LMFDB - Embedded newform 1849.4.a.i.1.5

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			1.5
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)

$f(q)$	$=$	$q-4.85844 q^{2} -5.73018 q^{3} +15.6044 q^{4} +14.4569 q^{5} +27.8397 q^{6} -13.1859 q^{7} -36.9457 q^{8} +5.83494 q^{9} +O(q^{10})$	\(q-4.85844 q^{2} -5.73018 q^{3} +15.6044 q^{4} +14.4569 q^{5} +27.8397 q^{6} -13.1859 q^{7} -36.9457 q^{8} +5.83494 q^{9} -70.2380 q^{10} -56.6297 q^{11} -89.4162 q^{12} -68.5859 q^{13} +64.0631 q^{14} -82.8407 q^{15} +54.6629 q^{16} +23.3842 q^{17} -28.3487 q^{18} -119.755 q^{19} +225.592 q^{20} +75.5578 q^{21} +275.132 q^{22} -49.8515 q^{23} +211.705 q^{24} +84.0024 q^{25} +333.220 q^{26} +121.280 q^{27} -205.759 q^{28} +290.660 q^{29} +402.477 q^{30} +58.9050 q^{31} +29.9890 q^{32} +324.498 q^{33} -113.611 q^{34} -190.628 q^{35} +91.0510 q^{36} +147.330 q^{37} +581.820 q^{38} +393.009 q^{39} -534.121 q^{40} +216.626 q^{41} -367.093 q^{42} -883.674 q^{44} +84.3552 q^{45} +242.201 q^{46} -233.374 q^{47} -313.228 q^{48} -169.131 q^{49} -408.121 q^{50} -133.996 q^{51} -1070.24 q^{52} +712.940 q^{53} -589.229 q^{54} -818.690 q^{55} +487.164 q^{56} +686.215 q^{57} -1412.15 q^{58} +70.0677 q^{59} -1292.68 q^{60} +328.266 q^{61} -286.186 q^{62} -76.9392 q^{63} -583.003 q^{64} -991.541 q^{65} -1576.55 q^{66} +307.039 q^{67} +364.898 q^{68} +285.658 q^{69} +926.155 q^{70} +1135.63 q^{71} -215.576 q^{72} +203.220 q^{73} -715.792 q^{74} -481.349 q^{75} -1868.70 q^{76} +746.715 q^{77} -1909.41 q^{78} +255.296 q^{79} +790.257 q^{80} -852.497 q^{81} -1052.47 q^{82} +665.658 q^{83} +1179.04 q^{84} +338.064 q^{85} -1665.53 q^{87} +2092.22 q^{88} -834.098 q^{89} -409.835 q^{90} +904.369 q^{91} -777.905 q^{92} -337.536 q^{93} +1133.83 q^{94} -1731.28 q^{95} -171.842 q^{96} +817.923 q^{97} +821.713 q^{98} -330.431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.85844	−1.71772	−0.858859	−	0.512212i	$-0.828826\pi$
$2$	−4.85844	−1.71772	−0.858859	+	0.512212i	$0.828826\pi$
$3$	−5.73018	−1.10277	−0.551387	−	0.834250i	$-0.685901\pi$
$3$	−5.73018	−1.10277	−0.551387	+	0.834250i	$0.685901\pi$
$4$	15.6044	1.95055
$5$	14.4569	1.29307	0.646533	−	0.762886i	$-0.276218\pi$
$5$	14.4569	1.29307	0.646533	+	0.762886i	$0.276218\pi$
$6$	27.8397	1.89425
$7$	−13.1859	−0.711974	−0.355987	−	0.934491i	$-0.615855\pi$
$7$	−13.1859	−0.711974	−0.355987	+	0.934491i	$0.615855\pi$
$8$	−36.9457	−1.63278
$9$	5.83494	0.216109
$10$	−70.2380	−2.22112
$11$	−56.6297	−1.55223	−0.776113	−	0.630594i	$-0.782811\pi$
$11$	−56.6297	−1.55223	−0.776113	+	0.630594i	$0.782811\pi$
$12$	−89.4162	−2.15102
$13$	−68.5859	−1.46325	−0.731627	−	0.681705i	$-0.761239\pi$
$13$	−68.5859	−1.46325	−0.731627	+	0.681705i	$0.761239\pi$
$14$	64.0631	1.22297
$15$	−82.8407	−1.42596
$16$	54.6629	0.854108
$17$	23.3842	0.333618	0.166809	−	0.985989i	$-0.446654\pi$
$17$	23.3842	0.333618	0.166809	+	0.985989i	$0.446654\pi$
$18$	−28.3487	−0.371214
$19$	−119.755	−1.44598	−0.722989	−	0.690859i	$-0.757232\pi$
$19$	−119.755	−1.44598	−0.722989	+	0.690859i	$0.757232\pi$
$20$	225.592	2.52220
$21$	75.5578	0.785146
$22$	275.132	2.66629
$23$	−49.8515	−0.451946	−0.225973	−	0.974134i	$-0.572556\pi$
$23$	−49.8515	−0.451946	−0.225973	+	0.974134i	$0.572556\pi$
$24$	211.705	1.80059
$25$	84.0024	0.672019
$26$	333.220	2.51346
$27$	121.280	0.864454
$28$	−205.759	−1.38874
$29$	290.660	1.86118	0.930590	−	0.366064i	$-0.119295\pi$
$29$	290.660	1.86118	0.930590	+	0.366064i	$0.119295\pi$
$30$	402.477	2.44939
$31$	58.9050	0.341279	0.170639	−	0.985334i	$-0.445417\pi$
$31$	58.9050	0.341279	0.170639	+	0.985334i	$0.445417\pi$
$32$	29.9890	0.165667
$33$	324.498	1.71175
$34$	−113.611	−0.573062
$35$	−190.628	−0.920629
$36$	91.0510	0.421532
$37$	147.330	0.654617	0.327309	−	0.944918i	$-0.393858\pi$
$37$	147.330	0.654617	0.327309	+	0.944918i	$0.393858\pi$
$38$	581.820	2.48378
$39$	393.009	1.61364
$40$	−534.121	−2.11130
$41$	216.626	0.825154	0.412577	−	0.910923i	$-0.364629\pi$
$41$	216.626	0.825154	0.412577	+	0.910923i	$0.364629\pi$
$42$	−367.093	−1.34866
$43$	0	0
$43$	0	0
$44$	−883.674	−3.02770
$45$	84.3552	0.279443
$46$	242.201	0.776316
$47$	−233.374	−0.724277	−0.362139	−	0.932124i	$-0.617953\pi$
$47$	−233.374	−0.724277	−0.362139	+	0.932124i	$0.617953\pi$
$48$	−313.228	−0.941888
$49$	−169.131	−0.493093
$50$	−408.121	−1.15434
$51$	−133.996	−0.367905
$52$	−1070.24	−2.85416
$53$	712.940	1.84773	0.923866	−	0.382716i	$-0.125011\pi$
$53$	712.940	1.84773	0.923866	+	0.382716i	$0.125011\pi$
$54$	−589.229	−1.48489
$55$	−818.690	−2.00713
$56$	487.164	1.16250
$57$	686.215	1.59459
$58$	−1412.15	−3.19698
$59$	70.0677	0.154611	0.0773054	−	0.997007i	$-0.475368\pi$
$59$	70.0677	0.154611	0.0773054	+	0.997007i	$0.475368\pi$
$60$	−1292.68	−2.78141
$61$	328.266	0.689019	0.344509	−	0.938783i	$-0.388045\pi$
$61$	328.266	0.689019	0.344509	+	0.938783i	$0.388045\pi$
$62$	−286.186	−0.586221
$63$	−76.9392	−0.153864
$64$	−583.003	−1.13868
$65$	−991.541	−1.89208
$66$	−1576.55	−2.94031
$67$	307.039	0.559863	0.279932	−	0.960020i	$-0.409688\pi$
$67$	307.039	0.559863	0.279932	+	0.960020i	$0.409688\pi$
$68$	364.898	0.650740
$69$	285.658	0.498394
$70$	926.155	1.58138
$71$	1135.63	1.89823	0.949114	−	0.314933i	$-0.101982\pi$
$71$	1135.63	1.89823	0.949114	+	0.314933i	$0.101982\pi$
$72$	−215.576	−0.352859
$73$	203.220	0.325824	0.162912	−	0.986641i	$-0.447911\pi$
$73$	203.220	0.325824	0.162912	+	0.986641i	$0.447911\pi$
$74$	−715.792	−1.12445
$75$	−481.349	−0.741085
$76$	−1868.70	−2.82046
$77$	746.715	1.10514
$78$	−1909.41	−2.77177
$79$	255.296	0.363583	0.181791	−	0.983337i	$-0.441810\pi$
$79$	255.296	0.363583	0.181791	+	0.983337i	$0.441810\pi$
$80$	790.257	1.10442
$81$	−852.497	−1.16941
$82$	−1052.47	−1.41738
$83$	665.658	0.880306	0.440153	−	0.897923i	$-0.354924\pi$
$83$	665.658	0.880306	0.440153	+	0.897923i	$0.354924\pi$
$84$	1179.04	1.53147
$85$	338.064	0.431390
$86$	0	0
$87$	−1665.53	−2.05246
$88$	2092.22	2.53445
$89$	−834.098	−0.993419	−0.496709	−	0.867917i	$-0.665458\pi$
$89$	−834.098	−0.993419	−0.496709	+	0.867917i	$0.665458\pi$
$90$	−409.835	−0.480004
$91$	904.369	1.04180
$92$	−777.905	−0.881545
$93$	−337.536	−0.376353
$94$	1133.83	1.24410
$95$	−1731.28	−1.86974
$96$	−171.842	−0.182693
$97$	817.923	0.856160	0.428080	−	0.903741i	$-0.359190\pi$
$97$	817.923	0.856160	0.428080	+	0.903741i	$0.359190\pi$
$98$	821.713	0.846995
$99$	−330.431	−0.335450
$100$	1310.81	1.31081
$101$	−642.462	−0.632944	−0.316472	−	0.948602i	$-0.602498\pi$
$101$	−642.462	−0.632944	−0.316472	+	0.948602i	$0.602498\pi$
$102$	651.010	0.631957
$103$	76.9496	0.0736123	0.0368062	−	0.999322i	$-0.488282\pi$
$103$	76.9496	0.0736123	0.0368062	+	0.999322i	$0.488282\pi$
$104$	2533.95	2.38918
$105$	1092.33	1.01524
$106$	−3463.77	−3.17388
$107$	−843.742	−0.762315	−0.381157	−	0.924510i	$-0.624474\pi$
$107$	−843.742	−0.762315	−0.381157	+	0.924510i	$0.624474\pi$
$108$	1892.50	1.68616
$109$	−1162.50	−1.02154	−0.510769	−	0.859718i	$-0.670639\pi$
$109$	−1162.50	−1.02154	−0.510769	+	0.859718i	$0.670639\pi$
$110$	3977.56	3.44768
$111$	−844.225	−0.721894
$112$	−720.782	−0.608103
$113$	884.391	0.736252	0.368126	−	0.929776i	$-0.379999\pi$
$113$	884.391	0.736252	0.368126	+	0.929776i	$0.379999\pi$
$114$	−3333.93	−2.73905
$115$	−720.699	−0.584396
$116$	4535.58	3.63033
$117$	−400.195	−0.316222
$118$	−340.420	−0.265578
$119$	−308.343	−0.237527
$120$	3060.61	2.32828
$121$	1875.92	1.40941
$122$	−1594.86	−1.18354
$123$	−1241.31	−0.909958
$124$	919.179	0.665683
$125$	−592.699	−0.424101
$126$	373.804	0.264295
$127$	−582.571	−0.407046	−0.203523	−	0.979070i	$-0.565239\pi$
$127$	−582.571	−0.407046	−0.203523	+	0.979070i	$0.565239\pi$
$128$	2592.57	1.79026
$129$	0	0
$130$	4817.34	3.25007
$131$	−903.044	−0.602285	−0.301142	−	0.953579i	$-0.597368\pi$
$131$	−903.044	−0.602285	−0.301142	+	0.953579i	$0.597368\pi$
$132$	5063.61	3.33887
$133$	1579.08	1.02950
$134$	−1491.73	−0.961687
$135$	1753.33	1.11780
$136$	−863.947	−0.544727
$137$	2121.22	1.32283	0.661415	−	0.750020i	$-0.269956\pi$
$137$	2121.22	1.32283	0.661415	+	0.750020i	$0.269956\pi$
$138$	−1387.85	−0.856100
$139$	1042.17	0.635939	0.317970	−	0.948101i	$-0.396999\pi$
$139$	1042.17	0.635939	0.317970	+	0.948101i	$0.396999\pi$
$140$	−2974.64	−1.79574
$141$	1337.27	0.798713
$142$	−5517.38	−3.26062
$143$	3884.00	2.27130
$144$	318.955	0.184580
$145$	4202.05	2.40663
$146$	−987.334	−0.559673
$147$	969.151	0.543770
$148$	2298.99	1.27687
$149$	−323.453	−0.177841	−0.0889205	−	0.996039i	$-0.528342\pi$
$149$	−323.453	−0.177841	−0.0889205	+	0.996039i	$0.528342\pi$
$150$	2338.60	1.27297
$151$	−864.578	−0.465949	−0.232975	−	0.972483i	$-0.574846\pi$
$151$	−864.578	−0.465949	−0.232975	+	0.972483i	$0.574846\pi$
$152$	4424.42	2.36097
$153$	136.446	0.0720979
$154$	−3627.87	−1.89833
$155$	851.584	0.441296
$156$	6132.69	3.14749
$157$	−577.261	−0.293442	−0.146721	−	0.989178i	$-0.546872\pi$
$157$	−577.261	−0.293442	−0.146721	+	0.989178i	$0.546872\pi$
$158$	−1240.34	−0.624533
$159$	−4085.27	−2.03763
$160$	433.548	0.214219
$161$	657.339	0.321774
$162$	4141.80	2.00871
$163$	−1803.66	−0.866707	−0.433353	−	0.901224i	$-0.642670\pi$
$163$	−1803.66	−0.866707	−0.433353	+	0.901224i	$0.642670\pi$
$164$	3380.33	1.60951
$165$	4691.24	2.21341
$166$	−3234.06	−1.51212
$167$	−2552.51	−1.18275	−0.591374	−	0.806397i	$-0.701414\pi$
$167$	−2552.51	−1.18275	−0.591374	+	0.806397i	$0.701414\pi$
$168$	−2791.53	−1.28197
$169$	2507.03	1.14111
$170$	−1642.46	−0.741007
$171$	−698.761	−0.312489
$172$	0	0
$173$	−676.365	−0.297243	−0.148622	−	0.988894i	$-0.547484\pi$
$173$	−676.365	−0.297243	−0.148622	+	0.988894i	$0.547484\pi$
$174$	8091.89	3.52554
$175$	−1107.65	−0.478460
$176$	−3095.54	−1.32577
$177$	−401.500	−0.170501
$178$	4052.42	1.70641
$179$	−1530.14	−0.638927	−0.319464	−	0.947598i	$-0.603503\pi$
$179$	−1530.14	−0.638927	−0.319464	+	0.947598i	$0.603503\pi$
$180$	1316.32	0.545069
$181$	2614.23	1.07356	0.536780	−	0.843722i	$-0.319641\pi$
$181$	2614.23	1.07356	0.536780	+	0.843722i	$0.319641\pi$
$182$	−4393.82	−1.78952
$183$	−1881.02	−0.759832
$184$	1841.80	0.737930
$185$	2129.93	0.846463
$186$	1639.90	0.646469
$187$	−1324.24	−0.517851
$188$	−3641.66	−1.41274
$189$	−1599.18	−0.615469
$190$	8411.33	3.21169
$191$	−3942.47	−1.49355	−0.746773	−	0.665079i	$-0.768398\pi$
$191$	−3942.47	−1.49355	−0.746773	+	0.665079i	$0.768398\pi$
$192$	3340.71	1.25570
$193$	−80.0135	−0.0298420	−0.0149210	−	0.999889i	$-0.504750\pi$
$193$	−80.0135	−0.0298420	−0.0149210	+	0.999889i	$0.504750\pi$
$194$	−3973.83	−1.47064
$195$	5681.70	2.08654
$196$	−2639.19	−0.961806
$197$	2777.66	1.00457	0.502284	−	0.864703i	$-0.332493\pi$
$197$	2777.66	1.00457	0.502284	+	0.864703i	$0.332493\pi$
$198$	1605.38	0.576208
$199$	2219.08	0.790484	0.395242	−	0.918577i	$-0.370661\pi$
$199$	2219.08	0.790484	0.395242	+	0.918577i	$0.370661\pi$
$200$	−3103.53	−1.09726
$201$	−1759.39	−0.617402
$202$	3121.36	1.08722
$203$	−3832.62	−1.32511
$204$	−2090.93	−0.717619
$205$	3131.75	1.06698
$206$	−373.855	−0.126445
$207$	−290.881	−0.0976696
$208$	−3749.11	−1.24978
$209$	6781.66	2.24449
$210$	−5307.03	−1.74390
$211$	−3231.50	−1.05434	−0.527169	−	0.849760i	$-0.676747\pi$
$211$	−3231.50	−1.05434	−0.527169	+	0.849760i	$0.676747\pi$
$212$	11125.0	3.60410
$213$	−6507.35	−2.09332
$214$	4099.27	1.30944
$215$	0	0
$216$	−4480.76	−1.41147
$217$	−776.717	−0.242982
$218$	5647.96	1.75471
$219$	−1164.49	−0.359310
$220$	−12775.2	−3.91502
$221$	−1603.83	−0.488168
$222$	4101.61	1.24001
$223$	2987.09	0.896996	0.448498	−	0.893784i	$-0.351959\pi$
$223$	2987.09	0.896996	0.448498	+	0.893784i	$0.351959\pi$
$224$	−395.433	−0.117951
$225$	490.149	0.145229
$226$	−4296.76	−1.26467
$227$	−2015.14	−0.589206	−0.294603	−	0.955620i	$-0.595187\pi$
$227$	−2015.14	−0.589206	−0.294603	+	0.955620i	$0.595187\pi$
$228$	10708.0	3.11033
$229$	−4594.18	−1.32573	−0.662865	−	0.748739i	$-0.730659\pi$
$229$	−4594.18	−1.32573	−0.662865	+	0.748739i	$0.730659\pi$
$230$	3501.47	1.00383
$231$	−4278.81	−1.21872
$232$	−10738.6	−3.03890
$233$	919.717	0.258595	0.129298	−	0.991606i	$-0.458728\pi$
$233$	919.717	0.258595	0.129298	+	0.991606i	$0.458728\pi$
$234$	1944.32	0.543181
$235$	−3373.86	−0.936538
$236$	1093.37	0.301577
$237$	−1462.89	−0.400950
$238$	1498.07	0.408005
$239$	1476.81	0.399695	0.199847	−	0.979827i	$-0.435955\pi$
$239$	1476.81	0.399695	0.199847	+	0.979827i	$0.435955\pi$
$240$	−4528.32	−1.21792
$241$	−5049.60	−1.34968	−0.674841	−	0.737963i	$-0.735788\pi$
$241$	−5049.60	−1.34968	−0.674841	+	0.737963i	$0.735788\pi$
$242$	−9114.05	−2.42096
$243$	1610.41	0.425135
$244$	5122.41	1.34397
$245$	−2445.11	−0.637602
$246$	6030.81	1.56305
$247$	8213.48	2.11583
$248$	−2176.28	−0.557235
$249$	−3814.34	−0.970778
$250$	2879.59	0.728486
$251$	−292.300	−0.0735052	−0.0367526	−	0.999324i	$-0.511701\pi$
$251$	−292.300	−0.0735052	−0.0367526	+	0.999324i	$0.511701\pi$
$252$	−1200.59	−0.300120
$253$	2823.08	0.701523
$254$	2830.39	0.699190
$255$	−1937.17	−0.475726
$256$	−7931.84	−1.93648
$257$	−4.22507	−0.00102550	−0.000512749	−	1.00000i	$-0.500163\pi$
$257$	−4.22507	−0.00102550	−0.000512749		1.00000i	$0.500163\pi$
$258$	0	0
$259$	−1942.68	−0.466070
$260$	−15472.4	−3.69061
$261$	1695.98	0.402217
$262$	4387.38	1.03456
$263$	8246.98	1.93358	0.966788	−	0.255580i	$-0.0822666\pi$
$263$	8246.98	1.93358	0.966788	+	0.255580i	$0.0822666\pi$
$264$	−11988.8	−2.79492
$265$	10306.9	2.38924
$266$	−7671.85	−1.76839
$267$	4779.53	1.09552
$268$	4791.18	1.09204
$269$	3136.78	0.710976	0.355488	−	0.934681i	$-0.384315\pi$
$269$	3136.78	0.710976	0.355488	+	0.934681i	$0.384315\pi$
$270$	−8518.44	−1.92006
$271$	−1246.03	−0.279303	−0.139652	−	0.990201i	$-0.544598\pi$
$271$	−1246.03	−0.279303	−0.139652	+	0.990201i	$0.544598\pi$
$272$	1278.25	0.284946
$273$	−5182.20	−1.14887
$274$	−10305.8	−2.27225
$275$	−4757.03	−1.04313
$276$	4457.53	0.972145
$277$	1353.84	0.293662	0.146831	−	0.989162i	$-0.453093\pi$
$277$	1353.84	0.293662	0.146831	+	0.989162i	$0.453093\pi$
$278$	−5063.31	−1.09236
$279$	343.707	0.0737534
$280$	7042.88	1.50319
$281$	−5032.93	−1.06847	−0.534234	−	0.845337i	$-0.679400\pi$
$281$	−5032.93	−1.06847	−0.534234	+	0.845337i	$0.679400\pi$
$282$	−6497.05	−1.37196
$283$	−1540.76	−0.323636	−0.161818	−	0.986821i	$-0.551736\pi$
$283$	−1540.76	−0.323636	−0.161818	+	0.986821i	$0.551736\pi$
$284$	17720.8	3.70260
$285$	9920.55	2.06190
$286$	−18870.2	−3.90146
$287$	−2856.42	−0.587488
$288$	174.984	0.0358022
$289$	−4366.18	−0.888699
$290$	−20415.4	−4.13391
$291$	−4686.85	−0.944150
$292$	3171.14	0.635537
$293$	−2032.88	−0.405331	−0.202665	−	0.979248i	$-0.564960\pi$
$293$	−2032.88	−0.405331	−0.202665	+	0.979248i	$0.564960\pi$
$294$	−4708.56	−0.934044
$295$	1012.96	0.199922
$296$	−5443.19	−1.06885
$297$	−6868.02	−1.34183
$298$	1571.48	0.305481
$299$	3419.11	0.661312
$300$	−7511.17	−1.44553
$301$	0	0
$302$	4200.50	0.800369
$303$	3681.42	0.697994
$304$	−6546.14	−1.23502
$305$	4745.71	0.890947
$306$	−662.913	−0.123844
$307$	−9698.57	−1.80302	−0.901509	−	0.432761i	$-0.857539\pi$
$307$	−9698.57	−1.80302	−0.901509	+	0.432761i	$0.857539\pi$
$308$	11652.1	2.15564
$309$	−440.935	−0.0811777
$310$	−4137.37	−0.758022
$311$	−8337.39	−1.52016	−0.760081	−	0.649829i	$-0.774841\pi$
$311$	−8337.39	−1.52016	−0.760081	+	0.649829i	$0.774841\pi$
$312$	−14520.0	−2.63472
$313$	−9108.79	−1.64492	−0.822459	−	0.568825i	$-0.807398\pi$
$313$	−9108.79	−1.64492	−0.822459	+	0.568825i	$0.807398\pi$
$314$	2804.59	0.504051
$315$	−1112.30	−0.198956
$316$	3983.75	0.709188
$317$	3842.07	0.680733	0.340366	−	0.940293i	$-0.389449\pi$
$317$	3842.07	0.680733	0.340366	+	0.940293i	$0.389449\pi$
$318$	19848.0	3.50007
$319$	−16460.0	−2.88897
$320$	−8428.43	−1.47239
$321$	4834.79	0.840660
$322$	−3193.64	−0.552716
$323$	−2800.37	−0.482405
$324$	−13302.7	−2.28099
$325$	−5761.38	−0.983335
$326$	8762.95	1.48876
$327$	6661.36	1.12653
$328$	−8003.40	−1.34730
$329$	3077.25	0.515666
$330$	−22792.1	−3.80201
$331$	2360.71	0.392014	0.196007	−	0.980603i	$-0.437202\pi$
$331$	2360.71	0.392014	0.196007	+	0.980603i	$0.437202\pi$
$332$	10387.2	1.71709
$333$	859.659	0.141469
$334$	12401.2	2.03163
$335$	4438.84	0.723940
$336$	4130.21	0.670599
$337$	−66.5688	−0.0107603	−0.00538017	−	0.999986i	$-0.501713\pi$
$337$	−66.5688	−0.0107603	−0.00538017	+	0.999986i	$0.501713\pi$
$338$	−12180.2	−1.96011
$339$	−5067.72	−0.811919
$340$	5275.29	0.841450
$341$	−3335.77	−0.529742
$342$	3394.89	0.536768
$343$	6752.93	1.06304
$344$	0	0
$345$	4129.73	0.644456
$346$	3286.08	0.510580
$347$	−2886.72	−0.446592	−0.223296	−	0.974751i	$-0.571682\pi$
$347$	−2886.72	−0.446592	−0.223296	+	0.974751i	$0.571682\pi$
$348$	−25989.7	−4.00343
$349$	−7743.50	−1.18768	−0.593840	−	0.804583i	$-0.702389\pi$
$349$	−7743.50	−1.18768	−0.593840	+	0.804583i	$0.702389\pi$
$350$	5381.45	0.821859
$351$	−8318.07	−1.26492
$352$	−1698.27	−0.257153
$353$	−2857.45	−0.430840	−0.215420	−	0.976521i	$-0.569112\pi$
$353$	−2857.45	−0.430840	−0.215420	+	0.976521i	$0.569112\pi$
$354$	1950.67	0.292872
$355$	16417.7	2.45453
$356$	−13015.6	−1.93772
$357$	1766.86	0.261939
$358$	7434.09	1.09750
$359$	−2242.44	−0.329670	−0.164835	−	0.986321i	$-0.552709\pi$
$359$	−2242.44	−0.329670	−0.164835	+	0.986321i	$0.552709\pi$
$360$	−3116.56	−0.456270
$361$	7482.16	1.09085
$362$	−12701.1	−1.84407
$363$	−10749.4	−1.55426
$364$	14112.2	2.03208
$365$	2937.94	0.421312
$366$	9138.84	1.30518
$367$	11678.8	1.66111	0.830557	−	0.556934i	$-0.188022\pi$
$367$	11678.8	1.66111	0.830557	+	0.556934i	$0.188022\pi$
$368$	−2725.03	−0.386011
$369$	1264.00	0.178323
$370$	−10348.1	−1.45398
$371$	−9400.78	−1.31554
$372$	−5267.06	−0.734097
$373$	4698.81	0.652266	0.326133	−	0.945324i	$-0.394254\pi$
$373$	4698.81	0.652266	0.326133	+	0.945324i	$0.394254\pi$
$374$	6433.75	0.889522
$375$	3396.27	0.467687
$376$	8622.15	1.18259
$377$	−19935.2	−2.72338
$378$	7769.54	1.05720
$379$	9794.57	1.32748	0.663738	−	0.747965i	$-0.268969\pi$
$379$	9794.57	1.32748	0.663738	+	0.747965i	$0.268969\pi$
$380$	−27015.7	−3.64704
$381$	3338.24	0.448879
$382$	19154.3	2.56549
$383$	4659.25	0.621610	0.310805	−	0.950474i	$-0.399401\pi$
$383$	4659.25	0.621610	0.310805	+	0.950474i	$0.399401\pi$
$384$	−14855.9	−1.97425
$385$	10795.2	1.42902
$386$	388.741	0.0512601
$387$	0	0
$388$	12763.2	1.66999
$389$	15017.9	1.95743	0.978713	−	0.205236i	$-0.0657961\pi$
$389$	15017.9	1.95743	0.978713	+	0.205236i	$0.0657961\pi$
$390$	−27604.2	−3.58409
$391$	−1165.74	−0.150777
$392$	6248.66	0.805115
$393$	5174.60	0.664184
$394$	−13495.1	−1.72557
$395$	3690.79	0.470137
$396$	−5156.19	−0.654313
$397$	5330.02	0.673819	0.336909	−	0.941537i	$-0.390618\pi$
$397$	5330.02	0.673819	0.336909	+	0.941537i	$0.390618\pi$
$398$	−10781.3	−1.35783
$399$	−9048.39	−1.13530
$400$	4591.82	0.573977
$401$	1881.10	0.234259	0.117130	−	0.993117i	$-0.462631\pi$
$401$	1881.10	0.234259	0.117130	+	0.993117i	$0.462631\pi$
$402$	8547.89	1.06052
$403$	−4040.05	−0.499378
$404$	−10025.3	−1.23459
$405$	−12324.5	−1.51212
$406$	18620.6	2.27617
$407$	−8343.23	−1.01611
$408$	4950.57	0.600710
$409$	8907.66	1.07691	0.538454	−	0.842655i	$-0.319009\pi$
$409$	8907.66	1.07691	0.538454	+	0.842655i	$0.319009\pi$
$410$	−15215.4	−1.83277
$411$	−12154.9	−1.45878
$412$	1200.76	0.143585
$413$	−923.908	−0.110079
$414$	1413.23	0.167769
$415$	9623.36	1.13829
$416$	−2056.82	−0.242413
$417$	−5971.81	−0.701297
$418$	−32948.3	−3.85539
$419$	−14129.0	−1.64736	−0.823682	−	0.567052i	$-0.808084\pi$
$419$	−14129.0	−1.64736	−0.823682	+	0.567052i	$0.808084\pi$
$420$	17045.2	1.98029
$421$	631.853	0.0731464	0.0365732	−	0.999331i	$-0.488356\pi$
$421$	631.853	0.0731464	0.0365732	+	0.999331i	$0.488356\pi$
$422$	15700.0	1.81106
$423$	−1361.72	−0.156523
$424$	−26340.0	−3.01695
$425$	1964.33	0.224198
$426$	31615.6	3.59572
$427$	−4328.50	−0.490563
$428$	−13166.1	−1.48694
$429$	−22256.0	−2.50473
$430$	0	0
$431$	−1391.25	−0.155485	−0.0777426	−	0.996973i	$-0.524771\pi$
$431$	−1391.25	−0.155485	−0.0777426	+	0.996973i	$0.524771\pi$
$432$	6629.50	0.738337
$433$	−11215.1	−1.24472	−0.622359	−	0.782732i	$-0.713825\pi$
$433$	−11215.1	−1.24472	−0.622359	+	0.782732i	$0.713825\pi$
$434$	3773.63	0.417374
$435$	−24078.5	−2.65396
$436$	−18140.2	−1.99257
$437$	5969.95	0.653504
$438$	5657.60	0.617193
$439$	4321.01	0.469774	0.234887	−	0.972023i	$-0.424528\pi$
$439$	4321.01	0.469774	0.234887	+	0.972023i	$0.424528\pi$
$440$	30247.1	3.27721
$441$	−986.870	−0.106562
$442$	7792.10	0.838535
$443$	−10333.2	−1.10823	−0.554113	−	0.832441i	$-0.686943\pi$
$443$	−10333.2	−1.10823	−0.554113	+	0.832441i	$0.686943\pi$
$444$	−13173.6	−1.40809
$445$	−12058.5	−1.28456
$446$	−14512.6	−1.54079
$447$	1853.44	0.196118
$448$	7687.44	0.810709
$449$	8737.55	0.918375	0.459188	−	0.888339i	$-0.348141\pi$
$449$	8737.55	0.918375	0.459188	+	0.888339i	$0.348141\pi$
$450$	−2381.36	−0.249463
$451$	−12267.5	−1.28083
$452$	13800.4	1.43610
$453$	4954.18	0.513836
$454$	9790.45	1.01209
$455$	13074.4	1.34711
$456$	−25352.7	−2.60362
$457$	11206.6	1.14709	0.573545	−	0.819174i	$-0.305568\pi$
$457$	11206.6	1.14709	0.573545	+	0.819174i	$0.305568\pi$
$458$	22320.5	2.27723
$459$	2836.03	0.288398
$460$	−11246.1	−1.13990
$461$	−14525.7	−1.46752	−0.733762	−	0.679407i	$-0.762237\pi$
$461$	−14525.7	−1.46752	−0.733762	+	0.679407i	$0.762237\pi$
$462$	20788.4	2.09342
$463$	4930.50	0.494903	0.247451	−	0.968900i	$-0.420407\pi$
$463$	4930.50	0.494903	0.247451	+	0.968900i	$0.420407\pi$
$464$	15888.3	1.58965
$465$	−4879.73	−0.486649
$466$	−4468.39	−0.444193
$467$	6108.04	0.605238	0.302619	−	0.953112i	$-0.402139\pi$
$467$	6108.04	0.605238	0.302619	+	0.953112i	$0.402139\pi$
$468$	−6244.81	−0.616809
$469$	−4048.60	−0.398608
$470$	16391.7	1.60871
$471$	3307.81	0.323600
$472$	−2588.70	−0.252446
$473$	0	0
$474$	7107.37	0.688718
$475$	−10059.7	−0.971725
$476$	−4811.52	−0.463310
$477$	4159.96	0.399311
$478$	−7175.00	−0.686563
$479$	−10162.4	−0.969382	−0.484691	−	0.874685i	$-0.661068\pi$
$479$	−10162.4	−0.969382	−0.484691	+	0.874685i	$0.661068\pi$
$480$	−2484.31	−0.236235
$481$	−10104.7	−0.957871
$482$	24533.2	2.31837
$483$	−3766.67	−0.354843
$484$	29272.7	2.74912
$485$	11824.6	1.10707
$486$	−7824.08	−0.730263
$487$	13884.5	1.29192	0.645961	−	0.763371i	$-0.276457\pi$
$487$	13884.5	1.29192	0.645961	+	0.763371i	$0.276457\pi$
$488$	−12128.0	−1.12502
$489$	10335.3	0.955781
$490$	11879.4	1.09522
$491$	14658.8	1.34733	0.673667	−	0.739035i	$-0.264718\pi$
$491$	14658.8	1.34733	0.673667	+	0.739035i	$0.264718\pi$
$492$	−19369.9	−1.77492
$493$	6796.86	0.620923
$494$	−39904.7	−3.63441
$495$	−4777.01	−0.433759
$496$	3219.92	0.291489
$497$	−14974.3	−1.35149
$498$	18531.7	1.66752
$499$	15383.3	1.38006	0.690029	−	0.723782i	$-0.257598\pi$
$499$	15383.3	1.38006	0.690029	+	0.723782i	$0.257598\pi$
$500$	−9248.73	−0.827232
$501$	14626.3	1.30430
$502$	1420.12	0.126261
$503$	−12847.1	−1.13882	−0.569409	−	0.822054i	$-0.692828\pi$
$503$	−12847.1	−1.13882	−0.569409	+	0.822054i	$0.692828\pi$
$504$	2842.57	0.251227
$505$	−9288.02	−0.818438
$506$	−13715.7	−1.20502
$507$	−14365.7	−1.25839
$508$	−9090.69	−0.793965
$509$	−14988.6	−1.30522	−0.652611	−	0.757693i	$-0.726326\pi$
$509$	−14988.6	−1.30522	−0.652611	+	0.757693i	$0.726326\pi$
$510$	9411.60	0.817162
$511$	−2679.65	−0.231978
$512$	17795.8	1.53607
$513$	−14523.8	−1.24998
$514$	20.5273	0.00176151
$515$	1112.45	0.0951856
$516$	0	0
$517$	13215.9	1.12424
$518$	9438.39	0.800577
$519$	3875.69	0.327792
$520$	36633.2	3.08937
$521$	10203.3	0.857997	0.428998	−	0.903305i	$-0.358867\pi$
$521$	10203.3	0.857997	0.428998	+	0.903305i	$0.358867\pi$
$522$	−8239.83	−0.690896
$523$	5487.11	0.458766	0.229383	−	0.973336i	$-0.426329\pi$
$523$	5487.11	0.458766	0.229383	+	0.973336i	$0.426329\pi$
$524$	−14091.5	−1.17479
$525$	6347.03	0.527633
$526$	−40067.4	−3.32134
$527$	1377.45	0.113857
$528$	17738.0	1.46202
$529$	−9681.83	−0.795745
$530$	−50075.5	−4.10404
$531$	408.841	0.0334128
$532$	24640.6	2.00809
$533$	−14857.5	−1.20741
$534$	−23221.1	−1.88179
$535$	−12197.9	−0.985723
$536$	−11343.8	−0.914136
$537$	8767.97	0.704592
$538$	−15239.8	−1.22126
$539$	9577.84	0.765393
$540$	27359.7	2.18032
$541$	13269.0	1.05449	0.527245	−	0.849713i	$-0.323225\pi$
$541$	13269.0	1.05449	0.527245	+	0.849713i	$0.323225\pi$
$542$	6053.78	0.479764
$543$	−14980.0	−1.18389
$544$	701.269	0.0552696
$545$	−16806.2	−1.32092
$546$	25177.4	1.97343
$547$	9377.89	0.733034	0.366517	−	0.930411i	$-0.380550\pi$
$547$	9377.89	0.733034	0.366517	+	0.930411i	$0.380550\pi$
$548$	33100.4	2.58025
$549$	1915.41	0.148903
$550$	23111.7	1.79180
$551$	−34807.9	−2.69122
$552$	−10553.8	−0.813770
$553$	−3366.32	−0.258861
$554$	−6577.55	−0.504429
$555$	−12204.9	−0.933457
$556$	16262.4	1.24043
$557$	10526.2	0.800735	0.400368	−	0.916355i	$-0.368882\pi$
$557$	10526.2	0.800735	0.400368	+	0.916355i	$0.368882\pi$
$558$	−1669.88	−0.126688
$559$	0	0
$560$	−10420.3	−0.786317
$561$	7588.14	0.571072
$562$	24452.2	1.83533
$563$	20928.1	1.56663	0.783315	−	0.621625i	$-0.213527\pi$
$563$	20928.1	1.56663	0.783315	+	0.621625i	$0.213527\pi$
$564$	20867.4	1.55793
$565$	12785.6	0.952022
$566$	7485.71	0.555915
$567$	11241.0	0.832586
$568$	−41956.5	−3.09940
$569$	−16353.3	−1.20486	−0.602431	−	0.798171i	$-0.705801\pi$
$569$	−16353.3	−1.20486	−0.602431	+	0.798171i	$0.705801\pi$
$570$	−48198.4	−3.54177
$571$	−4027.42	−0.295171	−0.147585	−	0.989049i	$-0.547150\pi$
$571$	−4027.42	−0.295171	−0.147585	+	0.989049i	$0.547150\pi$
$572$	60607.6	4.43030
$573$	22591.1	1.64704
$574$	13877.7	1.00914
$575$	−4187.65	−0.303716
$576$	−3401.79	−0.246078
$577$	18455.6	1.33157	0.665786	−	0.746143i	$-0.268096\pi$
$577$	18455.6	1.33157	0.665786	+	0.746143i	$0.268096\pi$
$578$	21212.8	1.52653
$579$	458.492	0.0329089
$580$	65570.6	4.69426
$581$	−8777.32	−0.626755
$582$	22770.8	1.62178
$583$	−40373.5	−2.86810
$584$	−7508.12	−0.532000
$585$	−5785.58	−0.408896
$586$	9876.61	0.696244
$587$	−12216.2	−0.858974	−0.429487	−	0.903073i	$-0.641306\pi$
$587$	−12216.2	−0.858974	−0.429487	+	0.903073i	$0.641306\pi$
$588$	15123.1	1.06065
$589$	−7054.14	−0.493482
$590$	−4921.42	−0.343409
$591$	−15916.5	−1.10781
$592$	8053.47	0.559114
$593$	15656.9	1.08424	0.542118	−	0.840302i	$-0.317622\pi$
$593$	15656.9	1.08424	0.542118	+	0.840302i	$0.317622\pi$
$594$	33367.9	2.30488
$595$	−4457.69	−0.307138
$596$	−5047.31	−0.346889
$597$	−12715.7	−0.871724
$598$	−16611.5	−1.13595
$599$	−7086.75	−0.483400	−0.241700	−	0.970351i	$-0.577705\pi$
$599$	−7086.75	−0.483400	−0.241700	+	0.970351i	$0.577705\pi$
$600$	17783.8	1.21003
$601$	−4349.45	−0.295204	−0.147602	−	0.989047i	$-0.547155\pi$
$601$	−4349.45	−0.295204	−0.147602	+	0.989047i	$0.547155\pi$
$602$	0	0
$603$	1791.56	0.120991
$604$	−13491.2	−0.908859
$605$	27120.0	1.82246
$606$	−17886.0	−1.19896
$607$	11528.1	0.770860	0.385430	−	0.922737i	$-0.374053\pi$
$607$	11528.1	0.770860	0.385430	+	0.922737i	$0.374053\pi$
$608$	−3591.32	−0.239551
$609$	21961.6	1.46130
$610$	−23056.8	−1.53040
$611$	16006.1	1.05980
$612$	2129.16	0.140631
$613$	19355.5	1.27530	0.637652	−	0.770324i	$-0.279906\pi$
$613$	19355.5	1.27530	0.637652	+	0.770324i	$0.279906\pi$
$614$	47119.9	3.09708
$615$	−17945.5	−1.17664
$616$	−27587.9	−1.80446
$617$	−13935.0	−0.909238	−0.454619	−	0.890686i	$-0.650225\pi$
$617$	−13935.0	−0.909238	−0.454619	+	0.890686i	$0.650225\pi$
$618$	2142.26	0.139440
$619$	15495.3	1.00615	0.503075	−	0.864243i	$-0.332202\pi$
$619$	15495.3	1.00615	0.503075	+	0.864243i	$0.332202\pi$
$620$	13288.5	0.860772
$621$	−6045.97	−0.390687
$622$	40506.7	2.61121
$623$	10998.4	0.707288
$624$	21483.0	1.37822
$625$	−19068.9	−1.22041
$626$	44254.5	2.82550
$627$	−38860.1	−2.47516
$628$	−9007.83	−0.572375
$629$	3445.19	0.218392
$630$	5404.06	0.341750
$631$	13393.6	0.844993	0.422496	−	0.906365i	$-0.361154\pi$
$631$	13393.6	0.844993	0.422496	+	0.906365i	$0.361154\pi$
$632$	−9432.09	−0.593652
$633$	18517.0	1.16270
$634$	−18666.5	−1.16931
$635$	−8422.18	−0.526337
$636$	−63748.3	−3.97451
$637$	11600.0	0.721521
$638$	79969.8	4.96244
$639$	6626.32	0.410224
$640$	37480.6	2.31492
$641$	−2195.86	−0.135306	−0.0676530	−	0.997709i	$-0.521551\pi$
$641$	−2195.86	−0.135306	−0.0676530	+	0.997709i	$0.521551\pi$
$642$	−23489.6	−1.44402
$643$	−19987.0	−1.22583	−0.612915	−	0.790149i	$-0.710003\pi$
$643$	−19987.0	−1.22583	−0.612915	+	0.790149i	$0.710003\pi$
$644$	10257.4	0.627637
$645$	0	0
$646$	13605.4	0.828635
$647$	−27112.0	−1.64743	−0.823713	−	0.567008i	$-0.808101\pi$
$647$	−27112.0	−1.64743	−0.823713	+	0.567008i	$0.808101\pi$
$648$	31496.1	1.90939
$649$	−3967.91	−0.239991
$650$	27991.3	1.68909
$651$	4450.73	0.267954
$652$	−28145.0	−1.69056
$653$	−15361.6	−0.920591	−0.460296	−	0.887766i	$-0.652257\pi$
$653$	−15361.6	−0.920591	−0.460296	+	0.887766i	$0.652257\pi$
$654$	−32363.8	−1.93505
$655$	−13055.2	−0.778794
$656$	11841.4	0.704771
$657$	1185.78	0.0704134
$658$	−14950.6	−0.885769
$659$	−276.285	−0.0163316	−0.00816580	−	0.999967i	$-0.502599\pi$
$659$	−276.285	−0.0163316	−0.00816580	+	0.999967i	$0.502599\pi$
$660$	73204.2	4.31738
$661$	1668.69	0.0981916	0.0490958	−	0.998794i	$-0.484366\pi$
$661$	1668.69	0.0981916	0.0490958	+	0.998794i	$0.484366\pi$
$662$	−11469.4	−0.673369
$663$	9190.22	0.538339
$664$	−24593.2	−1.43735
$665$	22828.6	1.33121
$666$	−4176.60	−0.243003
$667$	−14489.8	−0.841153
$668$	−39830.4	−2.30701
$669$	−17116.5	−0.989184
$670$	−21565.9	−1.24352
$671$	−18589.6	−1.06951
$672$	2265.90	0.130073
$673$	188.158	0.0107770	0.00538851	−	0.999985i	$-0.498285\pi$
$673$	188.158	0.0107770	0.00538851	+	0.999985i	$0.498285\pi$
$674$	323.421	0.0184832
$675$	10187.8	0.580930
$676$	39120.7	2.22580
$677$	−15768.2	−0.895154	−0.447577	−	0.894245i	$-0.647713\pi$
$677$	−15768.2	−0.895154	−0.447577	+	0.894245i	$0.647713\pi$
$678$	24621.2	1.39465
$679$	−10785.1	−0.609563
$680$	−12490.0	−0.704367
$681$	11547.1	0.649761
$682$	16206.6	0.909947
$683$	7660.10	0.429144	0.214572	−	0.976708i	$-0.431164\pi$
$683$	7660.10	0.429144	0.214572	+	0.976708i	$0.431164\pi$
$684$	−10903.8	−0.609526
$685$	30666.2	1.71051
$686$	−32808.7	−1.82601
$687$	26325.5	1.46198
$688$	0	0
$689$	−48897.6	−2.70370
$690$	−20064.1	−1.10699
$691$	5645.69	0.310814	0.155407	−	0.987851i	$-0.450331\pi$
$691$	5645.69	0.310814	0.155407	+	0.987851i	$0.450331\pi$
$692$	−10554.3	−0.579789
$693$	4357.04	0.238832
$694$	14025.0	0.767118
$695$	15066.5	0.822311
$696$	61534.3	3.35122
$697$	5065.64	0.275286
$698$	37621.3	2.04010
$699$	−5270.14	−0.285172
$700$	−17284.3	−0.933262
$701$	−16807.3	−0.905568	−0.452784	−	0.891620i	$-0.649569\pi$
$701$	−16807.3	−0.905568	−0.452784	+	0.891620i	$0.649569\pi$
$702$	40412.8	2.17277
$703$	−17643.4	−0.946562
$704$	33015.3	1.76749
$705$	19332.8	1.03279
$706$	13882.7	0.740062
$707$	8471.46	0.450640
$708$	−6265.19	−0.332571
$709$	2473.18	0.131005	0.0655023	−	0.997852i	$-0.479135\pi$
$709$	2473.18	0.131005	0.0655023	+	0.997852i	$0.479135\pi$
$710$	−79764.3	−4.21620
$711$	1489.64	0.0785735
$712$	30816.3	1.62204
$713$	−2936.50	−0.154240
$714$	−8584.18	−0.449937
$715$	56150.6	2.93694
$716$	−23877.0	−1.24626
$717$	−8462.39	−0.440773
$718$	10894.8	0.566280
$719$	1318.06	0.0683664	0.0341832	−	0.999416i	$-0.489117\pi$
$719$	1318.06	0.0683664	0.0341832	+	0.999416i	$0.489117\pi$
$720$	4611.10	0.238675
$721$	−1014.65	−0.0524100
$722$	−36351.6	−1.87378
$723$	28935.1	1.48839
$724$	40793.6	2.09404
$725$	24416.1	1.25075
$726$	52225.1	2.66977
$727$	−29579.7	−1.50901	−0.754505	−	0.656294i	$-0.772123\pi$
$727$	−29579.7	−1.50901	−0.754505	+	0.656294i	$0.772123\pi$
$728$	−33412.6	−1.70103
$729$	13789.5	0.700578
$730$	−14273.8	−0.723695
$731$	0	0
$732$	−29352.3	−1.48209
$733$	20648.4	1.04047	0.520237	−	0.854022i	$-0.325844\pi$
$733$	20648.4	1.04047	0.520237	+	0.854022i	$0.325844\pi$
$734$	−56740.8	−2.85332
$735$	14010.9	0.703131
$736$	−1495.00	−0.0748727
$737$	−17387.5	−0.869035
$738$	−6141.07	−0.306309
$739$	412.419	0.0205292	0.0102646	−	0.999947i	$-0.496733\pi$
$739$	412.419	0.0205292	0.0102646	+	0.999947i	$0.496733\pi$
$740$	33236.4	1.65107
$741$	−47064.7	−2.33328
$742$	45673.1	2.25972
$743$	−5178.96	−0.255717	−0.127858	−	0.991792i	$-0.540810\pi$
$743$	−5178.96	−0.255717	−0.127858	+	0.991792i	$0.540810\pi$
$744$	12470.5	0.614504
$745$	−4676.14	−0.229960
$746$	−22828.9	−1.12041
$747$	3884.07	0.190242
$748$	−20664.0	−1.01010
$749$	11125.5	0.542748
$750$	−16500.6	−0.803355
$751$	−34622.1	−1.68226	−0.841132	−	0.540831i	$-0.818110\pi$
$751$	−34622.1	−1.68226	−0.841132	+	0.540831i	$0.818110\pi$
$752$	−12756.9	−0.618611
$753$	1674.93	0.0810596
$754$	96853.8	4.67800
$755$	−12499.1	−0.602503
$756$	−24954.4	−1.20051
$757$	−18507.3	−0.888585	−0.444292	−	0.895882i	$-0.646545\pi$
$757$	−18507.3	−0.888585	−0.444292	+	0.895882i	$0.646545\pi$
$758$	−47586.4	−2.28023
$759$	−16176.7	−0.773620
$760$	63963.4	3.05289
$761$	−20023.6	−0.953817	−0.476909	−	0.878953i	$-0.658243\pi$
$761$	−20023.6	−0.953817	−0.476909	+	0.878953i	$0.658243\pi$
$762$	−16218.6	−0.771048
$763$	15328.7	0.727309
$764$	−61520.0	−2.91324
$765$	1972.58	0.0932273
$766$	−22636.7	−1.06775
$767$	−4805.66	−0.226235
$768$	45450.8	2.13550
$769$	−16391.2	−0.768636	−0.384318	−	0.923201i	$-0.625563\pi$
$769$	−16391.2	−0.768636	−0.384318	+	0.923201i	$0.625563\pi$
$770$	−52447.8	−2.45466
$771$	24.2104	0.00113089
$772$	−1248.57	−0.0582084
$773$	21244.9	0.988519	0.494260	−	0.869314i	$-0.335439\pi$
$773$	21244.9	0.988519	0.494260	+	0.869314i	$0.335439\pi$
$774$	0	0
$775$	4948.16	0.229346
$776$	−30218.7	−1.39792
$777$	11131.9	0.513970
$778$	−72963.6	−3.36230
$779$	−25942.0	−1.19315
$780$	88659.8	4.06991
$781$	−64310.2	−2.94648
$782$	5663.67	0.258993
$783$	35251.1	1.60890
$784$	−9245.20	−0.421155
$785$	−8345.41	−0.379440
$786$	−25140.5	−1.14088
$787$	2206.07	0.0999212	0.0499606	−	0.998751i	$-0.484090\pi$
$787$	2206.07	0.0999212	0.0499606	+	0.998751i	$0.484090\pi$
$788$	43343.8	1.95947
$789$	−47256.6	−2.13230
$790$	−17931.5	−0.807562
$791$	−11661.5	−0.524192
$792$	12208.0	0.547717
$793$	−22514.4	−1.00821
$794$	−25895.6	−1.15743
$795$	−59060.4	−2.63479
$796$	34627.5	1.54188
$797$	−39524.6	−1.75663	−0.878314	−	0.478085i	$-0.841331\pi$
$797$	−39524.6	−1.75663	−0.878314	+	0.478085i	$0.841331\pi$
$798$	43961.1	1.95013
$799$	−5457.26	−0.241632
$800$	2519.15	0.111332
$801$	−4866.92	−0.214687
$802$	−9139.23	−0.402391
$803$	−11508.3	−0.505752
$804$	−27454.3	−1.20428
$805$	9503.09	0.416075
$806$	19628.3	0.857790
$807$	−17974.3	−0.784046
$808$	23736.2	1.03346
$809$	−39225.2	−1.70468	−0.852339	−	0.522990i	$-0.824816\pi$
$809$	−39225.2	−1.70468	−0.852339	+	0.522990i	$0.824816\pi$
$810$	59877.7	2.59739
$811$	−10801.0	−0.467664	−0.233832	−	0.972277i	$-0.575127\pi$
$811$	−10801.0	−0.467664	−0.233832	+	0.972277i	$0.575127\pi$
$812$	−59805.9	−2.58470
$813$	7139.99	0.308008
$814$	40535.1	1.74540
$815$	−26075.3	−1.12071
$816$	−7324.60	−0.314231
$817$	0	0
$818$	−43277.3	−1.84982
$819$	5276.94	0.225142
$820$	48869.1	2.08120
$821$	25868.4	1.09965	0.549826	−	0.835279i	$-0.314694\pi$
$821$	25868.4	1.09965	0.549826	+	0.835279i	$0.314694\pi$
$822$	59054.0	2.50577
$823$	45014.4	1.90657	0.953283	−	0.302079i	$-0.0976806\pi$
$823$	45014.4	1.90657	0.953283	+	0.302079i	$0.0976806\pi$
$824$	−2842.96	−0.120193
$825$	27258.6	1.15033
$826$	4488.75	0.189084
$827$	46882.2	1.97129	0.985644	−	0.168839i	$-0.0540017\pi$
$827$	46882.2	1.97129	0.985644	+	0.168839i	$0.0540017\pi$
$828$	−4539.03	−0.190510
$829$	26628.6	1.11562	0.557810	−	0.829969i	$-0.311642\pi$
$829$	26628.6	1.11562	0.557810	+	0.829969i	$0.311642\pi$
$830$	−46754.5	−1.95527
$831$	−7757.75	−0.323843
$832$	39985.8	1.66618
$833$	−3955.00	−0.164505
$834$	29013.7	1.20463
$835$	−36901.4	−1.52937
$836$	105824.	4.37799
$837$	7143.97	0.295020
$838$	68644.8	2.82971
$839$	23832.3	0.980670	0.490335	−	0.871534i	$-0.336874\pi$
$839$	23832.3	0.980670	0.490335	+	0.871534i	$0.336874\pi$
$840$	−40357.0	−1.65768
$841$	60094.2	2.46399
$842$	−3069.82	−0.125645
$843$	28839.6	1.17828
$844$	−50425.7	−2.05654
$845$	36243.9	1.47553
$846$	6615.84	0.268862
$847$	−24735.8	−1.00346
$848$	38971.4	1.57816
$849$	8828.85	0.356897
$850$	−9543.58	−0.385108
$851$	−7344.60	−0.295852
$852$	−101543.	−4.08313
$853$	−8283.40	−0.332495	−0.166248	−	0.986084i	$-0.553165\pi$
$853$	−8283.40	−0.332495	−0.166248	+	0.986084i	$0.553165\pi$
$854$	21029.7	0.842649
$855$	−10101.9	−0.404069
$856$	31172.6	1.24470
$857$	−16912.0	−0.674098	−0.337049	−	0.941487i	$-0.609429\pi$
$857$	−16912.0	−0.674098	−0.337049	+	0.941487i	$0.609429\pi$
$858$	108129.	4.30242
$859$	−35911.2	−1.42640	−0.713199	−	0.700962i	$-0.752754\pi$
$859$	−35911.2	−1.42640	−0.713199	+	0.700962i	$0.752754\pi$
$860$	0	0
$861$	16367.8	0.647866
$862$	6759.30	0.267080
$863$	12877.6	0.507949	0.253975	−	0.967211i	$-0.418262\pi$
$863$	12877.6	0.507949	0.253975	+	0.967211i	$0.418262\pi$
$864$	3637.05	0.143212
$865$	−9778.15	−0.384355
$866$	54487.8	2.13807
$867$	25019.0	0.980033
$868$	−12120.2	−0.473949
$869$	−14457.3	−0.564363
$870$	116984.	4.55876
$871$	−21058.6	−0.819222
$872$	42949.5	1.66795
$873$	4772.53	0.185024
$874$	−29004.6	−1.12254
$875$	7815.29	0.301949
$876$	−18171.2	−0.700853
$877$	−40122.1	−1.54484	−0.772421	−	0.635110i	$-0.780955\pi$
$877$	−40122.1	−1.54484	−0.772421	+	0.635110i	$0.780955\pi$
$878$	−20993.4	−0.806939
$879$	11648.7	0.446988
$880$	−44752.0	−1.71431
$881$	−32354.6	−1.23729	−0.618646	−	0.785670i	$-0.712318\pi$
$881$	−32354.6	−1.23729	−0.618646	+	0.785670i	$0.712318\pi$
$882$	4794.65	0.183043
$883$	2575.95	0.0981741	0.0490870	−	0.998795i	$-0.484369\pi$
$883$	2575.95	0.0981741	0.0490870	+	0.998795i	$0.484369\pi$
$884$	−25026.8	−0.952199
$885$	−5804.46	−0.220469
$886$	50203.2	1.90362
$887$	171.714	0.00650009	0.00325004	−	0.999995i	$-0.498965\pi$
$887$	171.714	0.00650009	0.00325004	+	0.999995i	$0.498965\pi$
$888$	31190.5	1.17870
$889$	7681.75	0.289806
$890$	58585.4	2.20650
$891$	48276.6	1.81518
$892$	46611.8	1.74964
$893$	27947.5	1.04729
$894$	−9004.85	−0.336876
$895$	−22121.1	−0.826175
$896$	−34185.5	−1.27462
$897$	−19592.1	−0.729277
$898$	−42450.9	−1.57751
$899$	17121.3	0.635181
$900$	7648.50	0.283278
$901$	16671.5	0.616437
$902$	59600.8	2.20010
$903$	0	0
$904$	−32674.4	−1.20214
$905$	37793.7	1.38818
$906$	−24069.6	−0.882626
$907$	6826.29	0.249904	0.124952	−	0.992163i	$-0.460122\pi$
$907$	6826.29	0.249904	0.124952	+	0.992163i	$0.460122\pi$
$908$	−31445.2	−1.14928
$909$	−3748.73	−0.136785
$910$	−63521.1	−2.31396
$911$	2888.99	0.105067	0.0525337	−	0.998619i	$-0.483270\pi$
$911$	2888.99	0.105067	0.0525337	+	0.998619i	$0.483270\pi$
$912$	37510.5	1.36195
$913$	−37696.0	−1.36643
$914$	−54446.4	−1.97038
$915$	−27193.8	−0.982512
$916$	−71689.6	−2.58591
$917$	11907.5	0.428811
$918$	−13778.7	−0.495386
$919$	16257.1	0.583539	0.291770	−	0.956489i	$-0.405756\pi$
$919$	16257.1	0.583539	0.291770	+	0.956489i	$0.405756\pi$
$920$	26626.7	0.954193
$921$	55574.5	1.98832
$922$	70572.1	2.52079
$923$	−77888.0	−2.77759
$924$	−66768.5	−2.37719
$925$	12376.0	0.439915
$926$	−23954.6	−0.850103
$927$	448.996	0.0159083
$928$	8716.60	0.308337
$929$	46132.6	1.62924	0.814618	−	0.579998i	$-0.196947\pi$
$929$	46132.6	1.62924	0.814618	+	0.579998i	$0.196947\pi$
$930$	23707.9	0.835926
$931$	20254.2	0.713002
$932$	14351.7	0.504404
$933$	47774.7	1.67639
$934$	−29675.5	−1.03963
$935$	−19144.4	−0.669615
$936$	14785.5	0.516323
$937$	−14113.4	−0.492066	−0.246033	−	0.969262i	$-0.579127\pi$
$937$	−14113.4	−0.492066	−0.246033	+	0.969262i	$0.579127\pi$
$938$	19669.9	0.684696
$939$	52195.0	1.81397
$940$	−52647.2	−1.82677
$941$	−27642.6	−0.957622	−0.478811	−	0.877918i	$-0.658932\pi$
$941$	−27642.6	−0.957622	−0.478811	+	0.877918i	$0.658932\pi$
$942$	−16070.8	−0.555854
$943$	−10799.1	−0.372925
$944$	3830.11	0.132054
$945$	−23119.3	−0.795841
$946$	0	0
$947$	15987.3	0.548592	0.274296	−	0.961645i	$-0.411555\pi$
$947$	15987.3	0.548592	0.274296	+	0.961645i	$0.411555\pi$
$948$	−22827.6	−0.782074
$949$	−13938.0	−0.476763
$950$	48874.3	1.66915
$951$	−22015.8	−0.750694
$952$	11391.9	0.387831
$953$	44654.8	1.51785	0.758925	−	0.651178i	$-0.225725\pi$
$953$	44654.8	1.51785	0.758925	+	0.651178i	$0.225725\pi$
$954$	−20210.9	−0.685904
$955$	−56996.0	−1.93125
$956$	23044.8	0.779626
$957$	94318.6	3.18588
$958$	49373.6	1.66512
$959$	−27970.2	−0.941820
$960$	48296.4	1.62371
$961$	−26321.2	−0.883529
$962$	49093.2	1.64535
$963$	−4923.19	−0.164743
$964$	−78796.2	−2.63263
$965$	−1156.75	−0.0385876
$966$	18300.1	0.609521
$967$	−27849.4	−0.926140	−0.463070	−	0.886322i	$-0.653252\pi$
$967$	−27849.4	−0.926140	−0.463070	+	0.886322i	$0.653252\pi$
$968$	−69307.2	−2.30126
$969$	16046.6	0.531983
$970$	−57449.3	−1.90164
$971$	25393.9	0.839268	0.419634	−	0.907694i	$-0.362159\pi$
$971$	25393.9	0.839268	0.419634	+	0.907694i	$0.362159\pi$
$972$	25129.6	0.829250
$973$	−13742.0	−0.452772
$974$	−67456.9	−2.21916
$975$	33013.7	1.08440
$976$	17944.0	0.588497
$977$	−45241.2	−1.48147	−0.740734	−	0.671798i	$-0.765522\pi$
$977$	−45241.2	−1.48147	−0.740734	+	0.671798i	$0.765522\pi$
$978$	−50213.3	−1.64176
$979$	47234.7	1.54201
$980$	−38154.6	−1.24368
$981$	−6783.14	−0.220764
$982$	−71218.7	−2.31434
$983$	28920.1	0.938361	0.469180	−	0.883102i	$-0.344549\pi$
$983$	28920.1	0.938361	0.469180	+	0.883102i	$0.344549\pi$
$984$	45860.9	1.48577
$985$	40156.4	1.29897
$986$	−33022.1	−1.06657
$987$	−17633.2	−0.568663
$988$	128167.	4.12705
$989$	0	0
$990$	23208.8	0.745075
$991$	483.939	0.0155124	0.00775622	−	0.999970i	$-0.497531\pi$
$991$	483.939	0.0155124	0.00775622	+	0.999970i	$0.497531\pi$
$992$	1766.50	0.0565388
$993$	−13527.3	−0.432302
$994$	72751.8	2.32148
$995$	32081.0	1.02215
$996$	−59520.6	−1.89356
$997$	35131.0	1.11596	0.557978	−	0.829856i	$-0.311577\pi$
$997$	35131.0	1.11596	0.557978	+	0.829856i	$0.311577\pi$
$998$	−74738.6	−2.37055
$999$	17868.1	0.565886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.5	✓	50
43.42	odd	2		1849.4.a.j.1.46	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.5	✓	50	1.1	even	1	trivial
1849.4.a.j.1.46	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)

\(f(q)\)	\(=\)	\(q-4.85844 q^{2} -5.73018 q^{3} +15.6044 q^{4} +14.4569 q^{5} +27.8397 q^{6} -13.1859 q^{7} -36.9457 q^{8} +5.83494 q^{9} +O(q^{10})\)	\(q-4.85844 q^{2} -5.73018 q^{3} +15.6044 q^{4} +14.4569 q^{5} +27.8397 q^{6} -13.1859 q^{7} -36.9457 q^{8} +5.83494 q^{9} -70.2380 q^{10} -56.6297 q^{11} -89.4162 q^{12} -68.5859 q^{13} +64.0631 q^{14} -82.8407 q^{15} +54.6629 q^{16} +23.3842 q^{17} -28.3487 q^{18} -119.755 q^{19} +225.592 q^{20} +75.5578 q^{21} +275.132 q^{22} -49.8515 q^{23} +211.705 q^{24} +84.0024 q^{25} +333.220 q^{26} +121.280 q^{27} -205.759 q^{28} +290.660 q^{29} +402.477 q^{30} +58.9050 q^{31} +29.9890 q^{32} +324.498 q^{33} -113.611 q^{34} -190.628 q^{35} +91.0510 q^{36} +147.330 q^{37} +581.820 q^{38} +393.009 q^{39} -534.121 q^{40} +216.626 q^{41} -367.093 q^{42} -883.674 q^{44} +84.3552 q^{45} +242.201 q^{46} -233.374 q^{47} -313.228 q^{48} -169.131 q^{49} -408.121 q^{50} -133.996 q^{51} -1070.24 q^{52} +712.940 q^{53} -589.229 q^{54} -818.690 q^{55} +487.164 q^{56} +686.215 q^{57} -1412.15 q^{58} +70.0677 q^{59} -1292.68 q^{60} +328.266 q^{61} -286.186 q^{62} -76.9392 q^{63} -583.003 q^{64} -991.541 q^{65} -1576.55 q^{66} +307.039 q^{67} +364.898 q^{68} +285.658 q^{69} +926.155 q^{70} +1135.63 q^{71} -215.576 q^{72} +203.220 q^{73} -715.792 q^{74} -481.349 q^{75} -1868.70 q^{76} +746.715 q^{77} -1909.41 q^{78} +255.296 q^{79} +790.257 q^{80} -852.497 q^{81} -1052.47 q^{82} +665.658 q^{83} +1179.04 q^{84} +338.064 q^{85} -1665.53 q^{87} +2092.22 q^{88} -834.098 q^{89} -409.835 q^{90} +904.369 q^{91} -777.905 q^{92} -337.536 q^{93} +1133.83 q^{94} -1731.28 q^{95} -171.842 q^{96} +817.923 q^{97} +821.713 q^{98} -330.431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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