LMFDB - Embedded newform 6037.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.72738 q^{2} +0.874188 q^{3} +5.43862 q^{4} -1.32205 q^{5} -2.38425 q^{6} -0.0787567 q^{7} -9.37845 q^{8} -2.23580 q^{9} +O(q^{10})$	\(q-2.72738 q^{2} +0.874188 q^{3} +5.43862 q^{4} -1.32205 q^{5} -2.38425 q^{6} -0.0787567 q^{7} -9.37845 q^{8} -2.23580 q^{9} +3.60574 q^{10} +1.39027 q^{11} +4.75438 q^{12} -4.97614 q^{13} +0.214800 q^{14} -1.15572 q^{15} +14.7014 q^{16} +7.42427 q^{17} +6.09787 q^{18} +6.22831 q^{19} -7.19014 q^{20} -0.0688481 q^{21} -3.79180 q^{22} -4.46461 q^{23} -8.19852 q^{24} -3.25218 q^{25} +13.5718 q^{26} -4.57707 q^{27} -0.428328 q^{28} +4.74256 q^{29} +3.15210 q^{30} +7.19286 q^{31} -21.3394 q^{32} +1.21536 q^{33} -20.2488 q^{34} +0.104120 q^{35} -12.1597 q^{36} -6.55056 q^{37} -16.9870 q^{38} -4.35008 q^{39} +12.3988 q^{40} -5.17810 q^{41} +0.187775 q^{42} +5.95990 q^{43} +7.56115 q^{44} +2.95584 q^{45} +12.1767 q^{46} -1.14434 q^{47} +12.8518 q^{48} -6.99380 q^{49} +8.86994 q^{50} +6.49020 q^{51} -27.0633 q^{52} -11.3699 q^{53} +12.4834 q^{54} -1.83801 q^{55} +0.738615 q^{56} +5.44471 q^{57} -12.9348 q^{58} -11.2361 q^{59} -6.28553 q^{60} +11.1759 q^{61} -19.6177 q^{62} +0.176084 q^{63} +28.7980 q^{64} +6.57871 q^{65} -3.31474 q^{66} -10.0612 q^{67} +40.3778 q^{68} -3.90291 q^{69} -0.283976 q^{70} +6.57981 q^{71} +20.9683 q^{72} +6.04721 q^{73} +17.8659 q^{74} -2.84301 q^{75} +33.8734 q^{76} -0.109493 q^{77} +11.8643 q^{78} +15.8241 q^{79} -19.4360 q^{80} +2.70617 q^{81} +14.1227 q^{82} -3.45040 q^{83} -0.374439 q^{84} -9.81527 q^{85} -16.2549 q^{86} +4.14589 q^{87} -13.0386 q^{88} +5.45884 q^{89} -8.06171 q^{90} +0.391904 q^{91} -24.2813 q^{92} +6.28791 q^{93} +3.12105 q^{94} -8.23414 q^{95} -18.6547 q^{96} +7.93275 q^{97} +19.0748 q^{98} -3.10836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.72738	−1.92855	−0.964276	−	0.264900i	$-0.914661\pi$
$2$	−2.72738	−1.92855	−0.964276	+	0.264900i	$0.914661\pi$
$3$	0.874188	0.504712	0.252356	−	0.967634i	$-0.418795\pi$
$3$	0.874188	0.504712	0.252356	+	0.967634i	$0.418795\pi$
$4$	5.43862	2.71931
$5$	−1.32205	−0.591240	−0.295620	−	0.955306i	$-0.595526\pi$
$5$	−1.32205	−0.591240	−0.295620	+	0.955306i	$0.595526\pi$
$6$	−2.38425	−0.973364
$7$	−0.0787567	−0.0297672	−0.0148836	−	0.999889i	$-0.504738\pi$
$7$	−0.0787567	−0.0297672	−0.0148836	+	0.999889i	$0.504738\pi$
$8$	−9.37845	−3.31578
$9$	−2.23580	−0.745265
$10$	3.60574	1.14024
$11$	1.39027	0.419182	0.209591	−	0.977789i	$-0.432787\pi$
$11$	1.39027	0.419182	0.209591	+	0.977789i	$0.432787\pi$
$12$	4.75438	1.37247
$13$	−4.97614	−1.38013	−0.690066	−	0.723746i	$-0.742419\pi$
$13$	−4.97614	−1.38013	−0.690066	+	0.723746i	$0.742419\pi$
$14$	0.214800	0.0574076
$15$	−1.15572	−0.298406
$16$	14.7014	3.67535
$17$	7.42427	1.80065	0.900325	−	0.435219i	$-0.143329\pi$
$17$	7.42427	1.80065	0.900325	+	0.435219i	$0.143329\pi$
$18$	6.09787	1.43728
$19$	6.22831	1.42887	0.714436	−	0.699701i	$-0.246684\pi$
$19$	6.22831	1.42887	0.714436	+	0.699701i	$0.246684\pi$
$20$	−7.19014	−1.60776
$21$	−0.0688481	−0.0150239
$22$	−3.79180	−0.808414
$23$	−4.46461	−0.930936	−0.465468	−	0.885065i	$-0.654114\pi$
$23$	−4.46461	−0.930936	−0.465468	+	0.885065i	$0.654114\pi$
$24$	−8.19852	−1.67352
$25$	−3.25218	−0.650436
$26$	13.5718	2.66166
$27$	−4.57707	−0.880857
$28$	−0.428328	−0.0809464
$29$	4.74256	0.880672	0.440336	−	0.897833i	$-0.354859\pi$
$29$	4.74256	0.880672	0.440336	+	0.897833i	$0.354859\pi$
$30$	3.15210	0.575491
$31$	7.19286	1.29188	0.645938	−	0.763390i	$-0.276467\pi$
$31$	7.19286	1.29188	0.645938	+	0.763390i	$0.276467\pi$
$32$	−21.3394	−3.77231
$33$	1.21536	0.211566
$34$	−20.2488	−3.47265
$35$	0.104120	0.0175996
$36$	−12.1597	−2.02661
$37$	−6.55056	−1.07691	−0.538453	−	0.842656i	$-0.680991\pi$
$37$	−6.55056	−1.07691	−0.538453	+	0.842656i	$0.680991\pi$
$38$	−16.9870	−2.75565
$39$	−4.35008	−0.696570
$40$	12.3988	1.96042
$41$	−5.17810	−0.808683	−0.404342	−	0.914608i	$-0.632499\pi$
$41$	−5.17810	−0.808683	−0.404342	+	0.914608i	$0.632499\pi$
$42$	0.187775	0.0289743
$43$	5.95990	0.908877	0.454438	−	0.890778i	$-0.349840\pi$
$43$	5.95990	0.908877	0.454438	+	0.890778i	$0.349840\pi$
$44$	7.56115	1.13989
$45$	2.95584	0.440630
$46$	12.1767	1.79536
$47$	−1.14434	−0.166919	−0.0834594	−	0.996511i	$-0.526597\pi$
$47$	−1.14434	−0.166919	−0.0834594	+	0.996511i	$0.526597\pi$
$48$	12.8518	1.85499
$49$	−6.99380	−0.999114
$50$	8.86994	1.25440
$51$	6.49020	0.908810
$52$	−27.0633	−3.75301
$53$	−11.3699	−1.56178	−0.780889	−	0.624670i	$-0.785233\pi$
$53$	−11.3699	−1.56178	−0.780889	+	0.624670i	$0.785233\pi$
$54$	12.4834	1.69878
$55$	−1.83801	−0.247837
$56$	0.738615	0.0987016
$57$	5.44471	0.721169
$58$	−12.9348	−1.69842
$59$	−11.2361	−1.46281	−0.731407	−	0.681941i	$-0.761136\pi$
$59$	−11.2361	−1.46281	−0.731407	+	0.681941i	$0.761136\pi$
$60$	−6.28553	−0.811459
$61$	11.1759	1.43092	0.715462	−	0.698652i	$-0.246216\pi$
$61$	11.1759	1.43092	0.715462	+	0.698652i	$0.246216\pi$
$62$	−19.6177	−2.49145
$63$	0.176084	0.0221845
$64$	28.7980	3.59975
$65$	6.57871	0.815989
$66$	−3.31474	−0.408017
$67$	−10.0612	−1.22917	−0.614583	−	0.788852i	$-0.710676\pi$
$67$	−10.0612	−1.22917	−0.614583	+	0.788852i	$0.710676\pi$
$68$	40.3778	4.89653
$69$	−3.90291	−0.469855
$70$	−0.283976	−0.0339417
$71$	6.57981	0.780879	0.390440	−	0.920628i	$-0.372323\pi$
$71$	6.57981	0.780879	0.390440	+	0.920628i	$0.372323\pi$
$72$	20.9683	2.47114
$73$	6.04721	0.707773	0.353886	−	0.935288i	$-0.384860\pi$
$73$	6.04721	0.707773	0.353886	+	0.935288i	$0.384860\pi$
$74$	17.8659	2.07687
$75$	−2.84301	−0.328283
$76$	33.8734	3.88555
$77$	−0.109493	−0.0124779
$78$	11.8643	1.34337
$79$	15.8241	1.78035	0.890174	−	0.455621i	$-0.150583\pi$
$79$	15.8241	1.78035	0.890174	+	0.455621i	$0.150583\pi$
$80$	−19.4360	−2.17301
$81$	2.70617	0.300686
$82$	14.1227	1.55959
$83$	−3.45040	−0.378730	−0.189365	−	0.981907i	$-0.560643\pi$
$83$	−3.45040	−0.378730	−0.189365	+	0.981907i	$0.560643\pi$
$84$	−0.374439	−0.0408546
$85$	−9.81527	−1.06462
$86$	−16.2549	−1.75282
$87$	4.14589	0.444486
$88$	−13.0386	−1.38992
$89$	5.45884	0.578636	0.289318	−	0.957233i	$-0.406572\pi$
$89$	5.45884	0.578636	0.289318	+	0.957233i	$0.406572\pi$
$90$	−8.06171	−0.849778
$91$	0.391904	0.0410827
$92$	−24.2813	−2.53150
$93$	6.28791	0.652025
$94$	3.12105	0.321911
$95$	−8.23414	−0.844805
$96$	−18.6547	−1.90393
$97$	7.93275	0.805449	0.402724	−	0.915321i	$-0.368063\pi$
$97$	7.93275	0.805449	0.402724	+	0.915321i	$0.368063\pi$
$98$	19.0748	1.92684
$99$	−3.10836	−0.312402
$100$	−17.6874	−1.76874
$101$	−13.2821	−1.32162	−0.660811	−	0.750552i	$-0.729788\pi$
$101$	−13.2821	−1.32162	−0.660811	+	0.750552i	$0.729788\pi$
$102$	−17.7013	−1.75269
$103$	18.4556	1.81848	0.909241	−	0.416270i	$-0.136663\pi$
$103$	18.4556	1.81848	0.909241	+	0.416270i	$0.136663\pi$
$104$	46.6684	4.57622
$105$	0.0910208	0.00888272
$106$	31.0101	3.01197
$107$	−10.7262	−1.03694	−0.518469	−	0.855097i	$-0.673498\pi$
$107$	−10.7262	−1.03694	−0.518469	+	0.855097i	$0.673498\pi$
$108$	−24.8930	−2.39533
$109$	−0.442188	−0.0423540	−0.0211770	−	0.999776i	$-0.506741\pi$
$109$	−0.442188	−0.0423540	−0.0211770	+	0.999776i	$0.506741\pi$
$110$	5.01296	0.477967
$111$	−5.72642	−0.543528
$112$	−1.15783	−0.109405
$113$	0.610259	0.0574084	0.0287042	−	0.999588i	$-0.490862\pi$
$113$	0.610259	0.0574084	0.0287042	+	0.999588i	$0.490862\pi$
$114$	−14.8498	−1.39081
$115$	5.90245	0.550406
$116$	25.7930	2.39482
$117$	11.1256	1.02856
$118$	30.6451	2.82111
$119$	−0.584711	−0.0536003
$120$	10.8389	0.989449
$121$	−9.06715	−0.824286
$122$	−30.4809	−2.75961
$123$	−4.52663	−0.408153
$124$	39.1192	3.51301
$125$	10.9098	0.975803
$126$	−0.480248	−0.0427839
$127$	1.57468	0.139730	0.0698651	−	0.997556i	$-0.477743\pi$
$127$	1.57468	0.139730	0.0698651	+	0.997556i	$0.477743\pi$
$128$	−35.8644	−3.17000
$129$	5.21007	0.458722
$130$	−17.9427	−1.57368
$131$	−0.371895	−0.0324927	−0.0162463	−	0.999868i	$-0.505172\pi$
$131$	−0.371895	−0.0324927	−0.0162463	+	0.999868i	$0.505172\pi$
$132$	6.60987	0.575315
$133$	−0.490521	−0.0425335
$134$	27.4406	2.37051
$135$	6.05112	0.520798
$136$	−69.6281	−5.97056
$137$	3.98865	0.340773	0.170387	−	0.985377i	$-0.445498\pi$
$137$	3.98865	0.340773	0.170387	+	0.985377i	$0.445498\pi$
$138$	10.6447	0.906140
$139$	9.60096	0.814343	0.407171	−	0.913352i	$-0.366515\pi$
$139$	9.60096	0.814343	0.407171	+	0.913352i	$0.366515\pi$
$140$	0.566272	0.0478587
$141$	−1.00037	−0.0842460
$142$	−17.9457	−1.50597
$143$	−6.91817	−0.578527
$144$	−32.8693	−2.73911
$145$	−6.26991	−0.520688
$146$	−16.4931	−1.36498
$147$	−6.11389	−0.504265
$148$	−35.6260	−2.92844
$149$	−2.71332	−0.222284	−0.111142	−	0.993805i	$-0.535451\pi$
$149$	−2.71332	−0.222284	−0.111142	+	0.993805i	$0.535451\pi$
$150$	7.75399	0.633111
$151$	4.86235	0.395693	0.197846	−	0.980233i	$-0.436605\pi$
$151$	4.86235	0.395693	0.197846	+	0.980233i	$0.436605\pi$
$152$	−58.4118	−4.73783
$153$	−16.5991	−1.34196
$154$	0.298630	0.0240643
$155$	−9.50933	−0.763808
$156$	−23.6584	−1.89419
$157$	2.74002	0.218677	0.109339	−	0.994005i	$-0.465127\pi$
$157$	2.74002	0.218677	0.109339	+	0.994005i	$0.465127\pi$
$158$	−43.1583	−3.43349
$159$	−9.93944	−0.788249
$160$	28.2118	2.23034
$161$	0.351618	0.0277114
$162$	−7.38077	−0.579888
$163$	−20.4740	−1.60365	−0.801824	−	0.597561i	$-0.796137\pi$
$163$	−20.4740	−1.60365	−0.801824	+	0.597561i	$0.796137\pi$
$164$	−28.1617	−2.19906
$165$	−1.60676	−0.125086
$166$	9.41055	0.730401
$167$	24.4577	1.89260	0.946299	−	0.323294i	$-0.104790\pi$
$167$	24.4577	1.89260	0.946299	+	0.323294i	$0.104790\pi$
$168$	0.645688	0.0498159
$169$	11.7619	0.904765
$170$	26.7700	2.05317
$171$	−13.9252	−1.06489
$172$	32.4137	2.47152
$173$	−18.5693	−1.41180	−0.705900	−	0.708312i	$-0.749457\pi$
$173$	−18.5693	−1.41180	−0.705900	+	0.708312i	$0.749457\pi$
$174$	−11.3074	−0.857214
$175$	0.256131	0.0193617
$176$	20.4389	1.54064
$177$	−9.82245	−0.738301
$178$	−14.8883	−1.11593
$179$	1.79334	0.134041	0.0670204	−	0.997752i	$-0.478651\pi$
$179$	1.79334	0.134041	0.0670204	+	0.997752i	$0.478651\pi$
$180$	16.0757	1.19821
$181$	−18.8118	−1.39827	−0.699134	−	0.714991i	$-0.746431\pi$
$181$	−18.8118	−1.39827	−0.699134	+	0.714991i	$0.746431\pi$
$182$	−1.06887	−0.0792301
$183$	9.76981	0.722205
$184$	41.8711	3.08678
$185$	8.66018	0.636709
$186$	−17.1495	−1.25746
$187$	10.3217	0.754800
$188$	−6.22362	−0.453904
$189$	0.360475	0.0262207
$190$	22.4577	1.62925
$191$	6.42106	0.464611	0.232306	−	0.972643i	$-0.425373\pi$
$191$	6.42106	0.464611	0.232306	+	0.972643i	$0.425373\pi$
$192$	25.1749	1.81684
$193$	7.01836	0.505193	0.252596	−	0.967572i	$-0.418716\pi$
$193$	7.01836	0.505193	0.252596	+	0.967572i	$0.418716\pi$
$194$	−21.6357	−1.55335
$195$	5.75103	0.411840
$196$	−38.0366	−2.71690
$197$	−27.6067	−1.96690	−0.983449	−	0.181187i	$-0.942006\pi$
$197$	−27.6067	−1.96690	−0.983449	+	0.181187i	$0.942006\pi$
$198$	8.47769	0.602483
$199$	−2.94576	−0.208819	−0.104410	−	0.994534i	$-0.533295\pi$
$199$	−2.94576	−0.208819	−0.104410	+	0.994534i	$0.533295\pi$
$200$	30.5004	2.15670
$201$	−8.79534	−0.620375
$202$	36.2255	2.54882
$203$	−0.373508	−0.0262152
$204$	35.2978	2.47134
$205$	6.84572	0.478126
$206$	−50.3355	−3.50704
$207$	9.98196	0.693794
$208$	−73.1561	−5.07246
$209$	8.65902	0.598957
$210$	−0.248249	−0.0171308
$211$	11.0219	0.758776	0.379388	−	0.925238i	$-0.376135\pi$
$211$	11.0219	0.758776	0.379388	+	0.925238i	$0.376135\pi$
$212$	−61.8367	−4.24696
$213$	5.75199	0.394120
$214$	29.2544	1.99979
$215$	−7.87930	−0.537364
$216$	42.9258	2.92073
$217$	−0.566485	−0.0384555
$218$	1.20602	0.0816818
$219$	5.28640	0.357222
$220$	−9.99624	−0.673946
$221$	−36.9442	−2.48513
$222$	15.6181	1.04822
$223$	21.7996	1.45981	0.729904	−	0.683550i	$-0.239565\pi$
$223$	21.7996	1.45981	0.729904	+	0.683550i	$0.239565\pi$
$224$	1.68062	0.112291
$225$	7.27121	0.484747
$226$	−1.66441	−0.110715
$227$	−7.97627	−0.529404	−0.264702	−	0.964330i	$-0.585274\pi$
$227$	−7.97627	−0.529404	−0.264702	+	0.964330i	$0.585274\pi$
$228$	29.6117	1.96108
$229$	−16.9878	−1.12258	−0.561292	−	0.827618i	$-0.689696\pi$
$229$	−16.9878	−1.12258	−0.561292	+	0.827618i	$0.689696\pi$
$230$	−16.0982	−1.06149
$231$	−0.0957174	−0.00629775
$232$	−44.4779	−2.92012
$233$	−9.88128	−0.647344	−0.323672	−	0.946169i	$-0.604917\pi$
$233$	−9.88128	−0.647344	−0.323672	+	0.946169i	$0.604917\pi$
$234$	−30.3439	−1.98364
$235$	1.51287	0.0986890
$236$	−61.1089	−3.97785
$237$	13.8332	0.898564
$238$	1.59473	0.103371
$239$	5.57490	0.360611	0.180305	−	0.983611i	$-0.442291\pi$
$239$	5.57490	0.360611	0.180305	+	0.983611i	$0.442291\pi$
$240$	−16.9907	−1.09674
$241$	−13.0291	−0.839281	−0.419640	−	0.907690i	$-0.637844\pi$
$241$	−13.0291	−0.839281	−0.419640	+	0.907690i	$0.637844\pi$
$242$	24.7296	1.58968
$243$	16.0969	1.03262
$244$	60.7813	3.89113
$245$	9.24616	0.590716
$246$	12.3459	0.787143
$247$	−30.9929	−1.97203
$248$	−67.4578	−4.28358
$249$	−3.01629	−0.191150
$250$	−29.7552	−1.88189
$251$	−21.0473	−1.32850	−0.664248	−	0.747512i	$-0.731248\pi$
$251$	−21.0473	−1.32850	−0.664248	+	0.747512i	$0.731248\pi$
$252$	0.957654	0.0603265
$253$	−6.20701	−0.390232
$254$	−4.29476	−0.269477
$255$	−8.58039	−0.537325
$256$	40.2200	2.51375
$257$	−30.1348	−1.87976	−0.939879	−	0.341509i	$-0.889062\pi$
$257$	−30.1348	−1.87976	−0.939879	+	0.341509i	$0.889062\pi$
$258$	−14.2099	−0.884668
$259$	0.515900	0.0320565
$260$	35.7791	2.21893
$261$	−10.6034	−0.656334
$262$	1.01430	0.0626638
$263$	28.1446	1.73547	0.867736	−	0.497025i	$-0.165574\pi$
$263$	28.1446	1.73547	0.867736	+	0.497025i	$0.165574\pi$
$264$	−11.3982	−0.701508
$265$	15.0316	0.923385
$266$	1.33784	0.0820281
$267$	4.77205	0.292045
$268$	−54.7188	−3.34248
$269$	23.4280	1.42843	0.714217	−	0.699925i	$-0.246783\pi$
$269$	23.4280	1.42843	0.714217	+	0.699925i	$0.246783\pi$
$270$	−16.5037	−1.00439
$271$	−15.6810	−0.952551	−0.476276	−	0.879296i	$-0.658014\pi$
$271$	−15.6810	−0.952551	−0.476276	+	0.879296i	$0.658014\pi$
$272$	109.147	6.61801
$273$	0.342598	0.0207349
$274$	−10.8786	−0.657199
$275$	−4.52141	−0.272651
$276$	−21.2264	−1.27768
$277$	4.97360	0.298835	0.149417	−	0.988774i	$-0.452260\pi$
$277$	4.97360	0.298835	0.149417	+	0.988774i	$0.452260\pi$
$278$	−26.1855	−1.57050
$279$	−16.0818	−0.962790
$280$	−0.976488	−0.0583563
$281$	−13.2993	−0.793370	−0.396685	−	0.917955i	$-0.629839\pi$
$281$	−13.2993	−0.793370	−0.396685	+	0.917955i	$0.629839\pi$
$282$	2.72838	0.162473
$283$	−21.4946	−1.27772	−0.638859	−	0.769324i	$-0.720593\pi$
$283$	−21.4946	−1.27772	−0.638859	+	0.769324i	$0.720593\pi$
$284$	35.7851	2.12345
$285$	−7.19818	−0.426384
$286$	18.8685	1.11572
$287$	0.407810	0.0240723
$288$	47.7106	2.81137
$289$	38.1198	2.24234
$290$	17.1005	1.00417
$291$	6.93471	0.406520
$292$	32.8885	1.92465
$293$	−15.5092	−0.906054	−0.453027	−	0.891497i	$-0.649656\pi$
$293$	−15.5092	−0.906054	−0.453027	+	0.891497i	$0.649656\pi$
$294$	16.6749	0.972502
$295$	14.8547	0.864874
$296$	61.4341	3.57078
$297$	−6.36336	−0.369240
$298$	7.40025	0.428685
$299$	22.2165	1.28481
$300$	−15.4621	−0.892704
$301$	−0.469382	−0.0270547
$302$	−13.2615	−0.763114
$303$	−11.6111	−0.667039
$304$	91.5647	5.25159
$305$	−14.7751	−0.846018
$306$	45.2723	2.58804
$307$	−14.4830	−0.826586	−0.413293	−	0.910598i	$-0.635621\pi$
$307$	−14.4830	−0.826586	−0.413293	+	0.910598i	$0.635621\pi$
$308$	−0.595491	−0.0339313
$309$	16.1336	0.917811
$310$	25.9356	1.47304
$311$	−22.1023	−1.25330	−0.626652	−	0.779299i	$-0.715575\pi$
$311$	−22.1023	−1.25330	−0.626652	+	0.779299i	$0.715575\pi$
$312$	40.7970	2.30967
$313$	15.4829	0.875146	0.437573	−	0.899183i	$-0.355838\pi$
$313$	15.4829	0.875146	0.437573	+	0.899183i	$0.355838\pi$
$314$	−7.47309	−0.421731
$315$	−0.232792	−0.0131163
$316$	86.0612	4.84132
$317$	−23.9369	−1.34443	−0.672215	−	0.740356i	$-0.734657\pi$
$317$	−23.9369	−1.34443	−0.672215	+	0.740356i	$0.734657\pi$
$318$	27.1087	1.52018
$319$	6.59344	0.369162
$320$	−38.0725	−2.12832
$321$	−9.37668	−0.523355
$322$	−0.958997	−0.0534428
$323$	46.2406	2.57290
$324$	14.7178	0.817658
$325$	16.1833	0.897687
$326$	55.8405	3.09272
$327$	−0.386556	−0.0213766
$328$	48.5625	2.68142
$329$	0.0901242	0.00496871
$330$	4.38226	0.241236
$331$	12.6975	0.697918	0.348959	−	0.937138i	$-0.386535\pi$
$331$	12.6975	0.697918	0.348959	+	0.937138i	$0.386535\pi$
$332$	−18.7654	−1.02989
$333$	14.6457	0.802581
$334$	−66.7057	−3.64997
$335$	13.3014	0.726731
$336$	−1.01216	−0.0552180
$337$	−15.9606	−0.869427	−0.434714	−	0.900569i	$-0.643150\pi$
$337$	−15.9606	−0.869427	−0.434714	+	0.900569i	$0.643150\pi$
$338$	−32.0793	−1.74489
$339$	0.533481	0.0289747
$340$	−53.3815	−2.89502
$341$	10.0000	0.541531
$342$	37.9794	2.05369
$343$	1.10210	0.0595081
$344$	−55.8947	−3.01364
$345$	5.15985	0.277797
$346$	50.6457	2.72273
$347$	−13.5010	−0.724772	−0.362386	−	0.932028i	$-0.618038\pi$
$347$	−13.5010	−0.724772	−0.362386	+	0.932028i	$0.618038\pi$
$348$	22.5479	1.20870
$349$	−33.5715	−1.79704	−0.898520	−	0.438932i	$-0.855357\pi$
$349$	−33.5715	−1.79704	−0.898520	+	0.438932i	$0.855357\pi$
$350$	−0.698567	−0.0373400
$351$	22.7761	1.21570
$352$	−29.6675	−1.58129
$353$	−29.5585	−1.57324	−0.786621	−	0.617436i	$-0.788171\pi$
$353$	−29.5585	−1.57324	−0.786621	+	0.617436i	$0.788171\pi$
$354$	26.7896	1.42385
$355$	−8.69885	−0.461687
$356$	29.6886	1.57349
$357$	−0.511147	−0.0270528
$358$	−4.89114	−0.258505
$359$	−22.6550	−1.19569	−0.597844	−	0.801613i	$-0.703976\pi$
$359$	−22.6550	−1.19569	−0.597844	+	0.801613i	$0.703976\pi$
$360$	−27.7212	−1.46103
$361$	19.7918	1.04167
$362$	51.3069	2.69663
$363$	−7.92639	−0.416028
$364$	2.13142	0.111717
$365$	−7.99473	−0.418463
$366$	−26.6460	−1.39281
$367$	−9.85657	−0.514509	−0.257254	−	0.966344i	$-0.582818\pi$
$367$	−9.85657	−0.514509	−0.257254	+	0.966344i	$0.582818\pi$
$368$	−65.6360	−3.42151
$369$	11.5772	0.602684
$370$	−23.6196	−1.22793
$371$	0.895456	0.0464898
$372$	34.1976	1.77306
$373$	27.3126	1.41420	0.707098	−	0.707116i	$-0.250004\pi$
$373$	27.3126	1.41420	0.707098	+	0.707116i	$0.250004\pi$
$374$	−28.1513	−1.45567
$375$	9.53722	0.492500
$376$	10.7321	0.553466
$377$	−23.5996	−1.21544
$378$	−0.983153	−0.0505679
$379$	32.0341	1.64548	0.822740	−	0.568419i	$-0.192445\pi$
$379$	32.0341	1.64548	0.822740	+	0.568419i	$0.192445\pi$
$380$	−44.7824	−2.29729
$381$	1.37657	0.0705236
$382$	−17.5127	−0.896027
$383$	8.63436	0.441195	0.220598	−	0.975365i	$-0.429199\pi$
$383$	8.63436	0.441195	0.220598	+	0.975365i	$0.429199\pi$
$384$	−31.3522	−1.59994
$385$	0.144755	0.00737742
$386$	−19.1418	−0.974290
$387$	−13.3251	−0.677354
$388$	43.1432	2.19027
$389$	7.78585	0.394758	0.197379	−	0.980327i	$-0.436757\pi$
$389$	7.78585	0.394758	0.197379	+	0.980327i	$0.436757\pi$
$390$	−15.6853	−0.794254
$391$	−33.1465	−1.67629
$392$	65.5910	3.31284
$393$	−0.325106	−0.0163994
$394$	75.2941	3.79326
$395$	−20.9203	−1.05261
$396$	−16.9052	−0.849518
$397$	1.97331	0.0990374	0.0495187	−	0.998773i	$-0.484231\pi$
$397$	1.97331	0.0990374	0.0495187	+	0.998773i	$0.484231\pi$
$398$	8.03422	0.402719
$399$	−0.428807	−0.0214672
$400$	−47.8115	−2.39058
$401$	−13.6532	−0.681806	−0.340903	−	0.940098i	$-0.610733\pi$
$401$	−13.6532	−0.681806	−0.340903	+	0.940098i	$0.610733\pi$
$402$	23.9883	1.19643
$403$	−35.7926	−1.78296
$404$	−72.2366	−3.59390
$405$	−3.57770	−0.177777
$406$	1.01870	0.0505573
$407$	−9.10705	−0.451420
$408$	−60.8680	−3.01342
$409$	−25.5952	−1.26560	−0.632799	−	0.774316i	$-0.718094\pi$
$409$	−25.5952	−1.26560	−0.632799	+	0.774316i	$0.718094\pi$
$410$	−18.6709	−0.922090
$411$	3.48683	0.171992
$412$	100.373	4.94502
$413$	0.884917	0.0435439
$414$	−27.2246	−1.33802
$415$	4.56160	0.223920
$416$	106.188	5.20629
$417$	8.39304	0.411009
$418$	−23.6165	−1.15512
$419$	26.9072	1.31450	0.657252	−	0.753671i	$-0.271719\pi$
$419$	26.9072	1.31450	0.657252	+	0.753671i	$0.271719\pi$
$420$	0.495028	0.0241549
$421$	−1.76142	−0.0858463	−0.0429231	−	0.999078i	$-0.513667\pi$
$421$	−1.76142	−0.0858463	−0.0429231	+	0.999078i	$0.513667\pi$
$422$	−30.0609	−1.46334
$423$	2.55850	0.124399
$424$	106.632	5.17851
$425$	−24.1451	−1.17121
$426$	−15.6879	−0.760080
$427$	−0.880174	−0.0425946
$428$	−58.3356	−2.81976
$429$	−6.04778	−0.291990
$430$	21.4899	1.03633
$431$	36.3788	1.75231	0.876153	−	0.482034i	$-0.160102\pi$
$431$	36.3788	1.75231	0.876153	+	0.482034i	$0.160102\pi$
$432$	−67.2892	−3.23745
$433$	12.9978	0.624635	0.312317	−	0.949978i	$-0.398895\pi$
$433$	12.9978	0.624635	0.312317	+	0.949978i	$0.398895\pi$
$434$	1.54502	0.0741635
$435$	−5.48108	−0.262798
$436$	−2.40490	−0.115174
$437$	−27.8070	−1.33019
$438$	−14.4180	−0.688920
$439$	−33.8048	−1.61342	−0.806708	−	0.590950i	$-0.798753\pi$
$439$	−33.8048	−1.61342	−0.806708	+	0.590950i	$0.798753\pi$
$440$	17.2377	0.821774
$441$	15.6367	0.744605
$442$	100.761	4.79271
$443$	10.0520	0.477583	0.238792	−	0.971071i	$-0.423249\pi$
$443$	10.0520	0.477583	0.238792	+	0.971071i	$0.423249\pi$
$444$	−31.1438	−1.47802
$445$	−7.21687	−0.342112
$446$	−59.4558	−2.81531
$447$	−2.37195	−0.112189
$448$	−2.26804	−0.107155
$449$	8.09363	0.381962	0.190981	−	0.981594i	$-0.438833\pi$
$449$	8.09363	0.381962	0.190981	+	0.981594i	$0.438833\pi$
$450$	−19.8314	−0.934860
$451$	−7.19896	−0.338986
$452$	3.31897	0.156111
$453$	4.25061	0.199711
$454$	21.7543	1.02098
$455$	−0.518117	−0.0242897
$456$	−51.0629	−2.39124
$457$	10.1697	0.475718	0.237859	−	0.971300i	$-0.423554\pi$
$457$	10.1697	0.475718	0.237859	+	0.971300i	$0.423554\pi$
$458$	46.3322	2.16496
$459$	−33.9814	−1.58612
$460$	32.1012	1.49673
$461$	−12.6417	−0.588783	−0.294392	−	0.955685i	$-0.595117\pi$
$461$	−12.6417	−0.588783	−0.294392	+	0.955685i	$0.595117\pi$
$462$	0.261058	0.0121455
$463$	−20.8613	−0.969505	−0.484752	−	0.874651i	$-0.661090\pi$
$463$	−20.8613	−0.969505	−0.484752	+	0.874651i	$0.661090\pi$
$464$	69.7222	3.23677
$465$	−8.31294	−0.385503
$466$	26.9500	1.24844
$467$	6.01811	0.278485	0.139242	−	0.990258i	$-0.455533\pi$
$467$	6.01811	0.278485	0.139242	+	0.990258i	$0.455533\pi$
$468$	60.5081	2.79699
$469$	0.792383	0.0365888
$470$	−4.12619	−0.190327
$471$	2.39529	0.110369
$472$	105.377	4.85037
$473$	8.28588	0.380985
$474$	−37.7285	−1.73293
$475$	−20.2556	−0.929389
$476$	−3.18002	−0.145756
$477$	25.4208	1.16394
$478$	−15.2049	−0.695456
$479$	−1.06750	−0.0487753	−0.0243877	−	0.999703i	$-0.507764\pi$
$479$	−1.06750	−0.0487753	−0.0243877	+	0.999703i	$0.507764\pi$
$480$	24.6624	1.12568
$481$	32.5965	1.48627
$482$	35.5355	1.61860
$483$	0.307380	0.0139863
$484$	−49.3128	−2.24149
$485$	−10.4875	−0.476213
$486$	−43.9024	−1.99146
$487$	−23.5655	−1.06785	−0.533926	−	0.845531i	$-0.679284\pi$
$487$	−23.5655	−1.06785	−0.533926	+	0.845531i	$0.679284\pi$
$488$	−104.812	−4.74463
$489$	−17.8981	−0.809381
$490$	−25.2178	−1.13923
$491$	−32.7095	−1.47616	−0.738079	−	0.674715i	$-0.764267\pi$
$491$	−32.7095	−1.47616	−0.738079	+	0.674715i	$0.764267\pi$
$492$	−24.6186	−1.10989
$493$	35.2101	1.58578
$494$	84.5295	3.80316
$495$	4.10941	0.184704
$496$	105.745	4.74809
$497$	−0.518204	−0.0232446
$498$	8.22659	0.368642
$499$	−27.4578	−1.22918	−0.614589	−	0.788848i	$-0.710678\pi$
$499$	−27.4578	−1.22918	−0.614589	+	0.788848i	$0.710678\pi$
$500$	59.3343	2.65351
$501$	21.3807	0.955217
$502$	57.4042	2.56207
$503$	34.3216	1.53032	0.765162	−	0.643838i	$-0.222659\pi$
$503$	34.3216	1.53032	0.765162	+	0.643838i	$0.222659\pi$
$504$	−1.65139	−0.0735589
$505$	17.5597	0.781395
$506$	16.9289	0.752582
$507$	10.2821	0.456646
$508$	8.56409	0.379970
$509$	−20.0779	−0.889936	−0.444968	−	0.895546i	$-0.646785\pi$
$509$	−20.0779	−0.889936	−0.444968	+	0.895546i	$0.646785\pi$
$510$	23.4020	1.03626
$511$	−0.476258	−0.0210684
$512$	−37.9666	−1.67790
$513$	−28.5074	−1.25863
$514$	82.1892	3.62521
$515$	−24.3992	−1.07516
$516$	28.3356	1.24741
$517$	−1.59094	−0.0699694
$518$	−1.40706	−0.0618226
$519$	−16.2331	−0.712553
$520$	−61.6981	−2.70564
$521$	−32.9118	−1.44189	−0.720946	−	0.692991i	$-0.756293\pi$
$521$	−32.9118	−1.44189	−0.720946	+	0.692991i	$0.756293\pi$
$522$	28.9196	1.26577
$523$	4.86644	0.212795	0.106397	−	0.994324i	$-0.466068\pi$
$523$	4.86644	0.212795	0.106397	+	0.994324i	$0.466068\pi$
$524$	−2.02260	−0.0883577
$525$	0.223906	0.00977207
$526$	−76.7612	−3.34695
$527$	53.4017	2.32621
$528$	17.8674	0.777580
$529$	−3.06725	−0.133358
$530$	−40.9970	−1.78079
$531$	25.1216	1.09019
$532$	−2.66776	−0.115662
$533$	25.7669	1.11609
$534$	−13.0152	−0.563223
$535$	14.1805	0.613078
$536$	94.3580	4.07565
$537$	1.56772	0.0676521
$538$	−63.8973	−2.75481
$539$	−9.72327	−0.418811
$540$	32.9098	1.41621
$541$	−31.3170	−1.34642	−0.673211	−	0.739451i	$-0.735085\pi$
$541$	−31.3170	−1.34642	−0.673211	+	0.739451i	$0.735085\pi$
$542$	42.7680	1.83704
$543$	−16.4450	−0.705723
$544$	−158.430	−6.79261
$545$	0.584596	0.0250413
$546$	−0.934395	−0.0399884
$547$	11.8688	0.507473	0.253736	−	0.967273i	$-0.418340\pi$
$547$	11.8688	0.507473	0.253736	+	0.967273i	$0.418340\pi$
$548$	21.6927	0.926668
$549$	−24.9870	−1.06642
$550$	12.3316	0.525822
$551$	29.5381	1.25837
$552$	36.6032	1.55794
$553$	−1.24625	−0.0529960
$554$	−13.5649	−0.576318
$555$	7.57062	0.321355
$556$	52.2160	2.21445
$557$	12.6797	0.537254	0.268627	−	0.963244i	$-0.413430\pi$
$557$	12.6797	0.537254	0.268627	+	0.963244i	$0.413430\pi$
$558$	43.8611	1.85679
$559$	−29.6573	−1.25437
$560$	1.53071	0.0646844
$561$	9.02313	0.380957
$562$	36.2723	1.53006
$563$	−14.1264	−0.595356	−0.297678	−	0.954666i	$-0.596212\pi$
$563$	−14.1264	−0.595356	−0.297678	+	0.954666i	$0.596212\pi$
$564$	−5.44061	−0.229091
$565$	−0.806794	−0.0339421
$566$	58.6239	2.46415
$567$	−0.213129	−0.00895058
$568$	−61.7084	−2.58923
$569$	−31.2465	−1.30992	−0.654961	−	0.755663i	$-0.727315\pi$
$569$	−31.2465	−1.30992	−0.654961	+	0.755663i	$0.727315\pi$
$570$	19.6322	0.822303
$571$	−9.65942	−0.404234	−0.202117	−	0.979361i	$-0.564782\pi$
$571$	−9.65942	−0.404234	−0.202117	+	0.979361i	$0.564782\pi$
$572$	−37.6253	−1.57319
$573$	5.61321	0.234495
$574$	−1.11225	−0.0464246
$575$	14.5197	0.605514
$576$	−64.3865	−2.68277
$577$	−25.4771	−1.06062	−0.530312	−	0.847803i	$-0.677925\pi$
$577$	−25.4771	−1.06062	−0.530312	+	0.847803i	$0.677925\pi$
$578$	−103.967	−4.32447
$579$	6.13537	0.254977
$580$	−34.0997	−1.41591
$581$	0.271742	0.0112737
$582$	−18.9136	−0.783995
$583$	−15.8072	−0.654669
$584$	−56.7135	−2.34682
$585$	−14.7087	−0.608128
$586$	42.2994	1.74737
$587$	−6.39694	−0.264030	−0.132015	−	0.991248i	$-0.542145\pi$
$587$	−6.39694	−0.264030	−0.132015	+	0.991248i	$0.542145\pi$
$588$	−33.2512	−1.37125
$589$	44.7993	1.84592
$590$	−40.5145	−1.66795
$591$	−24.1335	−0.992718
$592$	−96.3023	−3.95800
$593$	0.332997	0.0136746	0.00683728	−	0.999977i	$-0.497824\pi$
$593$	0.332997	0.0136746	0.00683728	+	0.999977i	$0.497824\pi$
$594$	17.3553	0.712098
$595$	0.773018	0.0316906
$596$	−14.7567	−0.604458
$597$	−2.57515	−0.105394
$598$	−60.5930	−2.47783
$599$	−4.11481	−0.168127	−0.0840634	−	0.996460i	$-0.526790\pi$
$599$	−4.11481	−0.168127	−0.0840634	+	0.996460i	$0.526790\pi$
$600$	26.6631	1.08852
$601$	−35.1426	−1.43350	−0.716749	−	0.697332i	$-0.754370\pi$
$601$	−35.1426	−1.43350	−0.716749	+	0.697332i	$0.754370\pi$
$602$	1.28019	0.0521765
$603$	22.4947	0.916054
$604$	26.4445	1.07601
$605$	11.9872	0.487351
$606$	31.6679	1.28642
$607$	18.1566	0.736953	0.368477	−	0.929637i	$-0.379879\pi$
$607$	18.1566	0.736953	0.368477	+	0.929637i	$0.379879\pi$
$608$	−132.908	−5.39015
$609$	−0.326517	−0.0132311
$610$	40.2973	1.63159
$611$	5.69438	0.230370
$612$	−90.2765	−3.64921
$613$	−31.3030	−1.26431	−0.632157	−	0.774840i	$-0.717830\pi$
$613$	−31.3030	−1.26431	−0.632157	+	0.774840i	$0.717830\pi$
$614$	39.5006	1.59411
$615$	5.98444	0.241316
$616$	1.02687	0.0413740
$617$	−45.9066	−1.84813	−0.924065	−	0.382235i	$-0.875154\pi$
$617$	−45.9066	−1.84813	−0.924065	+	0.382235i	$0.875154\pi$
$618$	−44.0026	−1.77005
$619$	−27.2511	−1.09531	−0.547656	−	0.836703i	$-0.684480\pi$
$619$	−27.2511	−1.09531	−0.547656	+	0.836703i	$0.684480\pi$
$620$	−51.7177	−2.07703
$621$	20.4348	0.820021
$622$	60.2813	2.41706
$623$	−0.429920	−0.0172244
$624$	−63.9521	−2.56013
$625$	1.83757	0.0735026
$626$	−42.2278	−1.68776
$627$	7.56961	0.302301
$628$	14.9019	0.594652
$629$	−48.6331	−1.93913
$630$	0.634913	0.0252955
$631$	5.84546	0.232704	0.116352	−	0.993208i	$-0.462880\pi$
$631$	5.84546	0.232704	0.116352	+	0.993208i	$0.462880\pi$
$632$	−148.405	−5.90325
$633$	9.63518	0.382964
$634$	65.2851	2.59280
$635$	−2.08181	−0.0826141
$636$	−54.0569	−2.14349
$637$	34.8021	1.37891
$638$	−17.9829	−0.711948
$639$	−14.7111	−0.581962
$640$	47.4146	1.87423
$641$	−18.0692	−0.713691	−0.356846	−	0.934163i	$-0.616148\pi$
$641$	−18.0692	−0.713691	−0.356846	+	0.934163i	$0.616148\pi$
$642$	25.5738	1.00932
$643$	−42.8346	−1.68923	−0.844616	−	0.535372i	$-0.820171\pi$
$643$	−42.8346	−1.68923	−0.844616	+	0.535372i	$0.820171\pi$
$644$	1.91232	0.0753559
$645$	−6.88799	−0.271214
$646$	−126.116	−4.96196
$647$	−26.4066	−1.03815	−0.519075	−	0.854729i	$-0.673723\pi$
$647$	−26.4066	−1.03815	−0.519075	+	0.854729i	$0.673723\pi$
$648$	−25.3797	−0.997008
$649$	−15.6212	−0.613186
$650$	−44.1380	−1.73124
$651$	−0.495214	−0.0194090
$652$	−111.350	−4.36082
$653$	17.8946	0.700269	0.350134	−	0.936699i	$-0.386136\pi$
$653$	17.8946	0.700269	0.350134	+	0.936699i	$0.386136\pi$
$654$	1.05429	0.0412258
$655$	0.491665	0.0192109
$656$	−76.1252	−2.97219
$657$	−13.5203	−0.527478
$658$	−0.245803	−0.00958241
$659$	16.7641	0.653039	0.326519	−	0.945191i	$-0.394124\pi$
$659$	16.7641	0.653039	0.326519	+	0.945191i	$0.394124\pi$
$660$	−8.73859	−0.340149
$661$	5.26505	0.204787	0.102393	−	0.994744i	$-0.467350\pi$
$661$	5.26505	0.204787	0.102393	+	0.994744i	$0.467350\pi$
$662$	−34.6310	−1.34597
$663$	−32.2961	−1.25428
$664$	32.3594	1.25579
$665$	0.648494	0.0251475
$666$	−39.9445	−1.54782
$667$	−21.1737	−0.819849
$668$	133.016	5.14656
$669$	19.0569	0.736783
$670$	−36.2779	−1.40154
$671$	15.5375	0.599817
$672$	1.46918	0.0566748
$673$	7.19534	0.277360	0.138680	−	0.990337i	$-0.455714\pi$
$673$	7.19534	0.277360	0.138680	+	0.990337i	$0.455714\pi$
$674$	43.5306	1.67673
$675$	14.8854	0.572941
$676$	63.9688	2.46034
$677$	−9.45960	−0.363562	−0.181781	−	0.983339i	$-0.558186\pi$
$677$	−9.45960	−0.363562	−0.181781	+	0.983339i	$0.558186\pi$
$678$	−1.45501	−0.0558792
$679$	−0.624757	−0.0239760
$680$	92.0520	3.53003
$681$	−6.97276	−0.267197
$682$	−27.2739	−1.04437
$683$	3.88579	0.148686	0.0743428	−	0.997233i	$-0.476314\pi$
$683$	3.88579	0.148686	0.0743428	+	0.997233i	$0.476314\pi$
$684$	−75.7340	−2.89576
$685$	−5.27320	−0.201479
$686$	−3.00586	−0.114764
$687$	−14.8505	−0.566582
$688$	87.6188	3.34044
$689$	56.5782	2.15546
$690$	−14.0729	−0.535745
$691$	−15.9393	−0.606360	−0.303180	−	0.952933i	$-0.598048\pi$
$691$	−15.9393	−0.606360	−0.303180	+	0.952933i	$0.598048\pi$
$692$	−100.992	−3.83912
$693$	0.244804	0.00929934
$694$	36.8224	1.39776
$695$	−12.6930	−0.481472
$696$	−38.8820	−1.47382
$697$	−38.4436	−1.45616
$698$	91.5624	3.46569
$699$	−8.63809	−0.326723
$700$	1.39300	0.0526504
$701$	23.0955	0.872303	0.436152	−	0.899873i	$-0.356341\pi$
$701$	23.0955	0.872303	0.436152	+	0.899873i	$0.356341\pi$
$702$	−62.1192	−2.34454
$703$	−40.7989	−1.53876
$704$	40.0370	1.50895
$705$	1.32254	0.0498096
$706$	80.6175	3.03408
$707$	1.04606	0.0393410
$708$	−53.4206	−2.00767
$709$	14.8675	0.558360	0.279180	−	0.960239i	$-0.409937\pi$
$709$	14.8675	0.558360	0.279180	+	0.960239i	$0.409937\pi$
$710$	23.7251	0.890387
$711$	−35.3794	−1.32683
$712$	−51.1954	−1.91863
$713$	−32.1133	−1.20265
$714$	1.39409	0.0521726
$715$	9.14618	0.342048
$716$	9.75333	0.364499
$717$	4.87351	0.182005
$718$	61.7890	2.30595
$719$	26.9781	1.00611	0.503056	−	0.864254i	$-0.332209\pi$
$719$	26.9781	1.00611	0.503056	+	0.864254i	$0.332209\pi$
$720$	43.4549	1.61947
$721$	−1.45350	−0.0541312
$722$	−53.9798	−2.00892
$723$	−11.3899	−0.423596
$724$	−102.310	−3.80232
$725$	−15.4237	−0.572821
$726$	21.6183	0.802331
$727$	49.0409	1.81883	0.909414	−	0.415892i	$-0.136531\pi$
$727$	49.0409	1.81883	0.909414	+	0.415892i	$0.136531\pi$
$728$	−3.67545	−0.136221
$729$	5.95320	0.220489
$730$	21.8047	0.807028
$731$	44.2479	1.63657
$732$	53.1343	1.96390
$733$	−18.2358	−0.673554	−0.336777	−	0.941584i	$-0.609337\pi$
$733$	−18.2358	−0.673554	−0.336777	+	0.941584i	$0.609337\pi$
$734$	26.8826	0.992256
$735$	8.08288	0.298142
$736$	95.2722	3.51178
$737$	−13.9877	−0.515244
$738$	−31.5754	−1.16231
$739$	−33.8005	−1.24337	−0.621687	−	0.783266i	$-0.713552\pi$
$739$	−33.8005	−1.24337	−0.621687	+	0.783266i	$0.713552\pi$
$740$	47.0995	1.73141
$741$	−27.0936	−0.995309
$742$	−2.44225	−0.0896579
$743$	12.8484	0.471361	0.235680	−	0.971831i	$-0.424268\pi$
$743$	12.8484	0.471361	0.235680	+	0.971831i	$0.424268\pi$
$744$	−58.9708	−2.16197
$745$	3.58714	0.131423
$746$	−74.4921	−2.72735
$747$	7.71438	0.282254
$748$	56.1360	2.05254
$749$	0.844757	0.0308667
$750$	−26.0117	−0.949812
$751$	2.82903	0.103233	0.0516163	−	0.998667i	$-0.483563\pi$
$751$	2.82903	0.103233	0.0516163	+	0.998667i	$0.483563\pi$
$752$	−16.8233	−0.613484
$753$	−18.3993	−0.670509
$754$	64.3653	2.34405
$755$	−6.42828	−0.233949
$756$	1.96049	0.0713022
$757$	−5.94637	−0.216125	−0.108062	−	0.994144i	$-0.534465\pi$
$757$	−5.94637	−0.216125	−0.108062	+	0.994144i	$0.534465\pi$
$758$	−87.3692	−3.17339
$759$	−5.42610	−0.196955
$760$	77.2235	2.80119
$761$	−1.64252	−0.0595413	−0.0297707	−	0.999557i	$-0.509478\pi$
$761$	−1.64252	−0.0595413	−0.0297707	+	0.999557i	$0.509478\pi$
$762$	−3.75442	−0.136008
$763$	0.0348253	0.00126076
$764$	34.9217	1.26342
$765$	21.9449	0.793421
$766$	−23.5492	−0.850868
$767$	55.9123	2.01888
$768$	35.1599	1.26872
$769$	−42.3675	−1.52781	−0.763906	−	0.645328i	$-0.776721\pi$
$769$	−42.3675	−1.52781	−0.763906	+	0.645328i	$0.776721\pi$
$770$	−0.394804	−0.0142277
$771$	−26.3435	−0.948737
$772$	38.1702	1.37378
$773$	42.9838	1.54602	0.773011	−	0.634393i	$-0.218750\pi$
$773$	42.9838	1.54602	0.773011	+	0.634393i	$0.218750\pi$
$774$	36.3427	1.30631
$775$	−23.3925	−0.840282
$776$	−74.3969	−2.67069
$777$	0.450994	0.0161793
$778$	−21.2350	−0.761312
$779$	−32.2508	−1.15550
$780$	31.2777	1.11992
$781$	9.14771	0.327331
$782$	90.4032	3.23281
$783$	−21.7070	−0.775746
$784$	−102.818	−3.67209
$785$	−3.62245	−0.129291
$786$	0.886690	0.0316272
$787$	3.07675	0.109674	0.0548371	−	0.998495i	$-0.482536\pi$
$787$	3.07675	0.109674	0.0548371	+	0.998495i	$0.482536\pi$
$788$	−150.143	−5.34861
$789$	24.6037	0.875915
$790$	57.0576	2.03002
$791$	−0.0480620	−0.00170889
$792$	29.1516	1.03586
$793$	−55.6126	−1.97486
$794$	−5.38196	−0.190999
$795$	13.1404	0.466044
$796$	−16.0209	−0.567845
$797$	−18.4906	−0.654971	−0.327485	−	0.944856i	$-0.606201\pi$
$797$	−18.4906	−0.654971	−0.327485	+	0.944856i	$0.606201\pi$
$798$	1.16952	0.0414006
$799$	−8.49587	−0.300562
$800$	69.3996	2.45365
$801$	−12.2048	−0.431237
$802$	37.2374	1.31490
$803$	8.40726	0.296686
$804$	−47.8345	−1.68699
$805$	−0.464857	−0.0163841
$806$	97.6203	3.43853
$807$	20.4805	0.720948
$808$	124.566	4.38221
$809$	−18.0118	−0.633262	−0.316631	−	0.948549i	$-0.602552\pi$
$809$	−18.0118	−0.633262	−0.316631	+	0.948549i	$0.602552\pi$
$810$	9.75776	0.342853
$811$	48.1174	1.68963	0.844815	−	0.535058i	$-0.179710\pi$
$811$	48.1174	1.68963	0.844815	+	0.535058i	$0.179710\pi$
$812$	−2.03137	−0.0712872
$813$	−13.7081	−0.480765
$814$	24.8384	0.870586
$815$	27.0677	0.948140
$816$	95.4150	3.34019
$817$	37.1201	1.29867
$818$	69.8078	2.44077
$819$	−0.876217	−0.0306175
$820$	37.2313	1.30017
$821$	39.5749	1.38117	0.690587	−	0.723250i	$-0.257352\pi$
$821$	39.5749	1.38117	0.690587	+	0.723250i	$0.257352\pi$
$822$	−9.50991	−0.331696
$823$	6.29975	0.219595	0.109798	−	0.993954i	$-0.464980\pi$
$823$	6.29975	0.219595	0.109798	+	0.993954i	$0.464980\pi$
$824$	−173.085	−6.02969
$825$	−3.95256	−0.137610
$826$	−2.41351	−0.0839767
$827$	16.6752	0.579852	0.289926	−	0.957049i	$-0.406369\pi$
$827$	16.6752	0.579852	0.289926	+	0.957049i	$0.406369\pi$
$828$	54.2881	1.88664
$829$	46.5460	1.61661	0.808305	−	0.588763i	$-0.200385\pi$
$829$	46.5460	1.61661	0.808305	+	0.588763i	$0.200385\pi$
$830$	−12.4412	−0.431842
$831$	4.34786	0.150826
$832$	−143.303	−4.96813
$833$	−51.9238	−1.79905
$834$	−22.8910	−0.792652
$835$	−32.3344	−1.11898
$836$	47.0932	1.62875
$837$	−32.9222	−1.13796
$838$	−73.3864	−2.53509
$839$	−12.6646	−0.437229	−0.218614	−	0.975811i	$-0.570154\pi$
$839$	−12.6646	−0.437229	−0.218614	+	0.975811i	$0.570154\pi$
$840$	−0.853633	−0.0294531
$841$	−6.50809	−0.224417
$842$	4.80406	0.165559
$843$	−11.6261	−0.400424
$844$	59.9438	2.06335
$845$	−15.5499	−0.534933
$846$	−6.97803	−0.239909
$847$	0.714098	0.0245367
$848$	−167.153	−5.74007
$849$	−18.7903	−0.644880
$850$	65.8528	2.25873
$851$	29.2457	1.00253
$852$	31.2829	1.07173
$853$	−26.3221	−0.901250	−0.450625	−	0.892713i	$-0.648799\pi$
$853$	−26.3221	−0.901250	−0.450625	+	0.892713i	$0.648799\pi$
$854$	2.40057	0.0821459
$855$	18.4099	0.629604
$856$	100.595	3.43826
$857$	−34.6808	−1.18467	−0.592336	−	0.805691i	$-0.701794\pi$
$857$	−34.6808	−1.18467	−0.592336	+	0.805691i	$0.701794\pi$
$858$	16.4946	0.563117
$859$	−0.462843	−0.0157920	−0.00789600	−	0.999969i	$-0.502513\pi$
$859$	−0.462843	−0.0157920	−0.00789600	+	0.999969i	$0.502513\pi$
$860$	−42.8526	−1.46126
$861$	0.356502	0.0121496
$862$	−99.2190	−3.37941
$863$	−27.4267	−0.933615	−0.466808	−	0.884359i	$-0.654596\pi$
$863$	−27.4267	−0.933615	−0.466808	+	0.884359i	$0.654596\pi$
$864$	97.6720	3.32287
$865$	24.5496	0.834712
$866$	−35.4500	−1.20464
$867$	33.3238	1.13174
$868$	−3.08090	−0.104573
$869$	21.9997	0.746290
$870$	14.9490	0.506819
$871$	50.0657	1.69641
$872$	4.14704	0.140437
$873$	−17.7360	−0.600273
$874$	75.8403	2.56534
$875$	−0.859220	−0.0290469
$876$	28.7507	0.971397
$877$	−17.3918	−0.587279	−0.293640	−	0.955916i	$-0.594867\pi$
$877$	−17.3918	−0.587279	−0.293640	+	0.955916i	$0.594867\pi$
$878$	92.1987	3.11156
$879$	−13.5579	−0.457297
$880$	−27.0213	−0.910887
$881$	−7.42800	−0.250256	−0.125128	−	0.992141i	$-0.539934\pi$
$881$	−7.42800	−0.250256	−0.125128	+	0.992141i	$0.539934\pi$
$882$	−42.6473	−1.43601
$883$	−19.2315	−0.647193	−0.323596	−	0.946195i	$-0.604892\pi$
$883$	−19.2315	−0.647193	−0.323596	+	0.946195i	$0.604892\pi$
$884$	−200.925	−6.75785
$885$	12.9858	0.436513
$886$	−27.4156	−0.921044
$887$	−9.47318	−0.318078	−0.159039	−	0.987272i	$-0.550840\pi$
$887$	−9.47318	−0.318078	−0.159039	+	0.987272i	$0.550840\pi$
$888$	53.7049	1.80222
$889$	−0.124017	−0.00415938
$890$	19.6832	0.659781
$891$	3.76231	0.126042
$892$	118.560	3.96967
$893$	−7.12728	−0.238505
$894$	6.46921	0.216363
$895$	−2.37089	−0.0792503
$896$	2.82456	0.0943620
$897$	19.4214	0.648462
$898$	−22.0744	−0.736633
$899$	34.1126	1.13772
$900$	39.5454	1.31818
$901$	−84.4133	−2.81221
$902$	19.6343	0.653751
$903$	−0.410328	−0.0136549
$904$	−5.72328	−0.190354
$905$	24.8701	0.826711
$906$	−11.5930	−0.385153
$907$	40.6279	1.34903	0.674513	−	0.738263i	$-0.264354\pi$
$907$	40.6279	1.34903	0.674513	+	0.738263i	$0.264354\pi$
$908$	−43.3799	−1.43961
$909$	29.6962	0.984959
$910$	1.41310	0.0468440
$911$	−1.29030	−0.0427497	−0.0213748	−	0.999772i	$-0.506804\pi$
$911$	−1.29030	−0.0427497	−0.0213748	+	0.999772i	$0.506804\pi$
$912$	80.0447	2.65055
$913$	−4.79698	−0.158757
$914$	−27.7367	−0.917447
$915$	−12.9162	−0.426996
$916$	−92.3902	−3.05266
$917$	0.0292892	0.000967216 0
$918$	92.6803	3.05891
$919$	−3.18294	−0.104996	−0.0524978	−	0.998621i	$-0.516718\pi$
$919$	−3.18294	−0.104996	−0.0524978	+	0.998621i	$0.516718\pi$
$920$	−55.3558	−1.82503
$921$	−12.6608	−0.417188
$922$	34.4788	1.13550
$923$	−32.7420	−1.07772
$924$	−0.520571	−0.0171255
$925$	21.3036	0.700458
$926$	56.8967	1.86974
$927$	−41.2629	−1.35525
$928$	−101.204	−3.32217
$929$	−22.8688	−0.750302	−0.375151	−	0.926964i	$-0.622409\pi$
$929$	−22.8688	−0.750302	−0.375151	+	0.926964i	$0.622409\pi$
$930$	22.6726	0.743463
$931$	−43.5595	−1.42761
$932$	−53.7405	−1.76033
$933$	−19.3215	−0.632558
$934$	−16.4137	−0.537072
$935$	−13.6459	−0.446268
$936$	−104.341	−3.41050
$937$	−50.0587	−1.63535	−0.817673	−	0.575683i	$-0.804736\pi$
$937$	−50.0587	−1.63535	−0.817673	+	0.575683i	$0.804736\pi$
$938$	−2.16113	−0.0705635
$939$	13.5350	0.441697
$940$	8.22795	0.268366
$941$	51.8919	1.69163	0.845814	−	0.533478i	$-0.179115\pi$
$941$	51.8919	1.69163	0.845814	+	0.533478i	$0.179115\pi$
$942$	−6.53288	−0.212853
$943$	23.1182	0.752832
$944$	−165.186	−5.37635
$945$	−0.476566	−0.0155027
$946$	−22.5988	−0.734749
$947$	−23.7518	−0.771829	−0.385914	−	0.922535i	$-0.626114\pi$
$947$	−23.7518	−0.771829	−0.385914	+	0.922535i	$0.626114\pi$
$948$	75.2337	2.44348
$949$	−30.0918	−0.976820
$950$	55.2447	1.79237
$951$	−20.9253	−0.678551
$952$	5.48368	0.177727
$953$	7.96710	0.258080	0.129040	−	0.991639i	$-0.458811\pi$
$953$	7.96710	0.258080	0.129040	+	0.991639i	$0.458811\pi$
$954$	−69.3323	−2.24472
$955$	−8.48897	−0.274697
$956$	30.3198	0.980613
$957$	5.76391	0.186321
$958$	2.91148	0.0940657
$959$	−0.314133	−0.0101439
$960$	−33.2825	−1.07419
$961$	20.7372	0.668941
$962$	−88.9032	−2.86635
$963$	23.9815	0.772793
$964$	−70.8606	−2.28227
$965$	−9.27864	−0.298690
$966$	−0.838343	−0.0269733
$967$	10.8529	0.349006	0.174503	−	0.984657i	$-0.444168\pi$
$967$	10.8529	0.349006	0.174503	+	0.984657i	$0.444168\pi$
$968$	85.0358	2.73315
$969$	40.4230	1.29857
$970$	28.6035	0.918402
$971$	17.2954	0.555035	0.277518	−	0.960721i	$-0.410488\pi$
$971$	17.2954	0.555035	0.277518	+	0.960721i	$0.410488\pi$
$972$	87.5450	2.80801
$973$	−0.756139	−0.0242407
$974$	64.2721	2.05941
$975$	14.1472	0.453074
$976$	164.301	5.25914
$977$	−5.06220	−0.161954	−0.0809770	−	0.996716i	$-0.525804\pi$
$977$	−5.06220	−0.161954	−0.0809770	+	0.996716i	$0.525804\pi$
$978$	48.8150	1.56093
$979$	7.58926	0.242554
$980$	50.2864	1.60634
$981$	0.988643	0.0315649
$982$	89.2113	2.84685
$983$	−34.6675	−1.10572	−0.552861	−	0.833273i	$-0.686464\pi$
$983$	−34.6675	−1.10572	−0.552861	+	0.833273i	$0.686464\pi$
$984$	42.4528	1.35334
$985$	36.4975	1.16291
$986$	−96.0314	−3.05826
$987$	0.0787855	0.00250777
$988$	−168.559	−5.36257
$989$	−26.6087	−0.846106
$990$	−11.2079	−0.356212
$991$	4.73621	0.150451	0.0752253	−	0.997167i	$-0.476032\pi$
$991$	4.73621	0.150451	0.0752253	+	0.997167i	$0.476032\pi$
$992$	−153.491	−4.87336
$993$	11.1000	0.352248
$994$	1.41334	0.0448284
$995$	3.89445	0.123462
$996$	−16.4045	−0.519796
$997$	−56.8241	−1.79964	−0.899818	−	0.436266i	$-0.856301\pi$
$997$	−56.8241	−1.79964	−0.899818	+	0.436266i	$0.856301\pi$
$998$	74.8878	2.37053
$999$	29.9824	0.948600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.10	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.10	✓	243	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72738 q^{2} +0.874188 q^{3} +5.43862 q^{4} -1.32205 q^{5} -2.38425 q^{6} -0.0787567 q^{7} -9.37845 q^{8} -2.23580 q^{9} +O(q^{10})\)	\(q-2.72738 q^{2} +0.874188 q^{3} +5.43862 q^{4} -1.32205 q^{5} -2.38425 q^{6} -0.0787567 q^{7} -9.37845 q^{8} -2.23580 q^{9} +3.60574 q^{10} +1.39027 q^{11} +4.75438 q^{12} -4.97614 q^{13} +0.214800 q^{14} -1.15572 q^{15} +14.7014 q^{16} +7.42427 q^{17} +6.09787 q^{18} +6.22831 q^{19} -7.19014 q^{20} -0.0688481 q^{21} -3.79180 q^{22} -4.46461 q^{23} -8.19852 q^{24} -3.25218 q^{25} +13.5718 q^{26} -4.57707 q^{27} -0.428328 q^{28} +4.74256 q^{29} +3.15210 q^{30} +7.19286 q^{31} -21.3394 q^{32} +1.21536 q^{33} -20.2488 q^{34} +0.104120 q^{35} -12.1597 q^{36} -6.55056 q^{37} -16.9870 q^{38} -4.35008 q^{39} +12.3988 q^{40} -5.17810 q^{41} +0.187775 q^{42} +5.95990 q^{43} +7.56115 q^{44} +2.95584 q^{45} +12.1767 q^{46} -1.14434 q^{47} +12.8518 q^{48} -6.99380 q^{49} +8.86994 q^{50} +6.49020 q^{51} -27.0633 q^{52} -11.3699 q^{53} +12.4834 q^{54} -1.83801 q^{55} +0.738615 q^{56} +5.44471 q^{57} -12.9348 q^{58} -11.2361 q^{59} -6.28553 q^{60} +11.1759 q^{61} -19.6177 q^{62} +0.176084 q^{63} +28.7980 q^{64} +6.57871 q^{65} -3.31474 q^{66} -10.0612 q^{67} +40.3778 q^{68} -3.90291 q^{69} -0.283976 q^{70} +6.57981 q^{71} +20.9683 q^{72} +6.04721 q^{73} +17.8659 q^{74} -2.84301 q^{75} +33.8734 q^{76} -0.109493 q^{77} +11.8643 q^{78} +15.8241 q^{79} -19.4360 q^{80} +2.70617 q^{81} +14.1227 q^{82} -3.45040 q^{83} -0.374439 q^{84} -9.81527 q^{85} -16.2549 q^{86} +4.14589 q^{87} -13.0386 q^{88} +5.45884 q^{89} -8.06171 q^{90} +0.391904 q^{91} -24.2813 q^{92} +6.28791 q^{93} +3.12105 q^{94} -8.23414 q^{95} -18.6547 q^{96} +7.93275 q^{97} +19.0748 q^{98} -3.10836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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