LMFDB - Embedded newform 1849.4.a.i.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.928750 q^{2} +4.15887 q^{3} -7.13742 q^{4} -7.22084 q^{5} -3.86255 q^{6} -33.4889 q^{7} +14.0589 q^{8} -9.70384 q^{9} +O(q^{10})$	\(q-0.928750 q^{2} +4.15887 q^{3} -7.13742 q^{4} -7.22084 q^{5} -3.86255 q^{6} -33.4889 q^{7} +14.0589 q^{8} -9.70384 q^{9} +6.70635 q^{10} +21.8153 q^{11} -29.6836 q^{12} -37.7982 q^{13} +31.1028 q^{14} -30.0305 q^{15} +44.0422 q^{16} +87.4139 q^{17} +9.01244 q^{18} +115.186 q^{19} +51.5382 q^{20} -139.276 q^{21} -20.2609 q^{22} -3.50528 q^{23} +58.4690 q^{24} -72.8595 q^{25} +35.1051 q^{26} -152.646 q^{27} +239.025 q^{28} +149.824 q^{29} +27.8908 q^{30} +53.4626 q^{31} -153.375 q^{32} +90.7268 q^{33} -81.1857 q^{34} +241.818 q^{35} +69.2604 q^{36} +272.472 q^{37} -106.979 q^{38} -157.198 q^{39} -101.517 q^{40} -446.102 q^{41} +129.352 q^{42} -155.705 q^{44} +70.0699 q^{45} +3.25553 q^{46} +526.776 q^{47} +183.166 q^{48} +778.507 q^{49} +67.6683 q^{50} +363.543 q^{51} +269.782 q^{52} -262.810 q^{53} +141.770 q^{54} -157.525 q^{55} -470.817 q^{56} +479.044 q^{57} -139.149 q^{58} +575.151 q^{59} +214.340 q^{60} +112.448 q^{61} -49.6533 q^{62} +324.971 q^{63} -209.890 q^{64} +272.935 q^{65} -84.2625 q^{66} -6.38826 q^{67} -623.910 q^{68} -14.5780 q^{69} -224.588 q^{70} -570.402 q^{71} -136.425 q^{72} -424.131 q^{73} -253.059 q^{74} -303.013 q^{75} -822.133 q^{76} -730.570 q^{77} +145.997 q^{78} -395.839 q^{79} -318.022 q^{80} -372.832 q^{81} +414.317 q^{82} +472.458 q^{83} +994.071 q^{84} -631.202 q^{85} +623.098 q^{87} +306.698 q^{88} +836.438 q^{89} -65.0774 q^{90} +1265.82 q^{91} +25.0187 q^{92} +222.344 q^{93} -489.243 q^{94} -831.741 q^{95} -637.867 q^{96} -640.791 q^{97} -723.038 q^{98} -211.692 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * 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 $

$2$	−0.928750	−0.328363	−0.164181	−	0.986430i	$-0.552498\pi$
$2$	−0.928750	−0.328363	−0.164181	+	0.986430i	$0.552498\pi$
$3$	4.15887	0.800374	0.400187	−	0.916434i	$-0.368945\pi$
$3$	4.15887	0.800374	0.400187	+	0.916434i	$0.368945\pi$
$4$	−7.13742	−0.892178
$5$	−7.22084	−0.645851	−0.322926	−	0.946424i	$-0.604666\pi$
$5$	−7.22084	−0.645851	−0.322926	+	0.946424i	$0.604666\pi$
$6$	−3.86255	−0.262813
$7$	−33.4889	−1.80823	−0.904116	−	0.427288i	$-0.859469\pi$
$7$	−33.4889	−1.80823	−0.904116	+	0.427288i	$0.859469\pi$
$8$	14.0589	0.621321
$9$	−9.70384	−0.359401
$10$	6.70635	0.212074
$11$	21.8153	0.597959	0.298980	−	0.954259i	$-0.403354\pi$
$11$	21.8153	0.597959	0.298980	+	0.954259i	$0.403354\pi$
$12$	−29.6836	−0.714076
$13$	−37.7982	−0.806411	−0.403206	−	0.915109i	$-0.632104\pi$
$13$	−37.7982	−0.806411	−0.403206	+	0.915109i	$0.632104\pi$
$14$	31.1028	0.593756
$15$	−30.0305	−0.516923
$16$	44.0422	0.688159
$17$	87.4139	1.24712	0.623558	−	0.781777i	$-0.285686\pi$
$17$	87.4139	1.24712	0.623558	+	0.781777i	$0.285686\pi$
$18$	9.01244	0.118014
$19$	115.186	1.39082	0.695409	−	0.718614i	$-0.255223\pi$
$19$	115.186	1.39082	0.695409	+	0.718614i	$0.255223\pi$
$20$	51.5382	0.576214
$21$	−139.276	−1.44726
$22$	−20.2609	−0.196348
$23$	−3.50528	−0.0317783	−0.0158892	−	0.999874i	$-0.505058\pi$
$23$	−3.50528	−0.0317783	−0.0158892	+	0.999874i	$0.505058\pi$
$24$	58.4690	0.497289
$25$	−72.8595	−0.582876
$26$	35.1051	0.264795
$27$	−152.646	−1.08803
$28$	239.025	1.61326
$29$	149.824	0.959367	0.479683	−	0.877442i	$-0.340752\pi$
$29$	149.824	0.959367	0.479683	+	0.877442i	$0.340752\pi$
$30$	27.8908	0.169738
$31$	53.4626	0.309747	0.154874	−	0.987934i	$-0.450503\pi$
$31$	53.4626	0.309747	0.154874	+	0.987934i	$0.450503\pi$
$32$	−153.375	−0.847287
$33$	90.7268	0.478591
$34$	−81.1857	−0.409507
$35$	241.818	1.16785
$36$	69.2604	0.320650
$37$	272.472	1.21065	0.605327	−	0.795977i	$-0.293042\pi$
$37$	272.472	1.21065	0.605327	+	0.795977i	$0.293042\pi$
$38$	−106.979	−0.456693
$39$	−157.198	−0.645431
$40$	−101.517	−0.401281
$41$	−446.102	−1.69925	−0.849626	−	0.527385i	$-0.823173\pi$
$41$	−446.102	−1.69925	−0.849626	+	0.527385i	$0.823173\pi$
$42$	129.352	0.475227
$43$	0	0
$43$	0	0
$44$	−155.705	−0.533486
$45$	70.0699	0.232120
$46$	3.25553	0.0104348
$47$	526.776	1.63485	0.817427	−	0.576032i	$-0.195400\pi$
$47$	526.776	1.63485	0.817427	+	0.576032i	$0.195400\pi$
$48$	183.166	0.550785
$49$	778.507	2.26970
$50$	67.6683	0.191395
$51$	363.543	0.998160
$52$	269.782	0.719462
$53$	−262.810	−0.681128	−0.340564	−	0.940221i	$-0.610618\pi$
$53$	−262.810	−0.681128	−0.340564	+	0.940221i	$0.610618\pi$
$54$	141.770	0.357268
$55$	−157.525	−0.386193
$56$	−470.817	−1.12349
$57$	479.044	1.11317
$58$	−139.149	−0.315020
$59$	575.151	1.26912	0.634562	−	0.772872i	$-0.281181\pi$
$59$	575.151	1.26912	0.634562	+	0.772872i	$0.281181\pi$
$60$	214.340	0.461187
$61$	112.448	0.236024	0.118012	−	0.993012i	$-0.462348\pi$
$61$	112.448	0.236024	0.118012	+	0.993012i	$0.462348\pi$
$62$	−49.6533	−0.101709
$63$	324.971	0.649881
$64$	−209.890	−0.409942
$65$	272.935	0.520822
$66$	−84.2625	−0.157151
$67$	−6.38826	−0.0116485	−0.00582425	−	0.999983i	$-0.501854\pi$
$67$	−6.38826	−0.0116485	−0.00582425	+	0.999983i	$0.501854\pi$
$68$	−623.910	−1.11265
$69$	−14.5780	−0.0254346
$70$	−224.588	−0.383478
$71$	−570.402	−0.953440	−0.476720	−	0.879055i	$-0.658174\pi$
$71$	−570.402	−0.953440	−0.476720	+	0.879055i	$0.658174\pi$
$72$	−136.425	−0.223304
$73$	−424.131	−0.680010	−0.340005	−	0.940424i	$-0.610429\pi$
$73$	−424.131	−0.680010	−0.340005	+	0.940424i	$0.610429\pi$
$74$	−253.059	−0.397534
$75$	−303.013	−0.466519
$76$	−822.133	−1.24086
$77$	−730.570	−1.08125
$78$	145.997	0.211935
$79$	−395.839	−0.563739	−0.281869	−	0.959453i	$-0.590955\pi$
$79$	−395.839	−0.563739	−0.281869	+	0.959453i	$0.590955\pi$
$80$	−318.022	−0.444449
$81$	−372.832	−0.511429
$82$	414.317	0.557971
$83$	472.458	0.624807	0.312404	−	0.949949i	$-0.398866\pi$
$83$	472.458	0.624807	0.312404	+	0.949949i	$0.398866\pi$
$84$	994.071	1.29121
$85$	−631.202	−0.805452
$86$	0	0
$87$	623.098	0.767852
$88$	306.698	0.371525
$89$	836.438	0.996205	0.498102	−	0.867118i	$-0.334030\pi$
$89$	836.438	0.996205	0.498102	+	0.867118i	$0.334030\pi$
$90$	−65.0774	−0.0762195
$91$	1265.82	1.45818
$92$	25.0187	0.0283519
$93$	222.344	0.247913
$94$	−489.243	−0.536825
$95$	−831.741	−0.898262
$96$	−637.867	−0.678146
$97$	−640.791	−0.670747	−0.335374	−	0.942085i	$-0.608863\pi$
$97$	−640.791	−0.670747	−0.335374	+	0.942085i	$0.608863\pi$
$98$	−723.038	−0.745285
$99$	−211.692	−0.214907
$100$	520.029	0.520029
$101$	1626.00	1.60191	0.800957	−	0.598722i	$-0.204324\pi$
$101$	1626.00	1.60191	0.800957	+	0.598722i	$0.204324\pi$
$102$	−337.640	−0.327758
$103$	−539.444	−0.516049	−0.258024	−	0.966138i	$-0.583071\pi$
$103$	−539.444	−0.516049	−0.258024	+	0.966138i	$0.583071\pi$
$104$	−531.401	−0.501040
$105$	1005.69	0.934716
$106$	244.085	0.223657
$107$	257.349	0.232513	0.116257	−	0.993219i	$-0.462911\pi$
$107$	257.349	0.232513	0.116257	+	0.993219i	$0.462911\pi$
$108$	1089.50	0.970716
$109$	−1923.21	−1.69000	−0.844998	−	0.534769i	$-0.820399\pi$
$109$	−1923.21	−1.69000	−0.844998	+	0.534769i	$0.820399\pi$
$110$	146.301	0.126811
$111$	1133.18	0.968976
$112$	−1474.93	−1.24435
$113$	230.361	0.191774	0.0958872	−	0.995392i	$-0.469431\pi$
$113$	230.361	0.191774	0.0958872	+	0.995392i	$0.469431\pi$
$114$	−444.912	−0.365525
$115$	25.3111	0.0205241
$116$	−1069.36	−0.855926
$117$	366.788	0.289825
$118$	−534.171	−0.416733
$119$	−2927.40	−2.25508
$120$	−422.195	−0.321175
$121$	−855.094	−0.642445
$122$	−104.436	−0.0775014
$123$	−1855.28	−1.36004
$124$	−381.585	−0.276349
$125$	1428.71	1.02230
$126$	−301.817	−0.213397
$127$	−2386.40	−1.66739	−0.833695	−	0.552225i	$-0.813779\pi$
$127$	−2386.40	−1.66739	−0.833695	+	0.552225i	$0.813779\pi$
$128$	1421.94	0.981896
$129$	0	0
$130$	−253.488	−0.171018
$131$	702.752	0.468700	0.234350	−	0.972152i	$-0.424704\pi$
$131$	702.752	0.468700	0.234350	+	0.972152i	$0.424704\pi$
$132$	−647.555	−0.426988
$133$	−3857.46	−2.51492
$134$	5.93309	0.00382493
$135$	1102.23	0.702705
$136$	1228.94	0.774859
$137$	−406.925	−0.253766	−0.126883	−	0.991918i	$-0.540497\pi$
$137$	−406.925	−0.253766	−0.126883	+	0.991918i	$0.540497\pi$
$138$	13.5393	0.00835176
$139$	−630.082	−0.384481	−0.192241	−	0.981348i	$-0.561575\pi$
$139$	−630.082	−0.384481	−0.192241	+	0.981348i	$0.561575\pi$
$140$	−1725.96	−1.04193
$141$	2190.79	1.30849
$142$	529.761	0.313074
$143$	−824.579	−0.482201
$144$	−427.378	−0.247326
$145$	−1081.86	−0.619608
$146$	393.911	0.223290
$147$	3237.71	1.81661
$148$	−1944.75	−1.08012
$149$	−1284.41	−0.706193	−0.353097	−	0.935587i	$-0.614871\pi$
$149$	−1284.41	−0.706193	−0.353097	+	0.935587i	$0.614871\pi$
$150$	281.423	0.153187
$151$	909.515	0.490167	0.245084	−	0.969502i	$-0.421185\pi$
$151$	909.515	0.490167	0.245084	+	0.969502i	$0.421185\pi$
$152$	1619.39	0.864144
$153$	−848.251	−0.448216
$154$	678.517	0.355042
$155$	−386.044	−0.200051
$156$	1121.99	0.575839
$157$	−1974.99	−1.00396	−0.501979	−	0.864880i	$-0.667395\pi$
$157$	−1974.99	−1.00396	−0.501979	+	0.864880i	$0.667395\pi$
$158$	367.636	0.185111
$159$	−1092.99	−0.545157
$160$	1107.50	0.547221
$161$	117.388	0.0574626
$162$	346.268	0.167934
$163$	−1890.45	−0.908415	−0.454207	−	0.890896i	$-0.650077\pi$
$163$	−1890.45	−0.908415	−0.454207	+	0.890896i	$0.650077\pi$
$164$	3184.02	1.51604
$165$	−655.123	−0.309099
$166$	−438.795	−0.205163
$167$	3671.61	1.70130	0.850652	−	0.525729i	$-0.176208\pi$
$167$	3671.61	1.70130	0.850652	+	0.525729i	$0.176208\pi$
$168$	−1958.06	−0.899213
$169$	−768.293	−0.349701
$170$	586.229	0.264480
$171$	−1117.75	−0.499862
$172$	0	0
$173$	−2464.27	−1.08298	−0.541488	−	0.840709i	$-0.682139\pi$
$173$	−2464.27	−1.08298	−0.541488	+	0.840709i	$0.682139\pi$
$174$	−578.703	−0.252134
$175$	2439.98	1.05397
$176$	960.793	0.411491
$177$	2391.98	1.01577
$178$	−776.842	−0.327117
$179$	−1155.83	−0.482629	−0.241314	−	0.970447i	$-0.577579\pi$
$179$	−1155.83	−0.482629	−0.241314	+	0.970447i	$0.577579\pi$
$180$	−500.118	−0.207092
$181$	−124.784	−0.0512437	−0.0256218	−	0.999672i	$-0.508157\pi$
$181$	−124.784	−0.0512437	−0.0256218	+	0.999672i	$0.508157\pi$
$182$	−1175.63	−0.478811
$183$	467.655	0.188907
$184$	−49.2804	−0.0197445
$185$	−1967.48	−0.781903
$186$	−206.502	−0.0814055
$187$	1906.96	0.745725
$188$	−3759.82	−1.45858
$189$	5111.96	1.96741
$190$	772.480	0.294956
$191$	3922.64	1.48603	0.743016	−	0.669273i	$-0.233394\pi$
$191$	3922.64	1.48603	0.743016	+	0.669273i	$0.233394\pi$
$192$	−872.906	−0.328107
$193$	−3321.16	−1.23866	−0.619332	−	0.785129i	$-0.712596\pi$
$193$	−3321.16	−1.23866	−0.619332	+	0.785129i	$0.712596\pi$
$194$	595.135	0.220248
$195$	1135.10	0.416852
$196$	−5556.53	−2.02498
$197$	−1106.57	−0.400203	−0.200102	−	0.979775i	$-0.564127\pi$
$197$	−1106.57	−0.400203	−0.200102	+	0.979775i	$0.564127\pi$
$198$	196.609	0.0705676
$199$	−3689.82	−1.31440	−0.657198	−	0.753718i	$-0.728258\pi$
$199$	−3689.82	−1.31440	−0.657198	+	0.753718i	$0.728258\pi$
$200$	−1024.32	−0.362153
$201$	−26.5679	−0.00932316
$202$	−1510.15	−0.526009
$203$	−5017.45	−1.73476
$204$	−2594.76	−0.890536
$205$	3221.23	1.09746
$206$	501.009	0.169451
$207$	34.0147	0.0114212
$208$	−1664.72	−0.554939
$209$	2512.82	0.831652
$210$	−934.033	−0.306926
$211$	−802.568	−0.261853	−0.130927	−	0.991392i	$-0.541795\pi$
$211$	−802.568	−0.261853	−0.130927	+	0.991392i	$0.541795\pi$
$212$	1875.79	0.607687
$213$	−2372.23	−0.763109
$214$	−239.013	−0.0763486
$215$	0	0
$216$	−2146.04	−0.676015
$217$	−1790.40	−0.560094
$218$	1786.18	0.554932
$219$	−1763.90	−0.544263
$220$	1124.32	0.344553
$221$	−3304.09	−1.00569
$222$	−1052.44	−0.318176
$223$	4705.21	1.41293	0.706467	−	0.707746i	$-0.250288\pi$
$223$	4705.21	1.41293	0.706467	+	0.707746i	$0.250288\pi$
$224$	5136.37	1.53209
$225$	707.017	0.209486
$226$	−213.947	−0.0629716
$227$	1300.02	0.380112	0.190056	−	0.981773i	$-0.439133\pi$
$227$	1300.02	0.380112	0.190056	+	0.981773i	$0.439133\pi$
$228$	−3419.14	−0.993149
$229$	−4002.54	−1.15500	−0.577500	−	0.816391i	$-0.695972\pi$
$229$	−4002.54	−1.15500	−0.577500	+	0.816391i	$0.695972\pi$
$230$	−23.5077	−0.00673935
$231$	−3038.34	−0.865403
$232$	2106.36	0.596075
$233$	6770.78	1.90373	0.951864	−	0.306522i	$-0.0991654\pi$
$233$	6770.78	1.90373	0.951864	+	0.306522i	$0.0991654\pi$
$234$	−340.654	−0.0951679
$235$	−3803.76	−1.05587
$236$	−4105.10	−1.13228
$237$	−1646.24	−0.451202
$238$	2718.82	0.740483
$239$	−6033.44	−1.63293	−0.816467	−	0.577392i	$-0.804070\pi$
$239$	−6033.44	−1.63293	−0.816467	+	0.577392i	$0.804070\pi$
$240$	−1322.61	−0.355725
$241$	1721.55	0.460145	0.230073	−	0.973173i	$-0.426104\pi$
$241$	1721.55	0.460145	0.230073	+	0.973173i	$0.426104\pi$
$242$	794.168	0.210955
$243$	2570.89	0.678695
$244$	−802.587	−0.210575
$245$	−5621.47	−1.46589
$246$	1723.09	0.446586
$247$	−4353.84	−1.12157
$248$	751.624	0.192452
$249$	1964.89	0.500079
$250$	−1326.92	−0.335686
$251$	4782.06	1.20255	0.601277	−	0.799040i	$-0.294659\pi$
$251$	4782.06	1.20255	0.601277	+	0.799040i	$0.294659\pi$
$252$	−2319.46	−0.579809
$253$	−76.4687	−0.0190022
$254$	2216.37	0.547509
$255$	−2625.08	−0.644663
$256$	358.498	0.0875239
$257$	6028.06	1.46311	0.731556	−	0.681781i	$-0.238794\pi$
$257$	6028.06	1.46311	0.731556	+	0.681781i	$0.238794\pi$
$258$	0	0
$259$	−9124.80	−2.18914
$260$	−1948.05	−0.464666
$261$	−1453.87	−0.344798
$262$	−652.681	−0.153904
$263$	−1473.02	−0.345363	−0.172682	−	0.984978i	$-0.555243\pi$
$263$	−1473.02	−0.345363	−0.172682	+	0.984978i	$0.555243\pi$
$264$	1275.52	0.297359
$265$	1897.71	0.439907
$266$	3582.62	0.825806
$267$	3478.63	0.797337
$268$	45.5957	0.0103925
$269$	1629.48	0.369335	0.184668	−	0.982801i	$-0.440879\pi$
$269$	1629.48	0.369335	0.184668	+	0.982801i	$0.440879\pi$
$270$	−1023.70	−0.230742
$271$	−7123.49	−1.59676	−0.798379	−	0.602155i	$-0.794309\pi$
$271$	−7123.49	−1.59676	−0.798379	+	0.602155i	$0.794309\pi$
$272$	3849.90	0.858215
$273$	5264.38	1.16709
$274$	377.932	0.0833274
$275$	−1589.45	−0.348536
$276$	104.049	0.0226922
$277$	4593.78	0.996438	0.498219	−	0.867051i	$-0.333988\pi$
$277$	4593.78	0.996438	0.498219	+	0.867051i	$0.333988\pi$
$278$	585.189	0.126249
$279$	−518.792	−0.111324
$280$	3399.69	0.725609
$281$	−3196.86	−0.678678	−0.339339	−	0.940664i	$-0.610203\pi$
$281$	−3196.86	−0.678678	−0.339339	+	0.940664i	$0.610203\pi$
$282$	−2034.70	−0.429661
$283$	8652.58	1.81746	0.908732	−	0.417380i	$-0.137052\pi$
$283$	8652.58	1.81746	0.908732	+	0.417380i	$0.137052\pi$
$284$	4071.20	0.850638
$285$	−3459.10	−0.718945
$286$	765.828	0.158337
$287$	14939.5	3.07264
$288$	1488.33	0.304516
$289$	2728.19	0.555300
$290$	1004.77	0.203456
$291$	−2664.96	−0.536849
$292$	3027.20	0.606690
$293$	2526.24	0.503702	0.251851	−	0.967766i	$-0.418961\pi$
$293$	2526.24	0.503702	0.251851	+	0.967766i	$0.418961\pi$
$294$	−3007.02	−0.596507
$295$	−4153.07	−0.819665
$296$	3830.66	0.752204
$297$	−3330.02	−0.650597
$298$	1192.89	0.231888
$299$	132.494	0.0256264
$300$	2162.73	0.416218
$301$	0	0
$302$	−844.712	−0.160953
$303$	6762.33	1.28213
$304$	5073.06	0.957104
$305$	−811.967	−0.152436
$306$	787.813	0.147177
$307$	2682.30	0.498654	0.249327	−	0.968419i	$-0.419791\pi$
$307$	2682.30	0.498654	0.249327	+	0.968419i	$0.419791\pi$
$308$	5214.39	0.964666
$309$	−2243.48	−0.413032
$310$	358.539	0.0656891
$311$	−3757.40	−0.685089	−0.342544	−	0.939502i	$-0.611289\pi$
$311$	−3757.40	−0.685089	−0.342544	+	0.939502i	$0.611289\pi$
$312$	−2210.03	−0.401019
$313$	4548.20	0.821341	0.410670	−	0.911784i	$-0.365295\pi$
$313$	4548.20	0.821341	0.410670	+	0.911784i	$0.365295\pi$
$314$	1834.27	0.329663
$315$	−2346.56	−0.419727
$316$	2825.27	0.502955
$317$	−9653.47	−1.71039	−0.855193	−	0.518309i	$-0.826562\pi$
$317$	−9653.47	−1.71039	−0.855193	+	0.518309i	$0.826562\pi$
$318$	1015.12	0.179009
$319$	3268.45	0.573662
$320$	1515.58	0.264762
$321$	1070.28	0.186097
$322$	−109.024	−0.0188686
$323$	10068.9	1.73451
$324$	2661.06	0.456286
$325$	2753.96	0.470038
$326$	1755.76	0.298290
$327$	−7998.35	−1.35263
$328$	−6271.69	−1.05578
$329$	−17641.1	−2.95619
$330$	608.446	0.101497
$331$	5200.02	0.863501	0.431751	−	0.901993i	$-0.357896\pi$
$331$	5200.02	0.863501	0.431751	+	0.901993i	$0.357896\pi$
$332$	−3372.13	−0.557439
$333$	−2644.03	−0.435111
$334$	−3410.01	−0.558645
$335$	46.1286	0.00752320
$336$	−6134.01	−0.995946
$337$	−10242.7	−1.65566	−0.827829	−	0.560980i	$-0.810424\pi$
$337$	−10242.7	−1.65566	−0.827829	+	0.560980i	$0.810424\pi$
$338$	713.552	0.114829
$339$	958.039	0.153491
$340$	4505.15	0.718607
$341$	1166.30	0.185216
$342$	1038.11	0.164136
$343$	−14584.7	−2.29591
$344$	0	0
$345$	105.265	0.0164269
$346$	2288.69	0.355609
$347$	−5275.43	−0.816137	−0.408069	−	0.912951i	$-0.633798\pi$
$347$	−5275.43	−0.816137	−0.408069	+	0.912951i	$0.633798\pi$
$348$	−4447.32	−0.685061
$349$	76.7692	0.0117747	0.00588733	−	0.999983i	$-0.498126\pi$
$349$	76.7692	0.0117747	0.00588733	+	0.999983i	$0.498126\pi$
$350$	−2266.14	−0.346086
$351$	5769.76	0.877399
$352$	−3345.92	−0.506643
$353$	−1230.16	−0.185480	−0.0927402	−	0.995690i	$-0.529563\pi$
$353$	−1230.16	−0.185480	−0.0927402	+	0.995690i	$0.529563\pi$
$354$	−2221.55	−0.333542
$355$	4118.78	0.615781
$356$	−5970.01	−0.888792
$357$	−12174.6	−1.80490
$358$	1073.47	0.158477
$359$	498.064	0.0732223	0.0366112	−	0.999330i	$-0.488344\pi$
$359$	498.064	0.0732223	0.0366112	+	0.999330i	$0.488344\pi$
$360$	985.104	0.144221
$361$	6408.87	0.934374
$362$	115.893	0.0168265
$363$	−3556.22	−0.514196
$364$	−9034.71	−1.30095
$365$	3062.58	0.439186
$366$	−434.334	−0.0620301
$367$	−8123.76	−1.15547	−0.577734	−	0.816225i	$-0.696063\pi$
$367$	−8123.76	−1.15547	−0.577734	+	0.816225i	$0.696063\pi$
$368$	−154.380	−0.0218686
$369$	4328.90	0.610714
$370$	1827.30	0.256748
$371$	8801.23	1.23164
$372$	−1586.96	−0.221183
$373$	4460.89	0.619238	0.309619	−	0.950861i	$-0.399798\pi$
$373$	4460.89	0.619238	0.309619	+	0.950861i	$0.399798\pi$
$374$	−1771.09	−0.244868
$375$	5941.82	0.818224
$376$	7405.88	1.01577
$377$	−5663.09	−0.773644
$378$	−4747.73	−0.646024
$379$	−3176.29	−0.430488	−0.215244	−	0.976560i	$-0.569055\pi$
$379$	−3176.29	−0.430488	−0.215244	+	0.976560i	$0.569055\pi$
$380$	5936.49	0.801409
$381$	−9924.70	−1.33454
$382$	−3643.15	−0.487958
$383$	9741.88	1.29970	0.649852	−	0.760061i	$-0.274831\pi$
$383$	9741.88	1.29970	0.649852	+	0.760061i	$0.274831\pi$
$384$	5913.65	0.785884
$385$	5275.33	0.698326
$386$	3084.52	0.406731
$387$	0	0
$388$	4573.60	0.598426
$389$	−5989.93	−0.780723	−0.390362	−	0.920662i	$-0.627650\pi$
$389$	−5989.93	−0.780723	−0.390362	+	0.920662i	$0.627650\pi$
$390$	−1054.22	−0.136879
$391$	−306.410	−0.0396313
$392$	10944.9	1.41021
$393$	2922.65	0.375135
$394$	1027.73	0.131412
$395$	2858.29	0.364092
$396$	1510.93	0.191736
$397$	−6376.95	−0.806171	−0.403086	−	0.915162i	$-0.632062\pi$
$397$	−6376.95	−0.806171	−0.403086	+	0.915162i	$0.632062\pi$
$398$	3426.93	0.431599
$399$	−16042.7	−2.01288
$400$	−3208.89	−0.401112
$401$	11130.6	1.38613	0.693065	−	0.720875i	$-0.256260\pi$
$401$	11130.6	1.38613	0.693065	+	0.720875i	$0.256260\pi$
$402$	24.6749	0.00306138
$403$	−2020.79	−0.249784
$404$	−11605.5	−1.42919
$405$	2692.16	0.330307
$406$	4659.95	0.569630
$407$	5944.06	0.723922
$408$	5111.00	0.620177
$409$	−4881.98	−0.590216	−0.295108	−	0.955464i	$-0.595356\pi$
$409$	−4881.98	−0.590216	−0.295108	+	0.955464i	$0.595356\pi$
$410$	−2991.72	−0.360367
$411$	−1692.35	−0.203108
$412$	3850.24	0.460407
$413$	−19261.2	−2.29487
$414$	−31.5912	−0.00375029
$415$	−3411.54	−0.403533
$416$	5797.32	0.683261
$417$	−2620.43	−0.307729
$418$	−2333.78	−0.273084
$419$	−14222.9	−1.65831	−0.829156	−	0.559017i	$-0.811179\pi$
$419$	−14222.9	−1.65831	−0.829156	+	0.559017i	$0.811179\pi$
$420$	−7178.02	−0.833933
$421$	−11362.9	−1.31543	−0.657713	−	0.753269i	$-0.728476\pi$
$421$	−11362.9	−1.31543	−0.657713	+	0.753269i	$0.728476\pi$
$422$	745.385	0.0859829
$423$	−5111.75	−0.587569
$424$	−3694.82	−0.423199
$425$	−6368.93	−0.726914
$426$	2203.20	0.250576
$427$	−3765.75	−0.426786
$428$	−1836.81	−0.207443
$429$	−3429.31	−0.385941
$430$	0	0
$431$	−8523.94	−0.952631	−0.476315	−	0.879275i	$-0.658028\pi$
$431$	−8523.94	−0.952631	−0.476315	+	0.879275i	$0.658028\pi$
$432$	−6722.88	−0.748738
$433$	2382.07	0.264376	0.132188	−	0.991225i	$-0.457800\pi$
$433$	2382.07	0.264376	0.132188	+	0.991225i	$0.457800\pi$
$434$	1662.84	0.183914
$435$	−4499.29	−0.495918
$436$	13726.7	1.50778
$437$	−403.760	−0.0441979
$438$	1638.22	0.178716
$439$	7841.44	0.852509	0.426255	−	0.904603i	$-0.359833\pi$
$439$	7841.44	0.852509	0.426255	+	0.904603i	$0.359833\pi$
$440$	−2214.62	−0.239950
$441$	−7554.51	−0.815733
$442$	3068.68	0.330231
$443$	14488.4	1.55387	0.776934	−	0.629582i	$-0.216774\pi$
$443$	14488.4	1.55387	0.776934	+	0.629582i	$0.216774\pi$
$444$	−8087.96	−0.864499
$445$	−6039.78	−0.643400
$446$	−4369.96	−0.463955
$447$	−5341.68	−0.565219
$448$	7029.00	0.741270
$449$	−4280.14	−0.449871	−0.224936	−	0.974374i	$-0.572217\pi$
$449$	−4280.14	−0.449871	−0.224936	+	0.974374i	$0.572217\pi$
$450$	−656.642	−0.0687876
$451$	−9731.83	−1.01608
$452$	−1644.18	−0.171097
$453$	3782.55	0.392317
$454$	−1207.39	−0.124815
$455$	−9140.30	−0.941766
$456$	6734.82	0.691638
$457$	−5468.42	−0.559742	−0.279871	−	0.960038i	$-0.590292\pi$
$457$	−5468.42	−0.559742	−0.279871	+	0.960038i	$0.590292\pi$
$458$	3717.36	0.379259
$459$	−13343.4	−1.35690
$460$	−180.656	−0.0183111
$461$	−7987.57	−0.806981	−0.403490	−	0.914984i	$-0.632203\pi$
$461$	−7987.57	−0.806981	−0.403490	+	0.914984i	$0.632203\pi$
$462$	2821.86	0.284166
$463$	−2657.37	−0.266735	−0.133368	−	0.991067i	$-0.542579\pi$
$463$	−2657.37	−0.266735	−0.133368	+	0.991067i	$0.542579\pi$
$464$	6598.58	0.660197
$465$	−1605.51	−0.160115
$466$	−6288.36	−0.625113
$467$	2485.15	0.246250	0.123125	−	0.992391i	$-0.460708\pi$
$467$	2485.15	0.246250	0.123125	+	0.992391i	$0.460708\pi$
$468$	−2617.92	−0.258576
$469$	213.936	0.0210632
$470$	3532.74	0.346709
$471$	−8213.72	−0.803542
$472$	8085.98	0.788533
$473$	0	0
$474$	1528.95	0.148158
$475$	−8392.41	−0.810674
$476$	20894.1	2.01193
$477$	2550.27	0.244798
$478$	5603.56	0.536194
$479$	−536.798	−0.0512044	−0.0256022	−	0.999672i	$-0.508150\pi$
$479$	−536.798	−0.0512044	−0.0256022	+	0.999672i	$0.508150\pi$
$480$	4605.93	0.437982
$481$	−10299.0	−0.976285
$482$	−1598.89	−0.151095
$483$	488.201	0.0459916
$484$	6103.17	0.573175
$485$	4627.05	0.433203
$486$	−2387.72	−0.222858
$487$	−8983.76	−0.835920	−0.417960	−	0.908465i	$-0.637255\pi$
$487$	−8983.76	−0.835920	−0.417960	+	0.908465i	$0.637255\pi$
$488$	1580.89	0.146646
$489$	−7862.13	−0.727071
$490$	5220.94	0.481343
$491$	−15775.6	−1.44998	−0.724992	−	0.688757i	$-0.758157\pi$
$491$	−15775.6	−1.44998	−0.724992	+	0.688757i	$0.758157\pi$
$492$	13241.9	1.21340
$493$	13096.7	1.19644
$494$	4043.63	0.368282
$495$	1528.59	0.138798
$496$	2354.61	0.213155
$497$	19102.1	1.72404
$498$	−1824.89	−0.164207
$499$	9664.44	0.867014	0.433507	−	0.901150i	$-0.357276\pi$
$499$	9664.44	0.867014	0.433507	+	0.901150i	$0.357276\pi$
$500$	−10197.3	−0.912076
$501$	15269.7	1.36168
$502$	−4441.34	−0.394874
$503$	−5422.87	−0.480704	−0.240352	−	0.970686i	$-0.577263\pi$
$503$	−5422.87	−0.480704	−0.240352	+	0.970686i	$0.577263\pi$
$504$	4568.73	0.403784
$505$	−11741.1	−1.03460
$506$	71.0203	0.00623960
$507$	−3195.23	−0.279891
$508$	17032.7	1.48761
$509$	18023.2	1.56948	0.784738	−	0.619828i	$-0.212798\pi$
$509$	18023.2	1.56948	0.784738	+	0.619828i	$0.212798\pi$
$510$	2438.05	0.211683
$511$	14203.7	1.22962
$512$	−11708.5	−1.01064
$513$	−17582.8	−1.51325
$514$	−5598.56	−0.480432
$515$	3895.24	0.333291
$516$	0	0
$517$	11491.8	0.977576
$518$	8474.66	0.718833
$519$	−10248.6	−0.866785
$520$	3837.16	0.323597
$521$	1580.04	0.132865	0.0664325	−	0.997791i	$-0.478838\pi$
$521$	1580.04	0.132865	0.0664325	+	0.997791i	$0.478838\pi$
$522$	1350.28	0.113219
$523$	−12441.2	−1.04019	−0.520093	−	0.854110i	$-0.674103\pi$
$523$	−12441.2	−1.04019	−0.520093	+	0.854110i	$0.674103\pi$
$524$	−5015.84	−0.418164
$525$	10147.6	0.843574
$526$	1368.07	0.113404
$527$	4673.37	0.386291
$528$	3995.81	0.329347
$529$	−12154.7	−0.998990
$530$	−1762.50	−0.144449
$531$	−5581.17	−0.456125
$532$	27532.3	2.24376
$533$	16861.9	1.37030
$534$	−3230.78	−0.261816
$535$	−1858.28	−0.150169
$536$	−89.8117	−0.00723746
$537$	−4806.93	−0.386284
$538$	−1513.38	−0.121276
$539$	16983.3	1.35719
$540$	−7867.11	−0.626938
$541$	−14128.8	−1.12282	−0.561408	−	0.827539i	$-0.689740\pi$
$541$	−14128.8	−1.12282	−0.561408	+	0.827539i	$0.689740\pi$
$542$	6615.94	0.524316
$543$	−518.959	−0.0410141
$544$	−13407.1	−1.05667
$545$	13887.2	1.09149
$546$	−4889.30	−0.383228
$547$	8410.19	0.657393	0.328696	−	0.944436i	$-0.393391\pi$
$547$	8410.19	0.657393	0.328696	+	0.944436i	$0.393391\pi$
$548$	2904.40	0.226405
$549$	−1091.17	−0.0848273
$550$	1476.20	0.114446
$551$	17257.7	1.33430
$552$	−204.950	−0.0158030
$553$	13256.2	1.01937
$554$	−4266.47	−0.327193
$555$	−8182.48	−0.625814
$556$	4497.16	0.343025
$557$	−7911.88	−0.601862	−0.300931	−	0.953646i	$-0.597297\pi$
$557$	−7911.88	−0.601862	−0.300931	+	0.953646i	$0.597297\pi$
$558$	481.828	0.0365545
$559$	0	0
$560$	10650.2	0.803666
$561$	7930.78	0.596859
$562$	2969.08	0.222853
$563$	−2289.48	−0.171386	−0.0856929	−	0.996322i	$-0.527310\pi$
$563$	−2289.48	−0.171386	−0.0856929	+	0.996322i	$0.527310\pi$
$564$	−15636.6	−1.16741
$565$	−1663.40	−0.123858
$566$	−8036.08	−0.596787
$567$	12485.7	0.924782
$568$	−8019.21	−0.592392
$569$	8732.61	0.643392	0.321696	−	0.946843i	$-0.395747\pi$
$569$	8732.61	0.643392	0.321696	+	0.946843i	$0.395747\pi$
$570$	3212.64	0.236075
$571$	9031.46	0.661918	0.330959	−	0.943645i	$-0.392628\pi$
$571$	9031.46	0.661918	0.330959	+	0.943645i	$0.392628\pi$
$572$	5885.37	0.430209
$573$	16313.7	1.18938
$574$	−13875.0	−1.00894
$575$	255.393	0.0185228
$576$	2036.74	0.147334
$577$	1205.57	0.0869821	0.0434910	−	0.999054i	$-0.486152\pi$
$577$	1205.57	0.0869821	0.0434910	+	0.999054i	$0.486152\pi$
$578$	−2533.81	−0.182340
$579$	−13812.2	−0.991394
$580$	7721.66	0.552801
$581$	−15822.1	−1.12980
$582$	2475.09	0.176281
$583$	−5733.28	−0.407287
$584$	−5962.80	−0.422504
$585$	−2648.52	−0.187184
$586$	−2346.25	−0.165397
$587$	−3929.14	−0.276274	−0.138137	−	0.990413i	$-0.544111\pi$
$587$	−3929.14	−0.276274	−0.138137	+	0.990413i	$0.544111\pi$
$588$	−23108.9	−1.62074
$589$	6158.15	0.430802
$590$	3857.17	0.269147
$591$	−4602.09	−0.320312
$592$	12000.3	0.833123
$593$	−12857.6	−0.890386	−0.445193	−	0.895435i	$-0.646865\pi$
$593$	−12857.6	−0.890386	−0.445193	+	0.895435i	$0.646865\pi$
$594$	3092.76	0.213632
$595$	21138.3	1.45644
$596$	9167.36	0.630050
$597$	−15345.5	−1.05201
$598$	−123.053	−0.00841476
$599$	−16097.0	−1.09801	−0.549004	−	0.835820i	$-0.684993\pi$
$599$	−16097.0	−1.09801	−0.549004	+	0.835820i	$0.684993\pi$
$600$	−4260.02	−0.289858
$601$	242.345	0.0164483	0.00822416	−	0.999966i	$-0.497382\pi$
$601$	242.345	0.0164483	0.00822416	+	0.999966i	$0.497382\pi$
$602$	0	0
$603$	61.9906	0.00418649
$604$	−6491.59	−0.437316
$605$	6174.49	0.414924
$606$	−6280.51	−0.421004
$607$	2132.21	0.142576	0.0712882	−	0.997456i	$-0.477289\pi$
$607$	2132.21	0.142576	0.0712882	+	0.997456i	$0.477289\pi$
$608$	−17666.7	−1.17842
$609$	−20866.9	−1.38845
$610$	754.114	0.0500544
$611$	−19911.2	−1.31836
$612$	6054.32	0.399888
$613$	−26948.2	−1.77557	−0.887787	−	0.460254i	$-0.847758\pi$
$613$	−26948.2	−1.77557	−0.887787	+	0.460254i	$0.847758\pi$
$614$	−2491.19	−0.163740
$615$	13396.7	0.878382
$616$	−10271.0	−0.671802
$617$	−4081.93	−0.266341	−0.133170	−	0.991093i	$-0.542516\pi$
$617$	−4081.93	−0.266341	−0.133170	+	0.991093i	$0.542516\pi$
$618$	2083.63	0.135624
$619$	−3662.59	−0.237822	−0.118911	−	0.992905i	$-0.537940\pi$
$619$	−3662.59	−0.237822	−0.118911	+	0.992905i	$0.537940\pi$
$620$	2755.36	0.178481
$621$	535.069	0.0345758
$622$	3489.69	0.224958
$623$	−28011.4	−1.80137
$624$	−6923.34	−0.444159
$625$	−1209.06	−0.0773797
$626$	−4224.14	−0.269698
$627$	10450.5	0.665633
$628$	14096.3	0.895710
$629$	23817.9	1.50983
$630$	2179.37	0.137823
$631$	−15666.2	−0.988367	−0.494184	−	0.869358i	$-0.664533\pi$
$631$	−15666.2	−0.988367	−0.494184	+	0.869358i	$0.664533\pi$
$632$	−5565.05	−0.350263
$633$	−3337.77	−0.209581
$634$	8965.66	0.561627
$635$	17231.8	1.07689
$636$	7801.15	0.486377
$637$	−29426.2	−1.83031
$638$	−3035.58	−0.188369
$639$	5535.09	0.342668
$640$	−10267.6	−0.634159
$641$	−10576.0	−0.651679	−0.325839	−	0.945425i	$-0.605647\pi$
$641$	−10576.0	−0.651679	−0.325839	+	0.945425i	$0.605647\pi$
$642$	−994.024	−0.0611075
$643$	3630.64	0.222672	0.111336	−	0.993783i	$-0.464487\pi$
$643$	3630.64	0.222672	0.111336	+	0.993783i	$0.464487\pi$
$644$	−837.849	−0.0512669
$645$	0	0
$646$	−9351.47	−0.569549
$647$	20208.7	1.22795	0.613977	−	0.789324i	$-0.289569\pi$
$647$	20208.7	1.22795	0.613977	+	0.789324i	$0.289569\pi$
$648$	−5241.60	−0.317761
$649$	12547.1	0.758884
$650$	−2557.74	−0.154343
$651$	−7446.04	−0.448285
$652$	13493.0	0.810468
$653$	−13988.7	−0.838316	−0.419158	−	0.907913i	$-0.637675\pi$
$653$	−13988.7	−0.838316	−0.419158	+	0.907913i	$0.637675\pi$
$654$	7428.47	0.444153
$655$	−5074.46	−0.302711
$656$	−19647.3	−1.16936
$657$	4115.70	0.244397
$658$	16384.2	0.970704
$659$	−9951.46	−0.588245	−0.294123	−	0.955768i	$-0.595027\pi$
$659$	−9951.46	−0.588245	−0.294123	+	0.955768i	$0.595027\pi$
$660$	4675.89	0.275771
$661$	11708.5	0.688969	0.344484	−	0.938792i	$-0.388054\pi$
$661$	11708.5	0.688969	0.344484	+	0.938792i	$0.388054\pi$
$662$	−4829.52	−0.283542
$663$	−13741.3	−0.804927
$664$	6642.23	0.388206
$665$	27854.1	1.62426
$666$	2455.64	0.142874
$667$	−525.176	−0.0304871
$668$	−26205.8	−1.51787
$669$	19568.3	1.13088
$670$	−42.8419	−0.00247034
$671$	2453.08	0.141133
$672$	21361.5	1.22624
$673$	29959.1	1.71595	0.857977	−	0.513688i	$-0.171721\pi$
$673$	29959.1	1.71595	0.857977	+	0.513688i	$0.171721\pi$
$674$	9512.93	0.543657
$675$	11121.7	0.634186
$676$	5483.63	0.311995
$677$	6509.81	0.369560	0.184780	−	0.982780i	$-0.440843\pi$
$677$	6509.81	0.369560	0.184780	+	0.982780i	$0.440843\pi$
$678$	−889.779	−0.0504008
$679$	21459.4	1.21287
$680$	−8873.99	−0.500444
$681$	5406.61	0.304232
$682$	−1083.20	−0.0608181
$683$	18770.4	1.05158	0.525791	−	0.850614i	$-0.323770\pi$
$683$	18770.4	1.05158	0.525791	+	0.850614i	$0.323770\pi$
$684$	7977.85	0.445966
$685$	2938.34	0.163895
$686$	13545.5	0.753891
$687$	−16646.0	−0.924432
$688$	0	0
$689$	9933.77	0.549269
$690$	−97.7652	−0.00539400
$691$	−23467.6	−1.29197	−0.645985	−	0.763350i	$-0.723553\pi$
$691$	−23467.6	−1.29197	−0.645985	+	0.763350i	$0.723553\pi$
$692$	17588.5	0.966206
$693$	7089.33	0.388602
$694$	4899.55	0.267989
$695$	4549.72	0.248318
$696$	8760.07	0.477083
$697$	−38995.5	−2.11917
$698$	−71.2994	−0.00386636
$699$	28158.8	1.52369
$700$	−17415.2	−0.940333
$701$	12471.1	0.671938	0.335969	−	0.941873i	$-0.390936\pi$
$701$	12471.1	0.671938	0.335969	+	0.941873i	$0.390936\pi$
$702$	−5358.67	−0.288105
$703$	31385.1	1.68380
$704$	−4578.81	−0.245129
$705$	−15819.3	−0.845093
$706$	1142.51	0.0609048
$707$	−54453.1	−2.89663
$708$	−17072.5	−0.906250
$709$	29195.7	1.54650	0.773250	−	0.634102i	$-0.218630\pi$
$709$	29195.7	1.54650	0.773250	+	0.634102i	$0.218630\pi$
$710$	−3825.32	−0.202199
$711$	3841.16	0.202609
$712$	11759.4	0.618963
$713$	−187.401	−0.00984325
$714$	11307.2	0.592663
$715$	5954.15	0.311430
$716$	8249.63	0.430591
$717$	−25092.3	−1.30696
$718$	−462.577	−0.0240435
$719$	−14395.4	−0.746670	−0.373335	−	0.927697i	$-0.621786\pi$
$719$	−14395.4	−0.746670	−0.373335	+	0.927697i	$0.621786\pi$
$720$	3086.03	0.159736
$721$	18065.4	0.933135
$722$	−5952.24	−0.306814
$723$	7159.71	0.368288
$724$	890.635	0.0457185
$725$	−10916.1	−0.559192
$726$	3302.84	0.168843
$727$	19221.5	0.980587	0.490293	−	0.871557i	$-0.336890\pi$
$727$	19221.5	0.980587	0.490293	+	0.871557i	$0.336890\pi$
$728$	17796.0	0.905996
$729$	20758.5	1.05464
$730$	−2844.37	−0.144212
$731$	0	0
$732$	−3337.85	−0.168539
$733$	−1107.28	−0.0557958	−0.0278979	−	0.999611i	$-0.508881\pi$
$733$	−1107.28	−0.0557958	−0.0278979	+	0.999611i	$0.508881\pi$
$734$	7544.94	0.379412
$735$	−23378.9	−1.17326
$736$	537.624	0.0269254
$737$	−139.362	−0.00696533
$738$	−4020.47	−0.200536
$739$	−31591.9	−1.57257	−0.786283	−	0.617867i	$-0.787997\pi$
$739$	−31591.9	−1.57257	−0.786283	+	0.617867i	$0.787997\pi$
$740$	14042.7	0.697596
$741$	−18107.0	−0.897676
$742$	−8174.14	−0.404424
$743$	29466.4	1.45494	0.727468	−	0.686142i	$-0.240697\pi$
$743$	29466.4	1.45494	0.727468	+	0.686142i	$0.240697\pi$
$744$	3125.90	0.154034
$745$	9274.50	0.456096
$746$	−4143.05	−0.203335
$747$	−4584.66	−0.224557
$748$	−13610.8	−0.665319
$749$	−8618.35	−0.420437
$750$	−5518.46	−0.268674
$751$	−5615.56	−0.272856	−0.136428	−	0.990650i	$-0.543562\pi$
$751$	−5615.56	−0.272856	−0.136428	+	0.990650i	$0.543562\pi$
$752$	23200.4	1.12504
$753$	19888.0	0.962494
$754$	5259.59	0.254036
$755$	−6567.46	−0.316575
$756$	−36486.2	−1.75528
$757$	−18192.9	−0.873488	−0.436744	−	0.899586i	$-0.643869\pi$
$757$	−18192.9	−0.873488	−0.436744	+	0.899586i	$0.643869\pi$
$758$	2949.98	0.141356
$759$	−318.023	−0.0152088
$760$	−11693.4	−0.558109
$761$	27160.4	1.29378	0.646889	−	0.762584i	$-0.276070\pi$
$761$	27160.4	1.29378	0.646889	+	0.762584i	$0.276070\pi$
$762$	9217.57	0.438212
$763$	64406.0	3.05590
$764$	−27997.5	−1.32581
$765$	6125.08	0.289481
$766$	−9047.77	−0.426774
$767$	−21739.7	−1.02344
$768$	1490.94	0.0700518
$769$	−31551.5	−1.47955	−0.739776	−	0.672853i	$-0.765069\pi$
$769$	−31551.5	−1.47955	−0.739776	+	0.672853i	$0.765069\pi$
$770$	−4899.46	−0.229304
$771$	25069.9	1.17104
$772$	23704.5	1.10511
$773$	19613.7	0.912619	0.456309	−	0.889821i	$-0.349171\pi$
$773$	19613.7	0.912619	0.456309	+	0.889821i	$0.349171\pi$
$774$	0	0
$775$	−3895.25	−0.180544
$776$	−9008.81	−0.416749
$777$	−37948.8	−1.75213
$778$	5563.14	0.256360
$779$	−51384.8	−2.36335
$780$	−8101.69	−0.371906
$781$	−12443.5	−0.570119
$782$	284.579	0.0130134
$783$	−22870.1	−1.04382
$784$	34287.2	1.56192
$785$	14261.1	0.648408
$786$	−2714.41	−0.123180
$787$	19355.7	0.876693	0.438347	−	0.898806i	$-0.355564\pi$
$787$	19355.7	0.876693	0.438347	+	0.898806i	$0.355564\pi$
$788$	7898.08	0.357052
$789$	−6126.11	−0.276420
$790$	−2654.64	−0.119554
$791$	−7714.53	−0.346772
$792$	−2976.15	−0.133526
$793$	−4250.33	−0.190332
$794$	5922.59	0.264717
$795$	7892.32	0.352090
$796$	26335.8	1.17267
$797$	−15317.5	−0.680771	−0.340386	−	0.940286i	$-0.610558\pi$
$797$	−15317.5	−0.680771	−0.340386	+	0.940286i	$0.610558\pi$
$798$	14899.6	0.660954
$799$	46047.5	2.03885
$800$	11174.8	0.493863
$801$	−8116.66	−0.358038
$802$	−10337.6	−0.455153
$803$	−9252.53	−0.406618
$804$	189.626	0.00831792
$805$	−847.641	−0.0371123
$806$	1876.81	0.0820196
$807$	6776.79	0.295606
$808$	22859.8	0.995303
$809$	−39005.9	−1.69515	−0.847573	−	0.530678i	$-0.821937\pi$
$809$	−39005.9	−1.69515	−0.847573	+	0.530678i	$0.821937\pi$
$810$	−2500.34	−0.108461
$811$	28344.6	1.22727	0.613633	−	0.789591i	$-0.289707\pi$
$811$	28344.6	1.22727	0.613633	+	0.789591i	$0.289707\pi$
$812$	35811.6	1.54771
$813$	−29625.6	−1.27800
$814$	−5520.55	−0.237709
$815$	13650.6	0.586701
$816$	16011.2	0.686893
$817$	0	0
$818$	4534.14	0.193805
$819$	−12283.3	−0.524071
$820$	−22991.3	−0.979134
$821$	−17104.4	−0.727096	−0.363548	−	0.931575i	$-0.618435\pi$
$821$	−17104.4	−0.727096	−0.363548	+	0.931575i	$0.618435\pi$
$822$	1571.77	0.0666931
$823$	5202.60	0.220354	0.110177	−	0.993912i	$-0.464858\pi$
$823$	5202.60	0.220354	0.110177	+	0.993912i	$0.464858\pi$
$824$	−7583.98	−0.320632
$825$	−6610.31	−0.278959
$826$	17888.8	0.753549
$827$	31811.8	1.33761	0.668805	−	0.743438i	$-0.266806\pi$
$827$	31811.8	1.33761	0.668805	+	0.743438i	$0.266806\pi$
$828$	−242.777	−0.0101897
$829$	2820.60	0.118171	0.0590854	−	0.998253i	$-0.481182\pi$
$829$	2820.60	0.118171	0.0590854	+	0.998253i	$0.481182\pi$
$830$	3168.47	0.132505
$831$	19104.9	0.797523
$832$	7933.49	0.330582
$833$	68052.3	2.83058
$834$	2433.72	0.101047
$835$	−26512.1	−1.09879
$836$	−17935.1	−0.741982
$837$	−8160.86	−0.337014
$838$	13209.5	0.544528
$839$	−33523.4	−1.37945	−0.689723	−	0.724074i	$-0.742268\pi$
$839$	−33523.4	−1.37945	−0.689723	+	0.724074i	$0.742268\pi$
$840$	14138.9	0.580758
$841$	−1941.73	−0.0796152
$842$	10553.3	0.431937
$843$	−13295.3	−0.543196
$844$	5728.27	0.233620
$845$	5547.72	0.225855
$846$	4747.53	0.192936
$847$	28636.2	1.16169
$848$	−11574.7	−0.468725
$849$	35984.9	1.45465
$850$	5915.15	0.238692
$851$	−955.093	−0.0384726
$852$	16931.6	0.680829
$853$	−4185.92	−0.168023	−0.0840113	−	0.996465i	$-0.526773\pi$
$853$	−4185.92	−0.168023	−0.0840113	+	0.996465i	$0.526773\pi$
$854$	3497.44	0.140140
$855$	8071.08	0.322837
$856$	3618.04	0.144465
$857$	32627.5	1.30051	0.650254	−	0.759717i	$-0.274663\pi$
$857$	32627.5	1.30051	0.650254	+	0.759717i	$0.274663\pi$
$858$	3184.97	0.126729
$859$	−23475.1	−0.932433	−0.466217	−	0.884671i	$-0.654383\pi$
$859$	−23475.1	−0.932433	−0.466217	+	0.884671i	$0.654383\pi$
$860$	0	0
$861$	62131.2	2.45926
$862$	7916.61	0.312808
$863$	−2337.41	−0.0921975	−0.0460987	−	0.998937i	$-0.514679\pi$
$863$	−2337.41	−0.0921975	−0.0460987	+	0.998937i	$0.514679\pi$
$864$	23412.2	0.921873
$865$	17794.1	0.699441
$866$	−2212.35	−0.0868113
$867$	11346.2	0.444448
$868$	12778.9	0.499704
$869$	−8635.34	−0.337093
$870$	4178.72	0.162841
$871$	241.465	0.00939348
$872$	−27038.1	−1.05003
$873$	6218.14	0.241068
$874$	374.992	0.0145129
$875$	−47846.0	−1.84856
$876$	12589.7	0.485579
$877$	−31546.5	−1.21465	−0.607326	−	0.794453i	$-0.707758\pi$
$877$	−31546.5	−1.21465	−0.607326	+	0.794453i	$0.707758\pi$
$878$	−7282.74	−0.279932
$879$	10506.3	0.403150
$880$	−6937.73	−0.265762
$881$	−8467.25	−0.323801	−0.161901	−	0.986807i	$-0.551762\pi$
$881$	−8467.25	−0.323801	−0.161901	+	0.986807i	$0.551762\pi$
$882$	7016.25	0.267856
$883$	−33603.1	−1.28067	−0.640336	−	0.768095i	$-0.721205\pi$
$883$	−33603.1	−1.28067	−0.640336	+	0.768095i	$0.721205\pi$
$884$	23582.7	0.897254
$885$	−17272.1	−0.656039
$886$	−13456.1	−0.510232
$887$	−17129.2	−0.648415	−0.324207	−	0.945986i	$-0.605098\pi$
$887$	−17129.2	−0.648415	−0.324207	+	0.945986i	$0.605098\pi$
$888$	15931.2	0.602045
$889$	79917.8	3.01503
$890$	5609.45	0.211269
$891$	−8133.43	−0.305814
$892$	−33583.1	−1.26059
$893$	60677.3	2.27378
$894$	4961.09	0.185597
$895$	8346.04	0.311707
$896$	−47619.1	−1.77550
$897$	551.023	0.0205107
$898$	3975.18	0.147721
$899$	8009.98	0.297161
$900$	−5046.28	−0.186899
$901$	−22973.3	−0.849446
$902$	9038.44	0.333644
$903$	0	0
$904$	3238.61	0.119153
$905$	901.043	0.0330958
$906$	−3513.04	−0.128822
$907$	20927.5	0.766138	0.383069	−	0.923720i	$-0.374867\pi$
$907$	20927.5	0.766138	0.383069	+	0.923720i	$0.374867\pi$
$908$	−9278.80	−0.339127
$909$	−15778.5	−0.575730
$910$	8489.05	0.309241
$911$	46040.5	1.67441	0.837206	−	0.546888i	$-0.184188\pi$
$911$	46040.5	1.67441	0.837206	+	0.546888i	$0.184188\pi$
$912$	21098.2	0.766041
$913$	10306.8	0.373609
$914$	5078.80	0.183798
$915$	−3376.86	−0.122006
$916$	28567.8	1.03047
$917$	−23534.4	−0.847518
$918$	12392.7	0.445555
$919$	−21510.4	−0.772104	−0.386052	−	0.922477i	$-0.626162\pi$
$919$	−21510.4	−0.772104	−0.386052	+	0.922477i	$0.626162\pi$
$920$	355.846	0.0127520
$921$	11155.3	0.399110
$922$	7418.46	0.264982
$923$	21560.2	0.768865
$924$	21685.9	0.772094
$925$	−19852.2	−0.705661
$926$	2468.03	0.0875860
$927$	5234.68	0.185469
$928$	−22979.3	−0.812859
$929$	6327.56	0.223467	0.111733	−	0.993738i	$-0.464360\pi$
$929$	6327.56	0.223467	0.111733	+	0.993738i	$0.464360\pi$
$930$	1491.11	0.0525759
$931$	89673.3	3.15674
$932$	−48325.9	−1.69846
$933$	−15626.5	−0.548327
$934$	−2308.08	−0.0808594
$935$	−13769.8	−0.481628
$936$	5156.63	0.180075
$937$	−18761.8	−0.654133	−0.327066	−	0.945001i	$-0.606060\pi$
$937$	−18761.8	−0.654133	−0.327066	+	0.945001i	$0.606060\pi$
$938$	−198.693	−0.00691636
$939$	18915.4	0.657380
$940$	27149.1	0.942026
$941$	638.717	0.0221271	0.0110635	−	0.999939i	$-0.496478\pi$
$941$	638.717	0.0221271	0.0110635	+	0.999939i	$0.496478\pi$
$942$	7628.50	0.263853
$943$	1563.71	0.0539995
$944$	25330.9	0.873359
$945$	−36912.6	−1.27065
$946$	0	0
$947$	−11356.8	−0.389699	−0.194850	−	0.980833i	$-0.562422\pi$
$947$	−11356.8	−0.389699	−0.194850	+	0.980833i	$0.562422\pi$
$948$	11749.9	0.402552
$949$	16031.4	0.548368
$950$	7794.45	0.266195
$951$	−40147.5	−1.36895
$952$	−41155.9	−1.40112
$953$	18470.0	0.627809	0.313904	−	0.949455i	$-0.398363\pi$
$953$	18470.0	0.627809	0.313904	+	0.949455i	$0.398363\pi$
$954$	−2368.56	−0.0803827
$955$	−28324.7	−0.959756
$956$	43063.2	1.45687
$957$	13593.1	0.459144
$958$	498.551	0.0168136
$959$	13627.5	0.458868
$960$	6303.11	0.211908
$961$	−26932.8	−0.904057
$962$	9565.18	0.320576
$963$	−2497.28	−0.0835655
$964$	−12287.5	−0.410531
$965$	23981.5	0.799993
$966$	−453.417	−0.0151019
$967$	−29051.7	−0.966120	−0.483060	−	0.875587i	$-0.660475\pi$
$967$	−29051.7	−0.966120	−0.483060	+	0.875587i	$0.660475\pi$
$968$	−12021.7	−0.399164
$969$	41875.1	1.38826
$970$	−4297.37	−0.142248
$971$	−10491.2	−0.346734	−0.173367	−	0.984857i	$-0.555465\pi$
$971$	−10491.2	−0.346734	−0.173367	+	0.984857i	$0.555465\pi$
$972$	−18349.6	−0.605517
$973$	21100.8	0.695230
$974$	8343.67	0.274485
$975$	11453.4	0.376206
$976$	4952.44	0.162422
$977$	−1951.61	−0.0639075	−0.0319537	−	0.999489i	$-0.510173\pi$
$977$	−1951.61	−0.0639075	−0.0319537	+	0.999489i	$0.510173\pi$
$978$	7301.96	0.238743
$979$	18247.1	0.595690
$980$	40122.8	1.30783
$981$	18662.5	0.607387
$982$	14651.6	0.476121
$983$	−58691.5	−1.90434	−0.952172	−	0.305563i	$-0.901155\pi$
$983$	−58691.5	−1.90434	−0.952172	+	0.305563i	$0.901155\pi$
$984$	−26083.1	−0.845020
$985$	7990.38	0.258472
$986$	−12163.6	−0.392867
$987$	−73367.1	−2.36606
$988$	31075.2	1.00064
$989$	0	0
$990$	−1419.68	−0.0455762
$991$	−7723.20	−0.247564	−0.123782	−	0.992309i	$-0.539502\pi$
$991$	−7723.20	−0.247564	−0.123782	+	0.992309i	$0.539502\pi$
$992$	−8199.83	−0.262445
$993$	21626.2	0.691124
$994$	−17741.1	−0.566111
$995$	26643.6	0.848904
$996$	−14024.2	−0.446160
$997$	51198.5	1.62635	0.813176	−	0.582018i	$-0.197737\pi$
$997$	51198.5	1.62635	0.813176	+	0.582018i	$0.197737\pi$
$998$	−8975.85	−0.284695
$999$	−41591.9	−1.31723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.23	✓	50
43.42	odd	2		1849.4.a.j.1.28	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.23	✓	50	1.1	even	1	trivial
1849.4.a.j.1.28	yes	50	43.42	odd	2

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-0.928750 q^{2} +4.15887 q^{3} -7.13742 q^{4} -7.22084 q^{5} -3.86255 q^{6} -33.4889 q^{7} +14.0589 q^{8} -9.70384 q^{9} +O(q^{10})\)	\(q-0.928750 q^{2} +4.15887 q^{3} -7.13742 q^{4} -7.22084 q^{5} -3.86255 q^{6} -33.4889 q^{7} +14.0589 q^{8} -9.70384 q^{9} +6.70635 q^{10} +21.8153 q^{11} -29.6836 q^{12} -37.7982 q^{13} +31.1028 q^{14} -30.0305 q^{15} +44.0422 q^{16} +87.4139 q^{17} +9.01244 q^{18} +115.186 q^{19} +51.5382 q^{20} -139.276 q^{21} -20.2609 q^{22} -3.50528 q^{23} +58.4690 q^{24} -72.8595 q^{25} +35.1051 q^{26} -152.646 q^{27} +239.025 q^{28} +149.824 q^{29} +27.8908 q^{30} +53.4626 q^{31} -153.375 q^{32} +90.7268 q^{33} -81.1857 q^{34} +241.818 q^{35} +69.2604 q^{36} +272.472 q^{37} -106.979 q^{38} -157.198 q^{39} -101.517 q^{40} -446.102 q^{41} +129.352 q^{42} -155.705 q^{44} +70.0699 q^{45} +3.25553 q^{46} +526.776 q^{47} +183.166 q^{48} +778.507 q^{49} +67.6683 q^{50} +363.543 q^{51} +269.782 q^{52} -262.810 q^{53} +141.770 q^{54} -157.525 q^{55} -470.817 q^{56} +479.044 q^{57} -139.149 q^{58} +575.151 q^{59} +214.340 q^{60} +112.448 q^{61} -49.6533 q^{62} +324.971 q^{63} -209.890 q^{64} +272.935 q^{65} -84.2625 q^{66} -6.38826 q^{67} -623.910 q^{68} -14.5780 q^{69} -224.588 q^{70} -570.402 q^{71} -136.425 q^{72} -424.131 q^{73} -253.059 q^{74} -303.013 q^{75} -822.133 q^{76} -730.570 q^{77} +145.997 q^{78} -395.839 q^{79} -318.022 q^{80} -372.832 q^{81} +414.317 q^{82} +472.458 q^{83} +994.071 q^{84} -631.202 q^{85} +623.098 q^{87} +306.698 q^{88} +836.438 q^{89} -65.0774 q^{90} +1265.82 q^{91} +25.0187 q^{92} +222.344 q^{93} -489.243 q^{94} -831.741 q^{95} -637.867 q^{96} -640.791 q^{97} -723.038 q^{98} -211.692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

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