LMFDB - Embedded newform 6037.2.a.b.1.9

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:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.58809 q^{2} -2.19108 q^{3} +4.69820 q^{4} +0.221659 q^{5} +5.67071 q^{6} +0.704833 q^{7} -6.98319 q^{8} +1.80083 q^{9} +O(q^{10})$	\(q-2.58809 q^{2} -2.19108 q^{3} +4.69820 q^{4} +0.221659 q^{5} +5.67071 q^{6} +0.704833 q^{7} -6.98319 q^{8} +1.80083 q^{9} -0.573673 q^{10} +5.84789 q^{11} -10.2941 q^{12} +4.53018 q^{13} -1.82417 q^{14} -0.485672 q^{15} +8.67672 q^{16} +1.50986 q^{17} -4.66070 q^{18} -3.56997 q^{19} +1.04140 q^{20} -1.54435 q^{21} -15.1349 q^{22} -1.45557 q^{23} +15.3007 q^{24} -4.95087 q^{25} -11.7245 q^{26} +2.62748 q^{27} +3.31145 q^{28} +0.0946853 q^{29} +1.25696 q^{30} +1.02206 q^{31} -8.48973 q^{32} -12.8132 q^{33} -3.90765 q^{34} +0.156233 q^{35} +8.46065 q^{36} +8.86741 q^{37} +9.23941 q^{38} -9.92599 q^{39} -1.54789 q^{40} +1.54403 q^{41} +3.99690 q^{42} +0.515830 q^{43} +27.4746 q^{44} +0.399169 q^{45} +3.76715 q^{46} +9.35593 q^{47} -19.0114 q^{48} -6.50321 q^{49} +12.8133 q^{50} -3.30822 q^{51} +21.2837 q^{52} -0.0346419 q^{53} -6.80016 q^{54} +1.29624 q^{55} -4.92199 q^{56} +7.82209 q^{57} -0.245054 q^{58} -3.03560 q^{59} -2.28179 q^{60} +8.23193 q^{61} -2.64519 q^{62} +1.26928 q^{63} +4.61875 q^{64} +1.00416 q^{65} +33.1617 q^{66} +6.07412 q^{67} +7.09362 q^{68} +3.18927 q^{69} -0.404344 q^{70} +10.3162 q^{71} -12.5755 q^{72} +3.27118 q^{73} -22.9497 q^{74} +10.8477 q^{75} -16.7725 q^{76} +4.12178 q^{77} +25.6893 q^{78} -13.1027 q^{79} +1.92327 q^{80} -11.1595 q^{81} -3.99608 q^{82} +5.80581 q^{83} -7.25565 q^{84} +0.334674 q^{85} -1.33501 q^{86} -0.207463 q^{87} -40.8369 q^{88} -1.97381 q^{89} -1.03309 q^{90} +3.19302 q^{91} -6.83858 q^{92} -2.23942 q^{93} -24.2140 q^{94} -0.791317 q^{95} +18.6017 q^{96} +10.8935 q^{97} +16.8309 q^{98} +10.5310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * 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 $

$2$	−2.58809	−1.83006	−0.915028	−	0.403391i	$-0.867831\pi$
$2$	−2.58809	−1.83006	−0.915028	+	0.403391i	$0.867831\pi$
$3$	−2.19108	−1.26502	−0.632510	−	0.774552i	$-0.717975\pi$
$3$	−2.19108	−1.26502	−0.632510	+	0.774552i	$0.717975\pi$
$4$	4.69820	2.34910
$5$	0.221659	0.0991289	0.0495645	−	0.998771i	$-0.484217\pi$
$5$	0.221659	0.0991289	0.0495645	+	0.998771i	$0.484217\pi$
$6$	5.67071	2.31506
$7$	0.704833	0.266402	0.133201	−	0.991089i	$-0.457474\pi$
$7$	0.704833	0.266402	0.133201	+	0.991089i	$0.457474\pi$
$8$	−6.98319	−2.46893
$9$	1.80083	0.600276
$10$	−0.573673	−0.181411
$11$	5.84789	1.76320	0.881602	−	0.471993i	$-0.156465\pi$
$11$	5.84789	1.76320	0.881602	+	0.471993i	$0.156465\pi$
$12$	−10.2941	−2.97166
$13$	4.53018	1.25645	0.628223	−	0.778033i	$-0.283782\pi$
$13$	4.53018	1.25645	0.628223	+	0.778033i	$0.283782\pi$
$14$	−1.82417	−0.487530
$15$	−0.485672	−0.125400
$16$	8.67672	2.16918
$17$	1.50986	0.366194	0.183097	−	0.983095i	$-0.441388\pi$
$17$	1.50986	0.366194	0.183097	+	0.983095i	$0.441388\pi$
$18$	−4.66070	−1.09854
$19$	−3.56997	−0.819008	−0.409504	−	0.912308i	$-0.634298\pi$
$19$	−3.56997	−0.819008	−0.409504	+	0.912308i	$0.634298\pi$
$20$	1.04140	0.232864
$21$	−1.54435	−0.337004
$22$	−15.1349	−3.22676
$23$	−1.45557	−0.303508	−0.151754	−	0.988418i	$-0.548492\pi$
$23$	−1.45557	−0.303508	−0.151754	+	0.988418i	$0.548492\pi$
$24$	15.3007	3.12325
$25$	−4.95087	−0.990173
$26$	−11.7245	−2.29937
$27$	2.62748	0.505659
$28$	3.31145	0.625805
$29$	0.0946853	0.0175826	0.00879131	−	0.999961i	$-0.497202\pi$
$29$	0.0946853	0.0175826	0.00879131	+	0.999961i	$0.497202\pi$
$30$	1.25696	0.229489
$31$	1.02206	0.183568	0.0917840	−	0.995779i	$-0.470743\pi$
$31$	1.02206	0.183568	0.0917840	+	0.995779i	$0.470743\pi$
$32$	−8.48973	−1.50079
$33$	−12.8132	−2.23049
$34$	−3.90765	−0.670156
$35$	0.156233	0.0264081
$36$	8.46065	1.41011
$37$	8.86741	1.45779	0.728897	−	0.684624i	$-0.240033\pi$
$37$	8.86741	1.45779	0.728897	+	0.684624i	$0.240033\pi$
$38$	9.23941	1.49883
$39$	−9.92599	−1.58943
$40$	−1.54789	−0.244743
$41$	1.54403	0.241137	0.120568	−	0.992705i	$-0.461528\pi$
$41$	1.54403	0.241137	0.120568	+	0.992705i	$0.461528\pi$
$42$	3.99690	0.616735
$43$	0.515830	0.0786633	0.0393316	−	0.999226i	$-0.487477\pi$
$43$	0.515830	0.0786633	0.0393316	+	0.999226i	$0.487477\pi$
$44$	27.4746	4.14195
$45$	0.399169	0.0595047
$46$	3.76715	0.555436
$47$	9.35593	1.36470	0.682351	−	0.731024i	$-0.260957\pi$
$47$	9.35593	1.36470	0.682351	+	0.731024i	$0.260957\pi$
$48$	−19.0114	−2.74406
$49$	−6.50321	−0.929030
$50$	12.8133	1.81207
$51$	−3.30822	−0.463243
$52$	21.2837	2.95152
$53$	−0.0346419	−0.00475843	−0.00237921	−	0.999997i	$-0.500757\pi$
$53$	−0.0346419	−0.00475843	−0.00237921	+	0.999997i	$0.500757\pi$
$54$	−6.80016	−0.925385
$55$	1.29624	0.174785
$56$	−4.92199	−0.657728
$57$	7.82209	1.03606
$58$	−0.245054	−0.0321772
$59$	−3.03560	−0.395201	−0.197600	−	0.980283i	$-0.563315\pi$
$59$	−3.03560	−0.395201	−0.197600	+	0.980283i	$0.563315\pi$
$60$	−2.28179	−0.294578
$61$	8.23193	1.05399	0.526995	−	0.849868i	$-0.323319\pi$
$61$	8.23193	1.05399	0.526995	+	0.849868i	$0.323319\pi$
$62$	−2.64519	−0.335940
$63$	1.26928	0.159915
$64$	4.61875	0.577344
$65$	1.00416	0.124550
$66$	33.1617	4.08192
$67$	6.07412	0.742072	0.371036	−	0.928618i	$-0.379003\pi$
$67$	6.07412	0.742072	0.371036	+	0.928618i	$0.379003\pi$
$68$	7.09362	0.860228
$69$	3.18927	0.383943
$70$	−0.404344	−0.0483283
$71$	10.3162	1.22431	0.612153	−	0.790739i	$-0.290304\pi$
$71$	10.3162	1.22431	0.612153	+	0.790739i	$0.290304\pi$
$72$	−12.5755	−1.48204
$73$	3.27118	0.382863	0.191431	−	0.981506i	$-0.438687\pi$
$73$	3.27118	0.382863	0.191431	+	0.981506i	$0.438687\pi$
$74$	−22.9497	−2.66784
$75$	10.8477	1.25259
$76$	−16.7725	−1.92393
$77$	4.12178	0.469721
$78$	25.6893	2.90874
$79$	−13.1027	−1.47417	−0.737085	−	0.675800i	$-0.763798\pi$
$79$	−13.1027	−1.47417	−0.737085	+	0.675800i	$0.763798\pi$
$80$	1.92327	0.215028
$81$	−11.1595	−1.23994
$82$	−3.99608	−0.441293
$83$	5.80581	0.637270	0.318635	−	0.947877i	$-0.396776\pi$
$83$	5.80581	0.637270	0.318635	+	0.947877i	$0.396776\pi$
$84$	−7.25565	−0.791656
$85$	0.334674	0.0363005
$86$	−1.33501	−0.143958
$87$	−0.207463	−0.0222424
$88$	−40.8369	−4.35323
$89$	−1.97381	−0.209224	−0.104612	−	0.994513i	$-0.533360\pi$
$89$	−1.97381	−0.209224	−0.104612	+	0.994513i	$0.533360\pi$
$90$	−1.03309	−0.108897
$91$	3.19302	0.334720
$92$	−6.83858	−0.712971
$93$	−2.23942	−0.232217
$94$	−24.2140	−2.49748
$95$	−0.791317	−0.0811874
$96$	18.6017	1.89853
$97$	10.8935	1.10606	0.553032	−	0.833160i	$-0.313471\pi$
$97$	10.8935	1.10606	0.553032	+	0.833160i	$0.313471\pi$
$98$	16.8309	1.70018
$99$	10.5310	1.05841
$100$	−23.2602	−2.32602
$101$	5.43235	0.540539	0.270269	−	0.962785i	$-0.412887\pi$
$101$	5.43235	0.540539	0.270269	+	0.962785i	$0.412887\pi$
$102$	8.56196	0.847761
$103$	9.21047	0.907535	0.453767	−	0.891120i	$-0.350080\pi$
$103$	9.21047	0.907535	0.453767	+	0.891120i	$0.350080\pi$
$104$	−31.6351	−3.10208
$105$	−0.342318	−0.0334068
$106$	0.0896562	0.00870818
$107$	−6.49127	−0.627534	−0.313767	−	0.949500i	$-0.601591\pi$
$107$	−6.49127	−0.627534	−0.313767	+	0.949500i	$0.601591\pi$
$108$	12.3445	1.18785
$109$	−8.81516	−0.844339	−0.422170	−	0.906517i	$-0.638731\pi$
$109$	−8.81516	−0.844339	−0.422170	+	0.906517i	$0.638731\pi$
$110$	−3.35478	−0.319865
$111$	−19.4292	−1.84414
$112$	6.11564	0.577874
$113$	10.8309	1.01888	0.509441	−	0.860506i	$-0.329852\pi$
$113$	10.8309	1.01888	0.509441	+	0.860506i	$0.329852\pi$
$114$	−20.2443	−1.89605
$115$	−0.322641	−0.0300864
$116$	0.444851	0.0413034
$117$	8.15807	0.754214
$118$	7.85639	0.723240
$119$	1.06420	0.0975549
$120$	3.39154	0.309604
$121$	23.1978	2.10889
$122$	−21.3050	−1.92886
$123$	−3.38309	−0.305043
$124$	4.80186	0.431220
$125$	−2.20570	−0.197284
$126$	−3.28502	−0.292652
$127$	11.3700	1.00892	0.504461	−	0.863435i	$-0.331691\pi$
$127$	11.3700	1.00892	0.504461	+	0.863435i	$0.331691\pi$
$128$	5.02574	0.444216
$129$	−1.13022	−0.0995106
$130$	−2.59884	−0.227934
$131$	7.95476	0.695010	0.347505	−	0.937678i	$-0.387029\pi$
$131$	7.95476	0.695010	0.347505	+	0.937678i	$0.387029\pi$
$132$	−60.1989	−5.23965
$133$	−2.51624	−0.218185
$134$	−15.7204	−1.35803
$135$	0.582405	0.0501255
$136$	−10.5436	−0.904109
$137$	13.7214	1.17229	0.586147	−	0.810205i	$-0.300644\pi$
$137$	13.7214	1.17229	0.586147	+	0.810205i	$0.300644\pi$
$138$	−8.25412	−0.702638
$139$	2.18059	0.184955	0.0924776	−	0.995715i	$-0.470521\pi$
$139$	2.18059	0.184955	0.0924776	+	0.995715i	$0.470521\pi$
$140$	0.734013	0.0620354
$141$	−20.4996	−1.72638
$142$	−26.6992	−2.24055
$143$	26.4920	2.21537
$144$	15.6253	1.30211
$145$	0.0209879	0.00174295
$146$	−8.46611	−0.700660
$147$	14.2490	1.17524
$148$	41.6609	3.42451
$149$	−5.85503	−0.479663	−0.239831	−	0.970815i	$-0.577092\pi$
$149$	−5.85503	−0.479663	−0.239831	+	0.970815i	$0.577092\pi$
$150$	−28.0749	−2.29231
$151$	1.33704	0.108807	0.0544035	−	0.998519i	$-0.482674\pi$
$151$	1.33704	0.108807	0.0544035	+	0.998519i	$0.482674\pi$
$152$	24.9298	2.02208
$153$	2.71899	0.219818
$154$	−10.6675	−0.859615
$155$	0.226550	0.0181969
$156$	−46.6343	−3.73373
$157$	−11.8154	−0.942968	−0.471484	−	0.881875i	$-0.656281\pi$
$157$	−11.8154	−0.942968	−0.471484	+	0.881875i	$0.656281\pi$
$158$	33.9110	2.69781
$159$	0.0759030	0.00601950
$160$	−1.88183	−0.148771
$161$	−1.02594	−0.0808551
$162$	28.8818	2.26917
$163$	−22.7825	−1.78446	−0.892231	−	0.451579i	$-0.850861\pi$
$163$	−22.7825	−1.78446	−0.892231	+	0.451579i	$0.850861\pi$
$164$	7.25416	0.566454
$165$	−2.84016	−0.221106
$166$	−15.0260	−1.16624
$167$	15.1206	1.17007	0.585033	−	0.811010i	$-0.301082\pi$
$167$	15.1206	1.17007	0.585033	+	0.811010i	$0.301082\pi$
$168$	10.7845	0.832039
$169$	7.52255	0.578658
$170$	−0.866165	−0.0664318
$171$	−6.42890	−0.491631
$172$	2.42347	0.184788
$173$	16.9143	1.28597	0.642986	−	0.765878i	$-0.277695\pi$
$173$	16.9143	1.28597	0.642986	+	0.765878i	$0.277695\pi$
$174$	0.536933	0.0407048
$175$	−3.48954	−0.263784
$176$	50.7405	3.82471
$177$	6.65123	0.499937
$178$	5.10841	0.382891
$179$	−18.4652	−1.38015	−0.690077	−	0.723736i	$-0.742423\pi$
$179$	−18.4652	−1.38015	−0.690077	+	0.723736i	$0.742423\pi$
$180$	1.87538	0.139783
$181$	−22.9648	−1.70696	−0.853479	−	0.521127i	$-0.825512\pi$
$181$	−22.9648	−1.70696	−0.853479	+	0.521127i	$0.825512\pi$
$182$	−8.26383	−0.612556
$183$	−18.0368	−1.33332
$184$	10.1645	0.749340
$185$	1.96554	0.144509
$186$	5.79582	0.424970
$187$	8.82948	0.645675
$188$	43.9561	3.20583
$189$	1.85194	0.134709
$190$	2.04800	0.148577
$191$	11.5845	0.838227	0.419113	−	0.907934i	$-0.362341\pi$
$191$	11.5845	0.838227	0.419113	+	0.907934i	$0.362341\pi$
$192$	−10.1200	−0.730351
$193$	−13.4307	−0.966761	−0.483381	−	0.875410i	$-0.660591\pi$
$193$	−13.4307	−0.966761	−0.483381	+	0.875410i	$0.660591\pi$
$194$	−28.1933	−2.02416
$195$	−2.20018	−0.157558
$196$	−30.5534	−2.18239
$197$	−25.3382	−1.80527	−0.902634	−	0.430408i	$-0.858370\pi$
$197$	−25.3382	−1.80527	−0.902634	+	0.430408i	$0.858370\pi$
$198$	−27.2552	−1.93695
$199$	−2.57866	−0.182796	−0.0913982	−	0.995814i	$-0.529134\pi$
$199$	−2.57866	−0.182796	−0.0913982	+	0.995814i	$0.529134\pi$
$200$	34.5729	2.44467
$201$	−13.3089	−0.938736
$202$	−14.0594	−0.989216
$203$	0.0667374	0.00468405
$204$	−15.5427	−1.08821
$205$	0.342248	0.0239036
$206$	−23.8375	−1.66084
$207$	−2.62123	−0.182188
$208$	39.3071	2.72546
$209$	−20.8768	−1.44408
$210$	0.885949	0.0611363
$211$	19.8440	1.36612	0.683058	−	0.730364i	$-0.260650\pi$
$211$	19.8440	1.36612	0.683058	+	0.730364i	$0.260650\pi$
$212$	−0.162755	−0.0111780
$213$	−22.6036	−1.54877
$214$	16.8000	1.14842
$215$	0.114338	0.00779781
$216$	−18.3482	−1.24844
$217$	0.720384	0.0489029
$218$	22.8144	1.54519
$219$	−7.16742	−0.484329
$220$	6.08999	0.410587
$221$	6.83993	0.460104
$222$	50.2845	3.37487
$223$	−25.4849	−1.70660	−0.853299	−	0.521423i	$-0.825402\pi$
$223$	−25.4849	−1.70660	−0.853299	+	0.521423i	$0.825402\pi$
$224$	−5.98385	−0.399813
$225$	−8.91565	−0.594377
$226$	−28.0312	−1.86461
$227$	−24.5526	−1.62961	−0.814807	−	0.579732i	$-0.803157\pi$
$227$	−24.5526	−1.62961	−0.814807	+	0.579732i	$0.803157\pi$
$228$	36.7498	2.43381
$229$	7.31160	0.483164	0.241582	−	0.970380i	$-0.422334\pi$
$229$	7.31160	0.483164	0.241582	+	0.970380i	$0.422334\pi$
$230$	0.835023	0.0550598
$231$	−9.03116	−0.594206
$232$	−0.661206	−0.0434103
$233$	22.9836	1.50571	0.752853	−	0.658189i	$-0.228677\pi$
$233$	22.9836	1.50571	0.752853	+	0.658189i	$0.228677\pi$
$234$	−21.1138	−1.38025
$235$	2.07383	0.135282
$236$	−14.2619	−0.928368
$237$	28.7091	1.86485
$238$	−2.75424	−0.178531
$239$	8.59001	0.555642	0.277821	−	0.960633i	$-0.410388\pi$
$239$	8.59001	0.555642	0.277821	+	0.960633i	$0.410388\pi$
$240$	−4.21404	−0.272015
$241$	−27.7512	−1.78761	−0.893806	−	0.448453i	$-0.851975\pi$
$241$	−27.7512	−1.78761	−0.893806	+	0.448453i	$0.851975\pi$
$242$	−60.0379	−3.85938
$243$	16.5689	1.06290
$244$	38.6753	2.47593
$245$	−1.44150	−0.0920937
$246$	8.75573	0.558245
$247$	−16.1726	−1.02904
$248$	−7.13727	−0.453217
$249$	−12.7210	−0.806160
$250$	5.70855	0.361040
$251$	18.5685	1.17203	0.586016	−	0.810299i	$-0.300695\pi$
$251$	18.5685	1.17203	0.586016	+	0.810299i	$0.300695\pi$
$252$	5.96335	0.375656
$253$	−8.51202	−0.535146
$254$	−29.4265	−1.84638
$255$	−0.733296	−0.0459208
$256$	−22.2445	−1.39028
$257$	22.6728	1.41429	0.707146	−	0.707067i	$-0.249982\pi$
$257$	22.6728	1.41429	0.707146	+	0.707067i	$0.249982\pi$
$258$	2.92512	0.182110
$259$	6.25005	0.388359
$260$	4.71773	0.292581
$261$	0.170512	0.0105544
$262$	−20.5876	−1.27191
$263$	16.7885	1.03522	0.517611	−	0.855616i	$-0.326822\pi$
$263$	16.7885	1.03522	0.517611	+	0.855616i	$0.326822\pi$
$264$	89.4769	5.50692
$265$	−0.00767868	−0.000471698 0
$266$	6.51224	0.399291
$267$	4.32478	0.264672
$268$	28.5375	1.74320
$269$	−2.41380	−0.147172	−0.0735859	−	0.997289i	$-0.523444\pi$
$269$	−2.41380	−0.147172	−0.0735859	+	0.997289i	$0.523444\pi$
$270$	−1.50732	−0.0917324
$271$	7.65409	0.464953	0.232476	−	0.972602i	$-0.425317\pi$
$271$	7.65409	0.464953	0.232476	+	0.972602i	$0.425317\pi$
$272$	13.1006	0.794342
$273$	−6.99617	−0.423427
$274$	−35.5121	−2.14536
$275$	−28.9521	−1.74588
$276$	14.9839	0.901922
$277$	14.5968	0.877039	0.438519	−	0.898722i	$-0.355503\pi$
$277$	14.5968	0.877039	0.438519	+	0.898722i	$0.355503\pi$
$278$	−5.64356	−0.338478
$279$	1.84056	0.110191
$280$	−1.09100	−0.0651999
$281$	13.2342	0.789488	0.394744	−	0.918791i	$-0.370833\pi$
$281$	13.2342	0.789488	0.394744	+	0.918791i	$0.370833\pi$
$282$	53.0547	3.15936
$283$	−6.14852	−0.365491	−0.182746	−	0.983160i	$-0.558498\pi$
$283$	−6.14852	−0.365491	−0.182746	+	0.983160i	$0.558498\pi$
$284$	48.4675	2.87602
$285$	1.73384	0.102704
$286$	−68.5636	−4.05425
$287$	1.08828	0.0642392
$288$	−15.2885	−0.900886
$289$	−14.7203	−0.865902
$290$	−0.0543184	−0.00318969
$291$	−23.8685	−1.39919
$292$	15.3687	0.899384
$293$	−28.5901	−1.67025	−0.835127	−	0.550057i	$-0.814606\pi$
$293$	−28.5901	−1.67025	−0.835127	+	0.550057i	$0.814606\pi$
$294$	−36.8778	−2.15076
$295$	−0.672867	−0.0391758
$296$	−61.9229	−3.59919
$297$	15.3652	0.891581
$298$	15.1533	0.877809
$299$	−6.59401	−0.381341
$300$	50.9649	2.94246
$301$	0.363574	0.0209561
$302$	−3.46038	−0.199123
$303$	−11.9027	−0.683792
$304$	−30.9757	−1.77658
$305$	1.82468	0.104481
$306$	−7.03700	−0.402278
$307$	−21.7103	−1.23907	−0.619536	−	0.784968i	$-0.712679\pi$
$307$	−21.7103	−1.23907	−0.619536	+	0.784968i	$0.712679\pi$
$308$	19.3650	1.10342
$309$	−20.1809	−1.14805
$310$	−0.586330	−0.0333013
$311$	−15.7994	−0.895902	−0.447951	−	0.894058i	$-0.647846\pi$
$311$	−15.7994	−0.895902	−0.447951	+	0.894058i	$0.647846\pi$
$312$	69.3151	3.92419
$313$	−12.0213	−0.679485	−0.339743	−	0.940518i	$-0.610340\pi$
$313$	−12.0213	−0.679485	−0.339743	+	0.940518i	$0.610340\pi$
$314$	30.5792	1.72568
$315$	0.281348	0.0158522
$316$	−61.5592	−3.46298
$317$	−22.8885	−1.28555	−0.642773	−	0.766057i	$-0.722216\pi$
$317$	−22.8885	−1.28555	−0.642773	+	0.766057i	$0.722216\pi$
$318$	−0.196444	−0.0110160
$319$	0.553709	0.0310018
$320$	1.02379	0.0572314
$321$	14.2229	0.793843
$322$	2.65521	0.147969
$323$	−5.39015	−0.299916
$324$	−52.4296	−2.91276
$325$	−22.4283	−1.24410
$326$	58.9631	3.26566
$327$	19.3147	1.06811
$328$	−10.7822	−0.595350
$329$	6.59437	0.363559
$330$	7.35058	0.404636
$331$	−17.1450	−0.942375	−0.471187	−	0.882033i	$-0.656174\pi$
$331$	−17.1450	−0.942375	−0.471187	+	0.882033i	$0.656174\pi$
$332$	27.2769	1.49701
$333$	15.9687	0.875078
$334$	−39.1334	−2.14128
$335$	1.34638	0.0735608
$336$	−13.3999	−0.731022
$337$	−23.5025	−1.28026	−0.640130	−	0.768266i	$-0.721120\pi$
$337$	−23.5025	−1.28026	−0.640130	+	0.768266i	$0.721120\pi$
$338$	−19.4690	−1.05898
$339$	−23.7313	−1.28891
$340$	1.57237	0.0852735
$341$	5.97691	0.323668
$342$	16.6386	0.899711
$343$	−9.51751	−0.513897
$344$	−3.60214	−0.194214
$345$	0.706931	0.0380599
$346$	−43.7758	−2.35340
$347$	10.0773	0.540980	0.270490	−	0.962723i	$-0.412814\pi$
$347$	10.0773	0.540980	0.270490	+	0.962723i	$0.412814\pi$
$348$	−0.974704	−0.0522496
$349$	23.0316	1.23285	0.616426	−	0.787413i	$-0.288580\pi$
$349$	23.0316	1.23285	0.616426	+	0.787413i	$0.288580\pi$
$350$	9.03123	0.482739
$351$	11.9030	0.635334
$352$	−49.6470	−2.64619
$353$	10.5780	0.563008	0.281504	−	0.959560i	$-0.409167\pi$
$353$	10.5780	0.563008	0.281504	+	0.959560i	$0.409167\pi$
$354$	−17.2140	−0.914913
$355$	2.28667	0.121364
$356$	−9.27339	−0.491488
$357$	−2.33174	−0.123409
$358$	47.7896	2.52576
$359$	−13.5404	−0.714635	−0.357317	−	0.933983i	$-0.616309\pi$
$359$	−13.5404	−0.714635	−0.357317	+	0.933983i	$0.616309\pi$
$360$	−2.78748	−0.146913
$361$	−6.25529	−0.329226
$362$	59.4349	3.12383
$363$	−50.8282	−2.66779
$364$	15.0015	0.786291
$365$	0.725087	0.0379528
$366$	46.6809	2.44005
$367$	−4.72279	−0.246527	−0.123264	−	0.992374i	$-0.539336\pi$
$367$	−4.72279	−0.246527	−0.123264	+	0.992374i	$0.539336\pi$
$368$	−12.6296	−0.658363
$369$	2.78053	0.144748
$370$	−5.08700	−0.264460
$371$	−0.0244167	−0.00126765
$372$	−10.5213	−0.545502
$373$	11.4775	0.594285	0.297142	−	0.954833i	$-0.403966\pi$
$373$	11.4775	0.594285	0.297142	+	0.954833i	$0.403966\pi$
$374$	−22.8515	−1.18162
$375$	4.83286	0.249568
$376$	−65.3343	−3.36936
$377$	0.428942	0.0220916
$378$	−4.79298	−0.246524
$379$	−5.44052	−0.279461	−0.139730	−	0.990190i	$-0.544624\pi$
$379$	−5.44052	−0.279461	−0.139730	+	0.990190i	$0.544624\pi$
$380$	−3.71777	−0.190717
$381$	−24.9125	−1.27631
$382$	−29.9818	−1.53400
$383$	−3.62836	−0.185400	−0.0927002	−	0.995694i	$-0.529550\pi$
$383$	−3.62836	−0.185400	−0.0927002	+	0.995694i	$0.529550\pi$
$384$	−11.0118	−0.561943
$385$	0.913631	0.0465629
$386$	34.7598	1.76923
$387$	0.928920	0.0472197
$388$	51.1798	2.59826
$389$	−29.6586	−1.50375	−0.751874	−	0.659306i	$-0.770850\pi$
$389$	−29.6586	−1.50375	−0.751874	+	0.659306i	$0.770850\pi$
$390$	5.69427	0.288341
$391$	−2.19771	−0.111143
$392$	45.4132	2.29371
$393$	−17.4295	−0.879202
$394$	65.5774	3.30374
$395$	−2.90433	−0.146133
$396$	49.4769	2.48631
$397$	27.2954	1.36991	0.684957	−	0.728583i	$-0.259821\pi$
$397$	27.2954	1.36991	0.684957	+	0.728583i	$0.259821\pi$
$398$	6.67380	0.334527
$399$	5.51327	0.276009
$400$	−42.9573	−2.14786
$401$	7.41740	0.370407	0.185204	−	0.982700i	$-0.440706\pi$
$401$	7.41740	0.370407	0.185204	+	0.982700i	$0.440706\pi$
$402$	34.4446	1.71794
$403$	4.63013	0.230643
$404$	25.5223	1.26978
$405$	−2.47360	−0.122914
$406$	−0.172722	−0.00857206
$407$	51.8556	2.57039
$408$	23.1019	1.14372
$409$	−18.8556	−0.932350	−0.466175	−	0.884693i	$-0.654368\pi$
$409$	−18.8556	−0.932350	−0.466175	+	0.884693i	$0.654368\pi$
$410$	−0.885767	−0.0437449
$411$	−30.0646	−1.48298
$412$	43.2727	2.13189
$413$	−2.13959	−0.105282
$414$	6.78399	0.333415
$415$	1.28691	0.0631719
$416$	−38.4600	−1.88566
$417$	−4.77785	−0.233972
$418$	54.0310	2.64274
$419$	30.9639	1.51269	0.756343	−	0.654175i	$-0.226984\pi$
$419$	30.9639	1.51269	0.756343	+	0.654175i	$0.226984\pi$
$420$	−1.60828	−0.0784760
$421$	29.4432	1.43498	0.717488	−	0.696571i	$-0.245292\pi$
$421$	29.4432	1.43498	0.717488	+	0.696571i	$0.245292\pi$
$422$	−51.3580	−2.50007
$423$	16.8484	0.819198
$424$	0.241911	0.0117482
$425$	−7.47511	−0.362596
$426$	58.5001	2.83434
$427$	5.80214	0.280785
$428$	−30.4973	−1.47414
$429$	−58.0460	−2.80249
$430$	−0.295918	−0.0142704
$431$	0.567480	0.0273345	0.0136673	−	0.999907i	$-0.495649\pi$
$431$	0.567480	0.0273345	0.0136673	+	0.999907i	$0.495649\pi$
$432$	22.7979	1.09687
$433$	−22.2777	−1.07060	−0.535300	−	0.844662i	$-0.679801\pi$
$433$	−22.2777	−1.07060	−0.535300	+	0.844662i	$0.679801\pi$
$434$	−1.86442	−0.0894950
$435$	−0.0459861	−0.00220486
$436$	−41.4154	−1.98344
$437$	5.19635	0.248575
$438$	18.5499	0.886349
$439$	25.0143	1.19387	0.596935	−	0.802290i	$-0.296385\pi$
$439$	25.0143	1.19387	0.596935	+	0.802290i	$0.296385\pi$
$440$	−9.05187	−0.431531
$441$	−11.7112	−0.557674
$442$	−17.7024	−0.842015
$443$	8.87131	0.421489	0.210744	−	0.977541i	$-0.432411\pi$
$443$	8.87131	0.421489	0.210744	+	0.977541i	$0.432411\pi$
$444$	−91.2824	−4.33207
$445$	−0.437514	−0.0207401
$446$	65.9573	3.12317
$447$	12.8288	0.606783
$448$	3.25545	0.153805
$449$	−24.8325	−1.17192	−0.585959	−	0.810341i	$-0.699282\pi$
$449$	−24.8325	−1.17192	−0.585959	+	0.810341i	$0.699282\pi$
$450$	23.0745	1.08774
$451$	9.02930	0.425173
$452$	50.8856	2.39346
$453$	−2.92956	−0.137643
$454$	63.5444	2.98229
$455$	0.707762	0.0331804
$456$	−54.6232	−2.55797
$457$	−9.62760	−0.450360	−0.225180	−	0.974317i	$-0.572297\pi$
$457$	−9.62760	−0.450360	−0.225180	+	0.974317i	$0.572297\pi$
$458$	−18.9231	−0.884217
$459$	3.96713	0.185170
$460$	−1.51583	−0.0706760
$461$	−13.6020	−0.633506	−0.316753	−	0.948508i	$-0.602593\pi$
$461$	−13.6020	−0.633506	−0.316753	+	0.948508i	$0.602593\pi$
$462$	23.3734	1.08743
$463$	23.9242	1.11185	0.555925	−	0.831232i	$-0.312364\pi$
$463$	23.9242	1.11185	0.555925	+	0.831232i	$0.312364\pi$
$464$	0.821558	0.0381399
$465$	−0.496388	−0.0230194
$466$	−59.4836	−2.75552
$467$	26.0348	1.20475	0.602373	−	0.798215i	$-0.294222\pi$
$467$	26.0348	1.20475	0.602373	+	0.798215i	$0.294222\pi$
$468$	38.3283	1.77173
$469$	4.28124	0.197689
$470$	−5.36725	−0.247573
$471$	25.8884	1.19287
$472$	21.1982	0.975724
$473$	3.01651	0.138699
$474$	−74.3016	−3.41279
$475$	17.6745	0.810960
$476$	4.99982	0.229166
$477$	−0.0623840	−0.00285637
$478$	−22.2317	−1.01685
$479$	31.9145	1.45821	0.729105	−	0.684402i	$-0.239937\pi$
$479$	31.9145	1.45821	0.729105	+	0.684402i	$0.239937\pi$
$480$	4.12323	0.188199
$481$	40.1710	1.83164
$482$	71.8226	3.27143
$483$	2.24791	0.102283
$484$	108.988	4.95400
$485$	2.41464	0.109643
$486$	−42.8818	−1.94516
$487$	−0.470712	−0.0213300	−0.0106650	−	0.999943i	$-0.503395\pi$
$487$	−0.470712	−0.0213300	−0.0106650	+	0.999943i	$0.503395\pi$
$488$	−57.4852	−2.60223
$489$	49.9182	2.25738
$490$	3.73072	0.168537
$491$	15.9299	0.718907	0.359453	−	0.933163i	$-0.382963\pi$
$491$	15.9299	0.718907	0.359453	+	0.933163i	$0.382963\pi$
$492$	−15.8944	−0.716576
$493$	0.142961	0.00643866
$494$	41.8562	1.88320
$495$	2.33430	0.104919
$496$	8.86816	0.398192
$497$	7.27119	0.326157
$498$	32.9230	1.47532
$499$	−0.238983	−0.0106983	−0.00534917	−	0.999986i	$-0.501703\pi$
$499$	−0.238983	−0.0106983	−0.00534917	+	0.999986i	$0.501703\pi$
$500$	−10.3628	−0.463440
$501$	−33.1304	−1.48016
$502$	−48.0569	−2.14488
$503$	8.24796	0.367759	0.183879	−	0.982949i	$-0.441134\pi$
$503$	8.24796	0.367759	0.183879	+	0.982949i	$0.441134\pi$
$504$	−8.86365	−0.394818
$505$	1.20413	0.0535830
$506$	22.0299	0.979347
$507$	−16.4825	−0.732014
$508$	53.4184	2.37006
$509$	4.01036	0.177756	0.0888780	−	0.996043i	$-0.471672\pi$
$509$	4.01036	0.177756	0.0888780	+	0.996043i	$0.471672\pi$
$510$	1.89784	0.0840376
$511$	2.30564	0.101995
$512$	47.5194	2.10008
$513$	−9.38005	−0.414139
$514$	−58.6793	−2.58823
$515$	2.04158	0.0899630
$516$	−5.31002	−0.233761
$517$	54.7124	2.40625
$518$	−16.1757	−0.710718
$519$	−37.0606	−1.62678
$520$	−7.01221	−0.307506
$521$	20.9766	0.918999	0.459500	−	0.888178i	$-0.348029\pi$
$521$	20.9766	0.918999	0.459500	+	0.888178i	$0.348029\pi$
$522$	−0.441300	−0.0193152
$523$	11.8473	0.518048	0.259024	−	0.965871i	$-0.416599\pi$
$523$	11.8473	0.518048	0.259024	+	0.965871i	$0.416599\pi$
$524$	37.3731	1.63265
$525$	7.64585	0.333692
$526$	−43.4501	−1.89451
$527$	1.54317	0.0672216
$528$	−111.176	−4.83833
$529$	−20.8813	−0.907883
$530$	0.0198731	0.000863233 0
$531$	−5.46658	−0.237229
$532$	−11.8218	−0.512540
$533$	6.99473	0.302975
$534$	−11.1929	−0.484365
$535$	−1.43885	−0.0622068
$536$	−42.4168	−1.83213
$537$	40.4587	1.74592
$538$	6.24712	0.269333
$539$	−38.0300	−1.63807
$540$	2.73626	0.117750
$541$	35.1486	1.51116	0.755578	−	0.655058i	$-0.227356\pi$
$541$	35.1486	1.51116	0.755578	+	0.655058i	$0.227356\pi$
$542$	−19.8095	−0.850889
$543$	50.3176	2.15934
$544$	−12.8183	−0.549580
$545$	−1.95396	−0.0836985
$546$	18.1067	0.774895
$547$	28.2611	1.20836	0.604180	−	0.796848i	$-0.293501\pi$
$547$	28.2611	1.20836	0.604180	+	0.796848i	$0.293501\pi$
$548$	64.4657	2.75384
$549$	14.8243	0.632685
$550$	74.9306	3.19505
$551$	−0.338024	−0.0144003
$552$	−22.2713	−0.947930
$553$	−9.23522	−0.392722
$554$	−37.7779	−1.60503
$555$	−4.30666	−0.182807
$556$	10.2449	0.434479
$557$	−9.06621	−0.384148	−0.192074	−	0.981380i	$-0.561521\pi$
$557$	−9.06621	−0.384148	−0.192074	+	0.981380i	$0.561521\pi$
$558$	−4.76353	−0.201656
$559$	2.33680	0.0988362
$560$	1.35559	0.0572840
$561$	−19.3461	−0.816792
$562$	−34.2514	−1.44481
$563$	−31.0160	−1.30717	−0.653583	−	0.756854i	$-0.726735\pi$
$563$	−31.0160	−1.30717	−0.653583	+	0.756854i	$0.726735\pi$
$564$	−96.3112	−4.05543
$565$	2.40076	0.101001
$566$	15.9129	0.668869
$567$	−7.86559	−0.330324
$568$	−72.0399	−3.02273
$569$	6.01559	0.252187	0.126093	−	0.992018i	$-0.459756\pi$
$569$	6.01559	0.252187	0.126093	+	0.992018i	$0.459756\pi$
$570$	−4.48733	−0.187953
$571$	−38.1201	−1.59528	−0.797638	−	0.603137i	$-0.793917\pi$
$571$	−38.1201	−1.59528	−0.797638	+	0.603137i	$0.793917\pi$
$572$	124.465	5.20414
$573$	−25.3826	−1.06037
$574$	−2.81657	−0.117561
$575$	7.20635	0.300525
$576$	8.31757	0.346565
$577$	−9.22344	−0.383977	−0.191988	−	0.981397i	$-0.561494\pi$
$577$	−9.22344	−0.383977	−0.191988	+	0.981397i	$0.561494\pi$
$578$	38.0975	1.58465
$579$	29.4277	1.22297
$580$	0.0986053	0.00409436
$581$	4.09213	0.169770
$582$	61.7737	2.56060
$583$	−0.202582	−0.00839008
$584$	−22.8433	−0.945262
$585$	1.80831	0.0747644
$586$	73.9938	3.05666
$587$	−20.0466	−0.827412	−0.413706	−	0.910411i	$-0.635766\pi$
$587$	−20.0466	−0.827412	−0.413706	+	0.910411i	$0.635766\pi$
$588$	66.9449	2.76076
$589$	−3.64874	−0.150344
$590$	1.74144	0.0716940
$591$	55.5179	2.28370
$592$	76.9400	3.16222
$593$	−10.4139	−0.427649	−0.213824	−	0.976872i	$-0.568592\pi$
$593$	−10.4139	−0.427649	−0.213824	+	0.976872i	$0.568592\pi$
$594$	−39.7666	−1.63164
$595$	0.235889	0.00967051
$596$	−27.5081	−1.12678
$597$	5.65005	0.231241
$598$	17.0659	0.697876
$599$	27.2274	1.11248	0.556241	−	0.831021i	$-0.312243\pi$
$599$	27.2274	1.11248	0.556241	+	0.831021i	$0.312243\pi$
$600$	−75.7519	−3.09256
$601$	15.7871	0.643967	0.321984	−	0.946745i	$-0.395650\pi$
$601$	15.7871	0.643967	0.321984	+	0.946745i	$0.395650\pi$
$602$	−0.940962	−0.0383507
$603$	10.9384	0.445448
$604$	6.28170	0.255599
$605$	5.14200	0.209052
$606$	30.8052	1.25138
$607$	−13.9950	−0.568039	−0.284020	−	0.958818i	$-0.591668\pi$
$607$	−13.9950	−0.568039	−0.284020	+	0.958818i	$0.591668\pi$
$608$	30.3081	1.22916
$609$	−0.146227	−0.00592541
$610$	−4.72244	−0.191206
$611$	42.3841	1.71468
$612$	12.7744	0.516374
$613$	−12.1958	−0.492585	−0.246293	−	0.969196i	$-0.579212\pi$
$613$	−12.1958	−0.492585	−0.246293	+	0.969196i	$0.579212\pi$
$614$	56.1882	2.26757
$615$	−0.749891	−0.0302385
$616$	−28.7832	−1.15971
$617$	−5.31506	−0.213976	−0.106988	−	0.994260i	$-0.534121\pi$
$617$	−5.31506	−0.213976	−0.106988	+	0.994260i	$0.534121\pi$
$618$	52.2299	2.10099
$619$	17.3359	0.696789	0.348395	−	0.937348i	$-0.386727\pi$
$619$	17.3359	0.696789	0.348395	+	0.937348i	$0.386727\pi$
$620$	1.06438	0.0427464
$621$	−3.82449	−0.153472
$622$	40.8903	1.63955
$623$	−1.39121	−0.0557377
$624$	−86.1250	−3.44776
$625$	24.2654	0.970617
$626$	31.1123	1.24350
$627$	45.7427	1.82679
$628$	−55.5109	−2.21513
$629$	13.3885	0.533836
$630$	−0.728153	−0.0290103
$631$	22.8286	0.908791	0.454395	−	0.890800i	$-0.349855\pi$
$631$	22.8286	0.908791	0.454395	+	0.890800i	$0.349855\pi$
$632$	91.4988	3.63963
$633$	−43.4797	−1.72816
$634$	59.2374	2.35262
$635$	2.52025	0.100013
$636$	0.356608	0.0141404
$637$	−29.4607	−1.16728
$638$	−1.43305	−0.0567349
$639$	18.5777	0.734921
$640$	1.11400	0.0440347
$641$	3.22736	0.127473	0.0637364	−	0.997967i	$-0.479698\pi$
$641$	3.22736	0.127473	0.0637364	+	0.997967i	$0.479698\pi$
$642$	−36.8101	−1.45278
$643$	−2.43874	−0.0961744	−0.0480872	−	0.998843i	$-0.515313\pi$
$643$	−2.43874	−0.0961744	−0.0480872	+	0.998843i	$0.515313\pi$
$644$	−4.82006	−0.189937
$645$	−0.250524	−0.00986438
$646$	13.9502	0.548863
$647$	24.2512	0.953415	0.476707	−	0.879062i	$-0.341830\pi$
$647$	24.2512	0.953415	0.476707	+	0.879062i	$0.341830\pi$
$648$	77.9290	3.06134
$649$	−17.7518	−0.696820
$650$	58.0465	2.27677
$651$	−1.57842	−0.0618631
$652$	−107.037	−4.19188
$653$	36.1003	1.41272	0.706358	−	0.707855i	$-0.250337\pi$
$653$	36.1003	1.41272	0.706358	+	0.707855i	$0.250337\pi$
$654$	−49.9882	−1.95469
$655$	1.76324	0.0688956
$656$	13.3971	0.523069
$657$	5.89083	0.229823
$658$	−17.0668	−0.665334
$659$	−35.2138	−1.37173	−0.685867	−	0.727727i	$-0.740577\pi$
$659$	−35.2138	−1.37173	−0.685867	+	0.727727i	$0.740577\pi$
$660$	−13.3436	−0.519400
$661$	−20.4794	−0.796557	−0.398278	−	0.917265i	$-0.630392\pi$
$661$	−20.4794	−0.796557	−0.398278	+	0.917265i	$0.630392\pi$
$662$	44.3728	1.72460
$663$	−14.9868	−0.582040
$664$	−40.5431	−1.57338
$665$	−0.557746	−0.0216285
$666$	−41.3283	−1.60144
$667$	−0.137821	−0.00533646
$668$	71.0396	2.74860
$669$	55.8395	2.15888
$670$	−3.48456	−0.134620
$671$	48.1394	1.85840
$672$	13.1111	0.505771
$673$	32.7243	1.26143	0.630715	−	0.776014i	$-0.282762\pi$
$673$	32.7243	1.26143	0.630715	+	0.776014i	$0.282762\pi$
$674$	60.8265	2.34295
$675$	−13.0083	−0.500691
$676$	35.3425	1.35933
$677$	−4.42624	−0.170114	−0.0850571	−	0.996376i	$-0.527107\pi$
$677$	−4.42624	−0.170114	−0.0850571	+	0.996376i	$0.527107\pi$
$678$	61.4187	2.35877
$679$	7.67808	0.294658
$680$	−2.33709	−0.0896234
$681$	53.7967	2.06150
$682$	−15.4688	−0.592330
$683$	−11.2770	−0.431503	−0.215752	−	0.976448i	$-0.569220\pi$
$683$	−11.2770	−0.431503	−0.215752	+	0.976448i	$0.569220\pi$
$684$	−30.2043	−1.15489
$685$	3.04146	0.116208
$686$	24.6322	0.940460
$687$	−16.0203	−0.611213
$688$	4.47571	0.170635
$689$	−0.156934	−0.00597871
$690$	−1.82960	−0.0696517
$691$	27.2380	1.03618	0.518092	−	0.855325i	$-0.326643\pi$
$691$	27.2380	1.03618	0.518092	+	0.855325i	$0.326643\pi$
$692$	79.4670	3.02088
$693$	7.42262	0.281962
$694$	−26.0811	−0.990023
$695$	0.483348	0.0183344
$696$	1.44875	0.0549149
$697$	2.33126	0.0883029
$698$	−59.6078	−2.25619
$699$	−50.3589	−1.90475
$700$	−16.3946	−0.619656
$701$	28.5116	1.07687	0.538433	−	0.842668i	$-0.319016\pi$
$701$	28.5116	1.07687	0.538433	+	0.842668i	$0.319016\pi$
$702$	−30.8060	−1.16270
$703$	−31.6564	−1.19394
$704$	27.0099	1.01797
$705$	−4.54392	−0.171134
$706$	−27.3767	−1.03034
$707$	3.82890	0.144001
$708$	31.2488	1.17440
$709$	−11.5797	−0.434885	−0.217443	−	0.976073i	$-0.569771\pi$
$709$	−11.5797	−0.434885	−0.217443	+	0.976073i	$0.569771\pi$
$710$	−5.91812	−0.222103
$711$	−23.5957	−0.884908
$712$	13.7835	0.516560
$713$	−1.48769	−0.0557143
$714$	6.03476	0.225845
$715$	5.87219	0.219607
$716$	−86.7533	−3.24212
$717$	−18.8214	−0.702898
$718$	35.0437	1.30782
$719$	39.8732	1.48702	0.743511	−	0.668724i	$-0.233159\pi$
$719$	39.8732	1.48702	0.743511	+	0.668724i	$0.233159\pi$
$720$	3.46348	0.129076
$721$	6.49185	0.241769
$722$	16.1893	0.602502
$723$	60.8051	2.26137
$724$	−107.893	−4.00982
$725$	−0.468775	−0.0174099
$726$	131.548	4.88220
$727$	32.4888	1.20494	0.602471	−	0.798141i	$-0.294183\pi$
$727$	32.4888	1.20494	0.602471	+	0.798141i	$0.294183\pi$
$728$	−22.2975	−0.826400
$729$	−2.82526	−0.104639
$730$	−1.87659	−0.0694557
$731$	0.778830	0.0288061
$732$	−84.7406	−3.13210
$733$	46.1342	1.70401	0.852003	−	0.523537i	$-0.175388\pi$
$733$	46.1342	1.70401	0.852003	+	0.523537i	$0.175388\pi$
$734$	12.2230	0.451159
$735$	3.15843	0.116500
$736$	12.3574	0.455501
$737$	35.5208	1.30842
$738$	−7.19625	−0.264898
$739$	10.9428	0.402538	0.201269	−	0.979536i	$-0.435493\pi$
$739$	10.9428	0.402538	0.201269	+	0.979536i	$0.435493\pi$
$740$	9.23452	0.339468
$741$	35.4355	1.30176
$742$	0.0631927	0.00231988
$743$	−3.56653	−0.130843	−0.0654216	−	0.997858i	$-0.520839\pi$
$743$	−3.56653	−0.130843	−0.0654216	+	0.997858i	$0.520839\pi$
$744$	15.6383	0.573329
$745$	−1.29782	−0.0475484
$746$	−29.7049	−1.08757
$747$	10.4553	0.382538
$748$	41.4827	1.51676
$749$	−4.57526	−0.167176
$750$	−12.5079	−0.456723
$751$	−15.5350	−0.566879	−0.283439	−	0.958990i	$-0.591475\pi$
$751$	−15.5350	−0.566879	−0.283439	+	0.958990i	$0.591475\pi$
$752$	81.1788	2.96029
$753$	−40.6850	−1.48264
$754$	−1.11014	−0.0404289
$755$	0.296367	0.0107859
$756$	8.70078	0.316444
$757$	1.48658	0.0540306	0.0270153	−	0.999635i	$-0.491400\pi$
$757$	1.48658	0.0540306	0.0270153	+	0.999635i	$0.491400\pi$
$758$	14.0806	0.511429
$759$	18.6505	0.676971
$760$	5.52592	0.200446
$761$	−19.4897	−0.706501	−0.353251	−	0.935529i	$-0.614924\pi$
$761$	−19.4897	−0.706501	−0.353251	+	0.935529i	$0.614924\pi$
$762$	64.4757	2.33571
$763$	−6.21322	−0.224934
$764$	54.4265	1.96908
$765$	0.602689	0.0217903
$766$	9.39051	0.339293
$767$	−13.7518	−0.496549
$768$	48.7396	1.75874
$769$	−11.8389	−0.426920	−0.213460	−	0.976952i	$-0.568473\pi$
$769$	−11.8389	−0.426920	−0.213460	+	0.976952i	$0.568473\pi$
$770$	−2.36456	−0.0852127
$771$	−49.6780	−1.78911
$772$	−63.1001	−2.27102
$773$	−1.90972	−0.0686879	−0.0343439	−	0.999410i	$-0.510934\pi$
$773$	−1.90972	−0.0686879	−0.0343439	+	0.999410i	$0.510934\pi$
$774$	−2.40413	−0.0864146
$775$	−5.06010	−0.181764
$776$	−76.0713	−2.73080
$777$	−13.6943	−0.491282
$778$	76.7590	2.75194
$779$	−5.51214	−0.197493
$780$	−10.3369	−0.370121
$781$	60.3279	2.15870
$782$	5.68786	0.203398
$783$	0.248784	0.00889082
$784$	−56.4265	−2.01523
$785$	−2.61898	−0.0934754
$786$	45.1091	1.60899
$787$	−40.7722	−1.45337	−0.726686	−	0.686970i	$-0.758940\pi$
$787$	−40.7722	−1.45337	−0.726686	+	0.686970i	$0.758940\pi$
$788$	−119.044	−4.24076
$789$	−36.7849	−1.30958
$790$	7.51667	0.267431
$791$	7.63395	0.271432
$792$	−73.5402	−2.61314
$793$	37.2921	1.32428
$794$	−70.6428	−2.50702
$795$	0.0168246	0.000596707 0
$796$	−12.1151	−0.429407
$797$	1.20819	0.0427961	0.0213981	−	0.999771i	$-0.493188\pi$
$797$	1.20819	0.0427961	0.0213981	+	0.999771i	$0.493188\pi$
$798$	−14.2688	−0.505111
$799$	14.1261	0.499746
$800$	42.0315	1.48604
$801$	−3.55450	−0.125592
$802$	−19.1969	−0.677865
$803$	19.1295	0.675065
$804$	−62.5279	−2.20519
$805$	−0.227408	−0.00801507
$806$	−11.9832	−0.422090
$807$	5.28882	0.186175
$808$	−37.9351	−1.33455
$809$	12.5969	0.442885	0.221442	−	0.975173i	$-0.428924\pi$
$809$	12.5969	0.442885	0.221442	+	0.975173i	$0.428924\pi$
$810$	6.40191	0.224940
$811$	5.00382	0.175708	0.0878540	−	0.996133i	$-0.471999\pi$
$811$	5.00382	0.175708	0.0878540	+	0.996133i	$0.471999\pi$
$812$	0.313546	0.0110033
$813$	−16.7707	−0.588174
$814$	−134.207	−4.70395
$815$	−5.04994	−0.176892
$816$	−28.7045	−1.00486
$817$	−1.84150	−0.0644259
$818$	48.8000	1.70625
$819$	5.75008	0.200924
$820$	1.60795	0.0561520
$821$	−13.9475	−0.486772	−0.243386	−	0.969930i	$-0.578258\pi$
$821$	−13.9475	−0.486772	−0.243386	+	0.969930i	$0.578258\pi$
$822$	77.8098	2.71393
$823$	−36.4653	−1.27110	−0.635550	−	0.772059i	$-0.719227\pi$
$823$	−36.4653	−1.27110	−0.635550	+	0.772059i	$0.719227\pi$
$824$	−64.3185	−2.24064
$825$	63.4364	2.20857
$826$	5.53745	0.192672
$827$	16.3115	0.567207	0.283604	−	0.958942i	$-0.408470\pi$
$827$	16.3115	0.567207	0.283604	+	0.958942i	$0.408470\pi$
$828$	−12.3151	−0.427979
$829$	−42.4834	−1.47551	−0.737756	−	0.675068i	$-0.764114\pi$
$829$	−42.4834	−1.47551	−0.737756	+	0.675068i	$0.764114\pi$
$830$	−3.33064	−0.115608
$831$	−31.9828	−1.10947
$832$	20.9238	0.725401
$833$	−9.81893	−0.340206
$834$	12.3655	0.428182
$835$	3.35161	0.115987
$836$	−98.0835	−3.39229
$837$	2.68545	0.0928229
$838$	−80.1373	−2.76830
$839$	50.1047	1.72981	0.864903	−	0.501938i	$-0.167380\pi$
$839$	50.1047	1.72981	0.864903	+	0.501938i	$0.167380\pi$
$840$	2.39047	0.0824792
$841$	−28.9910	−0.999691
$842$	−76.2017	−2.62608
$843$	−28.9972	−0.998718
$844$	93.2311	3.20915
$845$	1.66744	0.0573617
$846$	−43.6052	−1.49918
$847$	16.3506	0.561812
$848$	−0.300578	−0.0103219
$849$	13.4719	0.462354
$850$	19.3462	0.663571
$851$	−12.9072	−0.442452
$852$	−106.196	−3.63822
$853$	−41.2506	−1.41239	−0.706196	−	0.708016i	$-0.749590\pi$
$853$	−41.2506	−1.41239	−0.706196	+	0.708016i	$0.749590\pi$
$854$	−15.0164	−0.513852
$855$	−1.42502	−0.0487348
$856$	45.3298	1.54934
$857$	−23.7106	−0.809940	−0.404970	−	0.914330i	$-0.632718\pi$
$857$	−23.7106	−0.809940	−0.404970	+	0.914330i	$0.632718\pi$
$858$	150.228	5.12871
$859$	51.1339	1.74467	0.872333	−	0.488913i	$-0.162606\pi$
$859$	51.1339	1.74467	0.872333	+	0.488913i	$0.162606\pi$
$860$	0.537185	0.0183178
$861$	−2.38451	−0.0812639
$862$	−1.46869	−0.0500237
$863$	34.2499	1.16588	0.582941	−	0.812515i	$-0.301902\pi$
$863$	34.2499	1.16588	0.582941	+	0.812515i	$0.301902\pi$
$864$	−22.3066	−0.758887
$865$	3.74921	0.127477
$866$	57.6568	1.95926
$867$	32.2534	1.09538
$868$	3.38451	0.114878
$869$	−76.6232	−2.59926
$870$	0.119016	0.00403502
$871$	27.5169	0.932374
$872$	61.5580	2.08462
$873$	19.6173	0.663944
$874$	−13.4486	−0.454907
$875$	−1.55465	−0.0525568
$876$	−33.6740	−1.13774
$877$	51.5335	1.74016	0.870081	−	0.492910i	$-0.164067\pi$
$877$	51.5335	1.74016	0.870081	+	0.492910i	$0.164067\pi$
$878$	−64.7394	−2.18485
$879$	62.6433	2.11290
$880$	11.2471	0.379139
$881$	−38.2008	−1.28702	−0.643510	−	0.765438i	$-0.722522\pi$
$881$	−38.2008	−1.28702	−0.643510	+	0.765438i	$0.722522\pi$
$882$	30.3095	1.02057
$883$	29.9756	1.00876	0.504380	−	0.863482i	$-0.331721\pi$
$883$	29.9756	1.00876	0.504380	+	0.863482i	$0.331721\pi$
$884$	32.1354	1.08083
$885$	1.47431	0.0495582
$886$	−22.9597	−0.771348
$887$	−55.8702	−1.87594	−0.937968	−	0.346721i	$-0.887295\pi$
$887$	−55.8702	−1.87594	−0.937968	+	0.346721i	$0.887295\pi$
$888$	135.678	4.55305
$889$	8.01393	0.268779
$890$	1.13232	0.0379556
$891$	−65.2595	−2.18628
$892$	−119.733	−4.00897
$893$	−33.4004	−1.11770
$894$	−33.2022	−1.11045
$895$	−4.09298	−0.136813
$896$	3.54231	0.118340
$897$	14.4480	0.482404
$898$	64.2687	2.14467
$899$	0.0967744	0.00322761
$900$	−41.8876	−1.39625
$901$	−0.0523043	−0.00174251
$902$	−23.3686	−0.778090
$903$	−0.796619	−0.0265098
$904$	−75.6340	−2.51555
$905$	−5.09035	−0.169209
$906$	7.58197	0.251894
$907$	32.0009	1.06257	0.531286	−	0.847193i	$-0.321709\pi$
$907$	32.0009	1.06257	0.531286	+	0.847193i	$0.321709\pi$
$908$	−115.353	−3.82813
$909$	9.78271	0.324472
$910$	−1.83175	−0.0607220
$911$	29.0415	0.962189	0.481094	−	0.876669i	$-0.340239\pi$
$911$	29.0415	0.962189	0.481094	+	0.876669i	$0.340239\pi$
$912$	67.8701	2.24740
$913$	33.9517	1.12364
$914$	24.9171	0.824184
$915$	−3.99802	−0.132170
$916$	34.3514	1.13500
$917$	5.60678	0.185152
$918$	−10.2673	−0.338871
$919$	−4.72429	−0.155840	−0.0779200	−	0.996960i	$-0.524828\pi$
$919$	−4.72429	−0.155840	−0.0779200	+	0.996960i	$0.524828\pi$
$920$	2.25306	0.0742813
$921$	47.5690	1.56745
$922$	35.2031	1.15935
$923$	46.7342	1.53827
$924$	−42.4302	−1.39585
$925$	−43.9014	−1.44347
$926$	−61.9179	−2.03475
$927$	16.5865	0.544771
$928$	−0.803853	−0.0263878
$929$	−30.8910	−1.01350	−0.506751	−	0.862093i	$-0.669153\pi$
$929$	−30.8910	−1.01350	−0.506751	+	0.862093i	$0.669153\pi$
$930$	1.28470	0.0421269
$931$	23.2163	0.760883
$932$	107.982	3.53706
$933$	34.6178	1.13333
$934$	−67.3803	−2.20475
$935$	1.95713	0.0640051
$936$	−56.9694	−1.86210
$937$	−25.3378	−0.827750	−0.413875	−	0.910334i	$-0.635825\pi$
$937$	−25.3378	−0.827750	−0.413875	+	0.910334i	$0.635825\pi$
$938$	−11.0802	−0.361783
$939$	26.3397	0.859562
$940$	9.74326	0.317790
$941$	−47.0802	−1.53477	−0.767385	−	0.641187i	$-0.778442\pi$
$941$	−47.0802	−1.53477	−0.767385	+	0.641187i	$0.778442\pi$
$942$	−67.0014	−2.18302
$943$	−2.24744	−0.0731868
$944$	−26.3390	−0.857262
$945$	0.410499	0.0133535
$946$	−7.80701	−0.253828
$947$	0.217403	0.00706465	0.00353232	−	0.999994i	$-0.498876\pi$
$947$	0.217403	0.00706465	0.00353232	+	0.999994i	$0.498876\pi$
$948$	134.881	4.38073
$949$	14.8190	0.481047
$950$	−45.7431	−1.48410
$951$	50.1505	1.62624
$952$	−7.43150	−0.240856
$953$	4.28728	0.138879	0.0694393	−	0.997586i	$-0.477879\pi$
$953$	4.28728	0.138879	0.0694393	+	0.997586i	$0.477879\pi$
$954$	0.161455	0.00522731
$955$	2.56781	0.0830925
$956$	40.3576	1.30526
$957$	−1.21322	−0.0392178
$958$	−82.5975	−2.66860
$959$	9.67127	0.312301
$960$	−2.24320	−0.0723989
$961$	−29.9554	−0.966303
$962$	−103.966	−3.35200
$963$	−11.6896	−0.376694
$964$	−130.381	−4.19929
$965$	−2.97703	−0.0958340
$966$	−5.81778	−0.187184
$967$	5.40073	0.173676	0.0868378	−	0.996222i	$-0.472324\pi$
$967$	5.40073	0.173676	0.0868378	+	0.996222i	$0.472324\pi$
$968$	−161.995	−5.20670
$969$	11.8103	0.379400
$970$	−6.24930	−0.200653
$971$	−6.58018	−0.211168	−0.105584	−	0.994410i	$-0.533671\pi$
$971$	−6.58018	−0.211168	−0.105584	+	0.994410i	$0.533671\pi$
$972$	77.8441	2.49685
$973$	1.53695	0.0492724
$974$	1.21824	0.0390351
$975$	49.1422	1.57381
$976$	71.4261	2.28630
$977$	−18.6673	−0.597219	−0.298609	−	0.954375i	$-0.596523\pi$
$977$	−18.6673	−0.597219	−0.298609	+	0.954375i	$0.596523\pi$
$978$	−129.193	−4.13113
$979$	−11.5426	−0.368905
$980$	−6.77244	−0.216338
$981$	−15.8746	−0.506836
$982$	−41.2280	−1.31564
$983$	16.4237	0.523835	0.261918	−	0.965090i	$-0.415645\pi$
$983$	16.4237	0.523835	0.261918	+	0.965090i	$0.415645\pi$
$984$	23.6247	0.753129
$985$	−5.61643	−0.178954
$986$	−0.369997	−0.0117831
$987$	−14.4488	−0.459910
$988$	−75.9823	−2.41732
$989$	−0.750827	−0.0238749
$990$	−6.04137	−0.192007
$991$	25.8923	0.822495	0.411248	−	0.911524i	$-0.365093\pi$
$991$	25.8923	0.822495	0.411248	+	0.911524i	$0.365093\pi$
$992$	−8.67705	−0.275497
$993$	37.5661	1.19212
$994$	−18.8185	−0.596886
$995$	−0.571583	−0.0181204
$996$	−59.7658	−1.89375
$997$	14.3871	0.455645	0.227822	−	0.973703i	$-0.426839\pi$
$997$	14.3871	0.455645	0.227822	+	0.973703i	$0.426839\pi$
$998$	0.618508	0.0195785
$999$	23.2990	0.737147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.9	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.9	✓	259	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)

\(f(q)\)	\(=\)	\(q-2.58809 q^{2} -2.19108 q^{3} +4.69820 q^{4} +0.221659 q^{5} +5.67071 q^{6} +0.704833 q^{7} -6.98319 q^{8} +1.80083 q^{9} +O(q^{10})\)	\(q-2.58809 q^{2} -2.19108 q^{3} +4.69820 q^{4} +0.221659 q^{5} +5.67071 q^{6} +0.704833 q^{7} -6.98319 q^{8} +1.80083 q^{9} -0.573673 q^{10} +5.84789 q^{11} -10.2941 q^{12} +4.53018 q^{13} -1.82417 q^{14} -0.485672 q^{15} +8.67672 q^{16} +1.50986 q^{17} -4.66070 q^{18} -3.56997 q^{19} +1.04140 q^{20} -1.54435 q^{21} -15.1349 q^{22} -1.45557 q^{23} +15.3007 q^{24} -4.95087 q^{25} -11.7245 q^{26} +2.62748 q^{27} +3.31145 q^{28} +0.0946853 q^{29} +1.25696 q^{30} +1.02206 q^{31} -8.48973 q^{32} -12.8132 q^{33} -3.90765 q^{34} +0.156233 q^{35} +8.46065 q^{36} +8.86741 q^{37} +9.23941 q^{38} -9.92599 q^{39} -1.54789 q^{40} +1.54403 q^{41} +3.99690 q^{42} +0.515830 q^{43} +27.4746 q^{44} +0.399169 q^{45} +3.76715 q^{46} +9.35593 q^{47} -19.0114 q^{48} -6.50321 q^{49} +12.8133 q^{50} -3.30822 q^{51} +21.2837 q^{52} -0.0346419 q^{53} -6.80016 q^{54} +1.29624 q^{55} -4.92199 q^{56} +7.82209 q^{57} -0.245054 q^{58} -3.03560 q^{59} -2.28179 q^{60} +8.23193 q^{61} -2.64519 q^{62} +1.26928 q^{63} +4.61875 q^{64} +1.00416 q^{65} +33.1617 q^{66} +6.07412 q^{67} +7.09362 q^{68} +3.18927 q^{69} -0.404344 q^{70} +10.3162 q^{71} -12.5755 q^{72} +3.27118 q^{73} -22.9497 q^{74} +10.8477 q^{75} -16.7725 q^{76} +4.12178 q^{77} +25.6893 q^{78} -13.1027 q^{79} +1.92327 q^{80} -11.1595 q^{81} -3.99608 q^{82} +5.80581 q^{83} -7.25565 q^{84} +0.334674 q^{85} -1.33501 q^{86} -0.207463 q^{87} -40.8369 q^{88} -1.97381 q^{89} -1.03309 q^{90} +3.19302 q^{91} -6.83858 q^{92} -2.23942 q^{93} -24.2140 q^{94} -0.791317 q^{95} +18.6017 q^{96} +10.8935 q^{97} +16.8309 q^{98} +10.5310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

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