$	−2.19447	−0.438894
$26$	−7.44279	−1.45965
$27$	−4.19166	−0.806685
$28$	1.54291	0.291582
$29$	6.29312	1.16860	0.584301	−	0.811537i	$-0.301369\pi$
$29$	6.29312	1.16860	0.584301	+	0.811537i	$0.301369\pi$
$30$	−3.53691	−0.645748
$31$	−10.0645	−1.80763	−0.903815	−	0.427923i	$-0.859245\pi$
$31$	−10.0645	−1.80763	−0.903815	+	0.427923i	$0.859245\pi$
$32$	−20.3933	−3.60506
$33$	−4.57330	−0.796109
$34$	−4.32795	−0.742237
$35$	0.479348	0.0810246
$36$	−12.9216	−2.15360
$37$	7.64888	1.25747	0.628734	−	0.777621i	$-0.283573\pi$
$37$	7.64888	1.25747	0.628734	+	0.777621i	$0.283573\pi$
$38$	2.79928	0.454103
$39$	2.12633	0.340485
$40$	−15.4433	−2.44179
$41$	−9.64721	−1.50664	−0.753320	−	0.657654i	$-0.771549\pi$
$41$	−9.64721	−1.50664	−0.753320	+	0.657654i	$0.771549\pi$
$42$	−0.604310	−0.0932471
$43$	0.886321	0.135163	0.0675813	−	0.997714i	$-0.478472\pi$
$43$	0.886321	0.135163	0.0675813	+	0.997714i	$0.478472\pi$
$44$	−31.7446	−4.78568
$45$	−4.01446	−0.598440
$46$	−11.4959	−1.69498
$47$	11.4726	1.67345	0.836724	−	0.547625i	$-0.184468\pi$
$47$	11.4726	1.67345	0.836724	+	0.547625i	$0.184468\pi$
$48$	11.0943	1.60132
$49$	−6.91810	−0.988300
$50$	5.96611	0.843735
$51$	1.23645	0.173137
$52$	14.7595	2.04677
$53$	7.67727	1.05455	0.527277	−	0.849693i	$-0.323213\pi$
$53$	7.67727	1.05455	0.527277	+	0.849693i	$0.323213\pi$
$54$	11.3959	1.55078
$55$	−9.86238	−1.32984
$56$	−2.63861	−0.352599
$57$	−0.799723	−0.105926
$58$	−17.1091	−2.24653
$59$	−1.79305	−0.233436	−0.116718	−	0.993165i	$-0.537237\pi$
$59$	−1.79305	−0.233436	−0.116718	+	0.993165i	$0.537237\pi$
$60$	7.01388	0.905488
$61$	11.1902	1.43276	0.716381	−	0.697709i	$-0.245797\pi$
$61$	11.1902	1.43276	0.716381	+	0.697709i	$0.245797\pi$
$62$	27.3623	3.47501
$63$	−0.685903	−0.0864157
$64$	26.8757	3.35946
$65$	4.58545	0.568755
$66$	12.4334	1.53045
$67$	11.9139	1.45551	0.727757	−	0.685835i	$-0.240563\pi$
$67$	11.9139	1.45551	0.727757	+	0.685835i	$0.240563\pi$
$68$	8.58256	1.04079
$69$	3.28426	0.395378
$70$	−1.30320	−0.155763
$71$	−10.0144	−1.18849	−0.594245	−	0.804284i	$-0.702549\pi$
$71$	−10.0144	−1.18849	−0.594245	+	0.804284i	$0.702549\pi$
$72$	22.0979	2.60426
$73$	6.68326	0.782217	0.391108	−	0.920345i	$-0.372092\pi$
$73$	6.68326	0.782217	0.391108	+	0.920345i	$0.372092\pi$
$74$	−20.7950	−2.41737
$75$	−1.70445	−0.196813
$76$	−5.55112	−0.636757
$77$	−1.68507	−0.192031
$78$	−5.78084	−0.654551
$79$	12.5463	1.41156	0.705782	−	0.708429i	$-0.250596\pi$
$79$	12.5463	1.41156	0.705782	+	0.708429i	$0.250596\pi$
$80$	23.9249	2.67489
$81$	3.93452	0.437169
$82$	26.2279	2.89638
$83$	−10.3837	−1.13976	−0.569882	−	0.821726i	$-0.693011\pi$
$83$	−10.3837	−1.13976	−0.569882	+	0.821726i	$0.693011\pi$
$84$	1.19838	0.130754
$85$	2.66642	0.289214
$86$	−2.40964	−0.259838
$87$	4.88788	0.524036
$88$	54.2882	5.78714
$89$	−4.50334	−0.477353	−0.238676	−	0.971099i	$-0.576714\pi$
$89$	−4.50334	−0.477353	−0.238676	+	0.971099i	$0.576714\pi$
$90$	10.9141	1.15045
$91$	0.783462	0.0821292
$92$	22.7970	2.37675
$93$	−7.81710	−0.810595
$94$	−31.1905	−3.21705
$95$	−1.72461	−0.176942
$96$	−15.8395	−1.61662
$97$	−5.79710	−0.588606	−0.294303	−	0.955712i	$-0.595088\pi$
$97$	−5.79710	−0.588606	−0.294303	+	0.955712i	$0.595088\pi$
$98$	18.8082	1.89992
$99$	14.1122	1.41833
$100$	−11.8311	−1.18311
$101$	−12.2652	−1.22044	−0.610218	−	0.792233i	$-0.708918\pi$
$101$	−12.2652	−1.22044	−0.610218	+	0.792233i	$0.708918\pi$
$102$	−3.36153	−0.332841
$103$	−13.4798	−1.32820	−0.664102	−	0.747642i	$-0.731186\pi$
$103$	−13.4798	−1.32820	−0.664102	+	0.747642i	$0.731186\pi$
$104$	−25.2410	−2.47508
$105$	0.372311	0.0363339
$106$	−20.8722	−2.02729
$107$	−10.2415	−0.990081	−0.495040	−	0.868870i	$-0.664847\pi$
$107$	−10.2415	−0.990081	−0.495040	+	0.868870i	$0.664847\pi$
$108$	−22.5986	−2.17455
$109$	9.45074	0.905217	0.452609	−	0.891709i	$-0.350494\pi$
$109$	9.45074	0.905217	0.452609	+	0.891709i	$0.350494\pi$
$110$	26.8128	2.55650
$111$	5.94091	0.563886
$112$	4.08777	0.386258
$113$	−3.83279	−0.360559	−0.180279	−	0.983615i	$-0.557700\pi$
$113$	−3.83279	−0.360559	−0.180279	+	0.983615i	$0.557700\pi$
$114$	2.17421	0.203633
$115$	7.08254	0.660451
$116$	33.9283	3.15016
$117$	−6.56136	−0.606598
$118$	4.87477	0.448759
$119$	0.455580	0.0417629
$120$	−11.9948	−1.09497
$121$	23.6695	2.15178
$122$	−30.4229	−2.75436
$123$	−7.49302	−0.675623
$124$	−54.2608	−4.87277
$125$	−12.0505	−1.07783
$126$	1.86477	0.166127
$127$	4.90761	0.435480	0.217740	−	0.976007i	$-0.430132\pi$
$127$	4.90761	0.435480	0.217740	+	0.976007i	$0.430132\pi$
$128$	−32.2804	−2.85321
$129$	0.688408	0.0606110
$130$	−12.4665	−1.09338
$131$	−21.4469	−1.87382	−0.936911	−	0.349568i	$-0.886328\pi$
$131$	−21.4469	−1.87382	−0.936911	+	0.349568i	$0.886328\pi$
$132$	−24.6561	−2.14604
$133$	−0.294665	−0.0255507
$134$	−32.3903	−2.79810
$135$	−7.02091	−0.604264
$136$	−14.6775	−1.25859
$137$	−9.94801	−0.849916	−0.424958	−	0.905213i	$-0.639711\pi$
$137$	−9.94801	−0.849916	−0.424958	+	0.905213i	$0.639711\pi$
$138$	−8.92891	−0.760079
$139$	−1.24228	−0.105369	−0.0526843	−	0.998611i	$-0.516778\pi$
$139$	−1.24228	−0.105369	−0.0526843	+	0.998611i	$0.516778\pi$
$140$	2.58432	0.218415
$141$	8.91079	0.750424
$142$	27.2261	2.28477
$143$	−16.1194	−1.34797
$144$	−34.2344	−2.85287
$145$	10.5408	0.875365
$146$	−18.1698	−1.50374
$147$	−5.37331	−0.443183
$148$	41.2376	3.38971
$149$	3.85257	0.315615	0.157808	−	0.987470i	$-0.449557\pi$
$149$	3.85257	0.315615	0.157808	+	0.987470i	$0.449557\pi$
$150$	4.63389	0.378356
$151$	−11.5679	−0.941383	−0.470692	−	0.882298i	$-0.655996\pi$
$151$	−11.5679	−0.941383	−0.470692	+	0.882298i	$0.655996\pi$
$152$	9.49328	0.770006
$153$	−3.81540	−0.308457
$154$	4.58120	0.369163
$155$	−16.8577	−1.35404
$156$	11.4637	0.917832
$157$	16.4542	1.31319	0.656595	−	0.754244i	$-0.271996\pi$
$157$	16.4542	1.31319	0.656595	+	0.754244i	$0.271996\pi$
$158$	−34.1095	−2.71361
$159$	5.96296	0.472894
$160$	−34.1582	−2.70044
$161$	1.21011	0.0953701
$162$	−10.6968	−0.840418
$163$	−2.69664	−0.211217	−0.105608	−	0.994408i	$-0.533679\pi$
$163$	−2.69664	−0.211217	−0.105608	+	0.994408i	$0.533679\pi$
$164$	−52.0113	−4.06140
$165$	−7.66014	−0.596341
$166$	28.2303	2.19110
$167$	−6.07722	−0.470269	−0.235135	−	0.971963i	$-0.575553\pi$
$167$	−6.07722	−0.470269	−0.235135	+	0.971963i	$0.575553\pi$
$168$	−2.04942	−0.158116
$169$	−5.50539	−0.423491
$170$	−7.24919	−0.555988
$171$	2.46777	0.188715
$172$	4.77845	0.364353
$173$	−14.3190	−1.08865	−0.544326	−	0.838874i	$-0.683214\pi$
$173$	−14.3190	−1.08865	−0.544326	+	0.838874i	$0.683214\pi$
$174$	−13.2887	−1.00741
$175$	−0.628019	−0.0474738
$176$	−84.1041	−6.33959
$177$	−1.39267	−0.104680
$178$	12.2432	0.917669
$179$	13.8595	1.03591	0.517955	−	0.855408i	$-0.326694\pi$
$179$	13.8595	1.03591	0.517955	+	0.855408i	$0.326694\pi$
$180$	−21.6433	−1.61319
$181$	−16.5516	−1.23027	−0.615135	−	0.788422i	$-0.710898\pi$
$181$	−16.5516	−1.23027	−0.615135	+	0.788422i	$0.710898\pi$
$182$	−2.13000	−0.157886
$183$	8.69149	0.642493
$184$	−38.9864	−2.87412
$185$	12.8117	0.941932
$186$	21.2523	1.55830
$187$	−9.37335	−0.685447
$188$	61.8525	4.51105
$189$	−1.19958	−0.0872567
$190$	4.68871	0.340155
$191$	−16.0048	−1.15807	−0.579034	−	0.815304i	$-0.696570\pi$
$191$	−16.0048	−1.15807	−0.579034	+	0.815304i	$0.696570\pi$
$192$	20.8744	1.50648
$193$	−9.94868	−0.716122	−0.358061	−	0.933698i	$-0.616562\pi$
$193$	−9.94868	−0.716122	−0.358061	+	0.933698i	$0.616562\pi$
$194$	15.7606	1.13154
$195$	3.56153	0.255047
$196$	−37.2978	−2.66413
$197$	−24.5433	−1.74864	−0.874318	−	0.485354i	$-0.838691\pi$
$197$	−24.5433	−1.74864	−0.874318	+	0.485354i	$0.838691\pi$
$198$	−38.3667	−2.72661
$199$	−3.51865	−0.249431	−0.124715	−	0.992193i	$-0.539802\pi$
$199$	−3.51865	−0.249431	−0.124715	+	0.992193i	$0.539802\pi$
$200$	20.2330	1.43069
$201$	9.25356	0.652696
$202$	33.3455	2.34618
$203$	1.80098	0.126404
$204$	6.66610	0.466720
$205$	−16.1588	−1.12858
$206$	36.6475	2.55336
$207$	−10.1345	−0.704395
$208$	39.1037	2.71135
$209$	6.06260	0.419359
$210$	−1.01220	−0.0698486
$211$	28.3742	1.95336	0.976679	−	0.214703i	$-0.0688784\pi$
$211$	28.3742	1.95336	0.976679	+	0.214703i	$0.0688784\pi$
$212$	41.3907	2.84272
$213$	−7.77821	−0.532954
$214$	27.8435	1.90334
$215$	1.48456	0.101246
$216$	38.6471	2.62961
$217$	−2.88028	−0.195526
$218$	−25.6937	−1.74020
$219$	5.19091	0.350769
$220$	−53.1713	−3.58481
$221$	4.35808	0.293156
$222$	−16.1515	−1.08402
$223$	−22.0999	−1.47992	−0.739958	−	0.672653i	$-0.765155\pi$
$223$	−22.0999	−1.47992	−0.739958	+	0.672653i	$0.765155\pi$
$224$	−5.83621	−0.389948
$225$	5.25956	0.350637
$226$	10.4202	0.693142
$227$	−20.3885	−1.35323	−0.676616	−	0.736336i	$-0.736554\pi$
$227$	−20.3885	−1.35323	−0.676616	+	0.736336i	$0.736554\pi$
$228$	−4.31157	−0.285541
$229$	1.71480	0.113317	0.0566586	−	0.998394i	$-0.481955\pi$
$229$	1.71480	0.113317	0.0566586	+	0.998394i	$0.481955\pi$
$230$	−19.2553	−1.26966
$231$	−1.30880	−0.0861126
$232$	−58.0226	−3.80937
$233$	−12.6315	−0.827516	−0.413758	−	0.910387i	$-0.635784\pi$
$233$	−12.6315	−0.827516	−0.413758	+	0.910387i	$0.635784\pi$
$234$	17.8384	1.16613
$235$	19.2162	1.25353
$236$	−9.66694	−0.629264
$237$	9.74472	0.632988
$238$	−1.23858	−0.0802855
$239$	−12.7421	−0.824216	−0.412108	−	0.911135i	$-0.635207\pi$
$239$	−12.7421	−0.824216	−0.412108	+	0.911135i	$0.635207\pi$
$240$	18.5826	1.19950
$241$	12.0466	0.775991	0.387996	−	0.921661i	$-0.373168\pi$
$241$	12.0466	0.775991	0.387996	+	0.921661i	$0.373168\pi$
$242$	−64.3504	−4.13660
$243$	15.6309	1.00272
$244$	60.3302	3.86225
$245$	−11.5876	−0.740306
$246$	20.3713	1.29882
$247$	−2.81877	−0.179354
$248$	92.7944	5.89245
$249$	−8.06509	−0.511104
$250$	32.7618	2.07204
$251$	17.5459	1.10749	0.553743	−	0.832688i	$-0.313199\pi$
$251$	17.5459	1.10749	0.553743	+	0.832688i	$0.313199\pi$
$252$	−3.69793	−0.232948
$253$	−24.8975	−1.56529
$254$	−13.3423	−0.837171
$255$	2.07102	0.129692
$256$	34.0093	2.12558
$257$	6.89542	0.430124	0.215062	−	0.976600i	$-0.431005\pi$
$257$	6.89542	0.430124	0.215062	+	0.976600i	$0.431005\pi$
$258$	−1.87158	−0.116519
$259$	2.18898	0.136016
$260$	24.7217	1.53317
$261$	−15.0829	−0.933609
$262$	58.3076	3.60226
$263$	−28.7719	−1.77415	−0.887076	−	0.461623i	$-0.847267\pi$
$263$	−28.7719	−1.77415	−0.887076	+	0.461623i	$0.847267\pi$
$264$	42.1658	2.59513
$265$	12.8592	0.789935
$266$	0.801105	0.0491189
$267$	−3.49776	−0.214059
$268$	64.2317	3.92358
$269$	3.22591	0.196687	0.0983437	−	0.995153i	$-0.468646\pi$
$269$	3.22591	0.196687	0.0983437	+	0.995153i	$0.468646\pi$
$270$	19.0878	1.16164
$271$	−2.89841	−0.176066	−0.0880328	−	0.996118i	$-0.528058\pi$
$271$	−2.89841	−0.176066	−0.0880328	+	0.996118i	$0.528058\pi$
$272$	22.7386	1.37873
$273$	0.608518	0.0368292
$274$	27.0457	1.63389
$275$	12.9212	0.779179
$276$	17.7065	1.06581
$277$	4.37992	0.263164	0.131582	−	0.991305i	$-0.457994\pi$
$277$	4.37992	0.263164	0.131582	+	0.991305i	$0.457994\pi$
$278$	3.37738	0.202562
$279$	24.1218	1.44414
$280$	−4.41959	−0.264121
$281$	−23.5271	−1.40351	−0.701756	−	0.712418i	$-0.747600\pi$
$281$	−23.5271	−1.40351	−0.701756	+	0.712418i	$0.747600\pi$
$282$	−24.2258	−1.44262
$283$	−19.6959	−1.17080	−0.585400	−	0.810744i	$-0.699063\pi$
$283$	−19.6959	−1.17080	−0.585400	+	0.810744i	$0.699063\pi$
$284$	−53.9909	−3.20377
$285$	−1.33951	−0.0793460
$286$	43.8238	2.59136
$287$	−2.76086	−0.162969
$288$	48.8773	2.88012
$289$	−14.4658	−0.850929
$290$	−28.6573	−1.68281
$291$	−4.50263	−0.263949
$292$	36.0317	2.10859
$293$	−1.03319	−0.0603598	−0.0301799	−	0.999544i	$-0.509608\pi$
$293$	−1.03319	−0.0603598	−0.0301799	+	0.999544i	$0.509608\pi$
$294$	14.6084	0.851980
$295$	−3.00331	−0.174860
$296$	−70.5227	−4.09905
$297$	24.6808	1.43213
$298$	−10.4740	−0.606742
$299$	11.5759	0.669454
$300$	−9.18926	−0.530542
$301$	0.253650	0.0146201
$302$	31.4497	1.80973
$303$	−9.52645	−0.547280
$304$	−14.7071	−0.843512
$305$	18.7433	1.07324
$306$	10.3729	0.592981
$307$	−16.4083	−0.936470	−0.468235	−	0.883604i	$-0.655110\pi$
$307$	−16.4083	−0.936470	−0.468235	+	0.883604i	$0.655110\pi$
$308$	−9.08476	−0.517652
$309$	−10.4698	−0.595607
$310$	45.8310	2.60303
$311$	−18.6475	−1.05740	−0.528702	−	0.848807i	$-0.677321\pi$
$311$	−18.6475	−1.05740	−0.528702	+	0.848807i	$0.677321\pi$
$312$	−19.6047	−1.10990
$313$	14.4425	0.816337	0.408169	−	0.912907i	$-0.366168\pi$
$313$	14.4425	0.816337	0.408169	+	0.912907i	$0.366168\pi$
$314$	−44.7341	−2.52449
$315$	−1.14887	−0.0647314
$316$	67.6410	3.80511
$317$	8.64657	0.485640	0.242820	−	0.970071i	$-0.421928\pi$
$317$	8.64657	0.485640	0.242820	+	0.970071i	$0.421928\pi$
$318$	−16.2115	−0.909096
$319$	−37.0544	−2.07465
$320$	45.0160	2.51647
$321$	−7.95459	−0.443982
$322$	−3.28993	−0.183341
$323$	−1.63910	−0.0912020
$324$	21.2123	1.17846
$325$	−6.00764	−0.333244
$326$	7.33134	0.406046
$327$	7.34042	0.405926
$328$	88.9473	4.91129
$329$	3.28325	0.181012
$330$	20.8256	1.14641
$331$	−26.5530	−1.45948	−0.729742	−	0.683723i	$-0.760360\pi$
$331$	−26.5530	−1.45948	−0.729742	+	0.683723i	$0.760360\pi$
$332$	−55.9822	−3.07242
$333$	−18.3323	−1.00460
$334$	16.5221	0.904051
$335$	19.9554	1.09028
$336$	3.17499	0.173210
$337$	−24.6658	−1.34363	−0.671816	−	0.740718i	$-0.734485\pi$
$337$	−24.6658	−1.34363	−0.671816	+	0.740718i	$0.734485\pi$
$338$	14.9675	0.814125
$339$	−2.97694	−0.161685
$340$	14.3755	0.779623
$341$	59.2604	3.20913
$342$	−6.70912	−0.362788
$343$	−3.98312	−0.215068
$344$	−8.17189	−0.440599
$345$	5.50103	0.296166
$346$	38.9290	2.09284
$347$	7.75477	0.416298	0.208149	−	0.978097i	$-0.433256\pi$
$347$	7.75477	0.416298	0.208149	+	0.978097i	$0.433256\pi$
$348$	26.3522	1.41263
$349$	−27.4501	−1.46937	−0.734684	−	0.678409i	$-0.762670\pi$
$349$	−27.4501	−1.46937	−0.734684	+	0.678409i	$0.762670\pi$
$350$	1.70740	0.0912642
$351$	−11.4752	−0.612501
$352$	120.077	6.40015
$353$	22.5188	1.19855	0.599277	−	0.800542i	$-0.295455\pi$
$353$	22.5188	1.19855	0.599277	+	0.800542i	$0.295455\pi$
$354$	3.78625	0.201237
$355$	−16.7738	−0.890262
$356$	−24.2790	−1.28678
$357$	0.353850	0.0187277
$358$	−37.6799	−1.99144
$359$	−2.25963	−0.119259	−0.0596294	−	0.998221i	$-0.518992\pi$
$359$	−2.25963	−0.119259	−0.0596294	+	0.998221i	$0.518992\pi$
$360$	37.0133	1.95077
$361$	−17.9398	−0.944202
$362$	44.9988	2.36508
$363$	18.3842	0.964921
$364$	4.22390	0.221393
$365$	11.1943	0.585935
$366$	−23.6295	−1.23514
$367$	−6.64138	−0.346677	−0.173339	−	0.984862i	$-0.555456\pi$
$367$	−6.64138	−0.346677	−0.173339	+	0.984862i	$0.555456\pi$
$368$	60.3983	3.14848
$369$	23.1218	1.20367
$370$	−34.8310	−1.81078
$371$	2.19710	0.114068
$372$	−42.1446	−2.18509
$373$	29.2392	1.51395	0.756973	−	0.653446i	$-0.226677\pi$
$373$	29.2392	1.51395	0.756973	+	0.653446i	$0.226677\pi$
$374$	25.4833	1.31771
$375$	−9.35969	−0.483332
$376$	−105.777	−5.45505
$377$	17.2282	0.887298
$378$	3.26130	0.167743
$379$	17.3138	0.889349	0.444675	−	0.895692i	$-0.353319\pi$
$379$	17.3138	0.889349	0.444675	+	0.895692i	$0.353319\pi$
$380$	−9.29797	−0.476976
$381$	3.81176	0.195282
$382$	43.5123	2.22628
$383$	−1.59035	−0.0812630	−0.0406315	−	0.999174i	$-0.512937\pi$
$383$	−1.59035	−0.0812630	−0.0406315	+	0.999174i	$0.512937\pi$
$384$	−25.0723	−1.27946
$385$	−2.82244	−0.143845
$386$	27.0475	1.37668
$387$	−2.12427	−0.107983
$388$	−31.2541	−1.58669
$389$	19.9732	1.01268	0.506342	−	0.862333i	$-0.330997\pi$
$389$	19.9732	1.01268	0.506342	+	0.862333i	$0.330997\pi$
$390$	−9.68275	−0.490305
$391$	6.73136	0.340419
$392$	63.7849	3.22163
$393$	−16.6579	−0.840278
$394$	66.7258	3.36160
$395$	21.0146	1.05736
$396$	76.0833	3.82333
$397$	2.80364	0.140711	0.0703554	−	0.997522i	$-0.477587\pi$
$397$	2.80364	0.140711	0.0703554	+	0.997522i	$0.477587\pi$
$398$	9.56616	0.479508
$399$	−0.228867	−0.0114577
$400$	−31.3453	−1.56727
$401$	−15.9283	−0.795421	−0.397711	−	0.917511i	$-0.630195\pi$
$401$	−15.9283	−0.795421	−0.397711	+	0.917511i	$0.630195\pi$
$402$	−25.1576	−1.25475
$403$	−27.5528	−1.37250
$404$	−66.1259	−3.28989
$405$	6.59021	0.327470
$406$	−4.89633	−0.243001
$407$	−45.0372	−2.23241
$408$	−11.4001	−0.564387
$409$	17.1977	0.850370	0.425185	−	0.905106i	$-0.360209\pi$
$409$	17.1977	0.850370	0.425185	+	0.905106i	$0.360209\pi$
$410$	43.9309	2.16959
$411$	−7.72666	−0.381128
$412$	−72.6741	−3.58040
$413$	−0.513141	−0.0252500
$414$	27.5526	1.35414
$415$	−17.3925	−0.853763
$416$	−55.8293	−2.73726
$417$	−0.964881	−0.0472504
$418$	−16.4824	−0.806180
$419$	23.7083	1.15823	0.579113	−	0.815247i	$-0.303399\pi$
$419$	23.7083	1.15823	0.579113	+	0.815247i	$0.303399\pi$
$420$	2.00725	0.0979439
$421$	18.6876	0.910779	0.455390	−	0.890292i	$-0.349500\pi$
$421$	18.6876	0.910779	0.455390	+	0.890292i	$0.349500\pi$
$422$	−77.1409	−3.75516
$423$	−27.4967	−1.33694
$424$	−70.7845	−3.43760
$425$	−3.49342	−0.169456
$426$	21.1466	1.02456
$427$	3.20245	0.154977
$428$	−55.2152	−2.66893
$429$	−12.5200	−0.604471
$430$	−4.03608	−0.194637
$431$	−35.8779	−1.72818	−0.864090	−	0.503338i	$-0.832105\pi$
$431$	−35.8779	−1.72818	−0.864090	+	0.503338i	$0.832105\pi$
$432$	−59.8728	−2.88063
$433$	−20.8102	−1.00007	−0.500036	−	0.866004i	$-0.666680\pi$
$433$	−20.8102	−1.00007	−0.500036	+	0.866004i	$0.666680\pi$
$434$	7.83060	0.375881
$435$	8.18707	0.392540
$436$	50.9521	2.44016
$437$	−4.35378	−0.208270
$438$	−14.1125	−0.674323
$439$	−20.6423	−0.985205	−0.492603	−	0.870254i	$-0.663954\pi$
$439$	−20.6423	−0.985205	−0.492603	+	0.870254i	$0.663954\pi$
$440$	90.9312	4.33498
$441$	16.5808	0.789563
$442$	−11.8483	−0.563567
$443$	−3.45252	−0.164034	−0.0820170	−	0.996631i	$-0.526136\pi$
$443$	−3.45252	−0.164034	−0.0820170	+	0.996631i	$0.526136\pi$
$444$	32.0294	1.52005
$445$	−7.54296	−0.357571
$446$	60.0829	2.84501
$447$	2.99231	0.141531
$448$	7.69136	0.363383
$449$	32.1167	1.51568	0.757841	−	0.652439i	$-0.226254\pi$
$449$	32.1167	1.51568	0.757841	+	0.652439i	$0.226254\pi$
$450$	−14.2992	−0.674069
$451$	56.8036	2.67478
$452$	−20.6638	−0.971946
$453$	−8.98483	−0.422144
$454$	55.4302	2.60147
$455$	1.31228	0.0615205
$456$	7.37346	0.345294
$457$	−8.15065	−0.381271	−0.190636	−	0.981661i	$-0.561055\pi$
$457$	−8.15065	−0.381271	−0.190636	+	0.981661i	$0.561055\pi$
$458$	−4.66203	−0.217842
$459$	−6.67278	−0.311459
$460$	38.1843	1.78035
$461$	28.5191	1.32827	0.664133	−	0.747615i	$-0.268801\pi$
$461$	28.5191	1.32827	0.664133	+	0.747615i	$0.268801\pi$
$462$	3.55823	0.165544
$463$	13.4653	0.625784	0.312892	−	0.949789i	$-0.398702\pi$
$463$	13.4653	0.625784	0.312892	+	0.949789i	$0.398702\pi$
$464$	89.8895	4.17302
$465$	−13.0934	−0.607193
$466$	34.3412	1.59083
$467$	1.84824	0.0855264	0.0427632	−	0.999085i	$-0.486384\pi$
$467$	1.84824	0.0855264	0.0427632	+	0.999085i	$0.486384\pi$
$468$	−35.3745	−1.63519
$469$	3.40955	0.157438
$470$	−52.2432	−2.40980
$471$	12.7800	0.588873
$472$	16.5320	0.760946
$473$	−5.21873	−0.239958
$474$	−26.4930	−1.21686
$475$	2.25951	0.103673
$476$	2.45618	0.112579
$477$	−18.4004	−0.842495
$478$	34.6419	1.58448
$479$	−7.82347	−0.357464	−0.178732	−	0.983898i	$-0.557199\pi$
$479$	−7.82347	−0.357464	−0.178732	+	0.983898i	$0.557199\pi$
$480$	−26.5308	−1.21096
$481$	20.9398	0.954772
$482$	−32.7512	−1.49177
$483$	0.939897	0.0427668
$484$	127.610	5.80047
$485$	−9.70997	−0.440907
$486$	−42.4958	−1.92765
$487$	−13.7905	−0.624905	−0.312453	−	0.949933i	$-0.601151\pi$
$487$	−13.7905	−0.624905	−0.312453	+	0.949933i	$0.601151\pi$
$488$	−103.174	−4.67047
$489$	−2.09449	−0.0947159
$490$	31.5033	1.42317
$491$	−13.5499	−0.611500	−0.305750	−	0.952112i	$-0.598907\pi$
$491$	−13.5499	−0.611500	−0.305750	+	0.952112i	$0.598907\pi$
$492$	−40.3973	−1.82125
$493$	10.0181	0.451194
$494$	7.66338	0.344792
$495$	23.6375	1.06243
$496$	−143.759	−6.45495
$497$	−2.86595	−0.128555
$498$	21.9266	0.982553
$499$	0.794090	0.0355483	0.0177742	−	0.999842i	$-0.494342\pi$
$499$	0.794090	0.0355483	0.0177742	+	0.999842i	$0.494342\pi$
$500$	−64.9684	−2.90548
$501$	−4.72019	−0.210883
$502$	−47.7020	−2.12904
$503$	−11.0715	−0.493654	−0.246827	−	0.969060i	$-0.579388\pi$
$503$	−11.0715	−0.493654	−0.246827	+	0.969060i	$0.579388\pi$
$504$	6.32404	0.281695
$505$	−20.5439	−0.914192
$506$	67.6889	3.00914
$507$	−4.27605	−0.189906
$508$	26.4585	1.17391
$509$	11.4240	0.506360	0.253180	−	0.967419i	$-0.418524\pi$
$509$	11.4240	0.506360	0.253180	+	0.967419i	$0.418524\pi$
$510$	−5.63047	−0.249321
$511$	1.91263	0.0846100
$512$	−27.9002	−1.23303
$513$	4.31589	0.190551
$514$	−18.7466	−0.826876
$515$	−22.5783	−0.994918
$516$	3.71144	0.163387
$517$	−67.5515	−2.97091
$518$	−5.95117	−0.261479
$519$	−11.1216	−0.488184
$520$	−42.2779	−1.85401
$521$	−21.0594	−0.922628	−0.461314	−	0.887237i	$-0.652622\pi$
$521$	−21.0594	−0.922628	−0.461314	+	0.887237i	$0.652622\pi$
$522$	41.0059	1.79478
$523$	−22.4926	−0.983535	−0.491767	−	0.870727i	$-0.663649\pi$
$523$	−22.4926	−0.983535	−0.491767	+	0.870727i	$0.663649\pi$
$524$	−115.627	−5.05120
$525$	−0.487785	−0.0212887
$526$	78.2222	3.41065
$527$	−16.0218	−0.697921
$528$	−65.3240	−2.84286
$529$	−5.12016	−0.222616
$530$	−34.9603	−1.51858
$531$	4.29747	0.186494
$532$	−1.58863	−0.0688761
$533$	−26.4105	−1.14396
$534$	9.50935	0.411510
$535$	−17.1542	−0.741640
$536$	−109.846	−4.74463
$537$	10.7647	0.464533
$538$	−8.77029	−0.378114
$539$	40.7344	1.75455
$540$	−37.8521	−1.62889
$541$	6.35885	0.273388	0.136694	−	0.990613i	$-0.456352\pi$
$541$	6.35885	0.273388	0.136694	+	0.990613i	$0.456352\pi$
$542$	7.87989	0.338470
$543$	−12.8557	−0.551690
$544$	−32.4645	−1.39190
$545$	15.8297	0.678071
$546$	−1.65438	−0.0708008
$547$	35.4903	1.51746	0.758728	−	0.651408i	$-0.225821\pi$
$547$	35.4903	1.51746	0.758728	+	0.651408i	$0.225821\pi$
$548$	−53.6330	−2.29109
$549$	−26.8200	−1.14465
$550$	−35.1289	−1.49790
$551$	−6.47963	−0.276042
$552$	−30.2809	−1.28884
$553$	3.59052	0.152685
$554$	−11.9077	−0.505910
$555$	9.95085	0.422390
$556$	−6.69753	−0.284038
$557$	0.413168	0.0175065	0.00875326	−	0.999962i	$-0.497214\pi$
$557$	0.413168	0.0175065	0.00875326	+	0.999962i	$0.497214\pi$
$558$	−65.5800	−2.77622
$559$	2.42642	0.102627
$560$	6.84690	0.289334
$561$	−7.28031	−0.307375
$562$	63.9632	2.69813
$563$	6.68044	0.281547	0.140774	−	0.990042i	$-0.455041\pi$
$563$	6.68044	0.281547	0.140774	+	0.990042i	$0.455041\pi$
$564$	48.0410	2.02289
$565$	−6.41982	−0.270084
$566$	53.5473	2.25076
$567$	1.12599	0.0472872
$568$	92.3328	3.87420
$569$	13.3154	0.558212	0.279106	−	0.960260i	$-0.409962\pi$
$569$	13.3154	0.558212	0.279106	+	0.960260i	$0.409962\pi$
$570$	3.64174	0.152536
$571$	−27.5362	−1.15236	−0.576178	−	0.817324i	$-0.695456\pi$
$571$	−27.5362	−1.15236	−0.576178	+	0.817324i	$0.695456\pi$
$572$	−86.9050	−3.63368
$573$	−12.4310	−0.519312
$574$	7.50596	0.313293
$575$	−9.27922	−0.386970
$576$	−64.4139	−2.68391
$577$	34.6159	1.44108	0.720540	−	0.693413i	$-0.243894\pi$
$577$	34.6159	1.44108	0.720540	+	0.693413i	$0.243894\pi$
$578$	39.3282	1.63584
$579$	−7.72718	−0.321130
$580$	56.8289	2.35969
$581$	−2.97165	−0.123285
$582$	12.2413	0.507418
$583$	−45.2044	−1.87218
$584$	−61.6198	−2.54984
$585$	−10.9901	−0.454385
$586$	2.80895	0.116036
$587$	37.7832	1.55948	0.779740	−	0.626103i	$-0.215351\pi$
$587$	37.7832	1.55948	0.779740	+	0.626103i	$0.215351\pi$
$588$	−28.9693	−1.19467
$589$	10.3628	0.426990
$590$	8.16511	0.336152
$591$	−19.0628	−0.784140
$592$	109.255	4.49035
$593$	−41.5243	−1.70520	−0.852599	−	0.522566i	$-0.824975\pi$
$593$	−41.5243	−1.70520	−0.852599	+	0.522566i	$0.824975\pi$
$594$	−67.0998	−2.75314
$595$	0.763083	0.0312834
$596$	20.7705	0.850793
$597$	−2.73295	−0.111852
$598$	−31.4715	−1.28697
$599$	9.55500	0.390407	0.195203	−	0.980763i	$-0.437463\pi$
$599$	9.55500	0.390407	0.195203	+	0.980763i	$0.437463\pi$
$600$	15.7151	0.641565
$601$	−3.44598	−0.140565	−0.0702823	−	0.997527i	$-0.522390\pi$
$601$	−3.44598	−0.140565	−0.0702823	+	0.997527i	$0.522390\pi$
$602$	−0.689597	−0.0281059
$603$	−28.5544	−1.16283
$604$	−62.3664	−2.53765
$605$	39.6458	1.61183
$606$	25.8996	1.05210
$607$	39.5196	1.60405	0.802026	−	0.597290i	$-0.203756\pi$
$607$	39.5196	1.60405	0.802026	+	0.597290i	$0.203756\pi$
$608$	20.9977	0.851570
$609$	1.39883	0.0566834
$610$	−50.9574	−2.06321
$611$	31.4077	1.27062
$612$	−20.5701	−0.831497
$613$	−14.2359	−0.574982	−0.287491	−	0.957783i	$-0.592821\pi$
$613$	−14.2359	−0.574982	−0.287491	+	0.957783i	$0.592821\pi$
$614$	44.6092	1.80028
$615$	−12.5506	−0.506089
$616$	15.5363	0.625977
$617$	−1.34464	−0.0541333	−0.0270667	−	0.999634i	$-0.508617\pi$
$617$	−1.34464	−0.0541333	−0.0270667	+	0.999634i	$0.508617\pi$
$618$	28.4643	1.14500
$619$	−0.352190	−0.0141557	−0.00707786	−	0.999975i	$-0.502253\pi$
$619$	−0.352190	−0.0141557	−0.00707786	+	0.999975i	$0.502253\pi$
$620$	−90.8854	−3.65004
$621$	−17.7242	−0.711249
$622$	50.6970	2.03277
$623$	−1.28878	−0.0516338
$624$	30.3720	1.21585
$625$	−9.21195	−0.368478
$626$	−39.2648	−1.56934
$627$	4.70884	0.188053
$628$	88.7101	3.53992
$629$	12.1764	0.485504
$630$	3.12343	0.124440
$631$	30.8908	1.22974	0.614872	−	0.788627i	$-0.289208\pi$
$631$	30.8908	1.22974	0.614872	+	0.788627i	$0.289208\pi$
$632$	−115.677	−4.60137
$633$	22.0383	0.875944
$634$	−23.5074	−0.933599
$635$	8.22011	0.326205
$636$	32.1483	1.27476
$637$	−18.9392	−0.750398
$638$	100.740	3.98833
$639$	24.0018	0.949497
$640$	−54.0687	−2.13725
$641$	45.2428	1.78698	0.893491	−	0.449081i	$-0.148248\pi$
$641$	45.2428	1.78698	0.893491	+	0.449081i	$0.148248\pi$
$642$	21.6261	0.853516
$643$	30.0501	1.18506	0.592531	−	0.805548i	$-0.298129\pi$
$643$	30.0501	1.18506	0.592531	+	0.805548i	$0.298129\pi$
$644$	6.52411	0.257086
$645$	1.15306	0.0454019
$646$	4.45622	0.175328
$647$	10.8704	0.427361	0.213681	−	0.976904i	$-0.431455\pi$
$647$	10.8704	0.427361	0.213681	+	0.976904i	$0.431455\pi$
$648$	−36.2763	−1.42507
$649$	10.5577	0.414424
$650$	16.3330	0.640632
$651$	−2.23712	−0.0876796
$652$	−14.5385	−0.569370
$653$	32.2029	1.26020	0.630098	−	0.776516i	$-0.283015\pi$
$653$	32.2029	1.26020	0.630098	+	0.776516i	$0.283015\pi$
$654$	−19.9564	−0.780357
$655$	−35.9229	−1.40362
$656$	−137.799	−5.38013
$657$	−16.0180	−0.624921
$658$	−8.92618	−0.347979
$659$	23.3307	0.908837	0.454418	−	0.890788i	$-0.349847\pi$
$659$	23.3307	0.908837	0.454418	+	0.890788i	$0.349847\pi$
$660$	−41.2983	−1.60754
$661$	−4.99815	−0.194405	−0.0972027	−	0.995265i	$-0.530990\pi$
$661$	−4.99815	−0.194405	−0.0972027	+	0.995265i	$0.530990\pi$
$662$	72.1896	2.80573
$663$	3.38494	0.131460
$664$	95.7383	3.71536
$665$	−0.493555	−0.0191392
$666$	49.8401	1.93126
$667$	26.6102	1.03035
$668$	−32.7643	−1.26769
$669$	−17.1650	−0.663639
$670$	−54.2528	−2.09597
$671$	−65.8890	−2.54362
$672$	−4.53300	−0.174864
$673$	−31.3777	−1.20952	−0.604761	−	0.796407i	$-0.706731\pi$
$673$	−31.3777	−1.20952	−0.604761	+	0.796407i	$0.706731\pi$
$674$	67.0589	2.58301
$675$	9.19847	0.354049
$676$	−29.6814	−1.14159
$677$	31.6084	1.21481	0.607405	−	0.794393i	$-0.292211\pi$
$677$	31.6084	1.21481	0.607405	+	0.794393i	$0.292211\pi$
$678$	8.09341	0.310826
$679$	−1.65903	−0.0636677
$680$	−24.5844	−0.942769
$681$	−15.8358	−0.606829
$682$	−161.111	−6.16927
$683$	−12.1091	−0.463342	−0.231671	−	0.972794i	$-0.574419\pi$
$683$	−12.1091	−0.463342	−0.231671	+	0.972794i	$0.574419\pi$
$684$	13.3045	0.508712
$685$	−16.6626	−0.636647
$686$	10.8289	0.413450
$687$	1.33189	0.0508148
$688$	12.6600	0.482658
$689$	21.0175	0.800704
$690$	−14.9557	−0.569352
$691$	13.5973	0.517267	0.258634	−	0.965975i	$-0.416728\pi$
$691$	13.5973	0.517267	0.258634	+	0.965975i	$0.416728\pi$
$692$	−77.1983	−2.93464
$693$	4.03866	0.153416
$694$	−21.0829	−0.800296
$695$	−2.08078	−0.0789285
$696$	−45.0663	−1.70824
$697$	−15.3576	−0.581709
$698$	74.6285	2.82473
$699$	−9.81091	−0.371083
$700$	−3.38586	−0.127974
$701$	−40.5949	−1.53325	−0.766624	−	0.642096i	$-0.778065\pi$
$701$	−40.5949	−1.53325	−0.766624	+	0.642096i	$0.778065\pi$
$702$	31.1977	1.17748
$703$	−7.87558	−0.297033
$704$	−158.246	−5.96414
$705$	14.9253	0.562120
$706$	−61.2218	−2.30411
$707$	−3.51010	−0.132011
$708$	−7.50835	−0.282181
$709$	−35.4611	−1.33177	−0.665885	−	0.746054i	$-0.731946\pi$
$709$	−35.4611	−1.33177	−0.665885	+	0.746054i	$0.731946\pi$
$710$	45.6030	1.71145
$711$	−30.0700	−1.12771
$712$	41.5208	1.55606
$713$	−42.5571	−1.59378
$714$	−0.962013	−0.0360024
$715$	−26.9995	−1.00973
$716$	74.7213	2.79247
$717$	−9.89681	−0.369603
$718$	6.14326	0.229264
$719$	22.5770	0.841979	0.420990	−	0.907065i	$-0.361683\pi$
$719$	22.5770	0.841979	0.420990	+	0.907065i	$0.361683\pi$
$720$	−57.3416	−2.13700
$721$	−3.85769	−0.143668
$722$	48.7731	1.81515
$723$	9.35665	0.347978
$724$	−89.2351	−3.31639
$725$	−13.8101	−0.512893
$726$	−49.9812	−1.85498
$727$	−33.2160	−1.23191	−0.615956	−	0.787781i	$-0.711230\pi$
$727$	−33.2160	−1.23191	−0.615956	+	0.787781i	$0.711230\pi$
$728$	−7.22353	−0.267722
$729$	0.337037	0.0124829
$730$	−30.4339	−1.12641
$731$	1.41095	0.0521859
$732$	46.8587	1.73195
$733$	−3.92461	−0.144959	−0.0724794	−	0.997370i	$-0.523091\pi$
$733$	−3.92461	−0.144959	−0.0724794	+	0.997370i	$0.523091\pi$
$734$	18.0559	0.666456
$735$	−9.00014	−0.331975
$736$	−86.2322	−3.17856
$737$	−70.1500	−2.58401
$738$	−62.8611	−2.31395
$739$	5.48372	0.201722	0.100861	−	0.994901i	$-0.467840\pi$
$739$	5.48372	0.201722	0.100861	+	0.994901i	$0.467840\pi$
$740$	69.0719	2.53913
$741$	−2.18935	−0.0804276
$742$	−5.97326	−0.219285
$743$	41.9463	1.53886	0.769430	−	0.638731i	$-0.220540\pi$
$743$	41.9463	1.53886	0.769430	+	0.638731i	$0.220540\pi$
$744$	72.0737	2.64235
$745$	6.45295	0.236418
$746$	−79.4925	−2.91043
$747$	24.8871	0.910570
$748$	−50.5348	−1.84774
$749$	−2.93093	−0.107094
$750$	25.4462	0.929163
$751$	1.46744	0.0535475	0.0267738	−	0.999642i	$-0.491477\pi$
$751$	1.46744	0.0535475	0.0267738	+	0.999642i	$0.491477\pi$
$752$	163.872	5.97579
$753$	13.6279	0.496630
$754$	−46.8384	−1.70575
$755$	−19.3759	−0.705162
$756$	−6.46734	−0.235215
$757$	24.5037	0.890601	0.445301	−	0.895381i	$-0.353097\pi$
$757$	24.5037	0.890601	0.445301	+	0.895381i	$0.353097\pi$
$758$	−47.0710	−1.70970
$759$	−19.3380	−0.701924
$760$	15.9010	0.576789
$761$	23.9544	0.868346	0.434173	−	0.900830i	$-0.357041\pi$
$761$	23.9544	0.868346	0.434173	+	0.900830i	$0.357041\pi$
$762$	−10.3630	−0.375413
$763$	2.70464	0.0979145
$764$	−86.2872	−3.12176
$765$	−6.39069	−0.231056
$766$	4.32368	0.156221
$767$	−4.90871	−0.177243
$768$	26.4151	0.953173
$769$	−15.6888	−0.565754	−0.282877	−	0.959156i	$-0.591289\pi$
$769$	−15.6888	−0.565754	−0.282877	+	0.959156i	$0.591289\pi$
$770$	7.67337	0.276529
$771$	5.35569	0.192881
$772$	−53.6366	−1.93043
$773$	2.69024	0.0967612	0.0483806	−	0.998829i	$-0.484594\pi$
$773$	2.69024	0.0967612	0.0483806	+	0.998829i	$0.484594\pi$
$774$	5.77526	0.207587
$775$	22.0862	0.793358
$776$	53.4493	1.91872
$777$	1.70019	0.0609938
$778$	−54.3012	−1.94679
$779$	9.93313	0.355891
$780$	19.2014	0.687521
$781$	58.9656	2.10995
$782$	−18.3005	−0.654426
$783$	−26.3786	−0.942694
$784$	−98.8166	−3.52917
$785$	27.5603	0.983671
$786$	45.2877	1.61536
$787$	−14.6904	−0.523655	−0.261828	−	0.965115i	$-0.584325\pi$
$787$	−14.6904	−0.523655	−0.261828	+	0.965115i	$0.584325\pi$
$788$	−132.321	−4.71374
$789$	−22.3472	−0.795583
$790$	−57.1325	−2.03268
$791$	−1.09688	−0.0390005
$792$	−130.114	−4.62341
$793$	30.6347	1.08787
$794$	−7.62226	−0.270504
$795$	9.98779	0.354230
$796$	−18.9702	−0.672382
$797$	44.5164	1.57685	0.788426	−	0.615130i	$-0.210896\pi$
$797$	44.5164	1.57685	0.788426	+	0.615130i	$0.210896\pi$
$798$	0.622221	0.0220264
$799$	18.2634	0.646113
$800$	44.7525	1.58224
$801$	10.7933	0.381362
$802$	43.3043	1.52913
$803$	−39.3516	−1.38869
$804$	49.8890	1.75945
$805$	2.02690	0.0714389
$806$	74.9077	2.63851
$807$	2.50558	0.0882005
$808$	113.086	3.97834
$809$	0.884733	0.0311056	0.0155528	−	0.999879i	$-0.495049\pi$
$809$	0.884733	0.0311056	0.0155528	+	0.999879i	$0.495049\pi$
$810$	−17.9168	−0.629532
$811$	−22.0729	−0.775085	−0.387542	−	0.921852i	$-0.626676\pi$
$811$	−22.0729	−0.775085	−0.387542	+	0.921852i	$0.626676\pi$
$812$	9.70969	0.340743
$813$	−2.25120	−0.0789531
$814$	122.443	4.29162
$815$	−4.51679	−0.158216
$816$	17.6612	0.618264
$817$	−0.912590	−0.0319275
$818$	−46.7553	−1.63476
$819$	−1.87775	−0.0656139
$820$	−87.1174	−3.04227
$821$	−16.1828	−0.564783	−0.282392	−	0.959299i	$-0.591128\pi$
$821$	−16.1828	−0.564783	−0.282392	+	0.959299i	$0.591128\pi$
$822$	21.0065	0.732684
$823$	−19.9634	−0.695879	−0.347940	−	0.937517i	$-0.613119\pi$
$823$	−19.9634	−0.695879	−0.347940	+	0.937517i	$0.613119\pi$
$824$	124.284	4.32964
$825$	10.0360	0.349407
$826$	1.39508	0.0485409
$827$	−20.2344	−0.703620	−0.351810	−	0.936072i	$-0.614434\pi$
$827$	−20.2344	−0.703620	−0.351810	+	0.936072i	$0.614434\pi$
$828$	−54.6383	−1.89881
$829$	−27.7151	−0.962586	−0.481293	−	0.876560i	$-0.659833\pi$
$829$	−27.7151	−0.962586	−0.481293	+	0.876560i	$0.659833\pi$
$830$	47.2849	1.64128
$831$	3.40190	0.118011
$832$	73.5757	2.55078
$833$	−11.0131	−0.381580
$834$	2.62322	0.0908348
$835$	−10.1792	−0.352264
$836$	32.6855	1.13045
$837$	42.1868	1.45819
$838$	−64.4557	−2.22659
$839$	−46.8928	−1.61892	−0.809459	−	0.587176i	$-0.800239\pi$
$839$	−46.8928	−1.61892	−0.809459	+	0.587176i	$0.800239\pi$
$840$	−3.43271	−0.118440
$841$	10.6033	0.365631
$842$	−50.8060	−1.75089
$843$	−18.2736	−0.629376
$844$	152.975	5.26560
$845$	−9.22137	−0.317225
$846$	74.7553	2.57014
$847$	6.77382	0.232751
$848$	109.660	3.76576
$849$	−15.2979	−0.525022
$850$	9.49755	0.325763
$851$	32.3429	1.10870
$852$	−41.9349	−1.43667
$853$	52.2677	1.78961	0.894805	−	0.446457i	$-0.147314\pi$
$853$	52.2677	1.78961	0.894805	+	0.446457i	$0.147314\pi$
$854$	−8.70650	−0.297930
$855$	4.13344	0.141361
$856$	94.4265	3.22743
$857$	24.0388	0.821151	0.410575	−	0.911827i	$-0.365328\pi$
$857$	24.0388	0.821151	0.410575	+	0.911827i	$0.365328\pi$
$858$	34.0381	1.16204
$859$	−39.1147	−1.33458	−0.667289	−	0.744799i	$-0.732545\pi$
$859$	−39.1147	−1.33458	−0.667289	+	0.744799i	$0.732545\pi$
$860$	8.00376	0.272926
$861$	−2.14437	−0.0730800
$862$	97.5414	3.32227
$863$	5.96931	0.203198	0.101599	−	0.994825i	$-0.467604\pi$
$863$	5.96931	0.203198	0.101599	+	0.994825i	$0.467604\pi$
$864$	85.4818	2.90815
$865$	−23.9839	−0.815476
$866$	56.5766	1.92255
$867$	−11.2356	−0.381582
$868$	−15.5285	−0.527072
$869$	−73.8734	−2.50599
$870$	−22.2582	−0.754623
$871$	32.6158	1.10514
$872$	−87.1360	−2.95080
$873$	13.8941	0.470244
$874$	11.8366	0.400380
$875$	−3.44865	−0.116586
$876$	27.9859	0.945557
$877$	−55.6428	−1.87892	−0.939462	−	0.342654i	$-0.888674\pi$
$877$	−55.6428	−1.87892	−0.939462	+	0.342654i	$0.888674\pi$
$878$	56.1203	1.89397
$879$	−0.802485	−0.0270672
$880$	−140.872	−4.74880
$881$	1.64744	0.0555035	0.0277518	−	0.999615i	$-0.491165\pi$
$881$	1.64744	0.0555035	0.0277518	+	0.999615i	$0.491165\pi$
$882$	−45.0783	−1.51787
$883$	32.1842	1.08308	0.541542	−	0.840674i	$-0.317841\pi$
$883$	32.1842	1.08308	0.541542	+	0.840674i	$0.317841\pi$
$884$	23.4959	0.790251
$885$	−2.33268	−0.0784123
$886$	9.38636	0.315341
$887$	23.8081	0.799397	0.399699	−	0.916647i	$-0.369115\pi$
$887$	23.8081	0.799397	0.399699	+	0.916647i	$0.369115\pi$
$888$	−54.7752	−1.83814
$889$	1.40447	0.0471045
$890$	20.5071	0.687398
$891$	−23.1668	−0.776117
$892$	−119.148	−3.98936
$893$	−11.8126	−0.395294
$894$	−8.13519	−0.272081
$895$	23.2143	0.775969
$896$	−9.23809	−0.308623
$897$	8.99107	0.300203
$898$	−87.3157	−2.91376
$899$	−63.3368	−2.11240
$900$	28.3560	0.945200
$901$	12.2216	0.407160
$902$	−154.432	−5.14202
$903$	0.197011	0.00655610
$904$	35.3384	1.17534
$905$	−27.7234	−0.921558
$906$	24.4271	0.811535
$907$	−42.9573	−1.42637	−0.713187	−	0.700973i	$-0.752749\pi$
$907$	−42.9573	−1.42637	−0.713187	+	0.700973i	$0.752749\pi$
$908$	−109.921	−3.64786
$909$	29.3965	0.975020
$910$	−3.56769	−0.118268
$911$	1.20152	0.0398081	0.0199040	−	0.999802i	$-0.493664\pi$
$911$	1.20152	0.0398081	0.0199040	+	0.999802i	$0.493664\pi$
$912$	−11.4231	−0.378256
$913$	61.1404	2.02345
$914$	22.1592	0.732960
$915$	14.5580	0.481272
$916$	9.24505	0.305465
$917$	−6.13773	−0.202686
$918$	18.1413	0.598752
$919$	−27.8314	−0.918073	−0.459037	−	0.888417i	$-0.651805\pi$
$919$	−27.8314	−0.918073	−0.459037	+	0.888417i	$0.651805\pi$
$920$	−65.3011	−2.15291
$921$	−12.7444	−0.419941
$922$	−77.5348	−2.55347
$923$	−27.4157	−0.902398
$924$	−7.05616	−0.232131
$925$	−16.7852	−0.551895
$926$	−36.6080	−1.20301
$927$	32.3075	1.06112
$928$	−128.337	−4.21288
$929$	−35.3260	−1.15901	−0.579505	−	0.814969i	$-0.696754\pi$
$929$	−35.3260	−1.15901	−0.579505	+	0.814969i	$0.696754\pi$
$930$	35.5971	1.16727
$931$	7.12314	0.233451
$932$	−68.1005	−2.23070
$933$	−14.4836	−0.474172
$934$	−5.02481	−0.164417
$935$	−15.7001	−0.513448
$936$	60.4958	1.97737
$937$	−2.85338	−0.0932157	−0.0466079	−	0.998913i	$-0.514841\pi$
$937$	−2.85338	−0.0932157	−0.0466079	+	0.998913i	$0.514841\pi$
$938$	−9.26954	−0.302661
$939$	11.2175	0.366070
$940$	103.601	3.37910
$941$	23.5288	0.767018	0.383509	−	0.923537i	$-0.374716\pi$
$941$	23.5288	0.767018	0.383509	+	0.923537i	$0.374716\pi$
$942$	−34.7451	−1.13206
$943$	−40.7928	−1.32840
$944$	−25.6116	−0.833586
$945$	−2.00926	−0.0653614
$946$	14.1882	0.461297
$947$	25.7916	0.838114	0.419057	−	0.907960i	$-0.362361\pi$
$947$	25.7916	0.838114	0.419057	+	0.907960i	$0.362361\pi$
$948$	52.5370	1.70632
$949$	18.2963	0.593923
$950$	−6.14293	−0.199303
$951$	6.71582	0.217775
$952$	−4.20045	−0.136137
$953$	−14.1177	−0.457319	−0.228659	−	0.973507i	$-0.573434\pi$
$953$	−14.1177	−0.457319	−0.228659	+	0.973507i	$0.573434\pi$
$954$	50.0251	1.61962
$955$	−26.8076	−0.867474
$956$	−68.6967	−2.22181
$957$	−28.7803	−0.930334
$958$	21.2697	0.687192
$959$	−2.84695	−0.0919328
$960$	34.9641	1.12846
$961$	70.2934	2.26753
$962$	−56.9290	−1.83546
$963$	24.5461	0.790986
$964$	64.9473	2.09181
$965$	−16.6638	−0.536426
$966$	−2.55530	−0.0822154
$967$	−32.3859	−1.04146	−0.520730	−	0.853722i	$-0.674340\pi$
$967$	−32.3859	−1.04146	−0.520730	+	0.853722i	$0.674340\pi$
$968$	−218.233	−7.01429
$969$	−1.27309	−0.0408977
$970$	26.3985	0.847605
$971$	−55.7842	−1.79020	−0.895100	−	0.445865i	$-0.852896\pi$
$971$	−55.7842	−1.79020	−0.895100	+	0.445865i	$0.852896\pi$
$972$	84.2715	2.70301
$973$	−0.355518	−0.0113974
$974$	37.4921	1.20133
$975$	−4.66616	−0.149437
$976$	159.839	5.11631
$977$	7.25606	0.232142	0.116071	−	0.993241i	$-0.462970\pi$
$977$	7.25606	0.232142	0.116071	+	0.993241i	$0.462970\pi$
$978$	5.69428	0.182083
$979$	26.5160	0.847456
$980$	−62.4727	−1.99562
$981$	−22.6509	−0.723188
$982$	36.8382	1.17555
$983$	41.7273	1.33090	0.665448	−	0.746445i	$-0.268241\pi$
$983$	41.7273	1.33090	0.665448	+	0.746445i	$0.268241\pi$
$984$	69.0857	2.20237
$985$	−41.1093	−1.30985
$986$	−27.2363	−0.867380
$987$	2.55011	0.0811710
$988$	−15.1969	−0.483478
$989$	3.74777	0.119172
$990$	−64.2632	−2.04242
$991$	−0.308961	−0.00981447	−0.00490723	−	0.999988i	$-0.501562\pi$
$991$	−0.308961	−0.00981447	−0.00490723	+	0.999988i	$0.501562\pi$
$992$	205.248	6.51662
$993$	−20.6238	−0.654476
$994$	7.79165	0.247136
$995$	−5.89364	−0.186841
$996$	−43.4816	−1.37777
$997$	57.2366	1.81270	0.906350	−	0.422527i	$-0.138857\pi$
$997$	57.2366	1.81270	0.906350	+	0.422527i	$0.138857\pi$
$998$	−2.15889	−0.0683385
$999$	−32.0615	−1.01438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.11	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.11	✓	243	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71870 q^{2} +0.776703 q^{3} +5.39133 q^{4} +1.67497 q^{5} -2.11162 q^{6} +0.286183 q^{7} -9.22001 q^{8} -2.39673 q^{9} +O(q^{10})\)	\(q-2.71870 q^{2} +0.776703 q^{3} +5.39133 q^{4} +1.67497 q^{5} -2.11162 q^{6} +0.286183 q^{7} -9.22001 q^{8} -2.39673 q^{9} -4.55375 q^{10} -5.88809 q^{11} +4.18746 q^{12} +2.73763 q^{13} -0.778045 q^{14} +1.30096 q^{15} +14.2838 q^{16} +1.59192 q^{17} +6.51600 q^{18} -1.02964 q^{19} +9.03033 q^{20} +0.222279 q^{21} +16.0079 q^{22} +4.22846 q^{23} -7.16121 q^{24} -2.19447 q^{25} -7.44279 q^{26} -4.19166 q^{27} +1.54291 q^{28} +6.29312 q^{29} -3.53691 q^{30} -10.0645 q^{31} -20.3933 q^{32} -4.57330 q^{33} -4.32795 q^{34} +0.479348 q^{35} -12.9216 q^{36} +7.64888 q^{37} +2.79928 q^{38} +2.12633 q^{39} -15.4433 q^{40} -9.64721 q^{41} -0.604310 q^{42} +0.886321 q^{43} -31.7446 q^{44} -4.01446 q^{45} -11.4959 q^{46} +11.4726 q^{47} +11.0943 q^{48} -6.91810 q^{49} +5.96611 q^{50} +1.23645 q^{51} +14.7595 q^{52} +7.67727 q^{53} +11.3959 q^{54} -9.86238 q^{55} -2.63861 q^{56} -0.799723 q^{57} -17.1091 q^{58} -1.79305 q^{59} +7.01388 q^{60} +11.1902 q^{61} +27.3623 q^{62} -0.685903 q^{63} +26.8757 q^{64} +4.58545 q^{65} +12.4334 q^{66} +11.9139 q^{67} +8.58256 q^{68} +3.28426 q^{69} -1.30320 q^{70} -10.0144 q^{71} +22.0979 q^{72} +6.68326 q^{73} -20.7950 q^{74} -1.70445 q^{75} -5.55112 q^{76} -1.68507 q^{77} -5.78084 q^{78} +12.5463 q^{79} +23.9249 q^{80} +3.93452 q^{81} +26.2279 q^{82} -10.3837 q^{83} +1.19838 q^{84} +2.66642 q^{85} -2.40964 q^{86} +4.88788 q^{87} +54.2882 q^{88} -4.50334 q^{89} +10.9141 q^{90} +0.783462 q^{91} +22.7970 q^{92} -7.81710 q^{93} -31.1905 q^{94} -1.72461 q^{95} -15.8395 q^{96} -5.79710 q^{97} +18.8082 q^{98} +14.1122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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