LMFDB - Embedded newform 1849.4.a.j.1.9

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			1.9
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)

$f(q)$	$=$	$q-4.08033 q^{2} -6.02226 q^{3} +8.64912 q^{4} +2.18258 q^{5} +24.5728 q^{6} +8.90728 q^{7} -2.64861 q^{8} +9.26767 q^{9} +O(q^{10})$	\(q-4.08033 q^{2} -6.02226 q^{3} +8.64912 q^{4} +2.18258 q^{5} +24.5728 q^{6} +8.90728 q^{7} -2.64861 q^{8} +9.26767 q^{9} -8.90564 q^{10} +2.96222 q^{11} -52.0873 q^{12} +15.9248 q^{13} -36.3447 q^{14} -13.1441 q^{15} -58.3857 q^{16} -54.4270 q^{17} -37.8152 q^{18} +136.251 q^{19} +18.8774 q^{20} -53.6420 q^{21} -12.0868 q^{22} +153.274 q^{23} +15.9506 q^{24} -120.236 q^{25} -64.9786 q^{26} +106.789 q^{27} +77.0401 q^{28} +69.4344 q^{29} +53.6321 q^{30} -13.1165 q^{31} +259.422 q^{32} -17.8393 q^{33} +222.080 q^{34} +19.4408 q^{35} +80.1572 q^{36} -306.611 q^{37} -555.948 q^{38} -95.9035 q^{39} -5.78080 q^{40} -27.1862 q^{41} +218.877 q^{42} +25.6206 q^{44} +20.2274 q^{45} -625.409 q^{46} -621.994 q^{47} +351.614 q^{48} -263.660 q^{49} +490.604 q^{50} +327.774 q^{51} +137.736 q^{52} -97.9357 q^{53} -435.734 q^{54} +6.46527 q^{55} -23.5919 q^{56} -820.538 q^{57} -283.315 q^{58} -417.172 q^{59} -113.684 q^{60} -608.416 q^{61} +53.5198 q^{62} +82.5498 q^{63} -591.443 q^{64} +34.7572 q^{65} +72.7902 q^{66} +772.902 q^{67} -470.745 q^{68} -923.057 q^{69} -79.3251 q^{70} +858.225 q^{71} -24.5464 q^{72} +14.7922 q^{73} +1251.07 q^{74} +724.095 q^{75} +1178.45 q^{76} +26.3853 q^{77} +391.318 q^{78} +872.351 q^{79} -127.431 q^{80} -893.337 q^{81} +110.929 q^{82} -1057.72 q^{83} -463.956 q^{84} -118.791 q^{85} -418.152 q^{87} -7.84576 q^{88} -444.661 q^{89} -82.5346 q^{90} +141.847 q^{91} +1325.69 q^{92} +78.9912 q^{93} +2537.94 q^{94} +297.378 q^{95} -1562.31 q^{96} +150.389 q^{97} +1075.82 q^{98} +27.4529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.08033	−1.44262	−0.721308	−	0.692615i	$-0.756459\pi$
$2$	−4.08033	−1.44262	−0.721308	+	0.692615i	$0.756459\pi$
$3$	−6.02226	−1.15899	−0.579493	−	0.814977i	$-0.696749\pi$
$3$	−6.02226	−1.15899	−0.579493	+	0.814977i	$0.696749\pi$
$4$	8.64912	1.08114
$5$	2.18258	0.195216	0.0976078	−	0.995225i	$-0.468881\pi$
$5$	2.18258	0.195216	0.0976078	+	0.995225i	$0.468881\pi$
$6$	24.5728	1.67197
$7$	8.90728	0.480948	0.240474	−	0.970656i	$-0.422697\pi$
$7$	8.90728	0.480948	0.240474	+	0.970656i	$0.422697\pi$
$8$	−2.64861	−0.117053
$9$	9.26767	0.343247
$10$	−8.90564	−0.281621
$11$	2.96222	0.0811948	0.0405974	−	0.999176i	$-0.487074\pi$
$11$	2.96222	0.0811948	0.0405974	+	0.999176i	$0.487074\pi$
$12$	−52.0873	−1.25302
$13$	15.9248	0.339750	0.169875	−	0.985466i	$-0.445664\pi$
$13$	15.9248	0.339750	0.169875	+	0.985466i	$0.445664\pi$
$14$	−36.3447	−0.693823
$15$	−13.1441	−0.226252
$16$	−58.3857	−0.912277
$17$	−54.4270	−0.776499	−0.388250	−	0.921554i	$-0.626920\pi$
$17$	−54.4270	−0.776499	−0.388250	+	0.921554i	$0.626920\pi$
$18$	−37.8152	−0.495174
$19$	136.251	1.64516	0.822580	−	0.568649i	$-0.192534\pi$
$19$	136.251	1.64516	0.822580	+	0.568649i	$0.192534\pi$
$20$	18.8774	0.211055
$21$	−53.6420	−0.557412
$22$	−12.0868	−0.117133
$23$	153.274	1.38956	0.694780	−	0.719223i	$-0.255502\pi$
$23$	153.274	1.38956	0.694780	+	0.719223i	$0.255502\pi$
$24$	15.9506	0.135663
$25$	−120.236	−0.961891
$26$	−64.9786	−0.490129
$27$	106.789	0.761167
$28$	77.0401	0.519972
$29$	69.4344	0.444608	0.222304	−	0.974977i	$-0.428642\pi$
$29$	69.4344	0.444608	0.222304	+	0.974977i	$0.428642\pi$
$30$	53.6321	0.326395
$31$	−13.1165	−0.0759935	−0.0379968	−	0.999278i	$-0.512098\pi$
$31$	−13.1165	−0.0759935	−0.0379968	+	0.999278i	$0.512098\pi$
$32$	259.422	1.43312
$33$	−17.8393	−0.0941036
$34$	222.080	1.12019
$35$	19.4408	0.0938886
$36$	80.1572	0.371098
$37$	−306.611	−1.36234	−0.681168	−	0.732127i	$-0.738528\pi$
$37$	−306.611	−1.36234	−0.681168	+	0.732127i	$0.738528\pi$
$38$	−555.948	−2.37333
$39$	−95.9035	−0.393765
$40$	−5.78080	−0.0228506
$41$	−27.1862	−0.103555	−0.0517776	−	0.998659i	$-0.516489\pi$
$41$	−27.1862	−0.103555	−0.0517776	+	0.998659i	$0.516489\pi$
$42$	218.877	0.804131
$43$	0	0
$43$	0	0
$44$	25.6206	0.0877829
$45$	20.2274	0.0670072
$46$	−625.409	−2.00460
$47$	−621.994	−1.93037	−0.965183	−	0.261576i	$-0.915758\pi$
$47$	−621.994	−1.93037	−0.965183	+	0.261576i	$0.915758\pi$
$48$	351.614	1.05732
$49$	−263.660	−0.768689
$50$	490.604	1.38764
$51$	327.774	0.899951
$52$	137.736	0.367317
$53$	−97.9357	−0.253821	−0.126910	−	0.991914i	$-0.540506\pi$
$53$	−97.9357	−0.253821	−0.126910	+	0.991914i	$0.540506\pi$
$54$	−435.734	−1.09807
$55$	6.46527	0.0158505
$56$	−23.5919	−0.0562965
$57$	−820.538	−1.90672
$58$	−283.315	−0.641399
$59$	−417.172	−0.920529	−0.460264	−	0.887782i	$-0.652245\pi$
$59$	−417.172	−0.920529	−0.460264	+	0.887782i	$0.652245\pi$
$60$	−113.684	−0.244610
$61$	−608.416	−1.27704	−0.638522	−	0.769604i	$-0.720454\pi$
$61$	−608.416	−1.27704	−0.638522	+	0.769604i	$0.720454\pi$
$62$	53.5198	0.109629
$63$	82.5498	0.165084
$64$	−591.443	−1.15516
$65$	34.7572	0.0663245
$66$	72.7902	0.135755
$67$	772.902	1.40933	0.704664	−	0.709541i	$-0.251098\pi$
$67$	772.902	1.40933	0.704664	+	0.709541i	$0.251098\pi$
$68$	−470.745	−0.839504
$69$	−923.057	−1.61048
$70$	−79.3251	−0.135445
$71$	858.225	1.43454	0.717272	−	0.696793i	$-0.245391\pi$
$71$	858.225	1.43454	0.717272	+	0.696793i	$0.245391\pi$
$72$	−24.5464	−0.0401781
$73$	14.7922	0.0237164	0.0118582	−	0.999930i	$-0.496225\pi$
$73$	14.7922	0.0237164	0.0118582	+	0.999930i	$0.496225\pi$
$74$	1251.07	1.96533
$75$	724.095	1.11482
$76$	1178.45	1.77865
$77$	26.3853	0.0390505
$78$	391.318	0.568052
$79$	872.351	1.24237	0.621185	−	0.783664i	$-0.286652\pi$
$79$	872.351	1.24237	0.621185	+	0.783664i	$0.286652\pi$
$80$	−127.431	−0.178091
$81$	−893.337	−1.22543
$82$	110.929	0.149390
$83$	−1057.72	−1.39880	−0.699399	−	0.714732i	$-0.746549\pi$
$83$	−1057.72	−1.39880	−0.699399	+	0.714732i	$0.746549\pi$
$84$	−463.956	−0.602640
$85$	−118.791	−0.151585
$86$	0	0
$87$	−418.152	−0.515295
$88$	−7.84576	−0.00950411
$89$	−444.661	−0.529596	−0.264798	−	0.964304i	$-0.585305\pi$
$89$	−444.661	−0.529596	−0.264798	+	0.964304i	$0.585305\pi$
$90$	−82.5346	−0.0966656
$91$	141.847	0.163402
$92$	1325.69	1.50231
$93$	78.9912	0.0880754
$94$	2537.94	2.78478
$95$	297.378	0.321161
$96$	−1562.31	−1.66096
$97$	150.389	0.157420	0.0787098	−	0.996898i	$-0.474920\pi$
$97$	150.389	0.157420	0.0787098	+	0.996898i	$0.474920\pi$
$98$	1075.82	1.10892
$99$	27.4529	0.0278699
$100$	−1039.94	−1.03994
$101$	400.658	0.394722	0.197361	−	0.980331i	$-0.436763\pi$
$101$	400.658	0.394722	0.197361	+	0.980331i	$0.436763\pi$
$102$	−1337.43	−1.29828
$103$	956.042	0.914579	0.457290	−	0.889318i	$-0.348820\pi$
$103$	956.042	0.914579	0.457290	+	0.889318i	$0.348820\pi$
$104$	−42.1786	−0.0397688
$105$	−117.078	−0.108816
$106$	399.610	0.366166
$107$	589.174	0.532314	0.266157	−	0.963930i	$-0.414246\pi$
$107$	589.174	0.532314	0.266157	+	0.963930i	$0.414246\pi$
$108$	923.629	0.822928
$109$	845.145	0.742662	0.371331	−	0.928500i	$-0.378901\pi$
$109$	845.145	0.742662	0.371331	+	0.928500i	$0.378901\pi$
$110$	−26.3805	−0.0228662
$111$	1846.49	1.57893
$112$	−520.058	−0.438758
$113$	−216.642	−0.180353	−0.0901767	−	0.995926i	$-0.528743\pi$
$113$	−216.642	−0.180353	−0.0901767	+	0.995926i	$0.528743\pi$
$114$	3348.07	2.75066
$115$	334.533	0.271264
$116$	600.546	0.480684
$117$	147.586	0.116618
$118$	1702.20	1.32797
$119$	−484.797	−0.373456
$120$	34.8135	0.0264835
$121$	−1322.23	−0.993407
$122$	2482.54	1.84228
$123$	163.722	0.120019
$124$	−113.446	−0.0821596
$125$	−535.247	−0.382992
$126$	−336.831	−0.238153
$127$	448.568	0.313417	0.156708	−	0.987645i	$-0.449912\pi$
$127$	448.568	0.313417	0.156708	+	0.987645i	$0.449912\pi$
$128$	337.906	0.233336
$129$	0	0
$130$	−141.821	−0.0956808
$131$	1293.46	0.862675	0.431338	−	0.902191i	$-0.358042\pi$
$131$	1293.46	0.862675	0.431338	+	0.902191i	$0.358042\pi$
$132$	−154.294	−0.101739
$133$	1213.62	0.791237
$134$	−3153.70	−2.03312
$135$	233.075	0.148592
$136$	144.156	0.0908917
$137$	2103.91	1.31204	0.656019	−	0.754744i	$-0.272239\pi$
$137$	2103.91	1.31204	0.656019	+	0.754744i	$0.272239\pi$
$138$	3766.38	2.32330
$139$	−2683.27	−1.63735	−0.818676	−	0.574255i	$-0.805292\pi$
$139$	−2683.27	−1.63735	−0.818676	+	0.574255i	$0.805292\pi$
$140$	168.146	0.101507
$141$	3745.81	2.23727
$142$	−3501.85	−2.06950
$143$	47.1728	0.0275859
$144$	−541.100	−0.313136
$145$	151.546	0.0867945
$146$	−60.3571	−0.0342136
$147$	1587.83	0.890899
$148$	−2651.91	−1.47288
$149$	−2733.30	−1.50283	−0.751413	−	0.659832i	$-0.770627\pi$
$149$	−2733.30	−1.50283	−0.751413	+	0.659832i	$0.770627\pi$
$150$	−2954.55	−1.60825
$151$	2187.16	1.17873	0.589367	−	0.807865i	$-0.299377\pi$
$151$	2187.16	1.17873	0.589367	+	0.807865i	$0.299377\pi$
$152$	−360.875	−0.192571
$153$	−504.411	−0.266531
$154$	−107.661	−0.0563348
$155$	−28.6278	−0.0148351
$156$	−829.480	−0.425715
$157$	2618.77	1.33122	0.665608	−	0.746302i	$-0.268172\pi$
$157$	2618.77	1.33122	0.665608	+	0.746302i	$0.268172\pi$
$158$	−3559.48	−1.79226
$159$	589.795	0.294175
$160$	566.209	0.279767
$161$	1365.26	0.668306
$162$	3645.11	1.76782
$163$	556.769	0.267543	0.133772	−	0.991012i	$-0.457291\pi$
$163$	556.769	0.267543	0.133772	+	0.991012i	$0.457291\pi$
$164$	−235.136	−0.111958
$165$	−38.9356	−0.0183705
$166$	4315.86	2.01793
$167$	−84.4752	−0.0391430	−0.0195715	−	0.999808i	$-0.506230\pi$
$167$	−84.4752	−0.0391430	−0.0195715	+	0.999808i	$0.506230\pi$
$168$	142.077	0.0652468
$169$	−1943.40	−0.884570
$170$	484.707	0.218679
$171$	1262.73	0.564697
$172$	0	0
$173$	−1870.04	−0.821829	−0.410914	−	0.911674i	$-0.634790\pi$
$173$	−1870.04	−0.821829	−0.410914	+	0.911674i	$0.634790\pi$
$174$	1706.20	0.743372
$175$	−1070.98	−0.462620
$176$	−172.951	−0.0740721
$177$	2512.32	1.06688
$178$	1814.37	0.764003
$179$	−590.661	−0.246637	−0.123319	−	0.992367i	$-0.539354\pi$
$179$	−590.661	−0.246637	−0.123319	+	0.992367i	$0.539354\pi$
$180$	174.949	0.0724441
$181$	1963.05	0.806147	0.403073	−	0.915168i	$-0.367942\pi$
$181$	1963.05	0.806147	0.403073	+	0.915168i	$0.367942\pi$
$182$	−578.783	−0.235726
$183$	3664.04	1.48007
$184$	−405.963	−0.162652
$185$	−669.201	−0.265949
$186$	−322.311	−0.127059
$187$	−161.225	−0.0630477
$188$	−5379.70	−2.08699
$189$	951.198	0.366082
$190$	−1213.40	−0.463312
$191$	−3347.99	−1.26833	−0.634167	−	0.773196i	$-0.718657\pi$
$191$	−3347.99	−1.26833	−0.634167	+	0.773196i	$0.718657\pi$
$192$	3561.82	1.33881
$193$	3819.93	1.42469	0.712344	−	0.701831i	$-0.247634\pi$
$193$	3819.93	1.42469	0.712344	+	0.701831i	$0.247634\pi$
$194$	−613.637	−0.227096
$195$	−209.317	−0.0768692
$196$	−2280.43	−0.831060
$197$	3154.91	1.14100	0.570502	−	0.821296i	$-0.306749\pi$
$197$	3154.91	1.14100	0.570502	+	0.821296i	$0.306749\pi$
$198$	−112.017	−0.0402055
$199$	5307.46	1.89063	0.945317	−	0.326154i	$-0.105753\pi$
$199$	5307.46	1.89063	0.945317	+	0.326154i	$0.105753\pi$
$200$	318.459	0.112592
$201$	−4654.62	−1.63339
$202$	−1634.82	−0.569432
$203$	618.472	0.213834
$204$	2834.95	0.972973
$205$	−59.3359	−0.0202156
$206$	−3900.97	−1.31939
$207$	1420.49	0.476962
$208$	−929.782	−0.309946
$209$	403.604	0.133578
$210$	477.717	0.156979
$211$	−2869.87	−0.936352	−0.468176	−	0.883635i	$-0.655089\pi$
$211$	−2869.87	−0.936352	−0.468176	+	0.883635i	$0.655089\pi$
$212$	−847.058	−0.274416
$213$	−5168.46	−1.66262
$214$	−2404.02	−0.767924
$215$	0	0
$216$	−282.842	−0.0890970
$217$	−116.833	−0.0365489
$218$	−3448.47	−1.07138
$219$	−89.0825	−0.0274869
$220$	55.9189	0.0171366
$221$	−866.740	−0.263816
$222$	−7534.29	−2.27779
$223$	−6510.38	−1.95501	−0.977506	−	0.210908i	$-0.932358\pi$
$223$	−6510.38	−1.95501	−0.977506	+	0.210908i	$0.932358\pi$
$224$	2310.75	0.689255
$225$	−1114.31	−0.330166
$226$	883.970	0.260181
$227$	1210.57	0.353958	0.176979	−	0.984215i	$-0.443368\pi$
$227$	1210.57	0.353958	0.176979	+	0.984215i	$0.443368\pi$
$228$	−7096.93	−2.06143
$229$	−1712.57	−0.494192	−0.247096	−	0.968991i	$-0.579476\pi$
$229$	−1712.57	−0.494192	−0.247096	+	0.968991i	$0.579476\pi$
$230$	−1365.00	−0.391329
$231$	−158.899	−0.0452589
$232$	−183.905	−0.0520428
$233$	−4497.51	−1.26456	−0.632278	−	0.774741i	$-0.717880\pi$
$233$	−4497.51	−1.26456	−0.632278	+	0.774741i	$0.717880\pi$
$234$	−602.200	−0.168235
$235$	−1357.55	−0.376838
$236$	−3608.17	−0.995220
$237$	−5253.53	−1.43989
$238$	1978.13	0.538753
$239$	6253.68	1.69254	0.846270	−	0.532754i	$-0.178843\pi$
$239$	6253.68	1.69254	0.846270	+	0.532754i	$0.178843\pi$
$240$	767.425	0.206405
$241$	4314.12	1.15310	0.576550	−	0.817062i	$-0.304399\pi$
$241$	4314.12	1.15310	0.576550	+	0.817062i	$0.304399\pi$
$242$	5395.12	1.43310
$243$	2496.62	0.659087
$244$	−5262.26	−1.38066
$245$	−575.459	−0.150060
$246$	−668.041	−0.173141
$247$	2169.77	0.558943
$248$	34.7406	0.00889528
$249$	6369.89	1.62119
$250$	2183.99	0.552510
$251$	−6821.84	−1.71550	−0.857750	−	0.514067i	$-0.828138\pi$
$251$	−6821.84	−1.71550	−0.857750	+	0.514067i	$0.828138\pi$
$252$	713.983	0.178479
$253$	454.032	0.112825
$254$	−1830.31	−0.452140
$255$	715.392	0.175685
$256$	3352.77	0.818548
$257$	2048.98	0.497322	0.248661	−	0.968591i	$-0.420009\pi$
$257$	2048.98	0.497322	0.248661	+	0.968591i	$0.420009\pi$
$258$	0	0
$259$	−2731.07	−0.655213
$260$	300.619	0.0717061
$261$	643.495	0.152611
$262$	−5277.76	−1.24451
$263$	−2225.75	−0.521847	−0.260923	−	0.965360i	$-0.584027\pi$
$263$	−2225.75	−0.521847	−0.260923	+	0.965360i	$0.584027\pi$
$264$	47.2493	0.0110151
$265$	−213.752	−0.0495498
$266$	−4951.99	−1.14145
$267$	2677.87	0.613794
$268$	6684.92	1.52368
$269$	−639.777	−0.145011	−0.0725054	−	0.997368i	$-0.523099\pi$
$269$	−639.777	−0.145011	−0.0725054	+	0.997368i	$0.523099\pi$
$270$	−951.023	−0.214361
$271$	2033.22	0.455754	0.227877	−	0.973690i	$-0.426822\pi$
$271$	2033.22	0.455754	0.227877	+	0.973690i	$0.426822\pi$
$272$	3177.76	0.708382
$273$	−854.240	−0.189381
$274$	−8584.66	−1.89277
$275$	−356.166	−0.0781005
$276$	−7983.63	−1.74115
$277$	855.321	0.185528	0.0927640	−	0.995688i	$-0.470430\pi$
$277$	855.321	0.185528	0.0927640	+	0.995688i	$0.470430\pi$
$278$	10948.6	2.36207
$279$	−121.560	−0.0260845
$280$	−51.4912	−0.0109900
$281$	6456.77	1.37074	0.685372	−	0.728194i	$-0.259640\pi$
$281$	6456.77	1.37074	0.685372	+	0.728194i	$0.259640\pi$
$282$	−15284.2	−3.22751
$283$	2550.24	0.535676	0.267838	−	0.963464i	$-0.413691\pi$
$283$	2550.24	0.535676	0.267838	+	0.963464i	$0.413691\pi$
$284$	7422.89	1.55094
$285$	−1790.89	−0.372221
$286$	−192.481	−0.0397959
$287$	−242.155	−0.0498047
$288$	2404.24	0.491913
$289$	−1950.70	−0.397049
$290$	−618.358	−0.125211
$291$	−905.683	−0.182447
$292$	127.939	0.0256407
$293$	−5438.66	−1.08440	−0.542201	−	0.840249i	$-0.682409\pi$
$293$	−5438.66	−1.08440	−0.542201	+	0.840249i	$0.682409\pi$
$294$	−6478.88	−1.28523
$295$	−910.511	−0.179702
$296$	812.092	0.159466
$297$	316.332	0.0618028
$298$	11152.8	2.16800
$299$	2440.86	0.472103
$300$	6262.78	1.20527
$301$	0	0
$302$	−8924.36	−1.70046
$303$	−2412.87	−0.457477
$304$	−7955.09	−1.50084
$305$	−1327.91	−0.249299
$306$	2058.17	0.384502
$307$	−5098.12	−0.947769	−0.473884	−	0.880587i	$-0.657149\pi$
$307$	−5098.12	−0.947769	−0.473884	+	0.880587i	$0.657149\pi$
$308$	228.210	0.0422190
$309$	−5757.54	−1.05998
$310$	116.811	0.0214014
$311$	608.278	0.110908	0.0554539	−	0.998461i	$-0.482339\pi$
$311$	608.278	0.110908	0.0554539	+	0.998461i	$0.482339\pi$
$312$	254.011	0.0460915
$313$	−8591.81	−1.55156	−0.775779	−	0.631005i	$-0.782643\pi$
$313$	−8591.81	−1.55156	−0.775779	+	0.631005i	$0.782643\pi$
$314$	−10685.5	−1.92043
$315$	180.171	0.0322270
$316$	7545.07	1.34317
$317$	−3275.74	−0.580391	−0.290196	−	0.956967i	$-0.593720\pi$
$317$	−3275.74	−0.580391	−0.290196	+	0.956967i	$0.593720\pi$
$318$	−2406.56	−0.424381
$319$	205.680	0.0360999
$320$	−1290.87	−0.225506
$321$	−3548.16	−0.616944
$322$	−5570.70	−0.964108
$323$	−7415.72	−1.27747
$324$	−7726.58	−1.32486
$325$	−1914.74	−0.326802
$326$	−2271.80	−0.385962
$327$	−5089.69	−0.860735
$328$	72.0055	0.0121215
$329$	−5540.28	−0.928406
$330$	158.870	0.0265016
$331$	7793.65	1.29419	0.647096	−	0.762409i	$-0.275983\pi$
$331$	7793.65	1.29419	0.647096	+	0.762409i	$0.275983\pi$
$332$	−9148.37	−1.51230
$333$	−2841.57	−0.467618
$334$	344.687	0.0564684
$335$	1686.92	0.275123
$336$	3131.93	0.508514
$337$	−1219.14	−0.197065	−0.0985324	−	0.995134i	$-0.531415\pi$
$337$	−1219.14	−0.197065	−0.0985324	+	0.995134i	$0.531415\pi$
$338$	7929.72	1.27609
$339$	1304.67	0.209027
$340$	−1027.44	−0.163884
$341$	−38.8540	−0.00617028
$342$	−5152.34	−0.814640
$343$	−5403.70	−0.850648
$344$	0	0
$345$	−2014.64	−0.314391
$346$	7630.38	1.18558
$347$	8942.44	1.38344	0.691722	−	0.722164i	$-0.256852\pi$
$347$	8942.44	1.38344	0.691722	+	0.722164i	$0.256852\pi$
$348$	−3616.65	−0.557105
$349$	−11578.0	−1.77581	−0.887904	−	0.460030i	$-0.847839\pi$
$349$	−11578.0	−1.77581	−0.887904	+	0.460030i	$0.847839\pi$
$350$	4369.95	0.667382
$351$	1700.59	0.258607
$352$	768.465	0.116362
$353$	−7587.38	−1.14401	−0.572005	−	0.820250i	$-0.693834\pi$
$353$	−7587.38	−1.14401	−0.572005	+	0.820250i	$0.693834\pi$
$354$	−10251.1	−1.53910
$355$	1873.14	0.280045
$356$	−3845.93	−0.572567
$357$	2919.57	0.432830
$358$	2410.09	0.355803
$359$	8406.81	1.23592	0.617959	−	0.786211i	$-0.287960\pi$
$359$	8406.81	1.23592	0.617959	+	0.786211i	$0.287960\pi$
$360$	−53.5745	−0.00784340
$361$	11705.3	1.70655
$362$	−8009.91	−1.16296
$363$	7962.79	1.15134
$364$	1226.85	0.176661
$365$	32.2851	0.00462981
$366$	−14950.5	−2.13518
$367$	−5733.44	−0.815486	−0.407743	−	0.913097i	$-0.633684\pi$
$367$	−5733.44	−0.815486	−0.407743	+	0.913097i	$0.633684\pi$
$368$	−8949.02	−1.26766
$369$	−251.952	−0.0355450
$370$	2730.56	0.383663
$371$	−872.341	−0.122075
$372$	683.204	0.0952218
$373$	3701.87	0.513875	0.256938	−	0.966428i	$-0.417286\pi$
$373$	3701.87	0.513875	0.256938	+	0.966428i	$0.417286\pi$
$374$	657.850	0.0909536
$375$	3223.40	0.443882
$376$	1647.42	0.225955
$377$	1105.73	0.151056
$378$	−3881.20	−0.528115
$379$	−1981.11	−0.268504	−0.134252	−	0.990947i	$-0.542863\pi$
$379$	−1981.11	−0.268504	−0.134252	+	0.990947i	$0.542863\pi$
$380$	2572.05	0.347220
$381$	−2701.39	−0.363246
$382$	13660.9	1.82972
$383$	−4324.44	−0.576942	−0.288471	−	0.957489i	$-0.593147\pi$
$383$	−4324.44	−0.576942	−0.288471	+	0.957489i	$0.593147\pi$
$384$	−2034.96	−0.270433
$385$	57.5880	0.00762327
$386$	−15586.6	−2.05528
$387$	0	0
$388$	1300.73	0.170192
$389$	−13257.2	−1.72793	−0.863967	−	0.503548i	$-0.832028\pi$
$389$	−13257.2	−1.72793	−0.863967	+	0.503548i	$0.832028\pi$
$390$	854.082	0.110893
$391$	−8342.25	−1.07899
$392$	698.333	0.0899774
$393$	−7789.58	−0.999828
$394$	−12873.1	−1.64603
$395$	1903.97	0.242530
$396$	237.443	0.0301312
$397$	2355.52	0.297784	0.148892	−	0.988853i	$-0.452429\pi$
$397$	2355.52	0.297784	0.148892	+	0.988853i	$0.452429\pi$
$398$	−21656.2	−2.72746
$399$	−7308.76	−0.917032
$400$	7020.09	0.877511
$401$	−3462.47	−0.431191	−0.215595	−	0.976483i	$-0.569169\pi$
$401$	−3462.47	−0.431191	−0.215595	+	0.976483i	$0.569169\pi$
$402$	18992.4	2.35636
$403$	−208.878	−0.0258188
$404$	3465.33	0.426750
$405$	−1949.78	−0.239223
$406$	−2523.57	−0.308480
$407$	−908.248	−0.110615
$408$	−868.145	−0.105342
$409$	7101.00	0.858489	0.429244	−	0.903188i	$-0.358780\pi$
$409$	7101.00	0.858489	0.429244	+	0.903188i	$0.358780\pi$
$410$	242.110	0.0291633
$411$	−12670.3	−1.52063
$412$	8268.92	0.988788
$413$	−3715.87	−0.442727
$414$	−5796.09	−0.688073
$415$	−2308.56	−0.273067
$416$	4131.25	0.486902
$417$	16159.4	1.89767
$418$	−1646.84	−0.192702
$419$	−7575.88	−0.883308	−0.441654	−	0.897185i	$-0.645608\pi$
$419$	−7575.88	−0.883308	−0.441654	+	0.897185i	$0.645608\pi$
$420$	−1012.62	−0.117645
$421$	2054.30	0.237816	0.118908	−	0.992905i	$-0.462061\pi$
$421$	2054.30	0.237816	0.118908	+	0.992905i	$0.462061\pi$
$422$	11710.0	1.35080
$423$	−5764.44	−0.662592
$424$	259.394	0.0297105
$425$	6544.10	0.746907
$426$	21089.0	2.39851
$427$	−5419.33	−0.614192
$428$	5095.83	0.575505
$429$	−284.087	−0.0319717
$430$	0	0
$431$	−17175.1	−1.91948	−0.959742	−	0.280884i	$-0.909372\pi$
$431$	−17175.1	−1.91948	−0.959742	+	0.280884i	$0.909372\pi$
$432$	−6234.94	−0.694395
$433$	7628.21	0.846624	0.423312	−	0.905984i	$-0.360867\pi$
$433$	7628.21	0.846624	0.423312	+	0.905984i	$0.360867\pi$
$434$	476.716	0.0527261
$435$	−912.650	−0.100594
$436$	7309.76	0.802922
$437$	20883.7	2.28605
$438$	363.486	0.0396531
$439$	−6478.18	−0.704298	−0.352149	−	0.935944i	$-0.614549\pi$
$439$	−6478.18	−0.704298	−0.352149	+	0.935944i	$0.614549\pi$
$440$	−17.1240	−0.00185535
$441$	−2443.52	−0.263850
$442$	3536.59	0.380584
$443$	3350.48	0.359336	0.179668	−	0.983727i	$-0.442498\pi$
$443$	3350.48	0.359336	0.179668	+	0.983727i	$0.442498\pi$
$444$	15970.5	1.70704
$445$	−970.508	−0.103385
$446$	26564.5	2.82033
$447$	16460.7	1.74175
$448$	−5268.15	−0.555573
$449$	−14358.1	−1.50913	−0.754567	−	0.656223i	$-0.772153\pi$
$449$	−14358.1	−1.50913	−0.754567	+	0.656223i	$0.772153\pi$
$450$	4546.76	0.476303
$451$	−80.5313	−0.00840814
$452$	−1873.76	−0.194987
$453$	−13171.7	−1.36614
$454$	−4939.53	−0.510625
$455$	309.592	0.0318987
$456$	2173.28	0.223187
$457$	−3151.07	−0.322540	−0.161270	−	0.986910i	$-0.551559\pi$
$457$	−3151.07	−0.322540	−0.161270	+	0.986910i	$0.551559\pi$
$458$	6987.86	0.712929
$459$	−5812.19	−0.591046
$460$	2893.41	0.293274
$461$	1289.67	0.130295	0.0651475	−	0.997876i	$-0.479248\pi$
$461$	1289.67	0.130295	0.0651475	+	0.997876i	$0.479248\pi$
$462$	648.363	0.0652912
$463$	9807.31	0.984416	0.492208	−	0.870478i	$-0.336190\pi$
$463$	9807.31	0.984416	0.492208	+	0.870478i	$0.336190\pi$
$464$	−4053.98	−0.405606
$465$	172.404	0.0171937
$466$	18351.3	1.82427
$467$	−2759.08	−0.273394	−0.136697	−	0.990613i	$-0.543649\pi$
$467$	−2759.08	−0.273394	−0.136697	+	0.990613i	$0.543649\pi$
$468$	1276.49	0.126081
$469$	6884.46	0.677814
$470$	5539.26	0.543632
$471$	−15770.9	−1.54286
$472$	1104.93	0.107751
$473$	0	0
$474$	21436.1	2.07720
$475$	−16382.3	−1.58246
$476$	−4193.06	−0.403758
$477$	−907.636	−0.0871233
$478$	−25517.1	−2.44168
$479$	6246.31	0.595828	0.297914	−	0.954593i	$-0.403709\pi$
$479$	6246.31	0.595828	0.297914	+	0.954593i	$0.403709\pi$
$480$	−3409.86	−0.324246
$481$	−4882.72	−0.462854
$482$	−17603.0	−1.66348
$483$	−8221.93	−0.774557
$484$	−11436.1	−1.07401
$485$	328.236	0.0307308
$486$	−10187.0	−0.950809
$487$	−7223.74	−0.672154	−0.336077	−	0.941835i	$-0.609100\pi$
$487$	−7223.74	−0.672154	−0.336077	+	0.941835i	$0.609100\pi$
$488$	1611.46	0.149482
$489$	−3353.01	−0.310079
$490$	2348.06	0.216479
$491$	9289.33	0.853812	0.426906	−	0.904296i	$-0.359603\pi$
$491$	9289.33	0.853812	0.426906	+	0.904296i	$0.359603\pi$
$492$	1416.05	0.129757
$493$	−3779.11	−0.345238
$494$	−8853.37	−0.806340
$495$	59.9180	0.00544064
$496$	765.818	0.0693271
$497$	7644.46	0.689941
$498$	−25991.3	−2.33875
$499$	3220.27	0.288896	0.144448	−	0.989512i	$-0.453859\pi$
$499$	3220.27	0.288896	0.144448	+	0.989512i	$0.453859\pi$
$500$	−4629.42	−0.414068
$501$	508.732	0.0453662
$502$	27835.4	2.47481
$503$	−164.938	−0.0146207	−0.00731035	−	0.999973i	$-0.502327\pi$
$503$	−164.938	−0.0146207	−0.00731035	+	0.999973i	$0.502327\pi$
$504$	−218.642	−0.0193236
$505$	874.466	0.0770559
$506$	−1852.60	−0.162763
$507$	11703.7	1.02520
$508$	3879.71	0.338847
$509$	−11574.1	−1.00788	−0.503940	−	0.863738i	$-0.668117\pi$
$509$	−11574.1	−1.00788	−0.503940	+	0.863738i	$0.668117\pi$
$510$	−2919.04	−0.253445
$511$	131.758	0.0114063
$512$	−16383.7	−1.41419
$513$	14550.0	1.25224
$514$	−8360.52	−0.717445
$515$	2086.64	0.178540
$516$	0	0
$517$	−1842.48	−0.156736
$518$	11143.7	0.945221
$519$	11261.9	0.952487
$520$	−92.0581	−0.00776349
$521$	−16300.3	−1.37069	−0.685343	−	0.728220i	$-0.740348\pi$
$521$	−16300.3	−1.37069	−0.685343	+	0.728220i	$0.740348\pi$
$522$	−2625.67	−0.220158
$523$	12912.3	1.07957	0.539785	−	0.841803i	$-0.318506\pi$
$523$	12912.3	1.07957	0.539785	+	0.841803i	$0.318506\pi$
$524$	11187.3	0.932672
$525$	6449.72	0.536169
$526$	9081.81	0.752824
$527$	713.893	0.0590089
$528$	1041.56	0.0858485
$529$	11326.0	0.930875
$530$	872.181	0.0714813
$531$	−3866.22	−0.315969
$532$	10496.8	0.855437
$533$	−432.935	−0.0351829
$534$	−10926.6	−0.885468
$535$	1285.92	0.103916
$536$	−2047.12	−0.164966
$537$	3557.12	0.285849
$538$	2610.50	0.209195
$539$	−781.020	−0.0624135
$540$	2015.89	0.160648
$541$	−2148.68	−0.170756	−0.0853780	−	0.996349i	$-0.527210\pi$
$541$	−2148.68	−0.170756	−0.0853780	+	0.996349i	$0.527210\pi$
$542$	−8296.22	−0.657478
$543$	−11822.0	−0.934312
$544$	−14119.6	−1.11281
$545$	1844.59	0.144979
$546$	3485.58	0.273204
$547$	−7515.40	−0.587450	−0.293725	−	0.955890i	$-0.594895\pi$
$547$	−7515.40	−0.587450	−0.293725	+	0.955890i	$0.594895\pi$
$548$	18197.0	1.41850
$549$	−5638.60	−0.438341
$550$	1453.28	0.112669
$551$	9460.49	0.731452
$552$	2444.82	0.188512
$553$	7770.28	0.597515
$554$	−3489.99	−0.267646
$555$	4030.11	0.308232
$556$	−23207.9	−1.77021
$557$	13442.7	1.02259	0.511297	−	0.859404i	$-0.329165\pi$
$557$	13442.7	1.02259	0.511297	+	0.859404i	$0.329165\pi$
$558$	496.004	0.0376300
$559$	0	0
$560$	−1135.07	−0.0856524
$561$	970.938	0.0730713
$562$	−26345.8	−1.97746
$563$	14488.6	1.08458	0.542291	−	0.840191i	$-0.317557\pi$
$563$	14488.6	1.08458	0.542291	+	0.840191i	$0.317557\pi$
$564$	32398.0	2.41880
$565$	−472.837	−0.0352078
$566$	−10405.8	−0.772774
$567$	−7957.21	−0.589368
$568$	−2273.10	−0.167918
$569$	−7940.71	−0.585047	−0.292524	−	0.956258i	$-0.594495\pi$
$569$	−7940.71	−0.585047	−0.292524	+	0.956258i	$0.594495\pi$
$570$	7307.41	0.536972
$571$	−16716.9	−1.22518	−0.612592	−	0.790400i	$-0.709873\pi$
$571$	−16716.9	−1.22518	−0.612592	+	0.790400i	$0.709873\pi$
$572$	408.003	0.0298242
$573$	20162.5	1.46998
$574$	988.072	0.0718490
$575$	−18429.1	−1.33660
$576$	−5481.29	−0.396506
$577$	22899.6	1.65221	0.826104	−	0.563518i	$-0.190552\pi$
$577$	22899.6	1.65221	0.826104	+	0.563518i	$0.190552\pi$
$578$	7959.51	0.572789
$579$	−23004.6	−1.65119
$580$	1310.74	0.0938370
$581$	−9421.44	−0.672749
$582$	3695.49	0.263201
$583$	−290.107	−0.0206089
$584$	−39.1788	−0.00277608
$585$	322.118	0.0227657
$586$	22191.6	1.56438
$587$	−21550.7	−1.51532	−0.757661	−	0.652648i	$-0.773658\pi$
$587$	−21550.7	−1.51532	−0.757661	+	0.652648i	$0.773658\pi$
$588$	13733.3	0.963186
$589$	−1787.14	−0.125022
$590$	3715.19	0.259240
$591$	−18999.7	−1.32241
$592$	17901.7	1.24283
$593$	26777.0	1.85430	0.927149	−	0.374694i	$-0.122252\pi$
$593$	26777.0	1.85430	0.927149	+	0.374694i	$0.122252\pi$
$594$	−1290.74	−0.0891577
$595$	−1058.11	−0.0729044
$596$	−23640.7	−1.62476
$597$	−31962.9	−2.19122
$598$	−9959.53	−0.681063
$599$	−8296.25	−0.565903	−0.282951	−	0.959134i	$-0.591313\pi$
$599$	−8296.25	−0.565903	−0.282951	+	0.959134i	$0.591313\pi$
$600$	−1917.85	−0.130493
$601$	−1874.08	−0.127197	−0.0635984	−	0.997976i	$-0.520258\pi$
$601$	−1874.08	−0.127197	−0.0635984	+	0.997976i	$0.520258\pi$
$602$	0	0
$603$	7163.00	0.483748
$604$	18917.0	1.27438
$605$	−2885.86	−0.193929
$606$	9845.30	0.659963
$607$	2574.28	0.172136	0.0860681	−	0.996289i	$-0.472570\pi$
$607$	2574.28	0.172136	0.0860681	+	0.996289i	$0.472570\pi$
$608$	35346.4	2.35771
$609$	−3724.60	−0.247830
$610$	5418.33	0.359642
$611$	−9905.15	−0.655842
$612$	−4362.71	−0.288157
$613$	8303.26	0.547089	0.273545	−	0.961859i	$-0.411804\pi$
$613$	8303.26	0.547089	0.273545	+	0.961859i	$0.411804\pi$
$614$	20802.0	1.36727
$615$	357.336	0.0234296
$616$	−69.8844	−0.00457098
$617$	−28299.9	−1.84653	−0.923267	−	0.384159i	$-0.874491\pi$
$617$	−28299.9	−1.84653	−0.923267	+	0.384159i	$0.874491\pi$
$618$	23492.7	1.52915
$619$	−24822.2	−1.61178	−0.805888	−	0.592069i	$-0.798311\pi$
$619$	−24822.2	−1.61178	−0.805888	+	0.592069i	$0.798311\pi$
$620$	−247.606	−0.0160388
$621$	16368.0	1.05769
$622$	−2481.98	−0.159997
$623$	−3960.73	−0.254708
$624$	5599.39	0.359223
$625$	13861.3	0.887125
$626$	35057.4	2.23830
$627$	−2430.61	−0.154816
$628$	22650.1	1.43923
$629$	16687.9	1.05785
$630$	−735.159	−0.0464911
$631$	−15805.6	−0.997162	−0.498581	−	0.866843i	$-0.666145\pi$
$631$	−15805.6	−0.997162	−0.498581	+	0.866843i	$0.666145\pi$
$632$	−2310.52	−0.145423
$633$	17283.1	1.08522
$634$	13366.1	0.837281
$635$	979.034	0.0611839
$636$	5101.20	0.318044
$637$	−4198.74	−0.261162
$638$	−839.243	−0.0520783
$639$	7953.75	0.492403
$640$	737.506	0.0455508
$641$	−4409.29	−0.271695	−0.135847	−	0.990730i	$-0.543376\pi$
$641$	−4409.29	−0.271695	−0.135847	+	0.990730i	$0.543376\pi$
$642$	14477.7	0.890013
$643$	−22435.9	−1.37603	−0.688014	−	0.725698i	$-0.741517\pi$
$643$	−22435.9	−1.37603	−0.688014	+	0.725698i	$0.741517\pi$
$644$	11808.3	0.722532
$645$	0	0
$646$	30258.6	1.84289
$647$	−7104.96	−0.431723	−0.215862	−	0.976424i	$-0.569256\pi$
$647$	−7104.96	−0.431723	−0.215862	+	0.976424i	$0.569256\pi$
$648$	2366.10	0.143440
$649$	−1235.76	−0.0747422
$650$	7812.79	0.471450
$651$	703.597	0.0423597
$652$	4815.56	0.289252
$653$	−6201.10	−0.371620	−0.185810	−	0.982586i	$-0.559491\pi$
$653$	−6201.10	−0.371620	−0.185810	+	0.982586i	$0.559491\pi$
$654$	20767.6	1.24171
$655$	2823.08	0.168408
$656$	1587.28	0.0944710
$657$	137.089	0.00814058
$658$	22606.2	1.33933
$659$	−24325.9	−1.43794	−0.718971	−	0.695041i	$-0.755386\pi$
$659$	−24325.9	−1.43794	−0.718971	+	0.695041i	$0.755386\pi$
$660$	−336.758	−0.0198611
$661$	4195.11	0.246855	0.123427	−	0.992354i	$-0.460611\pi$
$661$	4195.11	0.246855	0.123427	+	0.992354i	$0.460611\pi$
$662$	−31800.7	−1.86702
$663$	5219.74	0.305758
$664$	2801.50	0.163734
$665$	2648.83	0.154462
$666$	11594.5	0.674593
$667$	10642.5	0.617810
$668$	−730.636	−0.0423191
$669$	39207.3	2.26583
$670$	−6883.19	−0.396897
$671$	−1802.26	−0.103689
$672$	−13915.9	−0.798837
$673$	30476.3	1.74558	0.872789	−	0.488097i	$-0.162309\pi$
$673$	30476.3	1.74558	0.872789	+	0.488097i	$0.162309\pi$
$674$	4974.50	0.284289
$675$	−12839.9	−0.732160
$676$	−16808.7	−0.956343
$677$	−13889.1	−0.788482	−0.394241	−	0.919007i	$-0.628992\pi$
$677$	−13889.1	−0.788482	−0.394241	+	0.919007i	$0.628992\pi$
$678$	−5323.50	−0.301545
$679$	1339.56	0.0757106
$680$	314.631	0.0177435
$681$	−7290.38	−0.410232
$682$	158.537	0.00890134
$683$	−10181.3	−0.570388	−0.285194	−	0.958470i	$-0.592058\pi$
$683$	−10181.3	−0.570388	−0.285194	+	0.958470i	$0.592058\pi$
$684$	10921.5	0.610516
$685$	4591.95	0.256130
$686$	22048.9	1.22716
$687$	10313.6	0.572761
$688$	0	0
$689$	−1559.61	−0.0862357
$690$	8220.42	0.453545
$691$	−16877.9	−0.929182	−0.464591	−	0.885525i	$-0.653799\pi$
$691$	−16877.9	−0.929182	−0.464591	+	0.885525i	$0.653799\pi$
$692$	−16174.2	−0.888511
$693$	244.531	0.0134040
$694$	−36488.1	−1.99578
$695$	−5856.44	−0.319637
$696$	1107.52	0.0603169
$697$	1479.66	0.0804105
$698$	47242.1	2.56181
$699$	27085.2	1.46560
$700$	−9263.02	−0.500156
$701$	−22820.0	−1.22953	−0.614765	−	0.788710i	$-0.710749\pi$
$701$	−22820.0	−1.22953	−0.614765	+	0.788710i	$0.710749\pi$
$702$	−6938.98	−0.373070
$703$	−41775.9	−2.24126
$704$	−1751.98	−0.0937931
$705$	8175.53	0.436749
$706$	30959.1	1.65037
$707$	3568.77	0.189841
$708$	21729.4	1.15345
$709$	1810.88	0.0959226	0.0479613	−	0.998849i	$-0.484728\pi$
$709$	1810.88	0.0959226	0.0479613	+	0.998849i	$0.484728\pi$
$710$	−7643.05	−0.403998
$711$	8084.66	0.426440
$712$	1177.73	0.0619908
$713$	−2010.43	−0.105597
$714$	−11912.8	−0.624407
$715$	102.958	0.00538521
$716$	−5108.69	−0.266649
$717$	−37661.3	−1.96163
$718$	−34302.6	−1.78295
$719$	16290.1	0.844951	0.422476	−	0.906374i	$-0.361161\pi$
$719$	16290.1	0.844951	0.422476	+	0.906374i	$0.361161\pi$
$720$	−1180.99	−0.0611291
$721$	8515.74	0.439865
$722$	−47761.3	−2.46190
$723$	−25980.8	−1.33643
$724$	16978.7	0.871557
$725$	−8348.54	−0.427665
$726$	−32490.8	−1.66095
$727$	−9094.37	−0.463950	−0.231975	−	0.972722i	$-0.574519\pi$
$727$	−9094.37	−0.463950	−0.231975	+	0.972722i	$0.574519\pi$
$728$	−375.697	−0.0191267
$729$	9084.82	0.461557
$730$	−131.734	−0.00667903
$731$	0	0
$732$	31690.7	1.60017
$733$	−12269.4	−0.618256	−0.309128	−	0.951020i	$-0.600037\pi$
$733$	−12269.4	−0.618256	−0.309128	+	0.951020i	$0.600037\pi$
$734$	23394.4	1.17643
$735$	3465.57	0.173917
$736$	39762.7	1.99140
$737$	2289.51	0.114430
$738$	1028.05	0.0512778
$739$	1437.99	0.0715794	0.0357897	−	0.999359i	$-0.488605\pi$
$739$	1437.99	0.0715794	0.0357897	+	0.999359i	$0.488605\pi$
$740$	−5788.00	−0.287529
$741$	−13066.9	−0.647807
$742$	3559.44	0.176107
$743$	28488.6	1.40666	0.703328	−	0.710865i	$-0.251696\pi$
$743$	28488.6	1.40666	0.703328	+	0.710865i	$0.251696\pi$
$744$	−209.217	−0.0103095
$745$	−5965.65	−0.293375
$746$	−15104.9	−0.741325
$747$	−9802.63	−0.480133
$748$	−1394.45	−0.0681633
$749$	5247.94	0.256015
$750$	−13152.5	−0.640351
$751$	−16276.2	−0.790850	−0.395425	−	0.918498i	$-0.629403\pi$
$751$	−16276.2	−0.790850	−0.395425	+	0.918498i	$0.629403\pi$
$752$	36315.6	1.76103
$753$	41082.9	1.98824
$754$	−4511.75	−0.217915
$755$	4773.65	0.230107
$756$	8227.02	0.395786
$757$	12549.2	0.602519	0.301259	−	0.953542i	$-0.402593\pi$
$757$	12549.2	0.602519	0.301259	+	0.953542i	$0.402593\pi$
$758$	8083.60	0.387348
$759$	−2734.30	−0.130763
$760$	−787.637	−0.0375929
$761$	−20472.0	−0.975179	−0.487589	−	0.873073i	$-0.662124\pi$
$761$	−20472.0	−0.975179	−0.487589	+	0.873073i	$0.662124\pi$
$762$	11022.6	0.524024
$763$	7527.94	0.357182
$764$	−28957.1	−1.37125
$765$	−1100.92	−0.0520310
$766$	17645.2	0.832305
$767$	−6643.39	−0.312750
$768$	−20191.3	−0.948685
$769$	21892.6	1.02662	0.513309	−	0.858204i	$-0.328420\pi$
$769$	21892.6	1.02662	0.513309	+	0.858204i	$0.328420\pi$
$770$	−234.978	−0.0109974
$771$	−12339.5	−0.576389
$772$	33039.0	1.54029
$773$	33744.5	1.57012	0.785061	−	0.619419i	$-0.212632\pi$
$773$	33744.5	1.57012	0.785061	+	0.619419i	$0.212632\pi$
$774$	0	0
$775$	1577.08	0.0730975
$776$	−398.322	−0.0184264
$777$	16447.2	0.759383
$778$	54093.8	2.49275
$779$	−3704.13	−0.170365
$780$	−1810.41	−0.0831063
$781$	2542.25	0.116477
$782$	34039.2	1.55657
$783$	7414.82	0.338421
$784$	15394.0	0.701257
$785$	5715.67	0.259874
$786$	31784.1	1.44237
$787$	40966.7	1.85553	0.927767	−	0.373159i	$-0.121725\pi$
$787$	40966.7	1.85553	0.927767	+	0.373159i	$0.121725\pi$
$788$	27287.2	1.23358
$789$	13404.1	0.604813
$790$	−7768.85	−0.349877
$791$	−1929.69	−0.0867406
$792$	−72.7120	−0.00326226
$793$	−9688.91	−0.433876
$794$	−9611.30	−0.429587
$795$	1287.27	0.0574275
$796$	45904.9	2.04404
$797$	−253.103	−0.0112489	−0.00562445	−	0.999984i	$-0.501790\pi$
$797$	−253.103	−0.0112489	−0.00562445	+	0.999984i	$0.501790\pi$
$798$	29822.2	1.32292
$799$	33853.3	1.49893
$800$	−31192.0	−1.37850
$801$	−4120.98	−0.181782
$802$	14128.0	0.622042
$803$	43.8177	0.00192565
$804$	−40258.4	−1.76592
$805$	2979.78	0.130464
$806$	852.294	0.0372466
$807$	3852.91	0.168065
$808$	−1061.19	−0.0462034
$809$	−25849.5	−1.12339	−0.561694	−	0.827345i	$-0.689850\pi$
$809$	−25849.5	−1.12339	−0.561694	+	0.827345i	$0.689850\pi$
$810$	7955.74	0.345107
$811$	24298.3	1.05207	0.526036	−	0.850463i	$-0.323678\pi$
$811$	24298.3	1.05207	0.526036	+	0.850463i	$0.323678\pi$
$812$	5349.24	0.231184
$813$	−12244.6	−0.528212
$814$	3705.95	0.159574
$815$	1215.19	0.0522286
$816$	−19137.3	−0.821005
$817$	0	0
$818$	−28974.4	−1.23847
$819$	1314.59	0.0560873
$820$	−513.203	−0.0218559
$821$	−16567.0	−0.704253	−0.352127	−	0.935952i	$-0.614541\pi$
$821$	−16567.0	−0.704253	−0.352127	+	0.935952i	$0.614541\pi$
$822$	51699.1	2.19369
$823$	−19573.2	−0.829013	−0.414506	−	0.910046i	$-0.636046\pi$
$823$	−19573.2	−0.829013	−0.414506	+	0.910046i	$0.636046\pi$
$824$	−2532.18	−0.107054
$825$	2144.93	0.0905174
$826$	15162.0	0.638684
$827$	−34803.1	−1.46339	−0.731695	−	0.681632i	$-0.761270\pi$
$827$	−34803.1	−1.46339	−0.731695	+	0.681632i	$0.761270\pi$
$828$	12286.0	0.515663
$829$	8559.16	0.358591	0.179295	−	0.983795i	$-0.442618\pi$
$829$	8559.16	0.358591	0.179295	+	0.983795i	$0.442618\pi$
$830$	9419.70	0.393931
$831$	−5150.97	−0.215024
$832$	−9418.62	−0.392466
$833$	14350.2	0.596886
$834$	−65935.6	−2.73760
$835$	−184.374	−0.00764134
$836$	3490.82	0.144417
$837$	−1400.70	−0.0578438
$838$	30912.1	1.27427
$839$	−11133.3	−0.458124	−0.229062	−	0.973412i	$-0.573566\pi$
$839$	−11133.3	−0.458124	−0.229062	+	0.973412i	$0.573566\pi$
$840$	310.094	0.0127372
$841$	−19567.9	−0.802323
$842$	−8382.24	−0.343077
$843$	−38884.4	−1.58867
$844$	−24821.9	−1.01233
$845$	−4241.62	−0.172682
$846$	23520.8	0.955866
$847$	−11777.4	−0.477777
$848$	5718.05	0.231555
$849$	−15358.2	−0.620841
$850$	−26702.1	−1.07750
$851$	−46995.5	−1.89305
$852$	−44702.6	−1.79752
$853$	39508.0	1.58585	0.792923	−	0.609321i	$-0.208558\pi$
$853$	39508.0	1.58585	0.792923	+	0.609321i	$0.208558\pi$
$854$	22112.7	0.886043
$855$	2756.00	0.110238
$856$	−1560.49	−0.0623090
$857$	−25368.9	−1.01118	−0.505592	−	0.862773i	$-0.668726\pi$
$857$	−25368.9	−1.01118	−0.505592	+	0.862773i	$0.668726\pi$
$858$	1159.17	0.0461229
$859$	−15928.9	−0.632696	−0.316348	−	0.948643i	$-0.602457\pi$
$859$	−15928.9	−0.632696	−0.316348	+	0.948643i	$0.602457\pi$
$860$	0	0
$861$	1458.32	0.0577229
$862$	70080.3	2.76908
$863$	18377.5	0.724885	0.362442	−	0.932006i	$-0.381943\pi$
$863$	18377.5	0.724885	0.362442	+	0.932006i	$0.381943\pi$
$864$	27703.4	1.09084
$865$	−4081.50	−0.160434
$866$	−31125.6	−1.22135
$867$	11747.6	0.460174
$868$	−1010.50	−0.0395145
$869$	2584.10	0.100874
$870$	3723.91	0.145118
$871$	12308.3	0.478820
$872$	−2238.46	−0.0869310
$873$	1393.76	0.0540338
$874$	−85212.5	−3.29789
$875$	−4767.60	−0.184199
$876$	−770.485	−0.0297172
$877$	46868.1	1.80459	0.902293	−	0.431124i	$-0.141883\pi$
$877$	46868.1	1.80459	0.902293	+	0.431124i	$0.141883\pi$
$878$	26433.1	1.01603
$879$	32753.1	1.25681
$880$	−377.480	−0.0144600
$881$	−24976.8	−0.955153	−0.477577	−	0.878590i	$-0.658485\pi$
$881$	−24976.8	−0.955153	−0.477577	+	0.878590i	$0.658485\pi$
$882$	9970.36	0.380634
$883$	44574.5	1.69881	0.849406	−	0.527740i	$-0.176960\pi$
$883$	44574.5	1.69881	0.849406	+	0.527740i	$0.176960\pi$
$884$	−7496.54	−0.285221
$885$	5483.34	0.208272
$886$	−13671.1	−0.518384
$887$	−18914.5	−0.715994	−0.357997	−	0.933723i	$-0.616540\pi$
$887$	−18914.5	−0.715994	−0.357997	+	0.933723i	$0.616540\pi$
$888$	−4890.63	−0.184819
$889$	3995.52	0.150737
$890$	3960.00	0.149145
$891$	−2646.26	−0.0994984
$892$	−56309.1	−2.11364
$893$	−84747.1	−3.17576
$894$	−67165.1	−2.51268
$895$	−1289.16	−0.0481474
$896$	3009.83	0.112222
$897$	−14699.5	−0.547160
$898$	58585.8	2.17710
$899$	−910.739	−0.0337874
$900$	−9637.80	−0.356956
$901$	5330.35	0.197092
$902$	328.595	0.0121297
$903$	0	0
$904$	573.799	0.0211109
$905$	4284.51	0.157372
$906$	53744.8	1.97081
$907$	−9458.37	−0.346262	−0.173131	−	0.984899i	$-0.555388\pi$
$907$	−9458.37	−0.346262	−0.173131	+	0.984899i	$0.555388\pi$
$908$	10470.4	0.382678
$909$	3713.16	0.135487
$910$	−1263.24	−0.0460175
$911$	33612.0	1.22241	0.611206	−	0.791472i	$-0.290685\pi$
$911$	33612.0	1.22241	0.611206	+	0.791472i	$0.290685\pi$
$912$	47907.7	1.73945
$913$	−3133.21	−0.113575
$914$	12857.4	0.465302
$915$	7997.05	0.288934
$916$	−14812.2	−0.534290
$917$	11521.2	0.414902
$918$	23715.7	0.852651
$919$	−28693.2	−1.02993	−0.514963	−	0.857212i	$-0.672195\pi$
$919$	−28693.2	−1.02993	−0.514963	+	0.857212i	$0.672195\pi$
$920$	−886.046	−0.0317523
$921$	30702.2	1.09845
$922$	−5262.29	−0.187965
$923$	13667.1	0.487386
$924$	−1374.34	−0.0489312
$925$	36865.7	1.31042
$926$	−40017.1	−1.42013
$927$	8860.28	0.313927
$928$	18012.8	0.637176
$929$	−18092.0	−0.638946	−0.319473	−	0.947595i	$-0.603506\pi$
$929$	−18092.0	−0.638946	−0.319473	+	0.947595i	$0.603506\pi$
$930$	−703.468	−0.0248039
$931$	−35923.9	−1.26462
$932$	−38899.5	−1.36716
$933$	−3663.21	−0.128540
$934$	11258.0	0.394402
$935$	−351.885	−0.0123079
$936$	−390.898	−0.0136505
$937$	17209.8	0.600021	0.300010	−	0.953936i	$-0.403010\pi$
$937$	17209.8	0.600021	0.300010	+	0.953936i	$0.403010\pi$
$938$	−28090.9	−0.977825
$939$	51742.1	1.79823
$940$	−11741.6	−0.407414
$941$	−48758.8	−1.68915	−0.844576	−	0.535436i	$-0.820147\pi$
$941$	−48758.8	−1.68915	−0.844576	+	0.535436i	$0.820147\pi$
$942$	64350.7	2.22575
$943$	−4166.93	−0.143896
$944$	24356.9	0.839777
$945$	2076.06	0.0714649
$946$	0	0
$947$	−32685.7	−1.12159	−0.560794	−	0.827956i	$-0.689504\pi$
$947$	−32685.7	−1.12159	−0.560794	+	0.827956i	$0.689504\pi$
$948$	−45438.4	−1.55672
$949$	235.563	0.00805764
$950$	66845.2	2.28289
$951$	19727.4	0.672665
$952$	1284.04	0.0437142
$953$	14271.7	0.485105	0.242552	−	0.970138i	$-0.422015\pi$
$953$	14271.7	0.485105	0.242552	+	0.970138i	$0.422015\pi$
$954$	3703.46	0.125685
$955$	−7307.24	−0.247599
$956$	54088.8	1.82987
$957$	−1238.66	−0.0418392
$958$	−25487.0	−0.859550
$959$	18740.1	0.631022
$960$	7773.95	0.261358
$961$	−29619.0	−0.994225
$962$	19923.1	0.667720
$963$	5460.27	0.182715
$964$	37313.3	1.24666
$965$	8337.30	0.278121
$966$	33548.2	1.11739
$967$	18223.7	0.606034	0.303017	−	0.952985i	$-0.402006\pi$
$967$	18223.7	0.606034	0.303017	+	0.952985i	$0.402006\pi$
$968$	3502.06	0.116281
$969$	44659.4	1.48056
$970$	−1339.31	−0.0443327
$971$	27591.5	0.911899	0.455949	−	0.890006i	$-0.349300\pi$
$971$	27591.5	0.911899	0.455949	+	0.890006i	$0.349300\pi$
$972$	21593.5	0.712565
$973$	−23900.6	−0.787482
$974$	29475.3	0.969660
$975$	11531.1	0.378759
$976$	35522.8	1.16502
$977$	−26884.2	−0.880348	−0.440174	−	0.897912i	$-0.645083\pi$
$977$	−26884.2	−0.880348	−0.440174	+	0.897912i	$0.645083\pi$
$978$	13681.4	0.447324
$979$	−1317.18	−0.0430004
$980$	−4977.21	−0.162236
$981$	7832.52	0.254917
$982$	−37903.6	−1.23172
$983$	−11678.2	−0.378918	−0.189459	−	0.981889i	$-0.560673\pi$
$983$	−11678.2	−0.378918	−0.189459	+	0.981889i	$0.560673\pi$
$984$	−433.636	−0.0140486
$985$	6885.83	0.222742
$986$	15420.0	0.498046
$987$	33365.0	1.07601
$988$	18766.6	0.604296
$989$	0	0
$990$	−244.485	−0.00784875
$991$	37149.5	1.19081	0.595406	−	0.803425i	$-0.296991\pi$
$991$	37149.5	1.19081	0.595406	+	0.803425i	$0.296991\pi$
$992$	−3402.72	−0.108908
$993$	−46935.4	−1.49995
$994$	−31191.9	−0.995320
$995$	11583.9	0.369081
$996$	55093.9	1.75273
$997$	59233.9	1.88160	0.940800	−	0.338962i	$-0.110076\pi$
$997$	59233.9	1.88160	0.940800	+	0.338962i	$0.110076\pi$
$998$	−13139.8	−0.416765
$999$	−32742.6	−1.03697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.9	yes	50
43.42	odd	2		1849.4.a.i.1.42	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.42	✓	50	43.42	odd	2
1849.4.a.j.1.9	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)

\(f(q)\)	\(=\)	\(q-4.08033 q^{2} -6.02226 q^{3} +8.64912 q^{4} +2.18258 q^{5} +24.5728 q^{6} +8.90728 q^{7} -2.64861 q^{8} +9.26767 q^{9} +O(q^{10})\)	\(q-4.08033 q^{2} -6.02226 q^{3} +8.64912 q^{4} +2.18258 q^{5} +24.5728 q^{6} +8.90728 q^{7} -2.64861 q^{8} +9.26767 q^{9} -8.90564 q^{10} +2.96222 q^{11} -52.0873 q^{12} +15.9248 q^{13} -36.3447 q^{14} -13.1441 q^{15} -58.3857 q^{16} -54.4270 q^{17} -37.8152 q^{18} +136.251 q^{19} +18.8774 q^{20} -53.6420 q^{21} -12.0868 q^{22} +153.274 q^{23} +15.9506 q^{24} -120.236 q^{25} -64.9786 q^{26} +106.789 q^{27} +77.0401 q^{28} +69.4344 q^{29} +53.6321 q^{30} -13.1165 q^{31} +259.422 q^{32} -17.8393 q^{33} +222.080 q^{34} +19.4408 q^{35} +80.1572 q^{36} -306.611 q^{37} -555.948 q^{38} -95.9035 q^{39} -5.78080 q^{40} -27.1862 q^{41} +218.877 q^{42} +25.6206 q^{44} +20.2274 q^{45} -625.409 q^{46} -621.994 q^{47} +351.614 q^{48} -263.660 q^{49} +490.604 q^{50} +327.774 q^{51} +137.736 q^{52} -97.9357 q^{53} -435.734 q^{54} +6.46527 q^{55} -23.5919 q^{56} -820.538 q^{57} -283.315 q^{58} -417.172 q^{59} -113.684 q^{60} -608.416 q^{61} +53.5198 q^{62} +82.5498 q^{63} -591.443 q^{64} +34.7572 q^{65} +72.7902 q^{66} +772.902 q^{67} -470.745 q^{68} -923.057 q^{69} -79.3251 q^{70} +858.225 q^{71} -24.5464 q^{72} +14.7922 q^{73} +1251.07 q^{74} +724.095 q^{75} +1178.45 q^{76} +26.3853 q^{77} +391.318 q^{78} +872.351 q^{79} -127.431 q^{80} -893.337 q^{81} +110.929 q^{82} -1057.72 q^{83} -463.956 q^{84} -118.791 q^{85} -418.152 q^{87} -7.84576 q^{88} -444.661 q^{89} -82.5346 q^{90} +141.847 q^{91} +1325.69 q^{92} +78.9912 q^{93} +2537.94 q^{94} +297.378 q^{95} -1562.31 q^{96} +150.389 q^{97} +1075.82 q^{98} +27.4529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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