LMFDB - Embedded newform 6037.2.a.b.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.38263 q^{2} -0.344809 q^{3} +3.67692 q^{4} +0.273793 q^{5} +0.821552 q^{6} +0.727572 q^{7} -3.99549 q^{8} -2.88111 q^{9} +O(q^{10})$	\(q-2.38263 q^{2} -0.344809 q^{3} +3.67692 q^{4} +0.273793 q^{5} +0.821552 q^{6} +0.727572 q^{7} -3.99549 q^{8} -2.88111 q^{9} -0.652346 q^{10} +3.88366 q^{11} -1.26784 q^{12} -3.75219 q^{13} -1.73354 q^{14} -0.0944060 q^{15} +2.16593 q^{16} -5.98659 q^{17} +6.86461 q^{18} +5.86992 q^{19} +1.00671 q^{20} -0.250873 q^{21} -9.25334 q^{22} -2.71732 q^{23} +1.37768 q^{24} -4.92504 q^{25} +8.94009 q^{26} +2.02786 q^{27} +2.67523 q^{28} -1.73212 q^{29} +0.224935 q^{30} -10.6688 q^{31} +2.83038 q^{32} -1.33912 q^{33} +14.2638 q^{34} +0.199204 q^{35} -10.5936 q^{36} -0.0898831 q^{37} -13.9858 q^{38} +1.29379 q^{39} -1.09394 q^{40} -0.491956 q^{41} +0.597738 q^{42} +7.22234 q^{43} +14.2799 q^{44} -0.788825 q^{45} +6.47437 q^{46} -5.73624 q^{47} -0.746830 q^{48} -6.47064 q^{49} +11.7345 q^{50} +2.06423 q^{51} -13.7965 q^{52} +11.0244 q^{53} -4.83163 q^{54} +1.06332 q^{55} -2.90701 q^{56} -2.02400 q^{57} +4.12699 q^{58} -5.61526 q^{59} -0.347124 q^{60} -7.48540 q^{61} +25.4197 q^{62} -2.09621 q^{63} -11.0756 q^{64} -1.02732 q^{65} +3.19063 q^{66} +5.34242 q^{67} -22.0122 q^{68} +0.936956 q^{69} -0.474629 q^{70} -1.48365 q^{71} +11.5114 q^{72} +9.78980 q^{73} +0.214158 q^{74} +1.69820 q^{75} +21.5832 q^{76} +2.82565 q^{77} -3.08262 q^{78} -1.65606 q^{79} +0.593014 q^{80} +7.94410 q^{81} +1.17215 q^{82} -12.9137 q^{83} -0.922442 q^{84} -1.63908 q^{85} -17.2082 q^{86} +0.597249 q^{87} -15.5171 q^{88} +16.6571 q^{89} +1.87948 q^{90} -2.72999 q^{91} -9.99138 q^{92} +3.67868 q^{93} +13.6673 q^{94} +1.60714 q^{95} -0.975941 q^{96} +5.76518 q^{97} +15.4171 q^{98} -11.1893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.38263	−1.68477	−0.842387	−	0.538873i	$-0.818850\pi$
$2$	−2.38263	−1.68477	−0.842387	+	0.538873i	$0.818850\pi$
$3$	−0.344809	−0.199075	−0.0995377	−	0.995034i	$-0.531736\pi$
$3$	−0.344809	−0.199075	−0.0995377	+	0.995034i	$0.531736\pi$
$4$	3.67692	1.83846
$5$	0.273793	0.122444	0.0612219	−	0.998124i	$-0.480500\pi$
$5$	0.273793	0.122444	0.0612219	+	0.998124i	$0.480500\pi$
$6$	0.821552	0.335397
$7$	0.727572	0.274996	0.137498	−	0.990502i	$-0.456094\pi$
$7$	0.727572	0.274996	0.137498	+	0.990502i	$0.456094\pi$
$8$	−3.99549	−1.41262
$9$	−2.88111	−0.960369
$10$	−0.652346	−0.206290
$11$	3.88366	1.17097	0.585484	−	0.810684i	$-0.300904\pi$
$11$	3.88366	1.17097	0.585484	+	0.810684i	$0.300904\pi$
$12$	−1.26784	−0.365993
$13$	−3.75219	−1.04067	−0.520336	−	0.853962i	$-0.674193\pi$
$13$	−3.75219	−1.04067	−0.520336	+	0.853962i	$0.674193\pi$
$14$	−1.73354	−0.463307
$15$	−0.0944060	−0.0243755
$16$	2.16593	0.541481
$17$	−5.98659	−1.45196	−0.725980	−	0.687716i	$-0.758614\pi$
$17$	−5.98659	−1.45196	−0.725980	+	0.687716i	$0.758614\pi$
$18$	6.86461	1.61800
$19$	5.86992	1.34665	0.673326	−	0.739346i	$-0.264865\pi$
$19$	5.86992	1.34665	0.673326	+	0.739346i	$0.264865\pi$
$20$	1.00671	0.225108
$21$	−0.250873	−0.0547450
$22$	−9.25334	−1.97282
$23$	−2.71732	−0.566600	−0.283300	−	0.959031i	$-0.591429\pi$
$23$	−2.71732	−0.566600	−0.283300	+	0.959031i	$0.591429\pi$
$24$	1.37768	0.281218
$25$	−4.92504	−0.985008
$26$	8.94009	1.75330
$27$	2.02786	0.390261
$28$	2.67523	0.505571
$29$	−1.73212	−0.321646	−0.160823	−	0.986983i	$-0.551415\pi$
$29$	−1.73212	−0.321646	−0.160823	+	0.986983i	$0.551415\pi$
$30$	0.224935	0.0410673
$31$	−10.6688	−1.91616	−0.958082	−	0.286494i	$-0.907510\pi$
$31$	−10.6688	−1.91616	−0.958082	+	0.286494i	$0.907510\pi$
$32$	2.83038	0.500346
$33$	−1.33912	−0.233111
$34$	14.2638	2.44622
$35$	0.199204	0.0336716
$36$	−10.5936	−1.76560
$37$	−0.0898831	−0.0147767	−0.00738835	−	0.999973i	$-0.502352\pi$
$37$	−0.0898831	−0.0147767	−0.00738835	+	0.999973i	$0.502352\pi$
$38$	−13.9858	−2.26880
$39$	1.29379	0.207172
$40$	−1.09394	−0.172966
$41$	−0.491956	−0.0768306	−0.0384153	−	0.999262i	$-0.512231\pi$
$41$	−0.491956	−0.0768306	−0.0384153	+	0.999262i	$0.512231\pi$
$42$	0.597738	0.0922330
$43$	7.22234	1.10140	0.550698	−	0.834704i	$-0.314361\pi$
$43$	7.22234	1.10140	0.550698	+	0.834704i	$0.314361\pi$
$44$	14.2799	2.15278
$45$	−0.788825	−0.117591
$46$	6.47437	0.954593
$47$	−5.73624	−0.836717	−0.418358	−	0.908282i	$-0.637394\pi$
$47$	−5.73624	−0.836717	−0.418358	+	0.908282i	$0.637394\pi$
$48$	−0.746830	−0.107796
$49$	−6.47064	−0.924377
$50$	11.7345	1.65951
$51$	2.06423	0.289050
$52$	−13.7965	−1.91323
$53$	11.0244	1.51431	0.757156	−	0.653235i	$-0.226588\pi$
$53$	11.0244	1.51431	0.757156	+	0.653235i	$0.226588\pi$
$54$	−4.83163	−0.657502
$55$	1.06332	0.143378
$56$	−2.90701	−0.388465
$57$	−2.02400	−0.268085
$58$	4.12699	0.541901
$59$	−5.61526	−0.731045	−0.365522	−	0.930803i	$-0.619110\pi$
$59$	−5.61526	−0.731045	−0.365522	+	0.930803i	$0.619110\pi$
$60$	−0.347124	−0.0448135
$61$	−7.48540	−0.958407	−0.479203	−	0.877704i	$-0.659074\pi$
$61$	−7.48540	−0.958407	−0.479203	+	0.877704i	$0.659074\pi$
$62$	25.4197	3.22830
$63$	−2.09621	−0.264098
$64$	−11.0756	−1.38445
$65$	−1.02732	−0.127424
$66$	3.19063	0.392739
$67$	5.34242	0.652680	0.326340	−	0.945252i	$-0.394185\pi$
$67$	5.34242	0.652680	0.326340	+	0.945252i	$0.394185\pi$
$68$	−22.0122	−2.66937
$69$	0.936956	0.112796
$70$	−0.474629	−0.0567290
$71$	−1.48365	−0.176077	−0.0880387	−	0.996117i	$-0.528060\pi$
$71$	−1.48365	−0.176077	−0.0880387	+	0.996117i	$0.528060\pi$
$72$	11.5114	1.35664
$73$	9.78980	1.14581	0.572905	−	0.819622i	$-0.305816\pi$
$73$	9.78980	1.14581	0.572905	+	0.819622i	$0.305816\pi$
$74$	0.214158	0.0248954
$75$	1.69820	0.196091
$76$	21.5832	2.47577
$77$	2.82565	0.322012
$78$	−3.08262	−0.349038
$79$	−1.65606	−0.186321	−0.0931606	−	0.995651i	$-0.529697\pi$
$79$	−1.65606	−0.186321	−0.0931606	+	0.995651i	$0.529697\pi$
$80$	0.593014	0.0663010
$81$	7.94410	0.882678
$82$	1.17215	0.129442
$83$	−12.9137	−1.41746	−0.708732	−	0.705478i	$-0.750733\pi$
$83$	−12.9137	−1.41746	−0.708732	+	0.705478i	$0.750733\pi$
$84$	−0.922442	−0.100647
$85$	−1.63908	−0.177783
$86$	−17.2082	−1.85560
$87$	0.597249	0.0640318
$88$	−15.5171	−1.65413
$89$	16.6571	1.76565	0.882823	−	0.469706i	$-0.155640\pi$
$89$	16.6571	1.76565	0.882823	+	0.469706i	$0.155640\pi$
$90$	1.87948	0.198114
$91$	−2.72999	−0.286181
$92$	−9.99138	−1.04167
$93$	3.67868	0.381461
$94$	13.6673	1.40968
$95$	1.60714	0.164889
$96$	−0.975941	−0.0996065
$97$	5.76518	0.585365	0.292682	−	0.956210i	$-0.405452\pi$
$97$	5.76518	0.585365	0.292682	+	0.956210i	$0.405452\pi$
$98$	15.4171	1.55737
$99$	−11.1893	−1.12456
$100$	−18.1090	−1.81090
$101$	−9.67986	−0.963182	−0.481591	−	0.876396i	$-0.659941\pi$
$101$	−9.67986	−0.963182	−0.481591	+	0.876396i	$0.659941\pi$
$102$	−4.91829	−0.486983
$103$	7.41314	0.730438	0.365219	−	0.930922i	$-0.380994\pi$
$103$	7.41314	0.730438	0.365219	+	0.930922i	$0.380994\pi$
$104$	14.9919	1.47007
$105$	−0.0686872	−0.00670319
$106$	−26.2669	−2.55127
$107$	1.92792	0.186380	0.0931898	−	0.995648i	$-0.470294\pi$
$107$	1.92792	0.186380	0.0931898	+	0.995648i	$0.470294\pi$
$108$	7.45628	0.717481
$109$	−0.673701	−0.0645288	−0.0322644	−	0.999479i	$-0.510272\pi$
$109$	−0.673701	−0.0645288	−0.0322644	+	0.999479i	$0.510272\pi$
$110$	−2.53349	−0.241559
$111$	0.0309925	0.00294168
$112$	1.57587	0.148905
$113$	17.4808	1.64445	0.822227	−	0.569160i	$-0.192732\pi$
$113$	17.4808	1.64445	0.822227	+	0.569160i	$0.192732\pi$
$114$	4.82244	0.451663
$115$	−0.743982	−0.0693767
$116$	−6.36886	−0.591334
$117$	10.8105	0.999428
$118$	13.3791	1.23165
$119$	−4.35567	−0.399284
$120$	0.377198	0.0344334
$121$	4.08285	0.371168
$122$	17.8349	1.61470
$123$	0.169631	0.0152951
$124$	−39.2282	−3.52280
$125$	−2.71740	−0.243052
$126$	4.99450	0.444945
$127$	−11.6371	−1.03262	−0.516312	−	0.856400i	$-0.672696\pi$
$127$	−11.6371	−1.03262	−0.516312	+	0.856400i	$0.672696\pi$
$128$	20.7283	1.83214
$129$	−2.49033	−0.219261
$130$	2.44773	0.214680
$131$	12.6074	1.10151	0.550756	−	0.834666i	$-0.314339\pi$
$131$	12.6074	1.10151	0.550756	+	0.834666i	$0.314339\pi$
$132$	−4.92385	−0.428566
$133$	4.27079	0.370324
$134$	−12.7290	−1.09962
$135$	0.555212	0.0477850
$136$	23.9194	2.05107
$137$	17.4647	1.49211	0.746055	−	0.665884i	$-0.231945\pi$
$137$	17.4647	1.49211	0.746055	+	0.665884i	$0.231945\pi$
$138$	−2.23242	−0.190036
$139$	−2.93875	−0.249261	−0.124631	−	0.992203i	$-0.539775\pi$
$139$	−2.93875	−0.249261	−0.124631	+	0.992203i	$0.539775\pi$
$140$	0.732457	0.0619039
$141$	1.97791	0.166570
$142$	3.53500	0.296651
$143$	−14.5723	−1.21859
$144$	−6.24026	−0.520022
$145$	−0.474241	−0.0393835
$146$	−23.3255	−1.93043
$147$	2.23113	0.184021
$148$	−0.330493	−0.0271664
$149$	1.01379	0.0830527	0.0415264	−	0.999137i	$-0.486778\pi$
$149$	1.01379	0.0830527	0.0415264	+	0.999137i	$0.486778\pi$
$150$	−4.04617	−0.330369
$151$	9.77957	0.795850	0.397925	−	0.917418i	$-0.369730\pi$
$151$	9.77957	0.795850	0.397925	+	0.917418i	$0.369730\pi$
$152$	−23.4532	−1.90231
$153$	17.2480	1.39442
$154$	−6.73247	−0.542518
$155$	−2.92102	−0.234622
$156$	4.75716	0.380878
$157$	16.0977	1.28474	0.642368	−	0.766396i	$-0.277952\pi$
$157$	16.0977	1.28474	0.642368	+	0.766396i	$0.277952\pi$
$158$	3.94578	0.313909
$159$	−3.80129	−0.301462
$160$	0.774938	0.0612642
$161$	−1.97705	−0.155813
$162$	−18.9278	−1.48711
$163$	19.8423	1.55417	0.777083	−	0.629399i	$-0.216699\pi$
$163$	19.8423	1.55417	0.777083	+	0.629399i	$0.216699\pi$
$164$	−1.80888	−0.141250
$165$	−0.366641	−0.0285430
$166$	30.7686	2.38811
$167$	18.4378	1.42676	0.713378	−	0.700779i	$-0.247164\pi$
$167$	18.4378	1.42676	0.713378	+	0.700779i	$0.247164\pi$
$168$	1.00236	0.0773339
$169$	1.07895	0.0829964
$170$	3.90533	0.299525
$171$	−16.9119	−1.29328
$172$	26.5560	2.02488
$173$	−6.79800	−0.516843	−0.258421	−	0.966032i	$-0.583202\pi$
$173$	−6.79800	−0.516843	−0.258421	+	0.966032i	$0.583202\pi$
$174$	−1.42302	−0.107879
$175$	−3.58332	−0.270874
$176$	8.41173	0.634058
$177$	1.93619	0.145533
$178$	−39.6876	−2.97471
$179$	−2.04452	−0.152815	−0.0764074	−	0.997077i	$-0.524345\pi$
$179$	−2.04452	−0.152815	−0.0764074	+	0.997077i	$0.524345\pi$
$180$	−2.90045	−0.216187
$181$	−6.07758	−0.451743	−0.225872	−	0.974157i	$-0.572523\pi$
$181$	−6.07758	−0.451743	−0.225872	+	0.974157i	$0.572523\pi$
$182$	6.50456	0.482150
$183$	2.58103	0.190795
$184$	10.8570	0.800391
$185$	−0.0246093	−0.00180931
$186$	−8.76493	−0.642676
$187$	−23.2499	−1.70020
$188$	−21.0917	−1.53827
$189$	1.47541	0.107320
$190$	−3.82922	−0.277801
$191$	−15.4641	−1.11895	−0.559473	−	0.828849i	$-0.688996\pi$
$191$	−15.4641	−1.11895	−0.559473	+	0.828849i	$0.688996\pi$
$192$	3.81897	0.275610
$193$	1.30655	0.0940479	0.0470239	−	0.998894i	$-0.485026\pi$
$193$	1.30655	0.0940479	0.0470239	+	0.998894i	$0.485026\pi$
$194$	−13.7363	−0.986207
$195$	0.354230	0.0253669
$196$	−23.7921	−1.69943
$197$	9.53093	0.679051	0.339525	−	0.940597i	$-0.389734\pi$
$197$	9.53093	0.679051	0.339525	+	0.940597i	$0.389734\pi$
$198$	26.6598	1.89463
$199$	−19.5842	−1.38828	−0.694142	−	0.719838i	$-0.744216\pi$
$199$	−19.5842	−1.38828	−0.694142	+	0.719838i	$0.744216\pi$
$200$	19.6779	1.39144
$201$	−1.84211	−0.129933
$202$	23.0635	1.62274
$203$	−1.26024	−0.0884515
$204$	7.59001	0.531407
$205$	−0.134694	−0.00940742
$206$	−17.6628	−1.23062
$207$	7.82889	0.544145
$208$	−8.12697	−0.563504
$209$	22.7968	1.57689
$210$	0.163656	0.0112934
$211$	−3.19828	−0.220179	−0.110089	−	0.993922i	$-0.535114\pi$
$211$	−3.19828	−0.220179	−0.110089	+	0.993922i	$0.535114\pi$
$212$	40.5357	2.78400
$213$	0.511577	0.0350527
$214$	−4.59353	−0.314007
$215$	1.97742	0.134859
$216$	−8.10228	−0.551291
$217$	−7.76229	−0.526938
$218$	1.60518	0.108716
$219$	−3.37561	−0.228103
$220$	3.90974	0.263595
$221$	22.4628	1.51101
$222$	−0.0738436	−0.00495606
$223$	−11.6024	−0.776956	−0.388478	−	0.921458i	$-0.626999\pi$
$223$	−11.6024	−0.776956	−0.388478	+	0.921458i	$0.626999\pi$
$224$	2.05931	0.137593
$225$	14.1896	0.945971
$226$	−41.6502	−2.77053
$227$	23.5533	1.56329	0.781644	−	0.623725i	$-0.214382\pi$
$227$	23.5533	1.56329	0.781644	+	0.623725i	$0.214382\pi$
$228$	−7.44209	−0.492865
$229$	−13.1287	−0.867569	−0.433784	−	0.901017i	$-0.642822\pi$
$229$	−13.1287	−0.867569	−0.433784	+	0.901017i	$0.642822\pi$
$230$	1.77263	0.116884
$231$	−0.974308	−0.0641047
$232$	6.92066	0.454363
$233$	17.5241	1.14804	0.574022	−	0.818840i	$-0.305382\pi$
$233$	17.5241	1.14804	0.574022	+	0.818840i	$0.305382\pi$
$234$	−25.7573	−1.68381
$235$	−1.57054	−0.102451
$236$	−20.6469	−1.34400
$237$	0.571024	0.0370920
$238$	10.3780	0.672703
$239$	14.5925	0.943908	0.471954	−	0.881623i	$-0.343549\pi$
$239$	14.5925	0.943908	0.471954	+	0.881623i	$0.343549\pi$
$240$	−0.204476	−0.0131989
$241$	−26.4569	−1.70424	−0.852121	−	0.523345i	$-0.824684\pi$
$241$	−26.4569	−1.70424	−0.852121	+	0.523345i	$0.824684\pi$
$242$	−9.72793	−0.625335
$243$	−8.82277	−0.565981
$244$	−27.5232	−1.76199
$245$	−1.77161	−0.113184
$246$	−0.404167	−0.0257687
$247$	−22.0251	−1.40142
$248$	42.6269	2.70681
$249$	4.45276	0.282182
$250$	6.47456	0.409487
$251$	7.47031	0.471522	0.235761	−	0.971811i	$-0.424242\pi$
$251$	7.47031	0.471522	0.235761	+	0.971811i	$0.424242\pi$
$252$	−7.70762	−0.485534
$253$	−10.5532	−0.663471
$254$	27.7269	1.73974
$255$	0.565170	0.0353923
$256$	−27.2367	−1.70229
$257$	29.8196	1.86010	0.930048	−	0.367437i	$-0.119765\pi$
$257$	29.8196	1.86010	0.930048	+	0.367437i	$0.119765\pi$
$258$	5.93353	0.369405
$259$	−0.0653965	−0.00406354
$260$	−3.77739	−0.234264
$261$	4.99041	0.308899
$262$	−30.0387	−1.85580
$263$	−11.5992	−0.715237	−0.357618	−	0.933868i	$-0.616411\pi$
$263$	−11.5992	−0.715237	−0.357618	+	0.933868i	$0.616411\pi$
$264$	5.35045	0.329297
$265$	3.01838	0.185418
$266$	−10.1757	−0.623913
$267$	−5.74350	−0.351497
$268$	19.6437	1.19993
$269$	−4.85687	−0.296128	−0.148064	−	0.988978i	$-0.547304\pi$
$269$	−4.85687	−0.296128	−0.148064	+	0.988978i	$0.547304\pi$
$270$	−1.32286	−0.0805070
$271$	1.68960	0.102636	0.0513180	−	0.998682i	$-0.483658\pi$
$271$	1.68960	0.102636	0.0513180	+	0.998682i	$0.483658\pi$
$272$	−12.9665	−0.786210
$273$	0.941325	0.0569716
$274$	−41.6119	−2.51387
$275$	−19.1272	−1.15341
$276$	3.44511	0.207372
$277$	11.0402	0.663341	0.331671	−	0.943395i	$-0.392388\pi$
$277$	11.0402	0.663341	0.331671	+	0.943395i	$0.392388\pi$
$278$	7.00194	0.419949
$279$	30.7378	1.84022
$280$	−0.795917	−0.0475651
$281$	−26.7476	−1.59563	−0.797813	−	0.602905i	$-0.794010\pi$
$281$	−26.7476	−1.59563	−0.797813	+	0.602905i	$0.794010\pi$
$282$	−4.71262	−0.280632
$283$	−25.8292	−1.53539	−0.767694	−	0.640817i	$-0.778596\pi$
$283$	−25.8292	−1.53539	−0.767694	+	0.640817i	$0.778596\pi$
$284$	−5.45528	−0.323712
$285$	−0.554156	−0.0328254
$286$	34.7203	2.05305
$287$	−0.357933	−0.0211281
$288$	−8.15463	−0.480516
$289$	18.8392	1.10819
$290$	1.12994	0.0663523
$291$	−1.98788	−0.116532
$292$	35.9964	2.10653
$293$	0.702917	0.0410648	0.0205324	−	0.999789i	$-0.493464\pi$
$293$	0.702917	0.0410648	0.0205324	+	0.999789i	$0.493464\pi$
$294$	−5.31596	−0.310033
$295$	−1.53742	−0.0895119
$296$	0.359127	0.0208738
$297$	7.87552	0.456984
$298$	−2.41548	−0.139925
$299$	10.1959	0.589645
$300$	6.24414	0.360506
$301$	5.25477	0.302880
$302$	−23.3011	−1.34083
$303$	3.33770	0.191746
$304$	12.7138	0.729187
$305$	−2.04945	−0.117351
$306$	−41.0956	−2.34928
$307$	−24.5056	−1.39861	−0.699303	−	0.714825i	$-0.746506\pi$
$307$	−24.5056	−1.39861	−0.699303	+	0.714825i	$0.746506\pi$
$308$	10.3897	0.592007
$309$	−2.55612	−0.145412
$310$	6.95972	0.395285
$311$	29.4419	1.66950	0.834750	−	0.550629i	$-0.185612\pi$
$311$	29.4419	1.66950	0.834750	+	0.550629i	$0.185612\pi$
$312$	−5.16932	−0.292655
$313$	−13.0304	−0.736524	−0.368262	−	0.929722i	$-0.620047\pi$
$313$	−13.0304	−0.736524	−0.368262	+	0.929722i	$0.620047\pi$
$314$	−38.3549	−2.16449
$315$	−0.573927	−0.0323372
$316$	−6.08921	−0.342545
$317$	−4.15175	−0.233186	−0.116593	−	0.993180i	$-0.537197\pi$
$317$	−4.15175	−0.233186	−0.116593	+	0.993180i	$0.537197\pi$
$318$	9.05707	0.507895
$319$	−6.72696	−0.376637
$320$	−3.03242	−0.169517
$321$	−0.664765	−0.0371036
$322$	4.71057	0.262510
$323$	−35.1408	−1.95528
$324$	29.2098	1.62277
$325$	18.4797	1.02507
$326$	−47.2767	−2.61842
$327$	0.232298	0.0128461
$328$	1.96560	0.108532
$329$	−4.17353	−0.230094
$330$	0.873571	0.0480885
$331$	−8.52272	−0.468451	−0.234225	−	0.972182i	$-0.575255\pi$
$331$	−8.52272	−0.468451	−0.234225	+	0.972182i	$0.575255\pi$
$332$	−47.4828	−2.60596
$333$	0.258963	0.0141911
$334$	−43.9304	−2.40376
$335$	1.46271	0.0799166
$336$	−0.543373	−0.0296434
$337$	34.3300	1.87007	0.935037	−	0.354551i	$-0.115366\pi$
$337$	34.3300	1.87007	0.935037	+	0.354551i	$0.115366\pi$
$338$	−2.57075	−0.139830
$339$	−6.02752	−0.327370
$340$	−6.02678	−0.326848
$341$	−41.4338	−2.24377
$342$	40.2947	2.17889
$343$	−9.80086	−0.529197
$344$	−28.8568	−1.55585
$345$	0.256531	0.0138112
$346$	16.1971	0.870763
$347$	2.95835	0.158812	0.0794062	−	0.996842i	$-0.474698\pi$
$347$	2.95835	0.158812	0.0794062	+	0.996842i	$0.474698\pi$
$348$	2.19604	0.117720
$349$	−15.4111	−0.824937	−0.412469	−	0.910972i	$-0.635333\pi$
$349$	−15.4111	−0.824937	−0.412469	+	0.910972i	$0.635333\pi$
$350$	8.53773	0.456361
$351$	−7.60891	−0.406134
$352$	10.9923	0.585889
$353$	20.6918	1.10131	0.550657	−	0.834732i	$-0.314377\pi$
$353$	20.6918	1.10131	0.550657	+	0.834732i	$0.314377\pi$
$354$	−4.61323	−0.245190
$355$	−0.406213	−0.0215596
$356$	61.2468	3.24607
$357$	1.50187	0.0794876
$358$	4.87134	0.257458
$359$	−3.92504	−0.207156	−0.103578	−	0.994621i	$-0.533029\pi$
$359$	−3.92504	−0.207156	−0.103578	+	0.994621i	$0.533029\pi$
$360$	3.15174	0.166112
$361$	15.4559	0.813470
$362$	14.4806	0.761085
$363$	−1.40780	−0.0738905
$364$	−10.0380	−0.526133
$365$	2.68037	0.140297
$366$	−6.14964	−0.321447
$367$	4.98451	0.260189	0.130095	−	0.991502i	$-0.458472\pi$
$367$	4.98451	0.260189	0.130095	+	0.991502i	$0.458472\pi$
$368$	−5.88551	−0.306804
$369$	1.41738	0.0737857
$370$	0.0586349	0.00304828
$371$	8.02101	0.416430
$372$	13.5262	0.701302
$373$	−31.0404	−1.60721	−0.803607	−	0.595161i	$-0.797088\pi$
$373$	−31.0404	−1.60721	−0.803607	+	0.595161i	$0.797088\pi$
$374$	55.3959	2.86445
$375$	0.936984	0.0483856
$376$	22.9191	1.18196
$377$	6.49924	0.334728
$378$	−3.51536	−0.180811
$379$	27.1565	1.39494	0.697469	−	0.716615i	$-0.254310\pi$
$379$	27.1565	1.39494	0.697469	+	0.716615i	$0.254310\pi$
$380$	5.90933	0.303142
$381$	4.01257	0.205570
$382$	36.8453	1.88517
$383$	−22.8145	−1.16577	−0.582883	−	0.812556i	$-0.698075\pi$
$383$	−22.8145	−1.16577	−0.582883	+	0.812556i	$0.698075\pi$
$384$	−7.14730	−0.364734
$385$	0.773641	0.0394284
$386$	−3.11304	−0.158449
$387$	−20.8083	−1.05775
$388$	21.1981	1.07617
$389$	16.3515	0.829056	0.414528	−	0.910037i	$-0.363947\pi$
$389$	16.3515	0.829056	0.414528	+	0.910037i	$0.363947\pi$
$390$	−0.843998	−0.0427375
$391$	16.2675	0.822681
$392$	25.8534	1.30579
$393$	−4.34714	−0.219284
$394$	−22.7087	−1.14405
$395$	−0.453417	−0.0228139
$396$	−41.1420	−2.06747
$397$	−9.75609	−0.489644	−0.244822	−	0.969568i	$-0.578730\pi$
$397$	−9.75609	−0.489644	−0.244822	+	0.969568i	$0.578730\pi$
$398$	46.6618	2.33895
$399$	−1.47261	−0.0737225
$400$	−10.6673	−0.533363
$401$	−4.79423	−0.239412	−0.119706	−	0.992809i	$-0.538195\pi$
$401$	−4.79423	−0.239412	−0.119706	+	0.992809i	$0.538195\pi$
$402$	4.38907	0.218907
$403$	40.0312	1.99410
$404$	−35.5921	−1.77077
$405$	2.17503	0.108078
$406$	3.00269	0.149021
$407$	−0.349076	−0.0173031
$408$	−8.24760	−0.408317
$409$	1.51745	0.0750329	0.0375164	−	0.999296i	$-0.488055\pi$
$409$	1.51745	0.0750329	0.0375164	+	0.999296i	$0.488055\pi$
$410$	0.320925	0.0158494
$411$	−6.02198	−0.297043
$412$	27.2576	1.34288
$413$	−4.08551	−0.201035
$414$	−18.6533	−0.916762
$415$	−3.53568	−0.173560
$416$	−10.6201	−0.520695
$417$	1.01331	0.0496218
$418$	−54.3163	−2.65670
$419$	24.8570	1.21434	0.607172	−	0.794570i	$-0.292304\pi$
$419$	24.8570	1.21434	0.607172	+	0.794570i	$0.292304\pi$
$420$	−0.252558	−0.0123236
$421$	16.3819	0.798406	0.399203	−	0.916863i	$-0.369287\pi$
$421$	16.3819	0.798406	0.399203	+	0.916863i	$0.369287\pi$
$422$	7.62031	0.370951
$423$	16.5267	0.803557
$424$	−44.0477	−2.13915
$425$	29.4842	1.43019
$426$	−1.21890	−0.0590558
$427$	−5.44617	−0.263558
$428$	7.08883	0.342652
$429$	5.02464	0.242592
$430$	−4.71147	−0.227207
$431$	−10.4937	−0.505465	−0.252733	−	0.967536i	$-0.581329\pi$
$431$	−10.4937	−0.505465	−0.252733	+	0.967536i	$0.581329\pi$
$432$	4.39219	0.211319
$433$	31.5907	1.51815	0.759077	−	0.651001i	$-0.225651\pi$
$433$	31.5907	1.51815	0.759077	+	0.651001i	$0.225651\pi$
$434$	18.4947	0.887772
$435$	0.163522	0.00784029
$436$	−2.47715	−0.118634
$437$	−15.9504	−0.763013
$438$	8.04283	0.384301
$439$	19.7169	0.941037	0.470518	−	0.882390i	$-0.344067\pi$
$439$	19.7169	0.941037	0.470518	+	0.882390i	$0.344067\pi$
$440$	−4.24848	−0.202538
$441$	18.6426	0.887743
$442$	−53.5206	−2.54572
$443$	23.6026	1.12139	0.560696	−	0.828022i	$-0.310534\pi$
$443$	23.6026	1.12139	0.560696	+	0.828022i	$0.310534\pi$
$444$	0.113957	0.00540816
$445$	4.56058	0.216192
$446$	27.6443	1.30900
$447$	−0.349563	−0.0165338
$448$	−8.05830	−0.380719
$449$	−17.6689	−0.833845	−0.416923	−	0.908942i	$-0.636891\pi$
$449$	−17.6689	−0.833845	−0.416923	+	0.908942i	$0.636891\pi$
$450$	−33.8085	−1.59375
$451$	−1.91059	−0.0899662
$452$	64.2755	3.02327
$453$	−3.37208	−0.158434
$454$	−56.1188	−2.63379
$455$	−0.747451	−0.0350411
$456$	8.08687	0.378702
$457$	−30.1256	−1.40922	−0.704609	−	0.709596i	$-0.748878\pi$
$457$	−30.1256	−1.40922	−0.704609	+	0.709596i	$0.748878\pi$
$458$	31.2808	1.46166
$459$	−12.1399	−0.566644
$460$	−2.73556	−0.127546
$461$	2.65047	0.123445	0.0617223	−	0.998093i	$-0.480341\pi$
$461$	2.65047	0.123445	0.0617223	+	0.998093i	$0.480341\pi$
$462$	2.32141	0.108002
$463$	−18.2005	−0.845851	−0.422925	−	0.906165i	$-0.638997\pi$
$463$	−18.2005	−0.845851	−0.422925	+	0.906165i	$0.638997\pi$
$464$	−3.75164	−0.174165
$465$	1.00719	0.0467075
$466$	−41.7535	−1.93419
$467$	−17.4549	−0.807718	−0.403859	−	0.914821i	$-0.632331\pi$
$467$	−17.4549	−0.807718	−0.403859	+	0.914821i	$0.632331\pi$
$468$	39.7493	1.83741
$469$	3.88700	0.179485
$470$	3.74202	0.172606
$471$	−5.55063	−0.255760
$472$	22.4357	1.03269
$473$	28.0492	1.28970
$474$	−1.36054	−0.0624916
$475$	−28.9096	−1.32646
$476$	−16.0155	−0.734069
$477$	−31.7623	−1.45430
$478$	−34.7684	−1.59027
$479$	−16.5224	−0.754927	−0.377464	−	0.926024i	$-0.623204\pi$
$479$	−16.5224	−0.754927	−0.377464	+	0.926024i	$0.623204\pi$
$480$	−0.267205	−0.0121962
$481$	0.337259	0.0153777
$482$	63.0371	2.87126
$483$	0.681703	0.0310186
$484$	15.0123	0.682379
$485$	1.57846	0.0716743
$486$	21.0214	0.953549
$487$	13.0562	0.591632	0.295816	−	0.955245i	$-0.404408\pi$
$487$	13.0562	0.591632	0.295816	+	0.955245i	$0.404408\pi$
$488$	29.9078	1.35386
$489$	−6.84178	−0.309396
$490$	4.22110	0.190690
$491$	4.15659	0.187584	0.0937922	−	0.995592i	$-0.470101\pi$
$491$	4.15659	0.187584	0.0937922	+	0.995592i	$0.470101\pi$
$492$	0.623719	0.0281194
$493$	10.3695	0.467017
$494$	52.4776	2.36108
$495$	−3.06353	−0.137696
$496$	−23.1077	−1.03757
$497$	−1.07947	−0.0484206
$498$	−10.6093	−0.475413
$499$	23.2813	1.04221	0.521107	−	0.853491i	$-0.325519\pi$
$499$	23.2813	1.04221	0.521107	+	0.853491i	$0.325519\pi$
$500$	−9.99168	−0.446841
$501$	−6.35750	−0.284032
$502$	−17.7990	−0.794407
$503$	−7.95766	−0.354815	−0.177407	−	0.984138i	$-0.556771\pi$
$503$	−7.95766	−0.354815	−0.177407	+	0.984138i	$0.556771\pi$
$504$	8.37540	0.373070
$505$	−2.65027	−0.117936
$506$	25.1443	1.11780
$507$	−0.372033	−0.0165225
$508$	−42.7887	−1.89844
$509$	22.3243	0.989507	0.494754	−	0.869033i	$-0.335258\pi$
$509$	22.3243	0.989507	0.494754	+	0.869033i	$0.335258\pi$
$510$	−1.34659	−0.0596280
$511$	7.12279	0.315094
$512$	23.4383	1.03583
$513$	11.9034	0.525546
$514$	−71.0491	−3.13384
$515$	2.02966	0.0894376
$516$	−9.15674	−0.403103
$517$	−22.2776	−0.979770
$518$	0.155816	0.00684614
$519$	2.34401	0.102891
$520$	4.10466	0.180001
$521$	5.20158	0.227885	0.113943	−	0.993487i	$-0.463652\pi$
$521$	5.20158	0.227885	0.113943	+	0.993487i	$0.463652\pi$
$522$	−11.8903	−0.520425
$523$	7.32280	0.320204	0.160102	−	0.987100i	$-0.448818\pi$
$523$	7.32280	0.320204	0.160102	+	0.987100i	$0.448818\pi$
$524$	46.3564	2.02509
$525$	1.23556	0.0539243
$526$	27.6366	1.20501
$527$	63.8694	2.78219
$528$	−2.90044	−0.126225
$529$	−15.6162	−0.678964
$530$	−7.19169	−0.312387
$531$	16.1782	0.702073
$532$	15.7034	0.680827
$533$	1.84591	0.0799554
$534$	13.6846	0.592192
$535$	0.527851	0.0228210
$536$	−21.3456	−0.921989
$537$	0.704969	0.0304217
$538$	11.5721	0.498909
$539$	−25.1298	−1.08242
$540$	2.04147	0.0878510
$541$	28.7856	1.23759	0.618794	−	0.785553i	$-0.287621\pi$
$541$	28.7856	1.23759	0.618794	+	0.785553i	$0.287621\pi$
$542$	−4.02569	−0.172918
$543$	2.09560	0.0899310
$544$	−16.9443	−0.726482
$545$	−0.184454	−0.00790115
$546$	−2.24283	−0.0959842
$547$	−1.52056	−0.0650146	−0.0325073	−	0.999471i	$-0.510349\pi$
$547$	−1.52056	−0.0650146	−0.0325073	+	0.999471i	$0.510349\pi$
$548$	64.2164	2.74319
$549$	21.5662	0.920424
$550$	45.5730	1.94324
$551$	−10.1674	−0.433145
$552$	−3.74360	−0.159338
$553$	−1.20490	−0.0512377
$554$	−26.3047	−1.11758
$555$	0.00848551	0.000360190 0
$556$	−10.8055	−0.458257
$557$	−10.6899	−0.452947	−0.226474	−	0.974017i	$-0.572720\pi$
$557$	−10.6899	−0.452947	−0.226474	+	0.974017i	$0.572720\pi$
$558$	−73.2368	−3.10036
$559$	−27.0996	−1.14619
$560$	0.431461	0.0182325
$561$	8.01677	0.338468
$562$	63.7295	2.68827
$563$	−5.98815	−0.252371	−0.126185	−	0.992007i	$-0.540273\pi$
$563$	−5.98815	−0.252371	−0.126185	+	0.992007i	$0.540273\pi$
$564$	7.27261	0.306232
$565$	4.78611	0.201353
$566$	61.5415	2.58678
$567$	5.77990	0.242733
$568$	5.92793	0.248730
$569$	28.1697	1.18094	0.590468	−	0.807061i	$-0.298943\pi$
$569$	28.1697	1.18094	0.590468	+	0.807061i	$0.298943\pi$
$570$	1.32035	0.0553033
$571$	34.0126	1.42338	0.711692	−	0.702491i	$-0.247929\pi$
$571$	34.0126	1.42338	0.711692	+	0.702491i	$0.247929\pi$
$572$	−53.5811	−2.24034
$573$	5.33217	0.222754
$574$	0.852823	0.0355961
$575$	13.3829	0.558106
$576$	31.9100	1.32958
$577$	−5.05806	−0.210570	−0.105285	−	0.994442i	$-0.533575\pi$
$577$	−5.05806	−0.210570	−0.105285	+	0.994442i	$0.533575\pi$
$578$	−44.8869	−1.86705
$579$	−0.450512	−0.0187226
$580$	−1.74375	−0.0724051
$581$	−9.39566	−0.389798
$582$	4.73639	0.196330
$583$	42.8149	1.77321
$584$	−39.1151	−1.61859
$585$	2.95983	0.122374
$586$	−1.67479	−0.0691850
$587$	−40.5291	−1.67282	−0.836408	−	0.548107i	$-0.815349\pi$
$587$	−40.5291	−1.67282	−0.836408	+	0.548107i	$0.815349\pi$
$588$	8.20371	0.338315
$589$	−62.6247	−2.58041
$590$	3.66309	0.150807
$591$	−3.28635	−0.135182
$592$	−0.194680	−0.00800131
$593$	21.8112	0.895678	0.447839	−	0.894114i	$-0.352194\pi$
$593$	21.8112	0.895678	0.447839	+	0.894114i	$0.352194\pi$
$594$	−18.7644	−0.769914
$595$	−1.19255	−0.0488898
$596$	3.72762	0.152689
$597$	6.75279	0.276373
$598$	−24.2931	−0.993418
$599$	8.96796	0.366421	0.183210	−	0.983074i	$-0.441351\pi$
$599$	8.96796	0.366421	0.183210	+	0.983074i	$0.441351\pi$
$600$	−6.78513	−0.277002
$601$	1.89642	0.0773567	0.0386784	−	0.999252i	$-0.487685\pi$
$601$	1.89642	0.0773567	0.0386784	+	0.999252i	$0.487685\pi$
$602$	−12.5202	−0.510285
$603$	−15.3921	−0.626814
$604$	35.9587	1.46314
$605$	1.11785	0.0454472
$606$	−7.95250	−0.323048
$607$	28.4699	1.15556	0.577779	−	0.816193i	$-0.303919\pi$
$607$	28.4699	1.15556	0.577779	+	0.816193i	$0.303919\pi$
$608$	16.6141	0.673791
$609$	0.434542	0.0176085
$610$	4.88307	0.197710
$611$	21.5235	0.870747
$612$	63.4196	2.56358
$613$	−41.3037	−1.66824	−0.834120	−	0.551583i	$-0.814024\pi$
$613$	−41.3037	−1.66824	−0.834120	+	0.551583i	$0.814024\pi$
$614$	58.3877	2.35634
$615$	0.0464436	0.00187279
$616$	−11.2898	−0.454881
$617$	20.4279	0.822396	0.411198	−	0.911546i	$-0.365111\pi$
$617$	20.4279	0.822396	0.411198	+	0.911546i	$0.365111\pi$
$618$	6.09028	0.244987
$619$	44.7266	1.79771	0.898857	−	0.438241i	$-0.144398\pi$
$619$	44.7266	1.79771	0.898857	+	0.438241i	$0.144398\pi$
$620$	−10.7404	−0.431344
$621$	−5.51034	−0.221122
$622$	−70.1493	−2.81273
$623$	12.1192	0.485546
$624$	2.80225	0.112180
$625$	23.8812	0.955247
$626$	31.0467	1.24088
$627$	−7.86053	−0.313919
$628$	59.1901	2.36194
$629$	0.538093	0.0214552
$630$	1.36746	0.0544808
$631$	38.3115	1.52516	0.762578	−	0.646897i	$-0.223933\pi$
$631$	38.3115	1.52516	0.762578	+	0.646897i	$0.223933\pi$
$632$	6.61677	0.263201
$633$	1.10279	0.0438321
$634$	9.89208	0.392865
$635$	−3.18615	−0.126438
$636$	−13.9771	−0.554227
$637$	24.2791	0.961972
$638$	16.0279	0.634549
$639$	4.27457	0.169099
$640$	5.67525	0.224334
$641$	32.1230	1.26878	0.634391	−	0.773013i	$-0.281251\pi$
$641$	32.1230	1.26878	0.634391	+	0.773013i	$0.281251\pi$
$642$	1.58389	0.0625111
$643$	18.2031	0.717859	0.358930	−	0.933365i	$-0.383142\pi$
$643$	18.2031	0.717859	0.358930	+	0.933365i	$0.383142\pi$
$644$	−7.26945	−0.286456
$645$	−0.681833	−0.0268471
$646$	83.7274	3.29421
$647$	19.2504	0.756809	0.378405	−	0.925640i	$-0.376473\pi$
$647$	19.2504	0.756809	0.378405	+	0.925640i	$0.376473\pi$
$648$	−31.7406	−1.24689
$649$	−21.8078	−0.856031
$650$	−44.0303	−1.72701
$651$	2.67650	0.104900
$652$	72.9585	2.85727
$653$	40.7440	1.59444	0.797218	−	0.603691i	$-0.206304\pi$
$653$	40.7440	1.59444	0.797218	+	0.603691i	$0.206304\pi$
$654$	−0.553480	−0.0216428
$655$	3.45181	0.134873
$656$	−1.06554	−0.0416023
$657$	−28.2055	−1.10040
$658$	9.94398	0.387657
$659$	15.6498	0.609632	0.304816	−	0.952411i	$-0.401405\pi$
$659$	15.6498	0.609632	0.304816	+	0.952411i	$0.401405\pi$
$660$	−1.34811	−0.0524752
$661$	−26.2188	−1.01979	−0.509897	−	0.860235i	$-0.670316\pi$
$661$	−26.2188	−1.01979	−0.509897	+	0.860235i	$0.670316\pi$
$662$	20.3065	0.789234
$663$	−7.74538	−0.300806
$664$	51.5966	2.00234
$665$	1.16931	0.0453439
$666$	−0.617013	−0.0239088
$667$	4.70671	0.182245
$668$	67.7943	2.62304
$669$	4.00062	0.154673
$670$	−3.48511	−0.134641
$671$	−29.0708	−1.12226
$672$	−0.710067	−0.0273914
$673$	37.6070	1.44964	0.724821	−	0.688937i	$-0.241922\pi$
$673$	37.6070	1.44964	0.724821	+	0.688937i	$0.241922\pi$
$674$	−81.7956	−3.15065
$675$	−9.98727	−0.384410
$676$	3.96723	0.152586
$677$	−0.525690	−0.0202039	−0.0101020	−	0.999949i	$-0.503216\pi$
$677$	−0.525690	−0.0202039	−0.0101020	+	0.999949i	$0.503216\pi$
$678$	14.3614	0.551545
$679$	4.19458	0.160973
$680$	6.54894	0.251140
$681$	−8.12138	−0.311212
$682$	98.7215	3.78024
$683$	−43.0885	−1.64874	−0.824368	−	0.566054i	$-0.808469\pi$
$683$	−43.0885	−1.64874	−0.824368	+	0.566054i	$0.808469\pi$
$684$	−62.1836	−2.37765
$685$	4.78171	0.182700
$686$	23.3518	0.891577
$687$	4.52689	0.172712
$688$	15.6431	0.596386
$689$	−41.3655	−1.57590
$690$	−0.611219	−0.0232687
$691$	−39.1263	−1.48843	−0.744217	−	0.667938i	$-0.767177\pi$
$691$	−39.1263	−1.48843	−0.744217	+	0.667938i	$0.767177\pi$
$692$	−24.9957	−0.950196
$693$	−8.14099	−0.309251
$694$	−7.04865	−0.267563
$695$	−0.804606	−0.0305205
$696$	−2.38630	−0.0904526
$697$	2.94514	0.111555
$698$	36.7189	1.38983
$699$	−6.04247	−0.228547
$700$	−13.1756	−0.497991
$701$	40.7626	1.53958	0.769791	−	0.638296i	$-0.220360\pi$
$701$	40.7626	1.53958	0.769791	+	0.638296i	$0.220360\pi$
$702$	18.1292	0.684243
$703$	−0.527607	−0.0198991
$704$	−43.0139	−1.62115
$705$	0.541536	0.0203954
$706$	−49.3009	−1.85546
$707$	−7.04280	−0.264872
$708$	7.11923	0.267557
$709$	−27.1855	−1.02097	−0.510487	−	0.859886i	$-0.670535\pi$
$709$	−27.1855	−1.02097	−0.510487	+	0.859886i	$0.670535\pi$
$710$	0.967856	0.0363230
$711$	4.77128	0.178937
$712$	−66.5532	−2.49419
$713$	28.9904	1.08570
$714$	−3.57841	−0.133919
$715$	−3.98978	−0.149209
$716$	−7.51756	−0.280944
$717$	−5.03161	−0.187909
$718$	9.35192	0.349011
$719$	26.6368	0.993384	0.496692	−	0.867927i	$-0.334548\pi$
$719$	26.6368	0.993384	0.496692	+	0.867927i	$0.334548\pi$
$720$	−1.70854	−0.0636734
$721$	5.39359	0.200868
$722$	−36.8258	−1.37051
$723$	9.12258	0.339273
$724$	−22.3468	−0.830513
$725$	8.53074	0.316824
$726$	3.35427	0.124489
$727$	−21.0462	−0.780560	−0.390280	−	0.920696i	$-0.627622\pi$
$727$	−21.0462	−0.780560	−0.390280	+	0.920696i	$0.627622\pi$
$728$	10.9077	0.404265
$729$	−20.7901	−0.770005
$730$	−6.38634	−0.236369
$731$	−43.2372	−1.59918
$732$	9.49025	0.350770
$733$	−3.09646	−0.114370	−0.0571852	−	0.998364i	$-0.518213\pi$
$733$	−3.09646	−0.114370	−0.0571852	+	0.998364i	$0.518213\pi$
$734$	−11.8762	−0.438360
$735$	0.610867	0.0225322
$736$	−7.69105	−0.283496
$737$	20.7482	0.764268
$738$	−3.37709	−0.124312
$739$	51.3521	1.88902	0.944508	−	0.328488i	$-0.106539\pi$
$739$	51.3521	1.88902	0.944508	+	0.328488i	$0.106539\pi$
$740$	−0.0904866	−0.00332635
$741$	7.59443	0.278989
$742$	−19.1111	−0.701591
$743$	10.2072	0.374468	0.187234	−	0.982315i	$-0.440048\pi$
$743$	10.2072	0.374468	0.187234	+	0.982315i	$0.440048\pi$
$744$	−14.6981	−0.538859
$745$	0.277567	0.0101693
$746$	73.9579	2.70779
$747$	37.2058	1.36129
$748$	−85.4881	−3.12576
$749$	1.40270	0.0512537
$750$	−2.23248	−0.0815188
$751$	46.0065	1.67880	0.839401	−	0.543513i	$-0.182906\pi$
$751$	46.0065	1.67880	0.839401	+	0.543513i	$0.182906\pi$
$752$	−12.4243	−0.453067
$753$	−2.57583	−0.0938684
$754$	−15.4853	−0.563940
$755$	2.67757	0.0974468
$756$	5.42498	0.197305
$757$	33.6523	1.22311	0.611557	−	0.791201i	$-0.290544\pi$
$757$	33.6523	1.22311	0.611557	+	0.791201i	$0.290544\pi$
$758$	−64.7040	−2.35015
$759$	3.63882	0.132081
$760$	−6.42131	−0.232925
$761$	38.4039	1.39214	0.696071	−	0.717973i	$-0.254930\pi$
$761$	38.4039	1.39214	0.696071	+	0.717973i	$0.254930\pi$
$762$	−9.56046	−0.346339
$763$	−0.490166	−0.0177452
$764$	−56.8604	−2.05714
$765$	4.72237	0.170738
$766$	54.3585	1.96405
$767$	21.0695	0.760777
$768$	9.39144	0.338884
$769$	−25.8361	−0.931675	−0.465838	−	0.884870i	$-0.654247\pi$
$769$	−25.8361	−0.931675	−0.465838	+	0.884870i	$0.654247\pi$
$770$	−1.84330	−0.0664279
$771$	−10.2821	−0.370300
$772$	4.80410	0.172903
$773$	−15.2744	−0.549381	−0.274691	−	0.961533i	$-0.588575\pi$
$773$	−15.2744	−0.549381	−0.274691	+	0.961533i	$0.588575\pi$
$774$	49.5786	1.78206
$775$	52.5440	1.88744
$776$	−23.0347	−0.826898
$777$	0.0225493	0.000808951 0
$778$	−38.9597	−1.39677
$779$	−2.88774	−0.103464
$780$	1.30248	0.0466361
$781$	−5.76202	−0.206181
$782$	−38.7594	−1.38603
$783$	−3.51248	−0.125526
$784$	−14.0149	−0.500533
$785$	4.40743	0.157308
$786$	10.3576	0.369444
$787$	14.0074	0.499311	0.249656	−	0.968335i	$-0.419683\pi$
$787$	14.0074	0.499311	0.249656	+	0.968335i	$0.419683\pi$
$788$	35.0445	1.24841
$789$	3.99950	0.142386
$790$	1.08032	0.0384362
$791$	12.7185	0.452219
$792$	44.7066	1.58858
$793$	28.0866	0.997386
$794$	23.2451	0.824939
$795$	−1.04077	−0.0369121
$796$	−72.0095	−2.55231
$797$	3.84541	0.136212	0.0681058	−	0.997678i	$-0.478304\pi$
$797$	3.84541	0.136212	0.0681058	+	0.997678i	$0.478304\pi$
$798$	3.50867	0.124206
$799$	34.3405	1.21488
$800$	−13.9397	−0.492844
$801$	−47.9908	−1.69567
$802$	11.4229	0.403356
$803$	38.0203	1.34171
$804$	−6.77331	−0.238876
$805$	−0.541300	−0.0190783
$806$	−95.3796	−3.35960
$807$	1.67469	0.0589519
$808$	38.6758	1.36061
$809$	29.7136	1.04467	0.522337	−	0.852739i	$-0.325060\pi$
$809$	29.7136	1.04467	0.522337	+	0.852739i	$0.325060\pi$
$810$	−5.18230	−0.182088
$811$	−9.95679	−0.349630	−0.174815	−	0.984601i	$-0.555933\pi$
$811$	−9.95679	−0.349630	−0.174815	+	0.984601i	$0.555933\pi$
$812$	−4.63381	−0.162615
$813$	−0.582589	−0.0204323
$814$	0.831719	0.0291517
$815$	5.43266	0.190298
$816$	4.47096	0.156515
$817$	42.3945	1.48320
$818$	−3.61551	−0.126413
$819$	7.86540	0.274839
$820$	−0.495259	−0.0172952
$821$	32.6096	1.13808	0.569041	−	0.822309i	$-0.307314\pi$
$821$	32.6096	1.13808	0.569041	+	0.822309i	$0.307314\pi$
$822$	14.3482	0.500449
$823$	−2.71197	−0.0945335	−0.0472667	−	0.998882i	$-0.515051\pi$
$823$	−2.71197	−0.0945335	−0.0472667	+	0.998882i	$0.515051\pi$
$824$	−29.6191	−1.03183
$825$	6.59522	0.229616
$826$	9.73425	0.338698
$827$	−5.62022	−0.195434	−0.0977170	−	0.995214i	$-0.531154\pi$
$827$	−5.62022	−0.195434	−0.0977170	+	0.995214i	$0.531154\pi$
$828$	28.7862	1.00039
$829$	−19.6826	−0.683603	−0.341802	−	0.939772i	$-0.611037\pi$
$829$	−19.6826	−0.683603	−0.341802	+	0.939772i	$0.611037\pi$
$830$	8.42421	0.292409
$831$	−3.80676	−0.132055
$832$	41.5578	1.44076
$833$	38.7370	1.34216
$834$	−2.41433	−0.0836014
$835$	5.04812	0.174697
$836$	83.8221	2.89905
$837$	−21.6347	−0.747805
$838$	−59.2251	−2.04590
$839$	−10.6069	−0.366189	−0.183095	−	0.983095i	$-0.558611\pi$
$839$	−10.6069	−0.366189	−0.183095	+	0.983095i	$0.558611\pi$
$840$	0.274439	0.00946905
$841$	−25.9998	−0.896544
$842$	−39.0321	−1.34513
$843$	9.22279	0.317650
$844$	−11.7598	−0.404790
$845$	0.295409	0.0101624
$846$	−39.3771	−1.35381
$847$	2.97057	0.102070
$848$	23.8779	0.819971
$849$	8.90614	0.305658
$850$	−70.2498	−2.40955
$851$	0.244241	0.00837248
$852$	1.88103	0.0644430
$853$	44.6221	1.52783	0.763915	−	0.645317i	$-0.223275\pi$
$853$	44.6221	1.52783	0.763915	+	0.645317i	$0.223275\pi$
$854$	12.9762	0.444036
$855$	−4.63034	−0.158354
$856$	−7.70300	−0.263283
$857$	16.6250	0.567898	0.283949	−	0.958839i	$-0.408355\pi$
$857$	16.6250	0.567898	0.283949	+	0.958839i	$0.408355\pi$
$858$	−11.9719	−0.408713
$859$	−15.0058	−0.511991	−0.255996	−	0.966678i	$-0.582403\pi$
$859$	−15.0058	−0.511991	−0.255996	+	0.966678i	$0.582403\pi$
$860$	7.27083	0.247933
$861$	0.123419	0.00420609
$862$	25.0027	0.851595
$863$	−16.6937	−0.568259	−0.284130	−	0.958786i	$-0.591705\pi$
$863$	−16.6937	−0.568259	−0.284130	+	0.958786i	$0.591705\pi$
$864$	5.73961	0.195266
$865$	−1.86124	−0.0632841
$866$	−75.2690	−2.55775
$867$	−6.49593	−0.220613
$868$	−28.5413	−0.968756
$869$	−6.43158	−0.218176
$870$	−0.389613	−0.0132091
$871$	−20.0458	−0.679226
$872$	2.69176	0.0911547
$873$	−16.6101	−0.562166
$874$	38.0040	1.28550
$875$	−1.97711	−0.0668384
$876$	−12.4119	−0.419358
$877$	18.3947	0.621146	0.310573	−	0.950550i	$-0.399479\pi$
$877$	18.3947	0.621146	0.310573	+	0.950550i	$0.399479\pi$
$878$	−46.9781	−1.58543
$879$	−0.242372	−0.00817500
$880$	2.30307	0.0776364
$881$	−4.10415	−0.138272	−0.0691362	−	0.997607i	$-0.522024\pi$
$881$	−4.10415	−0.138272	−0.0691362	+	0.997607i	$0.522024\pi$
$882$	−44.4184	−1.49565
$883$	−17.4459	−0.587102	−0.293551	−	0.955943i	$-0.594837\pi$
$883$	−17.4459	−0.587102	−0.293551	+	0.955943i	$0.594837\pi$
$884$	82.5941	2.77794
$885$	0.530115	0.0178196
$886$	−56.2362	−1.88929
$887$	39.2535	1.31800	0.659002	−	0.752141i	$-0.270979\pi$
$887$	39.2535	1.31800	0.659002	+	0.752141i	$0.270979\pi$
$888$	−0.123830	−0.00415547
$889$	−8.46682	−0.283968
$890$	−10.8662	−0.364235
$891$	30.8522	1.03359
$892$	−42.6613	−1.42840
$893$	−33.6713	−1.12677
$894$	0.832879	0.0278556
$895$	−0.559775	−0.0187112
$896$	15.0813	0.503832
$897$	−3.51564	−0.117384
$898$	42.0984	1.40484
$899$	18.4795	0.616326
$900$	52.1739	1.73913
$901$	−65.9982	−2.19872
$902$	4.55223	0.151573
$903$	−1.81189	−0.0602960
$904$	−69.8443	−2.32299
$905$	−1.66400	−0.0553131
$906$	8.03442	0.266926
$907$	−51.1491	−1.69838	−0.849188	−	0.528090i	$-0.822908\pi$
$907$	−51.1491	−1.69838	−0.849188	+	0.528090i	$0.822908\pi$
$908$	86.6037	2.87404
$909$	27.8887	0.925010
$910$	1.78090	0.0590362
$911$	39.4156	1.30590	0.652948	−	0.757403i	$-0.273532\pi$
$911$	39.4156	1.30590	0.652948	+	0.757403i	$0.273532\pi$
$912$	−4.38383	−0.145163
$913$	−50.1525	−1.65981
$914$	71.7782	2.37421
$915$	0.706667	0.0233617
$916$	−48.2732	−1.59499
$917$	9.17278	0.302912
$918$	28.9250	0.954667
$919$	−18.1319	−0.598116	−0.299058	−	0.954235i	$-0.596672\pi$
$919$	−18.1319	−0.598116	−0.299058	+	0.954235i	$0.596672\pi$
$920$	2.97257	0.0980028
$921$	8.44974	0.278428
$922$	−6.31508	−0.207976
$923$	5.56696	0.183239
$924$	−3.58246	−0.117854
$925$	0.442678	0.0145552
$926$	43.3651	1.42507
$927$	−21.3580	−0.701490
$928$	−4.90255	−0.160934
$929$	3.60431	0.118254	0.0591268	−	0.998250i	$-0.481168\pi$
$929$	3.60431	0.118254	0.0591268	+	0.998250i	$0.481168\pi$
$930$	−2.39977	−0.0786916
$931$	−37.9821	−1.24481
$932$	64.4349	2.11064
$933$	−10.1518	−0.332356
$934$	41.5886	1.36082
$935$	−6.36565	−0.208179
$936$	−43.1931	−1.41181
$937$	−23.6915	−0.773969	−0.386984	−	0.922086i	$-0.626483\pi$
$937$	−23.6915	−0.773969	−0.386984	+	0.922086i	$0.626483\pi$
$938$	−9.26127	−0.302391
$939$	4.49301	0.146624
$940$	−5.77476	−0.188352
$941$	30.5075	0.994516	0.497258	−	0.867603i	$-0.334340\pi$
$941$	30.5075	0.994516	0.497258	+	0.867603i	$0.334340\pi$
$942$	13.2251	0.430897
$943$	1.33680	0.0435322
$944$	−12.1622	−0.395847
$945$	0.403957	0.0131407
$946$	−66.8307	−2.17285
$947$	21.3639	0.694235	0.347118	−	0.937822i	$-0.387160\pi$
$947$	21.3639	0.694235	0.347118	+	0.937822i	$0.387160\pi$
$948$	2.09961	0.0681922
$949$	−36.7332	−1.19241
$950$	68.8808	2.23479
$951$	1.43156	0.0464215
$952$	17.4031	0.564036
$953$	21.1411	0.684829	0.342414	−	0.939549i	$-0.388755\pi$
$953$	21.1411	0.684829	0.342414	+	0.939549i	$0.388755\pi$
$954$	75.6779	2.45016
$955$	−4.23396	−0.137008
$956$	53.6554	1.73534
$957$	2.31951	0.0749793
$958$	39.3667	1.27188
$959$	12.7068	0.410325
$960$	1.04560	0.0337467
$961$	82.8222	2.67168
$962$	−0.803563	−0.0259079
$963$	−5.55456	−0.178993
$964$	−97.2802	−3.13318
$965$	0.357725	0.0115156
$966$	−1.62425	−0.0522592
$967$	14.9665	0.481291	0.240646	−	0.970613i	$-0.422641\pi$
$967$	14.9665	0.481291	0.240646	+	0.970613i	$0.422641\pi$
$968$	−16.3130	−0.524320
$969$	12.1168	0.389249
$970$	−3.76089	−0.120755
$971$	5.33394	0.171174	0.0855871	−	0.996331i	$-0.472723\pi$
$971$	5.33394	0.171174	0.0855871	+	0.996331i	$0.472723\pi$
$972$	−32.4406	−1.04053
$973$	−2.13815	−0.0685459
$974$	−31.1080	−0.996766
$975$	−6.37196	−0.204066
$976$	−16.2128	−0.518959
$977$	−12.3985	−0.396663	−0.198331	−	0.980135i	$-0.563552\pi$
$977$	−12.3985	−0.396663	−0.198331	+	0.980135i	$0.563552\pi$
$978$	16.3014	0.521262
$979$	64.6905	2.06752
$980$	−6.51409	−0.208085
$981$	1.94100	0.0619715
$982$	−9.90362	−0.316037
$983$	−53.8935	−1.71894	−0.859468	−	0.511190i	$-0.829205\pi$
$983$	−53.8935	−1.71894	−0.859468	+	0.511190i	$0.829205\pi$
$984$	−0.677758	−0.0216061
$985$	2.60950	0.0831455
$986$	−24.7066	−0.786818
$987$	1.43907	0.0458061
$988$	−80.9845	−2.57646
$989$	−19.6254	−0.624052
$990$	7.29927	0.231986
$991$	37.9367	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$991$	37.9367	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$992$	−30.1966	−0.958744
$993$	2.93871	0.0932571
$994$	2.57197	0.0815778
$995$	−5.36200	−0.169987
$996$	16.3725	0.518782
$997$	−38.2290	−1.21072	−0.605362	−	0.795951i	$-0.706971\pi$
$997$	−38.2290	−1.21072	−0.605362	+	0.795951i	$0.706971\pi$
$998$	−55.4707	−1.75589
$999$	−0.182270	−0.00576677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.20	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.38263 q^{2} -0.344809 q^{3} +3.67692 q^{4} +0.273793 q^{5} +0.821552 q^{6} +0.727572 q^{7} -3.99549 q^{8} -2.88111 q^{9} +O(q^{10})\)	\(q-2.38263 q^{2} -0.344809 q^{3} +3.67692 q^{4} +0.273793 q^{5} +0.821552 q^{6} +0.727572 q^{7} -3.99549 q^{8} -2.88111 q^{9} -0.652346 q^{10} +3.88366 q^{11} -1.26784 q^{12} -3.75219 q^{13} -1.73354 q^{14} -0.0944060 q^{15} +2.16593 q^{16} -5.98659 q^{17} +6.86461 q^{18} +5.86992 q^{19} +1.00671 q^{20} -0.250873 q^{21} -9.25334 q^{22} -2.71732 q^{23} +1.37768 q^{24} -4.92504 q^{25} +8.94009 q^{26} +2.02786 q^{27} +2.67523 q^{28} -1.73212 q^{29} +0.224935 q^{30} -10.6688 q^{31} +2.83038 q^{32} -1.33912 q^{33} +14.2638 q^{34} +0.199204 q^{35} -10.5936 q^{36} -0.0898831 q^{37} -13.9858 q^{38} +1.29379 q^{39} -1.09394 q^{40} -0.491956 q^{41} +0.597738 q^{42} +7.22234 q^{43} +14.2799 q^{44} -0.788825 q^{45} +6.47437 q^{46} -5.73624 q^{47} -0.746830 q^{48} -6.47064 q^{49} +11.7345 q^{50} +2.06423 q^{51} -13.7965 q^{52} +11.0244 q^{53} -4.83163 q^{54} +1.06332 q^{55} -2.90701 q^{56} -2.02400 q^{57} +4.12699 q^{58} -5.61526 q^{59} -0.347124 q^{60} -7.48540 q^{61} +25.4197 q^{62} -2.09621 q^{63} -11.0756 q^{64} -1.02732 q^{65} +3.19063 q^{66} +5.34242 q^{67} -22.0122 q^{68} +0.936956 q^{69} -0.474629 q^{70} -1.48365 q^{71} +11.5114 q^{72} +9.78980 q^{73} +0.214158 q^{74} +1.69820 q^{75} +21.5832 q^{76} +2.82565 q^{77} -3.08262 q^{78} -1.65606 q^{79} +0.593014 q^{80} +7.94410 q^{81} +1.17215 q^{82} -12.9137 q^{83} -0.922442 q^{84} -1.63908 q^{85} -17.2082 q^{86} +0.597249 q^{87} -15.5171 q^{88} +16.6571 q^{89} +1.87948 q^{90} -2.72999 q^{91} -9.99138 q^{92} +3.67868 q^{93} +13.6673 q^{94} +1.60714 q^{95} -0.975941 q^{96} +5.76518 q^{97} +15.4171 q^{98} -11.1893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 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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