LMFDB - Embedded newform 1849.4.a.i.1.42

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			1.42
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	$-0.243541\pi$
$2$	4.08033	1.44262	0.721308	+	0.692615i	$0.243541\pi$
$3$	6.02226	1.15899	0.579493	−	0.814977i	$-0.303251\pi$
$3$	6.02226	1.15899	0.579493	+	0.814977i	$0.303251\pi$
$4$	8.64912	1.08114
$5$	−2.18258	−0.195216	−0.0976078	−	0.995225i	$-0.531119\pi$
$5$	−2.18258	−0.195216	−0.0976078	+	0.995225i	$0.531119\pi$
$6$	24.5728	1.67197
$7$	−8.90728	−0.480948	−0.240474	−	0.970656i	$-0.577303\pi$
$7$	−8.90728	−0.480948	−0.240474	+	0.970656i	$0.577303\pi$
$8$	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	$-0.807466\pi$
$19$	−136.251	−1.64516	−0.822580	+	0.568649i	$0.807466\pi$
$20$	−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	$-0.571358\pi$
$29$	−69.4344	−0.444608	−0.222304	+	0.974977i	$0.571358\pi$
$30$	−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	$-0.261472\pi$
$37$	306.611	1.36234	0.681168	+	0.732127i	$0.261472\pi$
$38$	−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	$-0.279546\pi$
$61$	608.416	1.27704	0.638522	+	0.769604i	$0.279546\pi$
$62$	−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	$-0.754609\pi$
$71$	−858.225	−1.43454	−0.717272	+	0.696793i	$0.754609\pi$
$72$	24.5464	0.0401781
$73$	−14.7922	−0.0237164	−0.0118582	−	0.999930i	$-0.503775\pi$
$73$	−14.7922	−0.0237164	−0.0118582	+	0.999930i	$0.503775\pi$
$74$	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	$-0.414695\pi$
$89$	444.661	0.529596	0.264798	+	0.964304i	$0.414695\pi$
$90$	−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	$-0.471257\pi$
$113$	216.642	0.180353	0.0901767	+	0.995926i	$0.471257\pi$
$114$	−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	$-0.641958\pi$
$131$	−1293.46	−0.862675	−0.431338	+	0.902191i	$0.641958\pi$
$132$	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	$-0.727761\pi$
$137$	−2103.91	−1.31204	−0.656019	+	0.754744i	$0.727761\pi$
$138$	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	$-0.229373\pi$
$149$	2733.30	1.50283	0.751413	+	0.659832i	$0.229373\pi$
$150$	−2954.55	−1.60825
$151$	−2187.16	−1.17873	−0.589367	−	0.807865i	$-0.700623\pi$
$151$	−2187.16	−1.17873	−0.589367	+	0.807865i	$0.700623\pi$
$152$	−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	$-0.731828\pi$
$157$	−2618.77	−1.33122	−0.665608	+	0.746302i	$0.731828\pi$
$158$	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	$-0.542709\pi$
$163$	−556.769	−0.267543	−0.133772	+	0.991012i	$0.542709\pi$
$164$	−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	$-0.460646\pi$
$179$	590.661	0.246637	0.123319	+	0.992367i	$0.460646\pi$
$180$	−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	$-0.281343\pi$
$191$	3347.99	1.26833	0.634167	+	0.773196i	$0.281343\pi$
$192$	−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	$-0.894247\pi$
$199$	−5307.46	−1.89063	−0.945317	+	0.326154i	$0.894247\pi$
$200$	−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	$-0.344911\pi$
$211$	2869.87	0.936352	0.468176	+	0.883635i	$0.344911\pi$
$212$	−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	$-0.0676422\pi$
$223$	6510.38	1.95501	0.977506	+	0.210908i	$0.0676422\pi$
$224$	2310.75	0.689255
$225$	−1114.31	−0.330166
$226$	883.970	0.260181
$227$	−1210.57	−0.353958	−0.176979	−	0.984215i	$-0.556632\pi$
$227$	−1210.57	−0.353958	−0.176979	+	0.984215i	$0.556632\pi$
$228$	−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	$-0.282120\pi$
$233$	4497.51	1.26456	0.632278	+	0.774741i	$0.282120\pi$
$234$	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	$-0.695601\pi$
$241$	−4314.12	−1.15310	−0.576550	+	0.817062i	$0.695601\pi$
$242$	−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	$-0.579991\pi$
$257$	−2048.98	−0.497322	−0.248661	+	0.968591i	$0.579991\pi$
$258$	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	$-0.415973\pi$
$263$	2225.75	0.521847	0.260923	+	0.965360i	$0.415973\pi$
$264$	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	$-0.529570\pi$
$277$	−855.321	−0.185528	−0.0927640	+	0.995688i	$0.529570\pi$
$278$	−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	$-0.217357\pi$
$313$	8591.81	1.55156	0.775779	+	0.631005i	$0.217357\pi$
$314$	−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	$-0.724017\pi$
$331$	−7793.65	−1.29419	−0.647096	+	0.762409i	$0.724017\pi$
$332$	−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	$-0.743148\pi$
$347$	−8942.44	−1.38344	−0.691722	+	0.722164i	$0.743148\pi$
$348$	−3616.65	−0.557105
$349$	11578.0	1.77581	0.887904	−	0.460030i	$-0.152161\pi$
$349$	11578.0	1.77581	0.887904	+	0.460030i	$0.152161\pi$
$350$	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	$-0.582714\pi$
$373$	−3701.87	−0.513875	−0.256938	+	0.966428i	$0.582714\pi$
$374$	−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	$-0.406853\pi$
$383$	4324.44	0.576942	0.288471	+	0.957489i	$0.406853\pi$
$384$	−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	$-0.167972\pi$
$389$	13257.2	1.72793	0.863967	+	0.503548i	$0.167972\pi$
$390$	−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	$-0.641220\pi$
$409$	−7101.00	−0.858489	−0.429244	+	0.903188i	$0.641220\pi$
$410$	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	$-0.354392\pi$
$419$	7575.88	0.883308	0.441654	+	0.897185i	$0.354392\pi$
$420$	1012.62	0.117645
$421$	−2054.30	−0.237816	−0.118908	−	0.992905i	$-0.537939\pi$
$421$	−2054.30	−0.237816	−0.118908	+	0.992905i	$0.537939\pi$
$422$	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	$-0.639133\pi$
$433$	−7628.21	−0.846624	−0.423312	+	0.905984i	$0.639133\pi$
$434$	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	$-0.227847\pi$
$449$	14358.1	1.50913	0.754567	+	0.656223i	$0.227847\pi$
$450$	−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	$-0.448441\pi$
$457$	3151.07	0.322540	0.161270	+	0.986910i	$0.448441\pi$
$458$	−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	$-0.663810\pi$
$463$	−9807.31	−0.984416	−0.492208	+	0.870478i	$0.663810\pi$
$464$	4053.98	0.405606
$465$	172.404	0.0171937
$466$	18351.3	1.82427
$467$	2759.08	0.273394	0.136697	−	0.990613i	$-0.456351\pi$
$467$	2759.08	0.273394	0.136697	+	0.990613i	$0.456351\pi$
$468$	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	$-0.640397\pi$
$491$	−9289.33	−0.853812	−0.426906	+	0.904296i	$0.640397\pi$
$492$	−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	$-0.546141\pi$
$499$	−3220.27	−0.288896	−0.144448	+	0.989512i	$0.546141\pi$
$500$	4629.42	0.414068
$501$	−508.732	−0.0453662
$502$	−27835.4	−2.47481
$503$	164.938	0.0146207	0.00731035	−	0.999973i	$-0.497673\pi$
$503$	164.938	0.0146207	0.00731035	+	0.999973i	$0.497673\pi$
$504$	−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	$-0.259652\pi$
$521$	16300.3	1.37069	0.685343	+	0.728220i	$0.259652\pi$
$522$	−2625.67	−0.220158
$523$	−12912.3	−1.07957	−0.539785	−	0.841803i	$-0.681494\pi$
$523$	−12912.3	−1.07957	−0.539785	+	0.841803i	$0.681494\pi$
$524$	−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	$-0.290127\pi$
$571$	16716.9	1.22518	0.612592	+	0.790400i	$0.290127\pi$
$572$	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	$-0.809448\pi$
$577$	−22899.6	−1.65221	−0.826104	+	0.563518i	$0.809448\pi$
$578$	−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	$-0.226342\pi$
$587$	21550.7	1.51532	0.757661	+	0.652648i	$0.226342\pi$
$588$	−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	$-0.877748\pi$
$593$	−26777.0	−1.85430	−0.927149	+	0.374694i	$0.877748\pi$
$594$	−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	$-0.479742\pi$
$601$	1874.08	0.127197	0.0635984	+	0.997976i	$0.479742\pi$
$602$	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	$-0.527430\pi$
$607$	−2574.28	−0.172136	−0.0860681	+	0.996289i	$0.527430\pi$
$608$	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	$-0.333855\pi$
$631$	15805.6	0.997162	0.498581	+	0.866843i	$0.333855\pi$
$632$	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	$-0.456624\pi$
$641$	4409.29	0.271695	0.135847	+	0.990730i	$0.456624\pi$
$642$	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	$-0.430744\pi$
$647$	7104.96	0.431723	0.215862	+	0.976424i	$0.430744\pi$
$648$	−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	$-0.440509\pi$
$653$	6201.10	0.371620	0.185810	+	0.982586i	$0.440509\pi$
$654$	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	$-0.837691\pi$
$673$	−30476.3	−1.74558	−0.872789	+	0.488097i	$0.837691\pi$
$674$	−4974.50	−0.284289
$675$	12839.9	0.732160
$676$	−16808.7	−0.956343
$677$	13889.1	0.788482	0.394241	−	0.919007i	$-0.371008\pi$
$677$	13889.1	0.788482	0.394241	+	0.919007i	$0.371008\pi$
$678$	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	$-0.346201\pi$
$691$	16877.9	0.929182	0.464591	+	0.885525i	$0.346201\pi$
$692$	−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	$-0.425481\pi$
$727$	9094.37	0.463950	0.231975	+	0.972722i	$0.425481\pi$
$728$	−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	$-0.399963\pi$
$733$	12269.4	0.618256	0.309128	+	0.951020i	$0.399963\pi$
$734$	−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	$-0.511395\pi$
$739$	−1437.99	−0.0715794	−0.0357897	+	0.999359i	$0.511395\pi$
$740$	−5788.00	−0.287529
$741$	−13066.9	−0.647807
$742$	3559.44	0.176107
$743$	−28488.6	−1.40666	−0.703328	−	0.710865i	$-0.748304\pi$
$743$	−28488.6	−1.40666	−0.703328	+	0.710865i	$0.748304\pi$
$744$	−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	$-0.370597\pi$
$751$	16276.2	0.790850	0.395425	+	0.918498i	$0.370597\pi$
$752$	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	$-0.597407\pi$
$757$	−12549.2	−0.602519	−0.301259	+	0.953542i	$0.597407\pi$
$758$	−8083.60	−0.387348
$759$	2734.30	0.130763
$760$	787.637	0.0375929
$761$	20472.0	0.975179	0.487589	−	0.873073i	$-0.337876\pi$
$761$	20472.0	0.975179	0.487589	+	0.873073i	$0.337876\pi$
$762$	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	$-0.787368\pi$
$773$	−33744.5	−1.57012	−0.785061	+	0.619419i	$0.787368\pi$
$774$	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	$-0.676322\pi$
$811$	−24298.3	−1.05207	−0.526036	+	0.850463i	$0.676322\pi$
$812$	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	$-0.557382\pi$
$829$	−8559.16	−0.358591	−0.179295	+	0.983795i	$0.557382\pi$
$830$	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	$-0.426434\pi$
$839$	11133.3	0.458124	0.229062	+	0.973412i	$0.426434\pi$
$840$	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	$-0.397543\pi$
$859$	15928.9	0.632696	0.316348	+	0.948643i	$0.397543\pi$
$860$	0	0
$861$	1458.32	0.0577229
$862$	−70080.3	−2.76908
$863$	−18377.5	−0.724885	−0.362442	−	0.932006i	$-0.618057\pi$
$863$	−18377.5	−0.724885	−0.362442	+	0.932006i	$0.618057\pi$
$864$	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	$-0.383460\pi$
$887$	18914.5	0.715994	0.357997	+	0.933723i	$0.383460\pi$
$888$	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	$-0.709315\pi$
$911$	−33612.0	−1.22241	−0.611206	+	0.791472i	$0.709315\pi$
$912$	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	$-0.396494\pi$
$929$	18092.0	0.638946	0.319473	+	0.947595i	$0.396494\pi$
$930$	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	$-0.596990\pi$
$937$	−17209.8	−0.600021	−0.300010	+	0.953936i	$0.596990\pi$
$938$	−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	$-0.577985\pi$
$953$	−14271.7	−0.485105	−0.242552	+	0.970138i	$0.577985\pi$
$954$	−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	$-0.439327\pi$
$983$	11678.2	0.378918	0.189459	+	0.981889i	$0.439327\pi$
$984$	−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	$-0.703009\pi$
$991$	−37149.5	−1.19081	−0.595406	+	0.803425i	$0.703009\pi$
$992$	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	$-0.889924\pi$
$997$	−59233.9	−1.88160	−0.940800	+	0.338962i	$0.889924\pi$
$998$	−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.i.1.42	✓	50
43.42	odd	2		1849.4.a.j.1.9	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.42	✓	50	1.1	even	1	trivial
1849.4.a.j.1.9	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)

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