LMFDB - Embedded newform 1849.4.a.i.1.30

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			1.30
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	$-0.439696\pi$
$2$	1.06529	0.376637	0.188319	+	0.982108i	$0.439696\pi$
$3$	0.463524	0.0892052	0.0446026	−	0.999005i	$-0.485798\pi$
$3$	0.463524	0.0892052	0.0446026	+	0.999005i	$0.485798\pi$
$4$	−6.86516	−0.858144
$5$	5.41130	0.484001	0.242001	−	0.970276i	$-0.422196\pi$
$5$	5.41130	0.484001	0.242001	+	0.970276i	$0.422196\pi$
$6$	0.493788	0.0335980
$7$	4.55619	0.246011	0.123005	−	0.992406i	$-0.460747\pi$
$7$	4.55619	0.246011	0.123005	+	0.992406i	$0.460747\pi$
$8$	−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	$-0.392283\pi$
$19$	54.9889	0.663964	0.331982	+	0.943286i	$0.392283\pi$
$20$	−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	$-0.409780\pi$
$29$	87.3472	0.559309	0.279654	+	0.960101i	$0.409780\pi$
$30$	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	$-0.720933\pi$
$37$	−287.935	−1.27936	−0.639680	+	0.768642i	$0.720933\pi$
$38$	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	$-0.631018\pi$
$61$	−381.217	−0.800162	−0.400081	+	0.916480i	$0.631018\pi$
$62$	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	$-0.588612\pi$
$71$	−328.805	−0.549605	−0.274802	+	0.961501i	$0.588612\pi$
$72$	424.162	0.694277
$73$	−1034.34	−1.65836	−0.829178	−	0.558985i	$-0.811191\pi$
$73$	−1034.34	−1.65836	−0.829178	+	0.558985i	$0.811191\pi$
$74$	−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	$-0.448449\pi$
$89$	270.772	0.322492	0.161246	+	0.986914i	$0.448449\pi$
$90$	−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	$-0.642469\pi$
$113$	−1039.73	−0.865568	−0.432784	+	0.901498i	$0.642469\pi$
$114$	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	$-0.622261\pi$
$131$	−1123.68	−0.749441	−0.374720	+	0.927138i	$0.622261\pi$
$132$	−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	$-0.257274\pi$
$137$	2215.34	1.38153	0.690764	+	0.723080i	$0.257274\pi$
$138$	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	$-0.649757\pi$
$149$	−1648.94	−0.906618	−0.453309	+	0.891353i	$0.649757\pi$
$150$	−47.2643	−0.0257274
$151$	−2643.96	−1.42492	−0.712459	−	0.701713i	$-0.752419\pi$
$151$	−2643.96	−1.42492	−0.712459	+	0.701713i	$0.752419\pi$
$152$	−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	$-0.485916\pi$
$157$	174.029	0.0884651	0.0442326	+	0.999021i	$0.485916\pi$
$158$	−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	$-0.266023\pi$
$163$	2791.23	1.34126	0.670631	+	0.741791i	$0.266023\pi$
$164$	−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	$-0.233678\pi$
$179$	3555.98	1.48484	0.742420	+	0.669934i	$0.233678\pi$
$180$	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	$-0.285270\pi$
$191$	3297.38	1.24916	0.624581	+	0.780960i	$0.285270\pi$
$192$	−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	$-0.822315\pi$
$199$	−4762.22	−1.69641	−0.848203	+	0.529672i	$0.822315\pi$
$200$	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	$-0.530222\pi$
$211$	−581.138	−0.189607	−0.0948037	+	0.995496i	$0.530222\pi$
$212$	−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	$-0.192089\pi$
$223$	5483.83	1.64675	0.823374	+	0.567500i	$0.192089\pi$
$224$	761.893	0.227260
$225$	2563.82	0.759649
$226$	−1107.61	−0.326005
$227$	−5427.63	−1.58698	−0.793490	−	0.608584i	$-0.791738\pi$
$227$	−5427.63	−1.58698	−0.793490	+	0.608584i	$0.791738\pi$
$228$	−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	$-0.533544\pi$
$233$	−748.209	−0.210373	−0.105186	+	0.994453i	$0.533544\pi$
$234$	−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	$-0.357848\pi$
$241$	3231.66	0.863774	0.431887	+	0.901928i	$0.357848\pi$
$242$	−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	$-0.667575\pi$
$257$	−4140.36	−1.00494	−0.502469	+	0.864595i	$0.667575\pi$
$258$	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	$-0.701237\pi$
$263$	−5040.77	−1.18185	−0.590926	+	0.806726i	$0.701237\pi$
$264$	−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	$-0.448813\pi$
$277$	1476.35	0.320236	0.160118	+	0.987098i	$0.448813\pi$
$278$	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	$-0.630307\pi$
$313$	−4408.24	−0.796065	−0.398032	+	0.917371i	$0.630307\pi$
$314$	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	$-0.805978\pi$
$331$	−9875.05	−1.63982	−0.819912	+	0.572489i	$0.805978\pi$
$332$	−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	$-0.193928\pi$
$347$	10601.8	1.64016	0.820081	+	0.572247i	$0.193928\pi$
$348$	−277.953	−0.0428156
$349$	−10990.8	−1.68574	−0.842870	−	0.538117i	$-0.819136\pi$
$349$	−10990.8	−1.68574	−0.842870	+	0.538117i	$0.819136\pi$
$350$	−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	$-0.290313\pi$
$373$	8819.35	1.22426	0.612129	+	0.790758i	$0.290313\pi$
$374$	−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	$-0.393849\pi$
$383$	4907.07	0.654673	0.327336	+	0.944908i	$0.393849\pi$
$384$	−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	$-0.541606\pi$
$389$	−1999.95	−0.260672	−0.130336	+	0.991470i	$0.541606\pi$
$390$	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	$-0.560155\pi$
$409$	−3107.78	−0.375720	−0.187860	+	0.982196i	$0.560155\pi$
$410$	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	$-0.101311\pi$
$419$	16291.9	1.89955	0.949776	+	0.312931i	$0.101311\pi$
$420$	−78.4558	−0.00911489
$421$	2863.80	0.331528	0.165764	−	0.986165i	$-0.446991\pi$
$421$	2863.80	0.331528	0.165764	+	0.986165i	$0.446991\pi$
$422$	−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	$-0.470436\pi$
$433$	1671.29	0.185489	0.0927447	+	0.995690i	$0.470436\pi$
$434$	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	$-0.331089\pi$
$449$	9630.11	1.01219	0.506095	+	0.862478i	$0.331089\pi$
$450$	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	$-0.407853\pi$
$457$	5577.69	0.570926	0.285463	+	0.958390i	$0.407853\pi$
$458$	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	$-0.507409\pi$
$463$	−463.742	−0.0465484	−0.0232742	+	0.999729i	$0.507409\pi$
$464$	3323.70	0.332541
$465$	68.0251	0.00678406
$466$	−797.060	−0.0792341
$467$	1238.06	0.122678	0.0613388	−	0.998117i	$-0.480463\pi$
$467$	1238.06	0.122678	0.0613388	+	0.998117i	$0.480463\pi$
$468$	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	$-0.655030\pi$
$491$	−10183.8	−0.936028	−0.468014	+	0.883721i	$0.655030\pi$
$492$	−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	$-0.360678\pi$
$499$	9449.18	0.847702	0.423851	+	0.905732i	$0.360678\pi$
$500$	8199.54	0.733389
$501$	880.162	0.0784885
$502$	−2842.91	−0.252759
$503$	14140.8	1.25349	0.626747	−	0.779223i	$-0.284386\pi$
$503$	14140.8	1.25349	0.626747	+	0.779223i	$0.284386\pi$
$504$	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	$-0.638152\pi$
$521$	−10001.7	−0.841038	−0.420519	+	0.907284i	$0.638152\pi$
$522$	−2492.36	−0.208980
$523$	−1686.23	−0.140982	−0.0704912	−	0.997512i	$-0.522457\pi$
$523$	−1686.23	−0.140982	−0.0704912	+	0.997512i	$0.522457\pi$
$524$	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	$-0.439789\pi$
$571$	5131.18	0.376065	0.188033	+	0.982163i	$0.439789\pi$
$572$	−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	$-0.238865\pi$
$577$	20274.6	1.46281	0.731405	+	0.681944i	$0.238865\pi$
$578$	−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	$-0.233873\pi$
$587$	21105.5	1.48402	0.742009	+	0.670390i	$0.233873\pi$
$588$	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	$-0.635176\pi$
$593$	−11899.5	−0.824035	−0.412017	+	0.911176i	$0.635176\pi$
$594$	−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	$-0.192253\pi$
$601$	24254.1	1.64616	0.823081	+	0.567924i	$0.192253\pi$
$602$	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	$-0.426663\pi$
$607$	6830.29	0.456726	0.228363	+	0.973576i	$0.426663\pi$
$608$	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	$-0.716763\pi$
$631$	−19957.6	−1.25911	−0.629555	+	0.776956i	$0.716763\pi$
$632$	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	$-0.739850\pi$
$641$	−22207.7	−1.36841	−0.684204	+	0.729290i	$0.739850\pi$
$642$	−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	$-0.554166\pi$
$647$	−5574.01	−0.338697	−0.169349	+	0.985556i	$0.554166\pi$
$648$	−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	$-0.661681\pi$
$653$	−16231.9	−0.972747	−0.486374	+	0.873751i	$0.661681\pi$
$654$	−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	$-0.625450\pi$
$673$	−13408.2	−0.767979	−0.383989	+	0.923337i	$0.625450\pi$
$674$	−4843.98	−0.276830
$675$	2386.31	0.136073
$676$	14944.4	0.850276
$677$	−32507.8	−1.84546	−0.922731	−	0.385445i	$-0.874048\pi$
$677$	−32507.8	−1.84546	−0.922731	+	0.385445i	$0.874048\pi$
$678$	−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	$-0.521151\pi$
$691$	−2412.12	−0.132795	−0.0663974	+	0.997793i	$0.521151\pi$
$692$	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	$-0.768261\pi$
$727$	−29265.4	−1.49298	−0.746488	+	0.665399i	$0.768261\pi$
$728$	−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	$-0.357937\pi$
$733$	17131.8	0.863270	0.431635	+	0.902048i	$0.357937\pi$
$734$	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	$-0.638811\pi$
$739$	−16971.4	−0.844794	−0.422397	+	0.906411i	$0.638811\pi$
$740$	10696.6	0.531373
$741$	114.401	0.00567156
$742$	1505.74	0.0744979
$743$	18171.5	0.897238	0.448619	−	0.893723i	$-0.351916\pi$
$743$	18171.5	0.897238	0.448619	+	0.893723i	$0.351916\pi$
$744$	−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	$-0.610296\pi$
$751$	−13978.9	−0.679223	−0.339612	+	0.940566i	$0.610296\pi$
$752$	−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	$-0.657448\pi$
$757$	−19774.5	−0.949426	−0.474713	+	0.880141i	$0.657448\pi$
$758$	2859.37	0.137015
$759$	649.543	0.0310631
$760$	−4712.10	−0.224902
$761$	34351.4	1.63632	0.818158	−	0.574994i	$-0.194996\pi$
$761$	34351.4	1.63632	0.818158	+	0.574994i	$0.194996\pi$
$762$	−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	$-0.181302\pi$
$773$	36197.4	1.68426	0.842129	+	0.539276i	$0.181302\pi$
$774$	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	$-0.759272\pi$
$811$	−33599.7	−1.45480	−0.727402	+	0.686212i	$0.759272\pi$
$812$	−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	$-0.316910\pi$
$829$	25969.3	1.08800	0.543999	+	0.839086i	$0.316910\pi$
$830$	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	$-0.681048\pi$
$839$	−26178.3	−1.07721	−0.538603	+	0.842560i	$0.681048\pi$
$840$	−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	$-0.221388\pi$
$859$	38656.8	1.53545	0.767726	+	0.640778i	$0.221388\pi$
$860$	0	0
$861$	603.063	0.0238703
$862$	−4650.83	−0.183768
$863$	11938.0	0.470886	0.235443	−	0.971888i	$-0.424346\pi$
$863$	11938.0	0.470886	0.235443	+	0.971888i	$0.424346\pi$
$864$	−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	$-0.181610\pi$
$887$	44465.6	1.68321	0.841606	+	0.540092i	$0.181610\pi$
$888$	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	$-0.643767\pi$
$911$	−24002.1	−0.872914	−0.436457	+	0.899725i	$0.643767\pi$
$912$	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	$-0.318397\pi$
$929$	30584.7	1.08014	0.540071	+	0.841619i	$0.318397\pi$
$930$	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	$-0.794655\pi$
$937$	−45835.7	−1.59807	−0.799033	+	0.601287i	$0.794655\pi$
$938$	−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	$-0.405456\pi$
$953$	17220.7	0.585343	0.292671	+	0.956213i	$0.405456\pi$
$954$	−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	$-0.484023\pi$
$983$	3092.53	0.100342	0.0501710	+	0.998741i	$0.484023\pi$
$984$	−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	$-0.566409\pi$
$991$	−12923.0	−0.414242	−0.207121	+	0.978315i	$0.566409\pi$
$992$	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	$-0.634787\pi$
$997$	−25871.0	−0.821807	−0.410904	+	0.911679i	$0.634787\pi$
$998$	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.i.1.30	✓	50
43.42	odd	2		1849.4.a.j.1.21	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.30	✓	50	1.1	even	1	trivial
1849.4.a.j.1.21	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)

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