LMFDB - Embedded newform 1849.4.a.j.1.21

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			1.21
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)

$f(q)$	$=$	$q-1.06529 q^{2} -0.463524 q^{3} -6.86516 q^{4} -5.41130 q^{5} +0.493788 q^{6} -4.55619 q^{7} +15.8357 q^{8} -26.7851 q^{9} +O(q^{10})$	\(q-1.06529 q^{2} -0.463524 q^{3} -6.86516 q^{4} -5.41130 q^{5} +0.493788 q^{6} -4.55619 q^{7} +15.8357 q^{8} -26.7851 q^{9} +5.76461 q^{10} +10.2865 q^{11} +3.18216 q^{12} +4.48831 q^{13} +4.85366 q^{14} +2.50827 q^{15} +38.0516 q^{16} -32.2212 q^{17} +28.5340 q^{18} -54.9889 q^{19} +37.1494 q^{20} +2.11190 q^{21} -10.9581 q^{22} +136.229 q^{23} -7.34023 q^{24} -95.7178 q^{25} -4.78136 q^{26} +24.9307 q^{27} +31.2789 q^{28} -87.3472 q^{29} -2.67203 q^{30} +27.1204 q^{31} -167.222 q^{32} -4.76801 q^{33} +34.3250 q^{34} +24.6549 q^{35} +183.884 q^{36} +287.935 q^{37} +58.5791 q^{38} -2.08044 q^{39} -85.6918 q^{40} +285.555 q^{41} -2.24979 q^{42} -70.6181 q^{44} +144.942 q^{45} -145.124 q^{46} -62.1624 q^{47} -17.6378 q^{48} -322.241 q^{49} +101.967 q^{50} +14.9353 q^{51} -30.8129 q^{52} +310.227 q^{53} -26.5584 q^{54} -55.6631 q^{55} -72.1505 q^{56} +25.4886 q^{57} +93.0501 q^{58} +561.966 q^{59} -17.2196 q^{60} +381.217 q^{61} -28.8911 q^{62} +122.038 q^{63} -126.273 q^{64} -24.2876 q^{65} +5.07932 q^{66} -167.929 q^{67} +221.204 q^{68} -63.1455 q^{69} -26.2646 q^{70} +328.805 q^{71} -424.162 q^{72} +1034.34 q^{73} -306.735 q^{74} +44.3675 q^{75} +377.507 q^{76} -46.8670 q^{77} +2.21627 q^{78} -496.972 q^{79} -205.909 q^{80} +711.643 q^{81} -304.199 q^{82} +374.134 q^{83} -14.4985 q^{84} +174.359 q^{85} +40.4875 q^{87} +162.893 q^{88} -270.772 q^{89} -154.406 q^{90} -20.4496 q^{91} -935.236 q^{92} -12.5709 q^{93} +66.2210 q^{94} +297.561 q^{95} +77.5112 q^{96} -1118.35 q^{97} +343.281 q^{98} -275.524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.06529	−0.376637	−0.188319	−	0.982108i	$-0.560304\pi$
$2$	−1.06529	−0.376637	−0.188319	+	0.982108i	$0.560304\pi$
$3$	−0.463524	−0.0892052	−0.0446026	−	0.999005i	$-0.514202\pi$
$3$	−0.463524	−0.0892052	−0.0446026	+	0.999005i	$0.514202\pi$
$4$	−6.86516	−0.858144
$5$	−5.41130	−0.484001	−0.242001	−	0.970276i	$-0.577804\pi$
$5$	−5.41130	−0.484001	−0.242001	+	0.970276i	$0.577804\pi$
$6$	0.493788	0.0335980
$7$	−4.55619	−0.246011	−0.123005	−	0.992406i	$-0.539253\pi$
$7$	−4.55619	−0.246011	−0.123005	+	0.992406i	$0.539253\pi$
$8$	15.8357	0.699846
$9$	−26.7851	−0.992042
$10$	5.76461	0.182293
$11$	10.2865	0.281953	0.140976	−	0.990013i	$-0.454976\pi$
$11$	10.2865	0.281953	0.140976	+	0.990013i	$0.454976\pi$
$12$	3.18216	0.0765509
$13$	4.48831	0.0957564	0.0478782	−	0.998853i	$-0.484754\pi$
$13$	4.48831	0.0957564	0.0478782	+	0.998853i	$0.484754\pi$
$14$	4.85366	0.0926569
$15$	2.50827	0.0431754
$16$	38.0516	0.594556
$17$	−32.2212	−0.459694	−0.229847	−	0.973227i	$-0.573823\pi$
$17$	−32.2212	−0.459694	−0.229847	+	0.973227i	$0.573823\pi$
$18$	28.5340	0.373640
$19$	−54.9889	−0.663964	−0.331982	−	0.943286i	$-0.607717\pi$
$19$	−54.9889	−0.663964	−0.331982	+	0.943286i	$0.607717\pi$
$20$	37.1494	0.415343
$21$	2.11190	0.0219454
$22$	−10.9581	−0.106194
$23$	136.229	1.23503	0.617517	−	0.786558i	$-0.288139\pi$
$23$	136.229	1.23503	0.617517	+	0.786558i	$0.288139\pi$
$24$	−7.34023	−0.0624299
$25$	−95.7178	−0.765743
$26$	−4.78136	−0.0360654
$27$	24.9307	0.177700
$28$	31.2789	0.211113
$29$	−87.3472	−0.559309	−0.279654	−	0.960101i	$-0.590220\pi$
$29$	−87.3472	−0.559309	−0.279654	+	0.960101i	$0.590220\pi$
$30$	−2.67203	−0.0162615
$31$	27.1204	0.157128	0.0785639	−	0.996909i	$-0.474967\pi$
$31$	27.1204	0.157128	0.0785639	+	0.996909i	$0.474967\pi$
$32$	−167.222	−0.923778
$33$	−4.76801	−0.0251517
$34$	34.3250	0.173138
$35$	24.6549	0.119070
$36$	183.884	0.851316
$37$	287.935	1.27936	0.639680	−	0.768642i	$-0.279067\pi$
$37$	287.935	1.27936	0.639680	+	0.768642i	$0.279067\pi$
$38$	58.5791	0.250073
$39$	−2.08044	−0.00854197
$40$	−85.6918	−0.338727
$41$	285.555	1.08771	0.543856	−	0.839179i	$-0.316964\pi$
$41$	285.555	1.08771	0.543856	+	0.839179i	$0.316964\pi$
$42$	−2.24979	−0.00826547
$43$	0	0
$43$	0	0
$44$	−70.6181	−0.241956
$45$	144.942	0.480150
$46$	−145.124	−0.465160
$47$	−62.1624	−0.192922	−0.0964608	−	0.995337i	$-0.530752\pi$
$47$	−62.1624	−0.192922	−0.0964608	+	0.995337i	$0.530752\pi$
$48$	−17.6378	−0.0530375
$49$	−322.241	−0.939479
$50$	101.967	0.288407
$51$	14.9353	0.0410071
$52$	−30.8129	−0.0821728
$53$	310.227	0.804019	0.402010	−	0.915635i	$-0.368312\pi$
$53$	310.227	0.804019	0.402010	+	0.915635i	$0.368312\pi$
$54$	−26.5584	−0.0669286
$55$	−55.6631	−0.136466
$56$	−72.1505	−0.172170
$57$	25.4886	0.0592290
$58$	93.0501	0.210657
$59$	561.966	1.24003	0.620015	−	0.784590i	$-0.287126\pi$
$59$	561.966	1.24003	0.620015	+	0.784590i	$0.287126\pi$
$60$	−17.2196	−0.0370507
$61$	381.217	0.800162	0.400081	−	0.916480i	$-0.368982\pi$
$61$	381.217	0.800162	0.400081	+	0.916480i	$0.368982\pi$
$62$	−28.8911	−0.0591802
$63$	122.038	0.244053
$64$	−126.273	−0.246627
$65$	−24.2876	−0.0463462
$66$	5.07932	0.00947305
$67$	−167.929	−0.306206	−0.153103	−	0.988210i	$-0.548927\pi$
$67$	−167.929	−0.306206	−0.153103	+	0.988210i	$0.548927\pi$
$68$	221.204	0.394484
$69$	−63.1455	−0.110171
$70$	−26.2646	−0.0448460
$71$	328.805	0.549605	0.274802	−	0.961501i	$-0.411388\pi$
$71$	328.805	0.549605	0.274802	+	0.961501i	$0.411388\pi$
$72$	−424.162	−0.694277
$73$	1034.34	1.65836	0.829178	−	0.558985i	$-0.188809\pi$
$73$	1034.34	1.65836	0.829178	+	0.558985i	$0.188809\pi$
$74$	−306.735	−0.481854
$75$	44.3675	0.0683082
$76$	377.507	0.569777
$77$	−46.8670	−0.0693635
$78$	2.21627	0.00321722
$79$	−496.972	−0.707768	−0.353884	−	0.935289i	$-0.615139\pi$
$79$	−496.972	−0.707768	−0.353884	+	0.935289i	$0.615139\pi$
$80$	−205.909	−0.287766
$81$	711.643	0.976191
$82$	−304.199	−0.409672
$83$	374.134	0.494777	0.247389	−	0.968916i	$-0.420428\pi$
$83$	374.134	0.494777	0.247389	+	0.968916i	$0.420428\pi$
$84$	−14.4985	−0.0188324
$85$	174.359	0.222493
$86$	0	0
$87$	40.4875	0.0498933
$88$	162.893	0.197324
$89$	−270.772	−0.322492	−0.161246	−	0.986914i	$-0.551551\pi$
$89$	−270.772	−0.322492	−0.161246	+	0.986914i	$0.551551\pi$
$90$	−154.406	−0.180842
$91$	−20.4496	−0.0235571
$92$	−935.236	−1.05984
$93$	−12.5709	−0.0140166
$94$	66.2210	0.0726615
$95$	297.561	0.321359
$96$	77.5112	0.0824058
$97$	−1118.35	−1.17063	−0.585314	−	0.810807i	$-0.699029\pi$
$97$	−1118.35	−1.17063	−0.585314	+	0.810807i	$0.699029\pi$
$98$	343.281	0.353843
$99$	−275.524	−0.279709
$100$	657.118	0.657118
$101$	4.71204	0.00464223	0.00232112	−	0.999997i	$-0.499261\pi$
$101$	4.71204	0.00464223	0.00232112	+	0.999997i	$0.499261\pi$
$102$	−15.9105	−0.0154448
$103$	1132.30	1.08319	0.541594	−	0.840640i	$-0.317821\pi$
$103$	1132.30	1.08319	0.541594	+	0.840640i	$0.317821\pi$
$104$	71.0756	0.0670148
$105$	−11.4281	−0.0106216
$106$	−330.482	−0.302823
$107$	−1718.40	−1.55256	−0.776279	−	0.630389i	$-0.782895\pi$
$107$	−1718.40	−1.55256	−0.776279	+	0.630389i	$0.782895\pi$
$108$	−171.153	−0.152493
$109$	−778.298	−0.683921	−0.341961	−	0.939714i	$-0.611091\pi$
$109$	−778.298	−0.683921	−0.341961	+	0.939714i	$0.611091\pi$
$110$	59.2974	0.0513980
$111$	−133.465	−0.114125
$112$	−173.370	−0.146267
$113$	1039.73	0.865568	0.432784	−	0.901498i	$-0.357531\pi$
$113$	1039.73	0.865568	0.432784	+	0.901498i	$0.357531\pi$
$114$	−27.1528	−0.0223078
$115$	−737.178	−0.597758
$116$	599.652	0.479968
$117$	−120.220	−0.0949944
$118$	−598.658	−0.467042
$119$	146.806	0.113090
$120$	39.7202	0.0302162
$121$	−1225.19	−0.920503
$122$	−406.107	−0.301371
$123$	−132.361	−0.0970294
$124$	−186.186	−0.134838
$125$	1194.37	0.854622
$126$	−130.006	−0.0919195
$127$	−289.845	−0.202516	−0.101258	−	0.994860i	$-0.532287\pi$
$127$	−289.845	−0.202516	−0.101258	+	0.994860i	$0.532287\pi$
$128$	1472.29	1.01667
$129$	0	0
$130$	25.8733	0.0174557
$131$	1123.68	0.749441	0.374720	−	0.927138i	$-0.377739\pi$
$131$	1123.68	0.749441	0.374720	+	0.927138i	$0.377739\pi$
$132$	32.7332	0.0215838
$133$	250.539	0.163342
$134$	178.893	0.115329
$135$	−134.907	−0.0860073
$136$	−510.247	−0.321715
$137$	−2215.34	−1.38153	−0.690764	−	0.723080i	$-0.742726\pi$
$137$	−2215.34	−1.38153	−0.690764	+	0.723080i	$0.742726\pi$
$138$	67.2684	0.0414947
$139$	1955.65	1.19335	0.596676	−	0.802482i	$-0.296488\pi$
$139$	1955.65	1.19335	0.596676	+	0.802482i	$0.296488\pi$
$140$	−169.260	−0.102179
$141$	28.8137	0.0172096
$142$	−350.273	−0.207002
$143$	46.1688	0.0269988
$144$	−1019.22	−0.589825
$145$	472.662	0.270706
$146$	−1101.87	−0.624598
$147$	149.366	0.0838064
$148$	−1976.72	−1.09787
$149$	1648.94	0.906618	0.453309	−	0.891353i	$-0.350243\pi$
$149$	1648.94	0.906618	0.453309	+	0.891353i	$0.350243\pi$
$150$	−47.2643	−0.0257274
$151$	2643.96	1.42492	0.712459	−	0.701713i	$-0.247581\pi$
$151$	2643.96	1.42492	0.712459	+	0.701713i	$0.247581\pi$
$152$	−870.788	−0.464673
$153$	863.051	0.456036
$154$	49.9270	0.0261249
$155$	−146.757	−0.0760501
$156$	14.2825	0.00733024
$157$	−174.029	−0.0884651	−0.0442326	−	0.999021i	$-0.514084\pi$
$157$	−174.029	−0.0884651	−0.0442326	+	0.999021i	$0.514084\pi$
$158$	529.419	0.266572
$159$	−143.798	−0.0717227
$160$	904.887	0.447110
$161$	−620.686	−0.303832
$162$	−758.107	−0.367670
$163$	−2791.23	−1.34126	−0.670631	−	0.741791i	$-0.733977\pi$
$163$	−2791.23	−1.34126	−0.670631	+	0.741791i	$0.733977\pi$
$164$	−1960.38	−0.933413
$165$	25.8011	0.0121734
$166$	−398.561	−0.186352
$167$	1898.85	0.879865	0.439932	−	0.898031i	$-0.355002\pi$
$167$	1898.85	0.879865	0.439932	+	0.898031i	$0.355002\pi$
$168$	33.4434	0.0153584
$169$	−2176.86	−0.990831
$170$	−185.743	−0.0837990
$171$	1472.88	0.658680
$172$	0	0
$173$	−1658.22	−0.728740	−0.364370	−	0.931254i	$-0.618716\pi$
$173$	−1658.22	−0.728740	−0.364370	+	0.931254i	$0.618716\pi$
$174$	−43.1309	−0.0187917
$175$	436.108	0.188381
$176$	391.416	0.167637
$177$	−260.485	−0.110617
$178$	288.451	0.121463
$179$	−3555.98	−1.48484	−0.742420	−	0.669934i	$-0.766322\pi$
$179$	−3555.98	−1.48484	−0.742420	+	0.669934i	$0.766322\pi$
$180$	−995.052	−0.412038
$181$	−3643.83	−1.49637	−0.748187	−	0.663488i	$-0.769075\pi$
$181$	−3643.83	−1.49637	−0.748187	+	0.663488i	$0.769075\pi$
$182$	21.7847	0.00887249
$183$	−176.703	−0.0713786
$184$	2157.29	0.864334
$185$	−1558.10	−0.619212
$186$	13.3917	0.00527918
$187$	−331.442	−0.129612
$188$	426.755	0.165555
$189$	−113.589	−0.0437163
$190$	−316.989	−0.121036
$191$	−3297.38	−1.24916	−0.624581	−	0.780960i	$-0.714730\pi$
$191$	−3297.38	−1.24916	−0.624581	+	0.780960i	$0.714730\pi$
$192$	58.5305	0.0220004
$193$	−3679.64	−1.37236	−0.686182	−	0.727430i	$-0.740715\pi$
$193$	−3679.64	−1.37236	−0.686182	+	0.727430i	$0.740715\pi$
$194$	1191.36	0.440902
$195$	11.2579	0.00413432
$196$	2212.24	0.806208
$197$	−2520.85	−0.911692	−0.455846	−	0.890059i	$-0.650663\pi$
$197$	−2520.85	−0.911692	−0.455846	+	0.890059i	$0.650663\pi$
$198$	293.513	0.105349
$199$	4762.22	1.69641	0.848203	−	0.529672i	$-0.177685\pi$
$199$	4762.22	1.69641	0.848203	+	0.529672i	$0.177685\pi$
$200$	−1515.76	−0.535902
$201$	77.8391	0.0273151
$202$	−5.01969	−0.00174844
$203$	397.970	0.137596
$204$	−102.533	−0.0351900
$205$	−1545.22	−0.526454
$206$	−1206.22	−0.407969
$207$	−3648.92	−1.22521
$208$	170.787	0.0569326
$209$	−565.640	−0.187206
$210$	12.1743	0.00400050
$211$	581.138	0.189607	0.0948037	−	0.995496i	$-0.469778\pi$
$211$	581.138	0.189607	0.0948037	+	0.995496i	$0.469778\pi$
$212$	−2129.76	−0.689964
$213$	−152.409	−0.0490276
$214$	1830.59	0.584752
$215$	0	0
$216$	394.795	0.124363
$217$	−123.565	−0.0386552
$218$	829.114	0.257590
$219$	−479.439	−0.147934
$220$	382.136	0.117107
$221$	−144.619	−0.0440187
$222$	142.179	0.0429839
$223$	−5483.83	−1.64675	−0.823374	−	0.567500i	$-0.807911\pi$
$223$	−5483.83	−1.64675	−0.823374	+	0.567500i	$0.807911\pi$
$224$	761.893	0.227260
$225$	2563.82	0.759649
$226$	−1107.61	−0.326005
$227$	5427.63	1.58698	0.793490	−	0.608584i	$-0.208262\pi$
$227$	5427.63	1.58698	0.793490	+	0.608584i	$0.208262\pi$
$228$	−174.983	−0.0508270
$229$	513.813	0.148269	0.0741347	−	0.997248i	$-0.476381\pi$
$229$	513.813	0.148269	0.0741347	+	0.997248i	$0.476381\pi$
$230$	785.309	0.225138
$231$	21.7240	0.00618758
$232$	−1383.20	−0.391430
$233$	748.209	0.210373	0.105186	−	0.994453i	$-0.466456\pi$
$233$	748.209	0.210373	0.105186	+	0.994453i	$0.466456\pi$
$234$	128.069	0.0357784
$235$	336.379	0.0933743
$236$	−3857.99	−1.06412
$237$	230.358	0.0631366
$238$	−156.391	−0.0425938
$239$	5232.24	1.41609	0.708045	−	0.706167i	$-0.249577\pi$
$239$	5232.24	1.41609	0.708045	+	0.706167i	$0.249577\pi$
$240$	95.4435	0.0256702
$241$	−3231.66	−0.863774	−0.431887	−	0.901928i	$-0.642152\pi$
$241$	−3231.66	−0.863774	−0.431887	+	0.901928i	$0.642152\pi$
$242$	1305.18	0.346696
$243$	−1002.99	−0.264782
$244$	−2617.12	−0.686655
$245$	1743.74	0.454709
$246$	141.003	0.0365449
$247$	−246.807	−0.0635788
$248$	429.471	0.109965
$249$	−173.420	−0.0441367
$250$	−1272.35	−0.321882
$251$	−2668.67	−0.671094	−0.335547	−	0.942023i	$-0.608921\pi$
$251$	−2668.67	−0.671094	−0.335547	+	0.942023i	$0.608921\pi$
$252$	−837.810	−0.209433
$253$	1401.32	0.348221
$254$	308.769	0.0762752
$255$	−80.8194	−0.0198475
$256$	−558.235	−0.136288
$257$	4140.36	1.00494	0.502469	−	0.864595i	$-0.332425\pi$
$257$	4140.36	1.00494	0.502469	+	0.864595i	$0.332425\pi$
$258$	0	0
$259$	−1311.89	−0.314736
$260$	166.738	0.0397718
$261$	2339.61	0.554858
$262$	−1197.05	−0.282267
$263$	5040.77	1.18185	0.590926	−	0.806726i	$-0.298763\pi$
$263$	5040.77	1.18185	0.590926	+	0.806726i	$0.298763\pi$
$264$	−75.5049	−0.0176023
$265$	−1678.73	−0.389146
$266$	−266.897	−0.0615208
$267$	125.509	0.0287680
$268$	1152.86	0.262769
$269$	−6767.05	−1.53381	−0.766904	−	0.641762i	$-0.778204\pi$
$269$	−6767.05	−1.53381	−0.766904	+	0.641762i	$0.778204\pi$
$270$	143.716	0.0323935
$271$	−7973.39	−1.78727	−0.893633	−	0.448799i	$-0.851852\pi$
$271$	−7973.39	−1.78727	−0.893633	+	0.448799i	$0.851852\pi$
$272$	−1226.07	−0.273314
$273$	9.47886	0.00210142
$274$	2359.98	0.520335
$275$	−984.597	−0.215903
$276$	433.504	0.0945430
$277$	−1476.35	−0.320236	−0.160118	−	0.987098i	$-0.551187\pi$
$277$	−1476.35	−0.320236	−0.160118	+	0.987098i	$0.551187\pi$
$278$	−2083.34	−0.449461
$279$	−726.423	−0.155878
$280$	390.428	0.0833304
$281$	−6880.43	−1.46068	−0.730341	−	0.683082i	$-0.760639\pi$
$281$	−6880.43	−1.46068	−0.730341	+	0.683082i	$0.760639\pi$
$282$	−30.6950	−0.00648178
$283$	−275.458	−0.0578597	−0.0289299	−	0.999581i	$-0.509210\pi$
$283$	−275.458	−0.0578597	−0.0289299	+	0.999581i	$0.509210\pi$
$284$	−2257.30	−0.471640
$285$	−137.927	−0.0286669
$286$	−49.1832	−0.0101687
$287$	−1301.04	−0.267589
$288$	4479.06	0.916427
$289$	−3874.79	−0.788681
$290$	−503.522	−0.101958
$291$	518.380	0.104426
$292$	−7100.88	−1.42311
$293$	−4500.88	−0.897420	−0.448710	−	0.893678i	$-0.648116\pi$
$293$	−4500.88	−0.897420	−0.448710	+	0.893678i	$0.648116\pi$
$294$	−159.119	−0.0315646
$295$	−3040.97	−0.600176
$296$	4559.66	0.895355
$297$	256.448	0.0501032
$298$	−1756.60	−0.341466
$299$	611.439	0.118262
$300$	−304.590	−0.0586183
$301$	0	0
$302$	−2816.59	−0.536677
$303$	−2.18414	−0.000414111 0
$304$	−2092.41	−0.394764
$305$	−2062.88	−0.387279
$306$	−919.400	−0.171760
$307$	−8303.21	−1.54361	−0.771806	−	0.635858i	$-0.780646\pi$
$307$	−8303.21	−1.54361	−0.771806	+	0.635858i	$0.780646\pi$
$308$	321.749	0.0595239
$309$	−524.846	−0.0966260
$310$	156.338	0.0286433
$311$	9034.89	1.64734	0.823668	−	0.567073i	$-0.191924\pi$
$311$	9034.89	1.64734	0.823668	+	0.567073i	$0.191924\pi$
$312$	−32.9452	−0.00597806
$313$	4408.24	0.796065	0.398032	−	0.917371i	$-0.369693\pi$
$313$	4408.24	0.796065	0.398032	+	0.917371i	$0.369693\pi$
$314$	185.392	0.0333193
$315$	−660.385	−0.118122
$316$	3411.79	0.607367
$317$	−1062.85	−0.188314	−0.0941569	−	0.995557i	$-0.530016\pi$
$317$	−1062.85	−0.188314	−0.0941569	+	0.995557i	$0.530016\pi$
$318$	153.186	0.0270134
$319$	−898.492	−0.157699
$320$	683.301	0.119368
$321$	796.518	0.138496
$322$	661.211	0.114434
$323$	1771.81	0.305220
$324$	−4885.54	−0.837713
$325$	−429.611	−0.0733248
$326$	2973.47	0.505170
$327$	360.760	0.0610093
$328$	4521.96	0.761231
$329$	283.223	0.0474608
$330$	−27.4857	−0.00458497
$331$	9875.05	1.63982	0.819912	−	0.572489i	$-0.194022\pi$
$331$	9875.05	1.63982	0.819912	+	0.572489i	$0.194022\pi$
$332$	−2568.49	−0.424590
$333$	−7712.39	−1.26918
$334$	−2022.83	−0.331390
$335$	908.714	0.148204
$336$	80.3612	0.0130478
$337$	−4547.10	−0.735004	−0.367502	−	0.930023i	$-0.619787\pi$
$337$	−4547.10	−0.735004	−0.367502	+	0.930023i	$0.619787\pi$
$338$	2318.98	0.373184
$339$	−481.937	−0.0772131
$340$	−1197.00	−0.190931
$341$	278.972	0.0443027
$342$	−1569.05	−0.248084
$343$	3030.96	0.477133
$344$	0	0
$345$	341.699	0.0533231
$346$	1766.49	0.274471
$347$	−10601.8	−1.64016	−0.820081	−	0.572247i	$-0.806072\pi$
$347$	−10601.8	−1.64016	−0.820081	+	0.572247i	$0.806072\pi$
$348$	−277.953	−0.0428156
$349$	10990.8	1.68574	0.842870	−	0.538117i	$-0.180864\pi$
$349$	10990.8	1.68574	0.842870	+	0.538117i	$0.180864\pi$
$350$	−464.582	−0.0709513
$351$	111.897	0.0170160
$352$	−1720.12	−0.260462
$353$	−290.232	−0.0437606	−0.0218803	−	0.999761i	$-0.506965\pi$
$353$	−290.232	−0.0437606	−0.0218803	+	0.999761i	$0.506965\pi$
$354$	277.492	0.0416625
$355$	−1779.26	−0.266010
$356$	1858.89	0.276745
$357$	−68.0480	−0.0100882
$358$	3788.15	0.559246
$359$	3441.15	0.505896	0.252948	−	0.967480i	$-0.418600\pi$
$359$	3441.15	0.505896	0.252948	+	0.967480i	$0.418600\pi$
$360$	2295.27	0.336031
$361$	−3835.22	−0.559152
$362$	3881.74	0.563590
$363$	567.904	0.0821136
$364$	140.389	0.0202154
$365$	−5597.10	−0.802646
$366$	188.240	0.0268838
$367$	6785.05	0.965060	0.482530	−	0.875880i	$-0.339718\pi$
$367$	6785.05	0.965060	0.482530	+	0.875880i	$0.339718\pi$
$368$	5183.74	0.734297
$369$	−7648.62	−1.07906
$370$	1659.83	0.233218
$371$	−1413.45	−0.197797
$372$	86.3014	0.0120283
$373$	−8819.35	−1.22426	−0.612129	−	0.790758i	$-0.709687\pi$
$373$	−8819.35	−1.22426	−0.612129	+	0.790758i	$0.709687\pi$
$374$	353.082	0.0488167
$375$	−553.619	−0.0762367
$376$	−984.386	−0.135016
$377$	−392.041	−0.0535574
$378$	121.005	0.0164652
$379$	2684.12	0.363784	0.181892	−	0.983319i	$-0.441778\pi$
$379$	2684.12	0.363784	0.181892	+	0.983319i	$0.441778\pi$
$380$	−2042.80	−0.275773
$381$	134.350	0.0180655
$382$	3512.67	0.470481
$383$	−4907.07	−0.654673	−0.327336	−	0.944908i	$-0.606151\pi$
$383$	−4907.07	−0.654673	−0.327336	+	0.944908i	$0.606151\pi$
$384$	−682.442	−0.0906920
$385$	253.611	0.0335720
$386$	3919.89	0.516884
$387$	0	0
$388$	7677.62	1.00457
$389$	1999.95	0.260672	0.130336	−	0.991470i	$-0.458394\pi$
$389$	1999.95	0.260672	0.130336	+	0.991470i	$0.458394\pi$
$390$	−11.9929	−0.00155714
$391$	−4389.48	−0.567738
$392$	−5102.92	−0.657491
$393$	−520.854	−0.0668540
$394$	2685.44	0.343377
$395$	2689.26	0.342561
$396$	1891.52	0.240031
$397$	9540.63	1.20612	0.603061	−	0.797695i	$-0.293947\pi$
$397$	9540.63	1.20612	0.603061	+	0.797695i	$0.293947\pi$
$398$	−5073.15	−0.638929
$399$	−116.131	−0.0145710
$400$	−3642.22	−0.455277
$401$	6723.57	0.837304	0.418652	−	0.908147i	$-0.362503\pi$
$401$	6723.57	0.837304	0.418652	+	0.908147i	$0.362503\pi$
$402$	−82.9213	−0.0102879
$403$	121.725	0.0150460
$404$	−32.3489	−0.00398371
$405$	−3850.91	−0.472478
$406$	−423.954	−0.0518238
$407$	2961.83	0.360719
$408$	236.511	0.0286987
$409$	3107.78	0.375720	0.187860	−	0.982196i	$-0.439845\pi$
$409$	3107.78	0.375720	0.187860	+	0.982196i	$0.439845\pi$
$410$	1646.11	0.198282
$411$	1026.86	0.123239
$412$	−7773.38	−0.929532
$413$	−2560.42	−0.305061
$414$	3887.16	0.461458
$415$	−2024.55	−0.239473
$416$	−750.543	−0.0884577
$417$	−906.490	−0.106453
$418$	602.571	0.0705089
$419$	−16291.9	−1.89955	−0.949776	−	0.312931i	$-0.898689\pi$
$419$	−16291.9	−1.89955	−0.949776	+	0.312931i	$0.898689\pi$
$420$	78.4558	0.00911489
$421$	−2863.80	−0.331528	−0.165764	−	0.986165i	$-0.553009\pi$
$421$	−2863.80	−0.331528	−0.165764	+	0.986165i	$0.553009\pi$
$422$	−619.081	−0.0714132
$423$	1665.03	0.191386
$424$	4912.67	0.562690
$425$	3084.15	0.352007
$426$	162.360	0.0184656
$427$	−1736.90	−0.196849
$428$	11797.1	1.33232
$429$	−21.4003	−0.00240843
$430$	0	0
$431$	−4365.79	−0.487918	−0.243959	−	0.969786i	$-0.578446\pi$
$431$	−4365.79	−0.487918	−0.243959	+	0.969786i	$0.578446\pi$
$432$	948.653	0.105653
$433$	−1671.29	−0.185489	−0.0927447	−	0.995690i	$-0.529564\pi$
$433$	−1671.29	−0.185489	−0.0927447	+	0.995690i	$0.529564\pi$
$434$	131.633	0.0145590
$435$	−219.090	−0.0241484
$436$	5343.14	0.586903
$437$	−7491.10	−0.820018
$438$	510.742	0.0557174
$439$	−5823.57	−0.633129	−0.316564	−	0.948571i	$-0.602529\pi$
$439$	−5823.57	−0.633129	−0.316564	+	0.948571i	$0.602529\pi$
$440$	−881.464	−0.0955049
$441$	8631.28	0.932003
$442$	154.061	0.0165791
$443$	−1022.42	−0.109654	−0.0548270	−	0.998496i	$-0.517461\pi$
$443$	−1022.42	−0.109654	−0.0548270	+	0.998496i	$0.517461\pi$
$444$	916.257	0.0979361
$445$	1465.23	0.156087
$446$	5841.88	0.620226
$447$	−764.321	−0.0808750
$448$	575.323	0.0606729
$449$	−9630.11	−1.01219	−0.506095	−	0.862478i	$-0.668911\pi$
$449$	−9630.11	−1.01219	−0.506095	+	0.862478i	$0.668911\pi$
$450$	−2731.21	−0.286112
$451$	2937.34	0.306683
$452$	−7137.88	−0.742782
$453$	−1225.54	−0.127110
$454$	−5782.00	−0.597715
$455$	110.659	0.0114017
$456$	403.631	0.0414512
$457$	−5577.69	−0.570926	−0.285463	−	0.958390i	$-0.592147\pi$
$457$	−5577.69	−0.570926	−0.285463	+	0.958390i	$0.592147\pi$
$458$	−547.360	−0.0558438
$459$	−803.298	−0.0816879
$460$	5060.84	0.512963
$461$	−4598.29	−0.464563	−0.232282	−	0.972649i	$-0.574619\pi$
$461$	−4598.29	−0.464563	−0.232282	+	0.972649i	$0.574619\pi$
$462$	−23.1423	−0.00233047
$463$	463.742	0.0465484	0.0232742	−	0.999729i	$-0.492591\pi$
$463$	463.742	0.0465484	0.0232742	+	0.999729i	$0.492591\pi$
$464$	−3323.70	−0.332541
$465$	68.0251	0.00678406
$466$	−797.060	−0.0792341
$467$	−1238.06	−0.122678	−0.0613388	−	0.998117i	$-0.519537\pi$
$467$	−1238.06	−0.122678	−0.0613388	+	0.998117i	$0.519537\pi$
$468$	825.329	0.0815189
$469$	765.116	0.0753300
$470$	−358.342	−0.0351683
$471$	80.6666	0.00789155
$472$	8899.14	0.867831
$473$	0	0
$474$	−245.398	−0.0237796
$475$	5263.42	0.508425
$476$	−1007.85	−0.0970474
$477$	−8309.49	−0.797621
$478$	−5573.86	−0.533352
$479$	6374.43	0.608048	0.304024	−	0.952664i	$-0.401670\pi$
$479$	6374.43	0.608048	0.304024	+	0.952664i	$0.401670\pi$
$480$	−419.437	−0.0398845
$481$	1292.34	0.122507
$482$	3442.66	0.325330
$483$	287.703	0.0271034
$484$	8411.11	0.789924
$485$	6051.71	0.566586
$486$	1068.48	0.0997267
$487$	−8076.69	−0.751519	−0.375759	−	0.926717i	$-0.622618\pi$
$487$	−8076.69	−0.751519	−0.375759	+	0.926717i	$0.622618\pi$
$488$	6036.85	0.559990
$489$	1293.80	0.119648
$490$	−1857.59	−0.171260
$491$	10183.8	0.936028	0.468014	−	0.883721i	$-0.344970\pi$
$491$	10183.8	0.936028	0.468014	+	0.883721i	$0.344970\pi$
$492$	908.681	0.0832653
$493$	2814.43	0.257111
$494$	262.921	0.0239461
$495$	1490.94	0.135380
$496$	1031.97	0.0934214
$497$	−1498.10	−0.135209
$498$	184.743	0.0166235
$499$	−9449.18	−0.847702	−0.423851	−	0.905732i	$-0.639322\pi$
$499$	−9449.18	−0.847702	−0.423851	+	0.905732i	$0.639322\pi$
$500$	−8199.54	−0.733389
$501$	−880.162	−0.0784885
$502$	2842.91	0.252759
$503$	−14140.8	−1.25349	−0.626747	−	0.779223i	$-0.715614\pi$
$503$	−14140.8	−1.25349	−0.626747	+	0.779223i	$0.715614\pi$
$504$	1932.56	0.170800
$505$	−25.4983	−0.00224685
$506$	−1492.81	−0.131153
$507$	1009.02	0.0883872
$508$	1989.83	0.173788
$509$	−192.153	−0.0167329	−0.00836643	−	0.999965i	$-0.502663\pi$
$509$	−192.153	−0.0167329	−0.00836643	+	0.999965i	$0.502663\pi$
$510$	86.0962	0.00747530
$511$	−4712.63	−0.407973
$512$	−11183.6	−0.965336
$513$	−1370.91	−0.117987
$514$	−4410.69	−0.378497
$515$	−6127.19	−0.524265
$516$	0	0
$517$	−639.430	−0.0543948
$518$	1397.54	0.118541
$519$	768.624	0.0650074
$520$	−384.611	−0.0324352
$521$	10001.7	0.841038	0.420519	−	0.907284i	$-0.361848\pi$
$521$	10001.7	0.841038	0.420519	+	0.907284i	$0.361848\pi$
$522$	−2492.36	−0.208980
$523$	1686.23	0.140982	0.0704912	−	0.997512i	$-0.477543\pi$
$523$	1686.23	0.140982	0.0704912	+	0.997512i	$0.477543\pi$
$524$	−7714.27	−0.643128
$525$	−202.146	−0.0168046
$526$	−5369.88	−0.445129
$527$	−873.853	−0.0722308
$528$	−181.431	−0.0149541
$529$	6391.44	0.525309
$530$	1788.34	0.146567
$531$	−15052.3	−1.23016
$532$	−1719.99	−0.140171
$533$	1281.66	0.104155
$534$	−133.704	−0.0108351
$535$	9298.77	0.751441
$536$	−2659.28	−0.214297
$537$	1648.28	0.132455
$538$	7208.87	0.577689
$539$	−3314.72	−0.264889
$540$	926.160	0.0738067
$541$	4269.53	0.339300	0.169650	−	0.985504i	$-0.445736\pi$
$541$	4269.53	0.339300	0.169650	+	0.985504i	$0.445736\pi$
$542$	8493.98	0.673151
$543$	1689.00	0.133484
$544$	5388.09	0.424656
$545$	4211.60	0.331019
$546$	−10.0977	−0.000791472 0
$547$	−5089.79	−0.397849	−0.198925	−	0.980015i	$-0.563745\pi$
$547$	−5089.79	−0.397849	−0.198925	+	0.980015i	$0.563745\pi$
$548$	15208.7	1.18555
$549$	−10211.0	−0.793795
$550$	1048.88	0.0813172
$551$	4803.12	0.371361
$552$	−999.955	−0.0771031
$553$	2264.29	0.174119
$554$	1572.74	0.120613
$555$	722.218	0.0552369
$556$	−13425.8	−1.02407
$557$	−211.814	−0.0161128	−0.00805641	−	0.999968i	$-0.502564\pi$
$557$	−211.814	−0.0161128	−0.00805641	+	0.999968i	$0.502564\pi$
$558$	773.852	0.0587093
$559$	0	0
$560$	938.158	0.0707936
$561$	153.631	0.0115621
$562$	7329.66	0.550148
$563$	9751.04	0.729942	0.364971	−	0.931019i	$-0.381079\pi$
$563$	9751.04	0.729942	0.364971	+	0.931019i	$0.381079\pi$
$564$	−197.811	−0.0147683
$565$	−5626.27	−0.418936
$566$	293.443	0.0217921
$567$	−3242.38	−0.240154
$568$	5206.86	0.384639
$569$	−13596.2	−1.00173	−0.500865	−	0.865526i	$-0.666985\pi$
$569$	−13596.2	−1.00173	−0.500865	+	0.865526i	$0.666985\pi$
$570$	146.932	0.0107970
$571$	−5131.18	−0.376065	−0.188033	−	0.982163i	$-0.560211\pi$
$571$	−5131.18	−0.376065	−0.188033	+	0.982163i	$0.560211\pi$
$572$	−316.956	−0.0231689
$573$	1528.41	0.111432
$574$	1385.99	0.100784
$575$	−13039.6	−0.945718
$576$	3382.24	0.244664
$577$	−20274.6	−1.46281	−0.731405	−	0.681944i	$-0.761135\pi$
$577$	−20274.6	−1.46281	−0.731405	+	0.681944i	$0.761135\pi$
$578$	4127.78	0.297047
$579$	1705.60	0.122422
$580$	−3244.90	−0.232305
$581$	−1704.62	−0.121721
$582$	−552.226	−0.0393307
$583$	3191.14	0.226695
$584$	16379.5	1.16059
$585$	650.547	0.0459774
$586$	4794.74	0.338002
$587$	−21105.5	−1.48402	−0.742009	−	0.670390i	$-0.766127\pi$
$587$	−21105.5	−1.48402	−0.742009	+	0.670390i	$0.766127\pi$
$588$	−1025.42	−0.0719180
$589$	−1491.32	−0.104327
$590$	3239.52	0.226049
$591$	1168.47	0.0813276
$592$	10956.4	0.760651
$593$	11899.5	0.824035	0.412017	−	0.911176i	$-0.364824\pi$
$593$	11899.5	0.824035	0.412017	+	0.911176i	$0.364824\pi$
$594$	−273.192	−0.0188707
$595$	−794.411	−0.0547356
$596$	−11320.2	−0.778009
$597$	−2207.40	−0.151328
$598$	−651.361	−0.0445420
$599$	25065.9	1.70979	0.854894	−	0.518802i	$-0.173622\pi$
$599$	25065.9	1.70979	0.854894	+	0.518802i	$0.173622\pi$
$600$	702.591	0.0478053
$601$	−24254.1	−1.64616	−0.823081	−	0.567924i	$-0.807747\pi$
$601$	−24254.1	−1.64616	−0.823081	+	0.567924i	$0.807747\pi$
$602$	0	0
$603$	4498.00	0.303769
$604$	−18151.2	−1.22279
$605$	6629.86	0.445525
$606$	2.32675	0.000155970 0
$607$	−6830.29	−0.456726	−0.228363	−	0.973576i	$-0.573337\pi$
$607$	−6830.29	−0.456726	−0.228363	+	0.973576i	$0.573337\pi$
$608$	9195.34	0.613355
$609$	−184.468	−0.0122743
$610$	2197.57	0.145864
$611$	−279.004	−0.0184735
$612$	−5924.98	−0.391345
$613$	−9630.02	−0.634507	−0.317253	−	0.948341i	$-0.602761\pi$
$613$	−9630.02	−0.634507	−0.317253	+	0.948341i	$0.602761\pi$
$614$	8845.33	0.581382
$615$	716.247	0.0469624
$616$	−742.172	−0.0485438
$617$	2856.28	0.186369	0.0931844	−	0.995649i	$-0.470295\pi$
$617$	2856.28	0.186369	0.0931844	+	0.995649i	$0.470295\pi$
$618$	559.113	0.0363929
$619$	16879.5	1.09603	0.548016	−	0.836468i	$-0.315383\pi$
$619$	16879.5	1.09603	0.548016	+	0.836468i	$0.315383\pi$
$620$	1007.51	0.0652620
$621$	3396.29	0.219466
$622$	−9624.78	−0.620448
$623$	1233.69	0.0793366
$624$	−79.1640	−0.00507868
$625$	5501.63	0.352105
$626$	−4696.06	−0.299828
$627$	262.188	0.0166998
$628$	1194.74	0.0759159
$629$	−9277.64	−0.588114
$630$	703.502	0.0444892
$631$	19957.6	1.25911	0.629555	−	0.776956i	$-0.283237\pi$
$631$	19957.6	1.25911	0.629555	+	0.776956i	$0.283237\pi$
$632$	−7869.90	−0.495329
$633$	−269.371	−0.0169140
$634$	1132.24	0.0709260
$635$	1568.44	0.0980182
$636$	987.194	0.0615484
$637$	−1446.32	−0.0899611
$638$	957.156	0.0593952
$639$	−8807.08	−0.545231
$640$	−7967.01	−0.492068
$641$	22207.7	1.36841	0.684204	−	0.729290i	$-0.260150\pi$
$641$	22207.7	1.36841	0.684204	+	0.729290i	$0.260150\pi$
$642$	−848.524	−0.0521629
$643$	−19400.5	−1.18986	−0.594932	−	0.803776i	$-0.702821\pi$
$643$	−19400.5	−1.18986	−0.594932	+	0.803776i	$0.702821\pi$
$644$	4261.11	0.260732
$645$	0	0
$646$	−1887.49	−0.114957
$647$	5574.01	0.338697	0.169349	−	0.985556i	$-0.445834\pi$
$647$	5574.01	0.338697	0.169349	+	0.985556i	$0.445834\pi$
$648$	11269.4	0.683183
$649$	5780.64	0.349630
$650$	457.661	0.0276168
$651$	57.2755	0.00344824
$652$	19162.2	1.15100
$653$	16231.9	0.972747	0.486374	−	0.873751i	$-0.338319\pi$
$653$	16231.9	0.972747	0.486374	+	0.873751i	$0.338319\pi$
$654$	−384.314	−0.0229784
$655$	−6080.59	−0.362730
$656$	10865.8	0.646705
$657$	−27704.9	−1.64516
$658$	−301.715	−0.0178755
$659$	−21111.1	−1.24791	−0.623955	−	0.781461i	$-0.714475\pi$
$659$	−21111.1	−1.24791	−0.623955	+	0.781461i	$0.714475\pi$
$660$	−177.129	−0.0104466
$661$	−12591.6	−0.740935	−0.370467	−	0.928845i	$-0.620802\pi$
$661$	−12591.6	−0.740935	−0.370467	+	0.928845i	$0.620802\pi$
$662$	−10519.8	−0.617619
$663$	67.0343	0.00392669
$664$	5924.68	0.346268
$665$	−1355.74	−0.0790579
$666$	8215.94	0.478020
$667$	−11899.2	−0.690766
$668$	−13035.9	−0.755051
$669$	2541.89	0.146898
$670$	−968.045	−0.0558192
$671$	3921.37	0.225608
$672$	−353.156	−0.0202727
$673$	13408.2	0.767979	0.383989	−	0.923337i	$-0.374550\pi$
$673$	13408.2	0.767979	0.383989	+	0.923337i	$0.374550\pi$
$674$	4843.98	0.276830
$675$	−2386.31	−0.136073
$676$	14944.4	0.850276
$677$	32507.8	1.84546	0.922731	−	0.385445i	$-0.125952\pi$
$677$	32507.8	1.84546	0.922731	+	0.385445i	$0.125952\pi$
$678$	513.404	0.0290813
$679$	5095.40	0.287987
$680$	2761.10	0.155711
$681$	−2515.83	−0.141567
$682$	−297.187	−0.0166860
$683$	−14676.1	−0.822203	−0.411101	−	0.911590i	$-0.634856\pi$
$683$	−14676.1	−0.822203	−0.411101	+	0.911590i	$0.634856\pi$
$684$	−10111.6	−0.565243
$685$	11987.9	0.668661
$686$	−3228.86	−0.179706
$687$	−238.164	−0.0132264
$688$	0	0
$689$	1392.40	0.0769900
$690$	−364.009	−0.0200835
$691$	2412.12	0.132795	0.0663974	−	0.997793i	$-0.478849\pi$
$691$	2412.12	0.132795	0.0663974	+	0.997793i	$0.478849\pi$
$692$	11383.9	0.625364
$693$	1255.34	0.0688115
$694$	11294.0	0.617746
$695$	−10582.6	−0.577584
$696$	641.148	0.0349176
$697$	−9200.93	−0.500014
$698$	−11708.4	−0.634913
$699$	−346.813	−0.0187663
$700$	−2993.95	−0.161658
$701$	13310.0	0.717136	0.358568	−	0.933504i	$-0.383265\pi$
$701$	13310.0	0.717136	0.358568	+	0.933504i	$0.383265\pi$
$702$	−119.202	−0.00640884
$703$	−15833.2	−0.849448
$704$	−1298.90	−0.0695372
$705$	−155.920	−0.00832947
$706$	309.182	0.0164819
$707$	−21.4689	−0.00114204
$708$	1788.27	0.0949254
$709$	31617.1	1.67476	0.837381	−	0.546620i	$-0.184086\pi$
$709$	31617.1	1.67476	0.837381	+	0.546620i	$0.184086\pi$
$710$	1895.43	0.100189
$711$	13311.5	0.702136
$712$	−4287.87	−0.225695
$713$	3694.59	0.194058
$714$	72.4910	0.00379959
$715$	−249.833	−0.0130674
$716$	24412.4	1.27421
$717$	−2425.27	−0.126323
$718$	−3665.82	−0.190539
$719$	15564.1	0.807294	0.403647	−	0.914915i	$-0.367742\pi$
$719$	15564.1	0.807294	0.403647	+	0.914915i	$0.367742\pi$
$720$	5515.29	0.285476
$721$	−5158.95	−0.266476
$722$	4085.63	0.210597
$723$	1497.95	0.0770531
$724$	25015.4	1.28410
$725$	8360.68	0.428287
$726$	−604.983	−0.0309270
$727$	29265.4	1.49298	0.746488	−	0.665399i	$-0.231739\pi$
$727$	29265.4	1.49298	0.746488	+	0.665399i	$0.231739\pi$
$728$	−323.834	−0.0164864
$729$	−18749.4	−0.952571
$730$	5962.54	0.302306
$731$	0	0
$732$	1213.10	0.0612531
$733$	−17131.8	−0.863270	−0.431635	−	0.902048i	$-0.642063\pi$
$733$	−17131.8	−0.863270	−0.431635	+	0.902048i	$0.642063\pi$
$734$	−7228.05	−0.363477
$735$	−808.266	−0.0405624
$736$	−22780.5	−1.14090
$737$	−1727.39	−0.0863356
$738$	8148.01	0.406412
$739$	16971.4	0.844794	0.422397	−	0.906411i	$-0.361189\pi$
$739$	16971.4	0.844794	0.422397	+	0.906411i	$0.361189\pi$
$740$	10696.6	0.531373
$741$	114.401	0.00567156
$742$	1505.74	0.0744979
$743$	−18171.5	−0.897238	−0.448619	−	0.893723i	$-0.648084\pi$
$743$	−18171.5	−0.897238	−0.448619	+	0.893723i	$0.648084\pi$
$744$	−199.070	−0.00980948
$745$	−8922.88	−0.438804
$746$	9395.17	0.461101
$747$	−10021.2	−0.490840
$748$	2275.40	0.111226
$749$	7829.34	0.381946
$750$	589.765	0.0287136
$751$	13978.9	0.679223	0.339612	−	0.940566i	$-0.389704\pi$
$751$	13978.9	0.679223	0.339612	+	0.940566i	$0.389704\pi$
$752$	−2365.38	−0.114703
$753$	1236.99	0.0598651
$754$	417.638	0.0201717
$755$	−14307.3	−0.689663
$756$	779.805	0.0375149
$757$	19774.5	0.949426	0.474713	−	0.880141i	$-0.342552\pi$
$757$	19774.5	0.949426	0.474713	+	0.880141i	$0.342552\pi$
$758$	−2859.37	−0.137015
$759$	−649.543	−0.0310631
$760$	4712.10	0.224902
$761$	−34351.4	−1.63632	−0.818158	−	0.574994i	$-0.805004\pi$
$761$	−34351.4	−1.63632	−0.818158	+	0.574994i	$0.805004\pi$
$762$	−143.122	−0.00680415
$763$	3546.07	0.168252
$764$	22637.0	1.07196
$765$	−4670.23	−0.220722
$766$	5227.46	0.246574
$767$	2522.28	0.118741
$768$	258.755	0.0121576
$769$	−19063.9	−0.893969	−0.446984	−	0.894542i	$-0.647502\pi$
$769$	−19063.9	−0.893969	−0.446984	+	0.894542i	$0.647502\pi$
$770$	−270.170	−0.0126445
$771$	−1919.16	−0.0896456
$772$	25261.3	1.17769
$773$	−36197.4	−1.68426	−0.842129	−	0.539276i	$-0.818698\pi$
$773$	−36197.4	−1.68426	−0.842129	+	0.539276i	$0.818698\pi$
$774$	0	0
$775$	−2595.90	−0.120320
$776$	−17709.8	−0.819260
$777$	608.091	0.0280761
$778$	−2130.53	−0.0981789
$779$	−15702.3	−0.722201
$780$	−77.2870	−0.00354785
$781$	3382.23	0.154963
$782$	4676.07	0.213831
$783$	−2177.62	−0.0993895
$784$	−12261.8	−0.558573
$785$	941.723	0.0428172
$786$	554.861	0.0251797
$787$	18293.2	0.828567	0.414284	−	0.910148i	$-0.364032\pi$
$787$	18293.2	0.828567	0.414284	+	0.910148i	$0.364032\pi$
$788$	17306.0	0.782363
$789$	−2336.51	−0.105427
$790$	−2864.85	−0.129021
$791$	−4737.18	−0.212939
$792$	−4363.12	−0.195753
$793$	1711.02	0.0766206
$794$	−10163.6	−0.454271
$795$	778.133	0.0347139
$796$	−32693.4	−1.45576
$797$	31454.9	1.39798	0.698989	−	0.715133i	$-0.253634\pi$
$797$	31454.9	1.39798	0.698989	+	0.715133i	$0.253634\pi$
$798$	123.713	0.00548797
$799$	2002.95	0.0886850
$800$	16006.1	0.707377
$801$	7252.67	0.319926
$802$	−7162.56	−0.315360
$803$	10639.7	0.467578
$804$	−534.377	−0.0234403
$805$	3358.72	0.147055
$806$	−129.672	−0.00566688
$807$	3136.69	0.136824
$808$	74.6185	0.00324885
$809$	25771.0	1.11998	0.559989	−	0.828500i	$-0.310805\pi$
$809$	25771.0	1.11998	0.559989	+	0.828500i	$0.310805\pi$
$810$	4102.34	0.177953
$811$	33599.7	1.45480	0.727402	−	0.686212i	$-0.240728\pi$
$811$	33599.7	1.45480	0.727402	+	0.686212i	$0.240728\pi$
$812$	−2732.12	−0.118077
$813$	3695.86	0.159433
$814$	−3155.21	−0.135860
$815$	15104.2	0.649173
$816$	568.312	0.0243810
$817$	0	0
$818$	−3310.69	−0.141510
$819$	547.745	0.0233697
$820$	10608.2	0.451773
$821$	36051.3	1.53252	0.766260	−	0.642531i	$-0.222116\pi$
$821$	36051.3	1.53252	0.766260	+	0.642531i	$0.222116\pi$
$822$	−1093.91	−0.0464166
$823$	5404.48	0.228905	0.114452	−	0.993429i	$-0.463489\pi$
$823$	5404.48	0.228905	0.114452	+	0.993429i	$0.463489\pi$
$824$	17930.7	0.758065
$825$	456.384	0.0192597
$826$	2727.59	0.114897
$827$	−19906.0	−0.837000	−0.418500	−	0.908217i	$-0.637444\pi$
$827$	−19906.0	−0.837000	−0.418500	+	0.908217i	$0.637444\pi$
$828$	25050.4	1.05140
$829$	−25969.3	−1.08800	−0.543999	−	0.839086i	$-0.683090\pi$
$829$	−25969.3	−1.08800	−0.543999	+	0.839086i	$0.683090\pi$
$830$	2156.74	0.0901944
$831$	684.324	0.0285667
$832$	−566.752	−0.0236161
$833$	10383.0	0.431873
$834$	965.676	0.0400943
$835$	−10275.2	−0.425856
$836$	3883.21	0.160650
$837$	676.130	0.0279217
$838$	17355.6	0.715442
$839$	26178.3	1.07721	0.538603	−	0.842560i	$-0.318952\pi$
$839$	26178.3	1.07721	0.538603	+	0.842560i	$0.318952\pi$
$840$	−180.973	−0.00743351
$841$	−16759.5	−0.687174
$842$	3050.78	0.124866
$843$	3189.24	0.130300
$844$	−3989.60	−0.162711
$845$	11779.6	0.479563
$846$	−1773.74	−0.0720833
$847$	5582.19	0.226454
$848$	11804.6	0.478034
$849$	127.681	0.00516139
$850$	−3285.52	−0.132579
$851$	39225.2	1.58005
$852$	1046.31	0.0420728
$853$	45066.9	1.80898	0.904490	−	0.426495i	$-0.140252\pi$
$853$	45066.9	1.80898	0.904490	+	0.426495i	$0.140252\pi$
$854$	1850.30	0.0741405
$855$	−7970.22	−0.318802
$856$	−27212.1	−1.08655
$857$	20163.4	0.803695	0.401848	−	0.915706i	$-0.368368\pi$
$857$	20163.4	0.803695	0.401848	+	0.915706i	$0.368368\pi$
$858$	22.7976	0.000907105 0
$859$	−38656.8	−1.53545	−0.767726	−	0.640778i	$-0.778612\pi$
$859$	−38656.8	−1.53545	−0.767726	+	0.640778i	$0.778612\pi$
$860$	0	0
$861$	603.063	0.0238703
$862$	4650.83	0.183768
$863$	−11938.0	−0.470886	−0.235443	−	0.971888i	$-0.575654\pi$
$863$	−11938.0	−0.470886	−0.235443	+	0.971888i	$0.575654\pi$
$864$	−4168.95	−0.164156
$865$	8973.12	0.352711
$866$	1780.41	0.0698622
$867$	1796.06	0.0703544
$868$	848.296	0.0331717
$869$	−5112.07	−0.199557
$870$	233.394	0.00909519
$871$	−753.717	−0.0293212
$872$	−12324.9	−0.478640
$873$	29955.1	1.16131
$874$	7980.20	0.308849
$875$	−5441.77	−0.210246
$876$	3291.43	0.126949
$877$	898.663	0.0346017	0.0173008	−	0.999850i	$-0.494493\pi$
$877$	898.663	0.0346017	0.0173008	+	0.999850i	$0.494493\pi$
$878$	6203.79	0.238460
$879$	2086.26	0.0800545
$880$	−2118.07	−0.0811364
$881$	−4887.81	−0.186918	−0.0934588	−	0.995623i	$-0.529792\pi$
$881$	−4887.81	−0.186918	−0.0934588	+	0.995623i	$0.529792\pi$
$882$	−9194.82	−0.351027
$883$	27593.4	1.05163	0.525816	−	0.850598i	$-0.323760\pi$
$883$	27593.4	1.05163	0.525816	+	0.850598i	$0.323760\pi$
$884$	992.831	0.0377744
$885$	1409.56	0.0535388
$886$	1089.18	0.0412998
$887$	−44465.6	−1.68321	−0.841606	−	0.540092i	$-0.818390\pi$
$887$	−44465.6	−1.68321	−0.841606	+	0.540092i	$0.818390\pi$
$888$	−2113.51	−0.0798703
$889$	1320.59	0.0498213
$890$	−1560.90	−0.0587880
$891$	7320.28	0.275240
$892$	37647.4	1.41315
$893$	3418.24	0.128093
$894$	814.224	0.0304605
$895$	19242.5	0.718665
$896$	−6708.03	−0.250111
$897$	−283.417	−0.0105496
$898$	10258.9	0.381228
$899$	−2368.89	−0.0878830
$900$	−17601.0	−0.651889
$901$	−9995.91	−0.369603
$902$	−3129.13	−0.115508
$903$	0	0
$904$	16464.8	0.605764
$905$	19717.8	0.724247
$906$	1305.56	0.0478744
$907$	−13410.8	−0.490958	−0.245479	−	0.969402i	$-0.578945\pi$
$907$	−13410.8	−0.490958	−0.245479	+	0.969402i	$0.578945\pi$
$908$	−37261.5	−1.36186
$909$	−126.213	−0.00460529
$910$	−117.884	−0.00429430
$911$	24002.1	0.872914	0.436457	−	0.899725i	$-0.356233\pi$
$911$	24002.1	0.872914	0.436457	+	0.899725i	$0.356233\pi$
$912$	969.884	0.0352150
$913$	3848.51	0.139504
$914$	5941.86	0.215032
$915$	956.194	0.0345473
$916$	−3527.40	−0.127237
$917$	−5119.71	−0.184371
$918$	855.746	0.0307667
$919$	28960.1	1.03950	0.519752	−	0.854317i	$-0.326024\pi$
$919$	28960.1	1.03950	0.519752	+	0.854317i	$0.326024\pi$
$920$	−11673.7	−0.418339
$921$	3848.73	0.137698
$922$	4898.52	0.174972
$923$	1475.78	0.0526282
$924$	−149.138	−0.00530984
$925$	−27560.6	−0.979660
$926$	−494.020	−0.0175318
$927$	−30328.7	−1.07457
$928$	14606.3	0.516678
$929$	−30584.7	−1.08014	−0.540071	−	0.841619i	$-0.681603\pi$
$929$	−30584.7	−1.08014	−0.540071	+	0.841619i	$0.681603\pi$
$930$	−72.4665	−0.00255513
$931$	17719.7	0.623780
$932$	−5136.57	−0.180530
$933$	−4187.88	−0.146951
$934$	1318.89	0.0462050
$935$	1793.53	0.0627324
$936$	−1903.77	−0.0664815
$937$	45835.7	1.59807	0.799033	−	0.601287i	$-0.205345\pi$
$937$	45835.7	1.59807	0.799033	+	0.601287i	$0.205345\pi$
$938$	−815.071	−0.0283721
$939$	−2043.32	−0.0710131
$940$	−2309.30	−0.0801287
$941$	−2785.96	−0.0965140	−0.0482570	−	0.998835i	$-0.515367\pi$
$941$	−2785.96	−0.0965140	−0.0482570	+	0.998835i	$0.515367\pi$
$942$	−85.9334	−0.00297225
$943$	38900.9	1.34336
$944$	21383.7	0.737268
$945$	614.663	0.0211587
$946$	0	0
$947$	−12107.3	−0.415454	−0.207727	−	0.978187i	$-0.566606\pi$
$947$	−12107.3	−0.415454	−0.207727	+	0.978187i	$0.566606\pi$
$948$	−1581.44	−0.0541803
$949$	4642.42	0.158798
$950$	−5607.07	−0.191492
$951$	492.655	0.0167986
$952$	2324.78	0.0791455
$953$	−17220.7	−0.585343	−0.292671	−	0.956213i	$-0.594544\pi$
$953$	−17220.7	−0.585343	−0.292671	+	0.956213i	$0.594544\pi$
$954$	8852.02	0.300414
$955$	17843.1	0.604597
$956$	−35920.2	−1.21521
$957$	416.472	0.0140675
$958$	−6790.62	−0.229014
$959$	10093.5	0.339871
$960$	−316.726	−0.0106482
$961$	−29055.5	−0.975311
$962$	−1376.72	−0.0461406
$963$	46027.5	1.54020
$964$	22185.9	0.741243
$965$	19911.6	0.664226
$966$	−306.487	−0.0102081
$967$	36590.1	1.21681	0.608407	−	0.793625i	$-0.291809\pi$
$967$	36590.1	1.21681	0.608407	+	0.793625i	$0.291809\pi$
$968$	−19401.7	−0.644210
$969$	−821.276	−0.0272272
$970$	−6446.83	−0.213397
$971$	14970.4	0.494771	0.247386	−	0.968917i	$-0.420429\pi$
$971$	14970.4	0.494771	0.247386	+	0.968917i	$0.420429\pi$
$972$	6885.70	0.227221
$973$	−8910.30	−0.293578
$974$	8604.02	0.283050
$975$	199.135	0.00654095
$976$	14505.9	0.475741
$977$	−55910.8	−1.83086	−0.915428	−	0.402483i	$-0.868147\pi$
$977$	−55910.8	−1.83086	−0.915428	+	0.402483i	$0.868147\pi$
$978$	−1378.27	−0.0450637
$979$	−2785.28	−0.0909276
$980$	−11971.1	−0.390206
$981$	20846.8	0.678479
$982$	−10848.7	−0.352543
$983$	−3092.53	−0.100342	−0.0501710	−	0.998741i	$-0.515977\pi$
$983$	−3092.53	−0.100342	−0.0501710	+	0.998741i	$0.515977\pi$
$984$	−2096.04	−0.0679057
$985$	13641.1	0.441260
$986$	−2998.19	−0.0968376
$987$	−131.281	−0.00423375
$988$	1694.37	0.0545598
$989$	0	0
$990$	−1588.29	−0.0509890
$991$	12923.0	0.414242	0.207121	−	0.978315i	$-0.433591\pi$
$991$	12923.0	0.414242	0.207121	+	0.978315i	$0.433591\pi$
$992$	−4535.12	−0.145151
$993$	−4577.32	−0.146281
$994$	1595.91	0.0509247
$995$	−25769.8	−0.821062
$996$	1190.55	0.0378757
$997$	25871.0	0.821807	0.410904	−	0.911679i	$-0.365213\pi$
$997$	25871.0	0.821807	0.410904	+	0.911679i	$0.365213\pi$
$998$	10066.1	0.319276
$999$	7178.43	0.227343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.21	yes	50
43.42	odd	2		1849.4.a.i.1.30	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.30	✓	50	43.42	odd	2
1849.4.a.j.1.21	yes	50	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-1.06529 q^{2} -0.463524 q^{3} -6.86516 q^{4} -5.41130 q^{5} +0.493788 q^{6} -4.55619 q^{7} +15.8357 q^{8} -26.7851 q^{9} +O(q^{10})\)	\(q-1.06529 q^{2} -0.463524 q^{3} -6.86516 q^{4} -5.41130 q^{5} +0.493788 q^{6} -4.55619 q^{7} +15.8357 q^{8} -26.7851 q^{9} +5.76461 q^{10} +10.2865 q^{11} +3.18216 q^{12} +4.48831 q^{13} +4.85366 q^{14} +2.50827 q^{15} +38.0516 q^{16} -32.2212 q^{17} +28.5340 q^{18} -54.9889 q^{19} +37.1494 q^{20} +2.11190 q^{21} -10.9581 q^{22} +136.229 q^{23} -7.34023 q^{24} -95.7178 q^{25} -4.78136 q^{26} +24.9307 q^{27} +31.2789 q^{28} -87.3472 q^{29} -2.67203 q^{30} +27.1204 q^{31} -167.222 q^{32} -4.76801 q^{33} +34.3250 q^{34} +24.6549 q^{35} +183.884 q^{36} +287.935 q^{37} +58.5791 q^{38} -2.08044 q^{39} -85.6918 q^{40} +285.555 q^{41} -2.24979 q^{42} -70.6181 q^{44} +144.942 q^{45} -145.124 q^{46} -62.1624 q^{47} -17.6378 q^{48} -322.241 q^{49} +101.967 q^{50} +14.9353 q^{51} -30.8129 q^{52} +310.227 q^{53} -26.5584 q^{54} -55.6631 q^{55} -72.1505 q^{56} +25.4886 q^{57} +93.0501 q^{58} +561.966 q^{59} -17.2196 q^{60} +381.217 q^{61} -28.8911 q^{62} +122.038 q^{63} -126.273 q^{64} -24.2876 q^{65} +5.07932 q^{66} -167.929 q^{67} +221.204 q^{68} -63.1455 q^{69} -26.2646 q^{70} +328.805 q^{71} -424.162 q^{72} +1034.34 q^{73} -306.735 q^{74} +44.3675 q^{75} +377.507 q^{76} -46.8670 q^{77} +2.21627 q^{78} -496.972 q^{79} -205.909 q^{80} +711.643 q^{81} -304.199 q^{82} +374.134 q^{83} -14.4985 q^{84} +174.359 q^{85} +40.4875 q^{87} +162.893 q^{88} -270.772 q^{89} -154.406 q^{90} -20.4496 q^{91} -935.236 q^{92} -12.5709 q^{93} +66.2210 q^{94} +297.561 q^{95} +77.5112 q^{96} -1118.35 q^{97} +343.281 q^{98} -275.524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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