LMFDB - Embedded newform 841.4.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,4,Mod(1,841)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, 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("841.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	841.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:	$49.6206063148$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.13458092.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 $ x^5 - x^4 - 14x^3 + 18x^2 + 20*x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.328194$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24125 q^{2} -1.84328 q^{3} -2.97681 q^{4} +18.3339 q^{5} +4.13124 q^{6} -16.8583 q^{7} +24.6017 q^{8} -23.6023 q^{9} +O(q^{10})$	\(q-2.24125 q^{2} -1.84328 q^{3} -2.97681 q^{4} +18.3339 q^{5} +4.13124 q^{6} -16.8583 q^{7} +24.6017 q^{8} -23.6023 q^{9} -41.0908 q^{10} -52.4385 q^{11} +5.48709 q^{12} -87.5580 q^{13} +37.7836 q^{14} -33.7945 q^{15} -31.3241 q^{16} -15.4072 q^{17} +52.8987 q^{18} -67.0156 q^{19} -54.5766 q^{20} +31.0745 q^{21} +117.528 q^{22} +132.679 q^{23} -45.3478 q^{24} +211.133 q^{25} +196.239 q^{26} +93.2741 q^{27} +50.1839 q^{28} +75.7418 q^{30} -90.2221 q^{31} -126.609 q^{32} +96.6587 q^{33} +34.5314 q^{34} -309.078 q^{35} +70.2597 q^{36} -11.1247 q^{37} +150.199 q^{38} +161.394 q^{39} +451.047 q^{40} +18.8392 q^{41} -69.6456 q^{42} +147.756 q^{43} +156.100 q^{44} -432.723 q^{45} -297.366 q^{46} -21.0963 q^{47} +57.7390 q^{48} -58.7983 q^{49} -473.201 q^{50} +28.3997 q^{51} +260.644 q^{52} -290.454 q^{53} -209.050 q^{54} -961.404 q^{55} -414.743 q^{56} +123.528 q^{57} -337.343 q^{59} +100.600 q^{60} -84.0147 q^{61} +202.210 q^{62} +397.895 q^{63} +534.355 q^{64} -1605.28 q^{65} -216.636 q^{66} +330.821 q^{67} +45.8644 q^{68} -244.564 q^{69} +692.721 q^{70} +492.420 q^{71} -580.659 q^{72} +347.053 q^{73} +24.9333 q^{74} -389.176 q^{75} +199.493 q^{76} +884.023 q^{77} -361.723 q^{78} +986.297 q^{79} -574.294 q^{80} +465.333 q^{81} -42.2234 q^{82} +594.382 q^{83} -92.5029 q^{84} -282.475 q^{85} -331.157 q^{86} -1290.08 q^{88} -1387.04 q^{89} +969.840 q^{90} +1476.08 q^{91} -394.960 q^{92} +166.304 q^{93} +47.2820 q^{94} -1228.66 q^{95} +233.375 q^{96} +334.003 q^{97} +131.781 q^{98} +1237.67 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) $ 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9} + 64 q^{10} - 12 q^{11} + 224 q^{12} + 14 q^{13} + 192 q^{14} + 74 q^{15} + 146 q^{16} - 66 q^{17} + 108 q^{18} - 214 q^{19} + 6 q^{20} - 98 q^{22} + 164 q^{23} + 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} + 540 q^{28} - 234 q^{30} - 420 q^{31} + 652 q^{32} - 576 q^{33} + 204 q^{34} - 52 q^{35} - 260 q^{36} - 378 q^{37} - 496 q^{38} + 374 q^{39} + 80 q^{40} + 1158 q^{41} + 348 q^{42} + 204 q^{43} - 784 q^{44} - 1506 q^{45} - 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} - 908 q^{50} + 228 q^{51} + 1482 q^{52} - 554 q^{53} + 918 q^{54} - 546 q^{55} + 608 q^{56} + 44 q^{57} + 440 q^{59} - 636 q^{60} - 618 q^{61} + 1250 q^{62} + 804 q^{63} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} + 2184 q^{70} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} + 1616 q^{77} - 1302 q^{78} - 272 q^{79} - 890 q^{80} + 1801 q^{81} + 92 q^{82} + 512 q^{83} + 3208 q^{84} + 1628 q^{85} + 2446 q^{86} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 2580 q^{91} + 3468 q^{92} - 40 q^{93} - 5942 q^{94} - 2244 q^{95} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} + 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9 + 64 * q^10 - 12 * q^11 + 224 * q^12 + 14 * q^13 + 192 * q^14 + 74 * q^15 + 146 * q^16 - 66 * q^17 + 108 * q^18 - 214 * q^19 + 6 * q^20 - 98 * q^22 + 164 * q^23 + 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 + 540 * q^28 - 234 * q^30 - 420 * q^31 + 652 * q^32 - 576 * q^33 + 204 * q^34 - 52 * q^35 - 260 * q^36 - 378 * q^37 - 496 * q^38 + 374 * q^39 + 80 * q^40 + 1158 * q^41 + 348 * q^42 + 204 * q^43 - 784 * q^44 - 1506 * q^45 - 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 - 908 * q^50 + 228 * q^51 + 1482 * q^52 - 554 * q^53 + 918 * q^54 - 546 * q^55 + 608 * q^56 + 44 * q^57 + 440 * q^59 - 636 * q^60 - 618 * q^61 + 1250 * q^62 + 804 * q^63 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 + 2184 * q^70 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 + 1616 * q^77 - 1302 * q^78 - 272 * q^79 - 890 * q^80 + 1801 * q^81 + 92 * q^82 + 512 * q^83 + 3208 * q^84 + 1628 * q^85 + 2446 * q^86 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 2580 * q^91 + 3468 * q^92 - 40 * q^93 - 5942 * q^94 - 2244 * q^95 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 + 238 * 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 $

$2$	−2.24125	−0.792400	−0.396200	−	0.918164i	$-0.629671\pi$
$2$	−2.24125	−0.792400	−0.396200	+	0.918164i	$0.629671\pi$
$3$	−1.84328	−0.354739	−0.177369	−	0.984144i	$-0.556759\pi$
$3$	−1.84328	−0.354739	−0.177369	+	0.984144i	$0.556759\pi$
$4$	−2.97681	−0.372101
$5$	18.3339	1.63984	0.819918	−	0.572481i	$-0.194019\pi$
$5$	18.3339	1.63984	0.819918	+	0.572481i	$0.194019\pi$
$6$	4.13124	0.281095
$7$	−16.8583	−0.910262	−0.455131	−	0.890425i	$-0.650408\pi$
$7$	−16.8583	−0.910262	−0.455131	+	0.890425i	$0.650408\pi$
$8$	24.6017	1.08725
$9$	−23.6023	−0.874160
$10$	−41.0908	−1.29941
$11$	−52.4385	−1.43735	−0.718673	−	0.695348i	$-0.755250\pi$
$11$	−52.4385	−1.43735	−0.718673	+	0.695348i	$0.755250\pi$
$12$	5.48709	0.131999
$13$	−87.5580	−1.86802	−0.934008	−	0.357252i	$-0.883714\pi$
$13$	−87.5580	−1.86802	−0.934008	+	0.357252i	$0.883714\pi$
$14$	37.7836	0.721292
$15$	−33.7945	−0.581713
$16$	−31.3241	−0.489439
$17$	−15.4072	−0.219812	−0.109906	−	0.993942i	$-0.535055\pi$
$17$	−15.4072	−0.219812	−0.109906	+	0.993942i	$0.535055\pi$
$18$	52.8987	0.692685
$19$	−67.0156	−0.809181	−0.404591	−	0.914498i	$-0.632586\pi$
$19$	−67.0156	−0.809181	−0.404591	+	0.914498i	$0.632586\pi$
$20$	−54.5766	−0.610185
$21$	31.0745	0.322905
$22$	117.528	1.13895
$23$	132.679	1.20285	0.601423	−	0.798931i	$-0.294601\pi$
$23$	132.679	1.20285	0.601423	+	0.798931i	$0.294601\pi$
$24$	−45.3478	−0.385691
$25$	211.133	1.68906
$26$	196.239	1.48022
$27$	93.2741	0.664837
$28$	50.1839	0.338710
$29$	0	0
$29$	0	0
$30$	75.7418	0.460950
$31$	−90.2221	−0.522721	−0.261361	−	0.965241i	$-0.584171\pi$
$31$	−90.2221	−0.522721	−0.261361	+	0.965241i	$0.584171\pi$
$32$	−126.609	−0.699422
$33$	96.6587	0.509882
$34$	34.5314	0.174179
$35$	−309.078	−1.49268
$36$	70.2597	0.325276
$37$	−11.1247	−0.0494296	−0.0247148	−	0.999695i	$-0.507868\pi$
$37$	−11.1247	−0.0494296	−0.0247148	+	0.999695i	$0.507868\pi$
$38$	150.199	0.641196
$39$	161.394	0.662658
$40$	451.047	1.78292
$41$	18.8392	0.0717608	0.0358804	−	0.999356i	$-0.488576\pi$
$41$	18.8392	0.0717608	0.0358804	+	0.999356i	$0.488576\pi$
$42$	−69.6456	−0.255870
$43$	147.756	0.524013	0.262007	−	0.965066i	$-0.415616\pi$
$43$	147.756	0.524013	0.262007	+	0.965066i	$0.415616\pi$
$44$	156.100	0.534839
$45$	−432.723	−1.43348
$46$	−297.366	−0.953136
$47$	−21.0963	−0.0654726	−0.0327363	−	0.999464i	$-0.510422\pi$
$47$	−21.0963	−0.0654726	−0.0327363	+	0.999464i	$0.510422\pi$
$48$	57.7390	0.173623
$49$	−58.7983	−0.171424
$50$	−473.201	−1.33841
$51$	28.3997	0.0779757
$52$	260.644	0.695092
$53$	−290.454	−0.752772	−0.376386	−	0.926463i	$-0.622833\pi$
$53$	−290.454	−0.752772	−0.376386	+	0.926463i	$0.622833\pi$
$54$	−209.050	−0.526817
$55$	−961.404	−2.35701
$56$	−414.743	−0.989686
$57$	123.528	0.287048
$58$	0	0
$59$	−337.343	−0.744379	−0.372190	−	0.928157i	$-0.621393\pi$
$59$	−337.343	−0.744379	−0.372190	+	0.928157i	$0.621393\pi$
$60$	100.600	0.216456
$61$	−84.0147	−0.176344	−0.0881720	−	0.996105i	$-0.528103\pi$
$61$	−84.0147	−0.176344	−0.0881720	+	0.996105i	$0.528103\pi$
$62$	202.210	0.414205
$63$	397.895	0.795715
$64$	534.355	1.04366
$65$	−1605.28	−3.06324
$66$	−216.636	−0.404031
$67$	330.821	0.603228	0.301614	−	0.953430i	$-0.402475\pi$
$67$	330.821	0.603228	0.301614	+	0.953430i	$0.402475\pi$
$68$	45.8644	0.0817922
$69$	−244.564	−0.426696
$70$	692.721	1.18280
$71$	492.420	0.823092	0.411546	−	0.911389i	$-0.364989\pi$
$71$	492.420	0.823092	0.411546	+	0.911389i	$0.364989\pi$
$72$	−580.659	−0.950434
$73$	347.053	0.556431	0.278216	−	0.960519i	$-0.410257\pi$
$73$	347.053	0.556431	0.278216	+	0.960519i	$0.410257\pi$
$74$	24.9333	0.0391681
$75$	−389.176	−0.599176
$76$	199.493	0.301098
$77$	884.023	1.30836
$78$	−361.723	−0.525090
$79$	986.297	1.40465	0.702324	−	0.711858i	$-0.252146\pi$
$79$	986.297	1.40465	0.702324	+	0.711858i	$0.252146\pi$
$80$	−574.294	−0.802600
$81$	465.333	0.638317
$82$	−42.2234	−0.0568633
$83$	594.382	0.786048	0.393024	−	0.919528i	$-0.371429\pi$
$83$	594.382	0.786048	0.393024	+	0.919528i	$0.371429\pi$
$84$	−92.5029	−0.120153
$85$	−282.475	−0.360455
$86$	−331.157	−0.415228
$87$	0	0
$88$	−1290.08	−1.56276
$89$	−1387.04	−1.65197	−0.825987	−	0.563689i	$-0.809382\pi$
$89$	−1387.04	−1.65197	−0.825987	+	0.563689i	$0.809382\pi$
$90$	969.840	1.13589
$91$	1476.08	1.70038
$92$	−394.960	−0.447581
$93$	166.304	0.185430
$94$	47.2820	0.0518805
$95$	−1228.66	−1.32692
$96$	233.375	0.248112
$97$	334.003	0.349617	0.174808	−	0.984602i	$-0.444069\pi$
$97$	334.003	0.349617	0.174808	+	0.984602i	$0.444069\pi$
$98$	131.781	0.135836
$99$	1237.67	1.25647
$100$	−628.502	−0.628502
$101$	245.919	0.242276	0.121138	−	0.992636i	$-0.461346\pi$
$101$	245.919	0.242276	0.121138	+	0.992636i	$0.461346\pi$
$102$	−63.6508	−0.0617880
$103$	−531.298	−0.508255	−0.254128	−	0.967171i	$-0.581788\pi$
$103$	−531.298	−0.508255	−0.254128	+	0.967171i	$0.581788\pi$
$104$	−2154.08	−2.03101
$105$	569.717	0.529511
$106$	650.979	0.596497
$107$	−429.030	−0.387625	−0.193812	−	0.981039i	$-0.562085\pi$
$107$	−429.030	−0.387625	−0.193812	+	0.981039i	$0.562085\pi$
$108$	−277.659	−0.247387
$109$	−967.263	−0.849972	−0.424986	−	0.905200i	$-0.639721\pi$
$109$	−967.263	−0.849972	−0.424986	+	0.905200i	$0.639721\pi$
$110$	2154.74	1.86770
$111$	20.5060	0.0175346
$112$	528.070	0.445518
$113$	1705.23	1.41960	0.709798	−	0.704405i	$-0.248786\pi$
$113$	1705.23	1.41960	0.709798	+	0.704405i	$0.248786\pi$
$114$	−276.858	−0.227457
$115$	2432.52	1.97247
$116$	0	0
$117$	2066.57	1.63295
$118$	756.070	0.589846
$119$	259.739	0.200086
$120$	−831.403	−0.632470
$121$	1418.80	1.06596
$122$	188.298	0.139735
$123$	−34.7259	−0.0254563
$124$	268.574	0.194505
$125$	1579.15	1.12995
$126$	−891.781	−0.630525
$127$	2670.28	1.86574	0.932870	−	0.360213i	$-0.117296\pi$
$127$	2670.28	1.86574	0.932870	+	0.360213i	$0.117296\pi$
$128$	−184.749	−0.127576
$129$	−272.355	−0.185888
$130$	3597.83	2.42731
$131$	−879.993	−0.586911	−0.293455	−	0.955973i	$-0.594805\pi$
$131$	−879.993	−0.586911	−0.293455	+	0.955973i	$0.594805\pi$
$132$	−287.735	−0.189728
$133$	1129.77	0.736567
$134$	−741.452	−0.477998
$135$	1710.08	1.09022
$136$	−379.044	−0.238991
$137$	−2064.15	−1.28724	−0.643620	−	0.765345i	$-0.722568\pi$
$137$	−2064.15	−1.28724	−0.643620	+	0.765345i	$0.722568\pi$
$138$	548.128	0.338114
$139$	605.130	0.369255	0.184628	−	0.982809i	$-0.440892\pi$
$139$	605.130	0.369255	0.184628	+	0.982809i	$0.440892\pi$
$140$	920.068	0.555428
$141$	38.8863	0.0232257
$142$	−1103.63	−0.652218
$143$	4591.41	2.68499
$144$	739.322	0.427848
$145$	0	0
$146$	−777.832	−0.440917
$147$	108.381	0.0608106
$148$	33.1163	0.0183928
$149$	−775.322	−0.426287	−0.213144	−	0.977021i	$-0.568370\pi$
$149$	−775.322	−0.426287	−0.213144	+	0.977021i	$0.568370\pi$
$150$	872.240	0.474787
$151$	427.925	0.230623	0.115311	−	0.993329i	$-0.463213\pi$
$151$	427.925	0.230623	0.115311	+	0.993329i	$0.463213\pi$
$152$	−1648.70	−0.879785
$153$	363.646	0.192151
$154$	−1981.31	−1.03675
$155$	−1654.12	−0.857177
$156$	−480.438	−0.246576
$157$	1680.93	0.854474	0.427237	−	0.904140i	$-0.359487\pi$
$157$	1680.93	0.854474	0.427237	+	0.904140i	$0.359487\pi$
$158$	−2210.54	−1.11304
$159$	535.387	0.267037
$160$	−2321.24	−1.14694
$161$	−2236.74	−1.09490
$162$	−1042.93	−0.505803
$163$	−2038.68	−0.979645	−0.489822	−	0.871822i	$-0.662938\pi$
$163$	−2038.68	−0.979645	−0.489822	+	0.871822i	$0.662938\pi$
$164$	−56.0808	−0.0267023
$165$	1772.13	0.836123
$166$	−1332.16	−0.622865
$167$	2543.12	1.17840	0.589199	−	0.807988i	$-0.299443\pi$
$167$	2543.12	1.17840	0.589199	+	0.807988i	$0.299443\pi$
$168$	764.486	0.351080
$169$	5469.40	2.48949
$170$	633.095	0.285625
$171$	1581.73	0.707354
$172$	−439.842	−0.194986
$173$	−306.031	−0.134492	−0.0672460	−	0.997736i	$-0.521421\pi$
$173$	−306.031	−0.134492	−0.0672460	+	0.997736i	$0.521421\pi$
$174$	0	0
$175$	−3559.34	−1.53749
$176$	1642.59	0.703493
$177$	621.817	0.264060
$178$	3108.69	1.30903
$179$	−478.797	−0.199927	−0.0999635	−	0.994991i	$-0.531873\pi$
$179$	−478.797	−0.199927	−0.0999635	+	0.994991i	$0.531873\pi$
$180$	1288.14	0.533400
$181$	−478.433	−0.196473	−0.0982367	−	0.995163i	$-0.531320\pi$
$181$	−478.433	−0.196473	−0.0982367	+	0.995163i	$0.531320\pi$
$182$	−3308.25	−1.34739
$183$	154.862	0.0625560
$184$	3264.13	1.30780
$185$	−203.960	−0.0810565
$186$	−372.729	−0.146934
$187$	807.931	0.315945
$188$	62.7998	0.0243625
$189$	−1572.44	−0.605176
$190$	2753.73	1.05146
$191$	−833.106	−0.315610	−0.157805	−	0.987470i	$-0.550442\pi$
$191$	−833.106	−0.315610	−0.157805	+	0.987470i	$0.550442\pi$
$192$	−984.963	−0.370227
$193$	1449.88	0.540751	0.270376	−	0.962755i	$-0.412852\pi$
$193$	1449.88	0.540751	0.270376	+	0.962755i	$0.412852\pi$
$194$	−748.582	−0.277037
$195$	2958.98	1.08665
$196$	175.031	0.0637870
$197$	−1993.27	−0.720886	−0.360443	−	0.932781i	$-0.617374\pi$
$197$	−1993.27	−0.720886	−0.360443	+	0.932781i	$0.617374\pi$
$198$	−2773.93	−0.995628
$199$	−356.359	−0.126943	−0.0634714	−	0.997984i	$-0.520217\pi$
$199$	−356.359	−0.126943	−0.0634714	+	0.997984i	$0.520217\pi$
$200$	5194.23	1.83644
$201$	−609.795	−0.213988
$202$	−551.165	−0.191979
$203$	0	0
$204$	−84.5407	−0.0290149
$205$	345.397	0.117676
$206$	1190.77	0.402742
$207$	−3131.53	−1.05148
$208$	2742.67	0.914280
$209$	3514.20	1.16307
$210$	−1276.88	−0.419585
$211$	−4131.66	−1.34803	−0.674017	−	0.738716i	$-0.735433\pi$
$211$	−4131.66	−1.34803	−0.674017	+	0.738716i	$0.735433\pi$
$212$	864.626	0.280107
$213$	−907.666	−0.291982
$214$	961.562	0.307154
$215$	2708.95	0.859296
$216$	2294.71	0.722847
$217$	1520.99	0.475813
$218$	2167.87	0.673518
$219$	−639.715	−0.197388
$220$	2861.92	0.877048
$221$	1349.02	0.410612
$222$	−45.9590	−0.0138944
$223$	1332.32	0.400086	0.200043	−	0.979787i	$-0.435892\pi$
$223$	1332.32	0.400086	0.200043	+	0.979787i	$0.435892\pi$
$224$	2134.41	0.636657
$225$	−4983.22	−1.47651
$226$	−3821.84	−1.12489
$227$	−1329.33	−0.388681	−0.194340	−	0.980934i	$-0.562257\pi$
$227$	−1329.33	−0.388681	−0.194340	+	0.980934i	$0.562257\pi$
$228$	−367.721	−0.106811
$229$	−5455.47	−1.57427	−0.787135	−	0.616780i	$-0.788437\pi$
$229$	−5455.47	−1.57427	−0.787135	+	0.616780i	$0.788437\pi$
$230$	−5451.89	−1.56299
$231$	−1629.50	−0.464126
$232$	0	0
$233$	−591.158	−0.166215	−0.0831075	−	0.996541i	$-0.526484\pi$
$233$	−591.158	−0.166215	−0.0831075	+	0.996541i	$0.526484\pi$
$234$	−4631.70	−1.29395
$235$	−386.778	−0.107364
$236$	1004.21	0.276985
$237$	−1818.02	−0.498283
$238$	−582.139	−0.158548
$239$	6946.01	1.87992	0.939959	−	0.341289i	$-0.110863\pi$
$239$	6946.01	1.87992	0.939959	+	0.341289i	$0.110863\pi$
$240$	1058.58	0.284713
$241$	7105.62	1.89923	0.949613	−	0.313426i	$-0.101477\pi$
$241$	7105.62	1.89923	0.949613	+	0.313426i	$0.101477\pi$
$242$	−3179.88	−0.844670
$243$	−3376.14	−0.891273
$244$	250.096	0.0656179
$245$	−1078.00	−0.281106
$246$	77.8293	0.0201716
$247$	5867.75	1.51156
$248$	−2219.62	−0.568331
$249$	−1095.61	−0.278842
$250$	−3539.27	−0.895372
$251$	4874.53	1.22581	0.612904	−	0.790158i	$-0.290001\pi$
$251$	4874.53	1.22581	0.612904	+	0.790158i	$0.290001\pi$
$252$	−1184.46	−0.296087
$253$	−6957.49	−1.72891
$254$	−5984.75	−1.47841
$255$	520.679	0.127867
$256$	−3860.77	−0.942570
$257$	2488.22	0.603934	0.301967	−	0.953318i	$-0.402357\pi$
$257$	2488.22	0.603934	0.301967	+	0.953318i	$0.402357\pi$
$258$	610.415	0.147298
$259$	187.544	0.0449939
$260$	4778.62	1.13984
$261$	0	0
$262$	1972.28	0.465068
$263$	2812.52	0.659419	0.329709	−	0.944082i	$-0.393049\pi$
$263$	2812.52	0.659419	0.329709	+	0.944082i	$0.393049\pi$
$264$	2377.97	0.554372
$265$	−5325.16	−1.23442
$266$	−2532.09	−0.583656
$267$	2556.69	0.586019
$268$	−984.793	−0.224462
$269$	5554.63	1.25900	0.629501	−	0.777000i	$-0.283259\pi$
$269$	5554.63	1.25900	0.629501	+	0.777000i	$0.283259\pi$
$270$	−3832.71	−0.863894
$271$	3168.41	0.710211	0.355105	−	0.934826i	$-0.384445\pi$
$271$	3168.41	0.710211	0.355105	+	0.934826i	$0.384445\pi$
$272$	482.617	0.107584
$273$	−2720.82	−0.603192
$274$	4626.26	1.02001
$275$	−11071.5	−2.42777
$276$	728.021	0.158774
$277$	3965.64	0.860189	0.430095	−	0.902784i	$-0.358480\pi$
$277$	3965.64	0.860189	0.430095	+	0.902784i	$0.358480\pi$
$278$	−1356.25	−0.292598
$279$	2129.45	0.456942
$280$	−7603.87	−1.62292
$281$	1655.16	0.351383	0.175692	−	0.984445i	$-0.443784\pi$
$281$	1655.16	0.351383	0.175692	+	0.984445i	$0.443784\pi$
$282$	−87.1539	−0.0184040
$283$	7786.09	1.63546	0.817730	−	0.575602i	$-0.195232\pi$
$283$	7786.09	1.63546	0.817730	+	0.575602i	$0.195232\pi$
$284$	−1465.84	−0.306274
$285$	2264.76	0.470711
$286$	−10290.5	−2.12758
$287$	−317.597	−0.0653211
$288$	2988.27	0.611407
$289$	−4675.62	−0.951683
$290$	0	0
$291$	−615.659	−0.124023
$292$	−1033.11	−0.207049
$293$	−8090.80	−1.61321	−0.806603	−	0.591094i	$-0.798696\pi$
$293$	−8090.80	−1.61321	−0.806603	+	0.591094i	$0.798696\pi$
$294$	−242.910	−0.0481863
$295$	−6184.83	−1.22066
$296$	−273.688	−0.0537426
$297$	−4891.16	−0.955601
$298$	1737.69	0.337790
$299$	−11617.1	−2.24694
$300$	1158.50	0.222954
$301$	−2490.91	−0.476989
$302$	−959.086	−0.182746
$303$	−453.297	−0.0859446
$304$	2099.20	0.396045
$305$	−1540.32	−0.289175
$306$	−815.020	−0.152260
$307$	6129.49	1.13951	0.569753	−	0.821816i	$-0.307039\pi$
$307$	6129.49	1.13951	0.569753	+	0.821816i	$0.307039\pi$
$308$	−2631.57	−0.486843
$309$	979.328	0.180298
$310$	3707.30	0.679228
$311$	8167.93	1.48926	0.744632	−	0.667476i	$-0.232625\pi$
$311$	8167.93	1.48926	0.744632	+	0.667476i	$0.232625\pi$
$312$	3970.56	0.720477
$313$	1877.25	0.339005	0.169502	−	0.985530i	$-0.445784\pi$
$313$	1877.25	0.339005	0.169502	+	0.985530i	$0.445784\pi$
$314$	−3767.37	−0.677086
$315$	7294.97	1.30484
$316$	−2936.02	−0.522671
$317$	−1222.93	−0.216677	−0.108338	−	0.994114i	$-0.534553\pi$
$317$	−1222.93	−0.216677	−0.108338	+	0.994114i	$0.534553\pi$
$318$	−1199.93	−0.211600
$319$	0	0
$320$	9796.82	1.71143
$321$	790.820	0.137506
$322$	5013.08	0.867603
$323$	1032.52	0.177867
$324$	−1385.21	−0.237519
$325$	−18486.4	−3.15520
$326$	4569.20	0.776271
$327$	1782.93	0.301518
$328$	463.478	0.0780222
$329$	355.648	0.0595972
$330$	−3971.79	−0.662545
$331$	−3769.03	−0.625876	−0.312938	−	0.949774i	$-0.601313\pi$
$331$	−3769.03	−0.625876	−0.312938	+	0.949774i	$0.601313\pi$
$332$	−1769.36	−0.292489
$333$	262.570	0.0432094
$334$	−5699.76	−0.933763
$335$	6065.25	0.989195
$336$	−973.380	−0.158042
$337$	10900.2	1.76193	0.880967	−	0.473179i	$-0.156893\pi$
$337$	10900.2	1.76193	0.880967	+	0.473179i	$0.156893\pi$
$338$	−12258.3	−1.97267
$339$	−3143.21	−0.503586
$340$	840.874	0.134126
$341$	4731.11	0.751332
$342$	−3545.04	−0.560508
$343$	6773.63	1.06630
$344$	3635.05	0.569735
$345$	−4483.82	−0.699712
$346$	685.892	0.106572
$347$	−8542.30	−1.32154	−0.660771	−	0.750588i	$-0.729770\pi$
$347$	−8542.30	−1.32154	−0.660771	+	0.750588i	$0.729770\pi$
$348$	0	0
$349$	−993.823	−0.152430	−0.0762151	−	0.997091i	$-0.524284\pi$
$349$	−993.823	−0.152430	−0.0762151	+	0.997091i	$0.524284\pi$
$350$	7977.35	1.21831
$351$	−8166.89	−1.24193
$352$	6639.19	1.00531
$353$	8191.10	1.23504	0.617519	−	0.786556i	$-0.288138\pi$
$353$	8191.10	1.23504	0.617519	+	0.786556i	$0.288138\pi$
$354$	−1393.65	−0.209241
$355$	9027.99	1.34974
$356$	4128.95	0.614702
$357$	−478.771	−0.0709783
$358$	1073.10	0.158422
$359$	4703.71	0.691510	0.345755	−	0.938325i	$-0.387623\pi$
$359$	4703.71	0.691510	0.345755	+	0.938325i	$0.387623\pi$
$360$	−10645.7	−1.55856
$361$	−2367.90	−0.345226
$362$	1072.29	0.155686
$363$	−2615.24	−0.378139
$364$	−4394.00	−0.632715
$365$	6362.85	0.912456
$366$	−347.085	−0.0495694
$367$	−9431.88	−1.34153	−0.670763	−	0.741672i	$-0.734033\pi$
$367$	−9431.88	−1.34153	−0.670763	+	0.741672i	$0.734033\pi$
$368$	−4156.05	−0.588720
$369$	−444.650	−0.0627305
$370$	457.125	0.0642292
$371$	4896.55	0.685219
$372$	−495.056	−0.0689986
$373$	−8281.46	−1.14959	−0.574796	−	0.818297i	$-0.694919\pi$
$373$	−8281.46	−1.14959	−0.574796	+	0.818297i	$0.694919\pi$
$374$	−1810.77	−0.250355
$375$	−2910.81	−0.400836
$376$	−519.006	−0.0711854
$377$	0	0
$378$	3524.23	0.479542
$379$	−6875.50	−0.931848	−0.465924	−	0.884825i	$-0.654278\pi$
$379$	−6875.50	−0.931848	−0.465924	+	0.884825i	$0.654278\pi$
$380$	3657.49	0.493750
$381$	−4922.06	−0.661850
$382$	1867.20	0.250089
$383$	−4826.61	−0.643938	−0.321969	−	0.946750i	$-0.604345\pi$
$383$	−4826.61	−0.643938	−0.321969	+	0.946750i	$0.604345\pi$
$384$	340.544	0.0452560
$385$	16207.6	2.14550
$386$	−3249.55	−0.428492
$387$	−3487.38	−0.458072
$388$	−994.263	−0.130093
$389$	−4970.57	−0.647861	−0.323930	−	0.946081i	$-0.605004\pi$
$389$	−4970.57	−0.647861	−0.323930	+	0.946081i	$0.605004\pi$
$390$	−6631.80	−0.861062
$391$	−2044.21	−0.264400
$392$	−1446.54	−0.186381
$393$	1622.07	0.208200
$394$	4467.41	0.571230
$395$	18082.7	2.30339
$396$	−3684.31	−0.467535
$397$	−12288.8	−1.55355	−0.776774	−	0.629779i	$-0.783145\pi$
$397$	−12288.8	−1.55355	−0.776774	+	0.629779i	$0.783145\pi$
$398$	798.689	0.100590
$399$	−2082.48	−0.261289
$400$	−6613.54	−0.826693
$401$	−11971.7	−1.49086	−0.745432	−	0.666581i	$-0.767757\pi$
$401$	−11971.7	−1.49086	−0.745432	+	0.666581i	$0.767757\pi$
$402$	1366.70	0.169564
$403$	7899.66	0.976452
$404$	−732.055	−0.0901512
$405$	8531.38	1.04673
$406$	0	0
$407$	583.365	0.0710475
$408$	698.683	0.0847794
$409$	−11147.7	−1.34772	−0.673861	−	0.738858i	$-0.735365\pi$
$409$	−11147.7	−1.34772	−0.673861	+	0.738858i	$0.735365\pi$
$410$	−774.120	−0.0932465
$411$	3804.79	0.456634
$412$	1581.57	0.189123
$413$	5687.03	0.677580
$414$	7018.54	0.833194
$415$	10897.4	1.28899
$416$	11085.6	1.30653
$417$	−1115.42	−0.130989
$418$	−7876.19	−0.921620
$419$	11557.3	1.34752	0.673762	−	0.738949i	$-0.264677\pi$
$419$	11557.3	1.34752	0.673762	+	0.738949i	$0.264677\pi$
$420$	−1695.94	−0.197032
$421$	12874.4	1.49040	0.745201	−	0.666840i	$-0.232353\pi$
$421$	12874.4	1.49040	0.745201	+	0.666840i	$0.232353\pi$
$422$	9260.07	1.06818
$423$	497.922	0.0572336
$424$	−7145.67	−0.818454
$425$	−3252.97	−0.371275
$426$	2034.30	0.231367
$427$	1416.34	0.160519
$428$	1277.14	0.144236
$429$	−8463.24	−0.952469
$430$	−6071.42	−0.680906
$431$	−4088.31	−0.456907	−0.228454	−	0.973555i	$-0.573367\pi$
$431$	−4088.31	−0.456907	−0.228454	+	0.973555i	$0.573367\pi$
$432$	−2921.73	−0.325397
$433$	3865.90	0.429060	0.214530	−	0.976717i	$-0.431178\pi$
$433$	3865.90	0.429060	0.214530	+	0.976717i	$0.431178\pi$
$434$	−3408.91	−0.377035
$435$	0	0
$436$	2879.36	0.316276
$437$	−8891.56	−0.973320
$438$	1433.76	0.156410
$439$	10662.4	1.15920	0.579600	−	0.814901i	$-0.303209\pi$
$439$	10662.4	1.15920	0.579600	+	0.814901i	$0.303209\pi$
$440$	−23652.2	−2.56267
$441$	1387.78	0.149852
$442$	−3023.50	−0.325369
$443$	−10288.9	−1.10347	−0.551736	−	0.834019i	$-0.686034\pi$
$443$	−10288.9	−1.10347	−0.551736	+	0.834019i	$0.686034\pi$
$444$	−61.0424	−0.00652465
$445$	−25429.8	−2.70897
$446$	−2986.07	−0.317028
$447$	1429.13	0.151221
$448$	−9008.30	−0.950005
$449$	−12426.2	−1.30608	−0.653041	−	0.757323i	$-0.726507\pi$
$449$	−12426.2	−1.30608	−0.653041	+	0.757323i	$0.726507\pi$
$450$	11168.6	1.16999
$451$	−987.901	−0.103145
$452$	−5076.14	−0.528234
$453$	−788.784	−0.0818108
$454$	2979.35	0.307991
$455$	27062.3	2.78835
$456$	3039.01	0.312094
$457$	−10657.8	−1.09092	−0.545462	−	0.838136i	$-0.683646\pi$
$457$	−10657.8	−1.09092	−0.545462	+	0.838136i	$0.683646\pi$
$458$	12227.1	1.24745
$459$	−1437.09	−0.146139
$460$	−7241.17	−0.733959
$461$	−9819.21	−0.992031	−0.496016	−	0.868314i	$-0.665204\pi$
$461$	−9819.21	−0.992031	−0.496016	+	0.868314i	$0.665204\pi$
$462$	3652.11	0.367774
$463$	−19210.5	−1.92827	−0.964135	−	0.265412i	$-0.914492\pi$
$463$	−19210.5	−1.92827	−0.964135	+	0.265412i	$0.914492\pi$
$464$	0	0
$465$	3049.01	0.304074
$466$	1324.93	0.131709
$467$	345.566	0.0342417	0.0171208	−	0.999853i	$-0.494550\pi$
$467$	345.566	0.0342417	0.0171208	+	0.999853i	$0.494550\pi$
$468$	−6151.80	−0.607622
$469$	−5577.08	−0.549095
$470$	866.865	0.0850756
$471$	−3098.41	−0.303115
$472$	−8299.24	−0.809329
$473$	−7748.10	−0.753188
$474$	4074.63	0.394839
$475$	−14149.2	−1.36676
$476$	−773.194	−0.0744523
$477$	6855.39	0.658043
$478$	−15567.7	−1.48965
$479$	253.709	0.0242009	0.0121005	−	0.999927i	$-0.496148\pi$
$479$	253.709	0.0242009	0.0121005	+	0.999927i	$0.496148\pi$
$480$	4278.68	0.406863
$481$	974.060	0.0923354
$482$	−15925.5	−1.50495
$483$	4122.93	0.388405
$484$	−4223.50	−0.396647
$485$	6123.58	0.573314
$486$	7566.76	0.706245
$487$	−13255.1	−1.23336	−0.616680	−	0.787214i	$-0.711523\pi$
$487$	−13255.1	−1.23336	−0.616680	+	0.787214i	$0.711523\pi$
$488$	−2066.91	−0.191731
$489$	3757.86	0.347518
$490$	2416.07	0.222749
$491$	6454.57	0.593260	0.296630	−	0.954993i	$-0.404137\pi$
$491$	6454.57	0.593260	0.296630	+	0.954993i	$0.404137\pi$
$492$	103.372	0.00947234
$493$	0	0
$494$	−13151.1	−1.19776
$495$	22691.4	2.06041
$496$	2826.12	0.255840
$497$	−8301.36	−0.749229
$498$	2455.54	0.220954
$499$	8090.41	0.725805	0.362902	−	0.931827i	$-0.381786\pi$
$499$	8090.41	0.725805	0.362902	+	0.931827i	$0.381786\pi$
$500$	−4700.84	−0.420455
$501$	−4687.67	−0.418023
$502$	−10925.0	−0.971330
$503$	18897.4	1.67513	0.837567	−	0.546334i	$-0.183977\pi$
$503$	18897.4	1.67513	0.837567	+	0.546334i	$0.183977\pi$
$504$	9788.91	0.865144
$505$	4508.66	0.397293
$506$	15593.4	1.36999
$507$	−10081.6	−0.883117
$508$	−7948.92	−0.694245
$509$	4265.15	0.371413	0.185707	−	0.982605i	$-0.440543\pi$
$509$	4265.15	0.371413	0.185707	+	0.982605i	$0.440543\pi$
$510$	−1166.97	−0.101322
$511$	−5850.72	−0.506498
$512$	10130.9	0.874469
$513$	−6250.82	−0.537974
$514$	−5576.72	−0.478558
$515$	−9740.77	−0.833455
$516$	810.750	0.0691691
$517$	1106.26	0.0941068
$518$	−420.333	−0.0356532
$519$	564.100	0.0477096
$520$	−39492.7	−3.33052
$521$	−3324.96	−0.279595	−0.139798	−	0.990180i	$-0.544645\pi$
$521$	−3324.96	−0.279595	−0.139798	+	0.990180i	$0.544645\pi$
$522$	0	0
$523$	13017.6	1.08838	0.544188	−	0.838964i	$-0.316838\pi$
$523$	13017.6	1.08838	0.544188	+	0.838964i	$0.316838\pi$
$524$	2619.57	0.218390
$525$	6560.84	0.545407
$526$	−6303.54	−0.522524
$527$	1390.07	0.114900
$528$	−3027.75	−0.249556
$529$	5436.69	0.446839
$530$	11935.0	0.978156
$531$	7962.09	0.650707
$532$	−3363.11	−0.274078
$533$	−1649.52	−0.134050
$534$	−5730.18	−0.464362
$535$	−7865.80	−0.635641
$536$	8138.78	0.655862
$537$	882.555	0.0709219
$538$	−12449.3	−0.997634
$539$	3083.29	0.246395
$540$	−5090.59	−0.405674
$541$	17906.8	1.42305	0.711527	−	0.702658i	$-0.248004\pi$
$541$	17906.8	1.42305	0.711527	+	0.702658i	$0.248004\pi$
$542$	−7101.19	−0.562771
$543$	881.885	0.0696967
$544$	1950.69	0.153741
$545$	−17733.7	−1.39382
$546$	6098.03	0.477970
$547$	1612.94	0.126078	0.0630389	−	0.998011i	$-0.479921\pi$
$547$	1612.94	0.126078	0.0630389	+	0.998011i	$0.479921\pi$
$548$	6144.58	0.478984
$549$	1982.94	0.154153
$550$	24813.9	1.92376
$551$	0	0
$552$	−6016.70	−0.463927
$553$	−16627.3	−1.27860
$554$	−8887.99	−0.681614
$555$	375.955	0.0287539
$556$	−1801.36	−0.137400
$557$	−7803.94	−0.593651	−0.296826	−	0.954932i	$-0.595928\pi$
$557$	−7803.94	−0.593651	−0.296826	+	0.954932i	$0.595928\pi$
$558$	−4772.63	−0.362081
$559$	−12937.2	−0.978865
$560$	9681.60	0.730576
$561$	−1489.24	−0.112078
$562$	−3709.63	−0.278436
$563$	12329.5	0.922958	0.461479	−	0.887151i	$-0.347319\pi$
$563$	12329.5	0.922958	0.461479	+	0.887151i	$0.347319\pi$
$564$	−115.757	−0.00864231
$565$	31263.5	2.32790
$566$	−17450.6	−1.29594
$567$	−7844.72	−0.581035
$568$	12114.4	0.894910
$569$	−1554.46	−0.114528	−0.0572640	−	0.998359i	$-0.518238\pi$
$569$	−1554.46	−0.114528	−0.0572640	+	0.998359i	$0.518238\pi$
$570$	−5075.88	−0.372992
$571$	15951.8	1.16911	0.584556	−	0.811353i	$-0.301269\pi$
$571$	15951.8	1.16911	0.584556	+	0.811353i	$0.301269\pi$
$572$	−13667.8	−0.999087
$573$	1535.64	0.111959
$574$	711.813	0.0517605
$575$	28012.9	2.03168
$576$	−12612.0	−0.912328
$577$	−10491.7	−0.756975	−0.378488	−	0.925606i	$-0.623556\pi$
$577$	−10491.7	−0.756975	−0.378488	+	0.925606i	$0.623556\pi$
$578$	10479.2	0.754114
$579$	−2672.54	−0.191825
$580$	0	0
$581$	−10020.3	−0.715509
$582$	1379.84	0.0982756
$583$	15231.0	1.08199
$584$	8538.11	0.604982
$585$	37888.4	2.67776
$586$	18133.5	1.27831
$587$	6437.47	0.452645	0.226323	−	0.974052i	$-0.427330\pi$
$587$	6437.47	0.452645	0.226323	+	0.974052i	$0.427330\pi$
$588$	−322.631	−0.0226277
$589$	6046.29	0.422976
$590$	13861.7	0.967251
$591$	3674.15	0.255726
$592$	348.473	0.0241928
$593$	11240.6	0.778411	0.389205	−	0.921151i	$-0.372750\pi$
$593$	11240.6	0.778411	0.389205	+	0.921151i	$0.372750\pi$
$594$	10962.3	0.757219
$595$	4762.04	0.328108
$596$	2307.99	0.158622
$597$	656.869	0.0450316
$598$	26036.8	1.78047
$599$	−15903.5	−1.08481	−0.542405	−	0.840117i	$-0.682486\pi$
$599$	−15903.5	−1.08481	−0.542405	+	0.840117i	$0.682486\pi$
$600$	−9574.41	−0.651456
$601$	−117.190	−0.00795385	−0.00397692	−	0.999992i	$-0.501266\pi$
$601$	−117.190	−0.00795385	−0.00397692	+	0.999992i	$0.501266\pi$
$602$	5582.75	0.377966
$603$	−7808.16	−0.527318
$604$	−1273.85	−0.0858151
$605$	26012.1	1.74801
$606$	1015.95	0.0681025
$607$	22047.8	1.47429	0.737143	−	0.675737i	$-0.236175\pi$
$607$	22047.8	1.47429	0.737143	+	0.675737i	$0.236175\pi$
$608$	8484.78	0.565959
$609$	0	0
$610$	3452.24	0.229143
$611$	1847.15	0.122304
$612$	−1082.51	−0.0714995
$613$	−12719.2	−0.838050	−0.419025	−	0.907975i	$-0.637628\pi$
$613$	−12719.2	−0.838050	−0.419025	+	0.907975i	$0.637628\pi$
$614$	−13737.7	−0.902945
$615$	−636.662	−0.0417442
$616$	21748.5	1.42252
$617$	−12736.9	−0.831064	−0.415532	−	0.909578i	$-0.636405\pi$
$617$	−12736.9	−0.831064	−0.415532	+	0.909578i	$0.636405\pi$
$618$	−2194.92	−0.142868
$619$	−28083.4	−1.82353	−0.911767	−	0.410709i	$-0.865281\pi$
$619$	−28083.4	−1.82353	−0.911767	+	0.410709i	$0.865281\pi$
$620$	4924.02	0.318957
$621$	12375.5	0.799697
$622$	−18306.4	−1.18009
$623$	23383.1	1.50373
$624$	−5055.51	−0.324331
$625$	2560.44	0.163868
$626$	−4207.38	−0.268628
$627$	−6477.64	−0.412587
$628$	−5003.80	−0.317951
$629$	171.401	0.0108652
$630$	−16349.8	−1.03396
$631$	281.496	0.0177594	0.00887969	−	0.999961i	$-0.497173\pi$
$631$	281.496	0.0177594	0.00887969	+	0.999961i	$0.497173\pi$
$632$	24264.6	1.52721
$633$	7615.79	0.478200
$634$	2740.89	0.171695
$635$	48956.7	3.05951
$636$	−1593.75	−0.0993650
$637$	5148.26	0.320222
$638$	0	0
$639$	−11622.3	−0.719514
$640$	−3387.18	−0.209203
$641$	8440.98	0.520123	0.260061	−	0.965592i	$-0.416257\pi$
$641$	8440.98	0.520123	0.260061	+	0.965592i	$0.416257\pi$
$642$	−1772.42	−0.108959
$643$	−1173.61	−0.0719792	−0.0359896	−	0.999352i	$-0.511458\pi$
$643$	−1173.61	−0.0719792	−0.0359896	+	0.999352i	$0.511458\pi$
$644$	6658.35	0.407416
$645$	−4993.34	−0.304825
$646$	−2314.14	−0.140942
$647$	−10845.7	−0.659025	−0.329513	−	0.944151i	$-0.606884\pi$
$647$	−10845.7	−0.659025	−0.329513	+	0.944151i	$0.606884\pi$
$648$	11448.0	0.694012
$649$	17689.8	1.06993
$650$	41432.5	2.50018
$651$	−2803.60	−0.168789
$652$	6068.78	0.364527
$653$	5282.40	0.316564	0.158282	−	0.987394i	$-0.449404\pi$
$653$	5282.40	0.316564	0.158282	+	0.987394i	$0.449404\pi$
$654$	−3995.99	−0.238923
$655$	−16133.7	−0.962437
$656$	−590.122	−0.0351225
$657$	−8191.26	−0.486410
$658$	−797.094	−0.0472249
$659$	19243.7	1.13752	0.568761	−	0.822503i	$-0.307423\pi$
$659$	19243.7	1.13752	0.568761	+	0.822503i	$0.307423\pi$
$660$	−5275.31	−0.311123
$661$	29196.9	1.71804	0.859021	−	0.511940i	$-0.171073\pi$
$661$	29196.9	1.71804	0.859021	+	0.511940i	$0.171073\pi$
$662$	8447.34	0.495944
$663$	−2486.62	−0.145660
$664$	14622.8	0.854633
$665$	20713.1	1.20785
$666$	−588.484	−0.0342392
$667$	0	0
$668$	−7570.39	−0.438484
$669$	−2455.84	−0.141926
$670$	−13593.7	−0.783838
$671$	4405.61	0.253467
$672$	−3934.31	−0.225847
$673$	19924.5	1.14121	0.570605	−	0.821224i	$-0.306709\pi$
$673$	19924.5	1.14121	0.570605	+	0.821224i	$0.306709\pi$
$674$	−24430.0	−1.39616
$675$	19693.2	1.12295
$676$	−16281.4	−0.926341
$677$	4980.43	0.282738	0.141369	−	0.989957i	$-0.454850\pi$
$677$	4980.43	0.282738	0.141369	+	0.989957i	$0.454850\pi$
$678$	7044.70	0.399041
$679$	−5630.71	−0.318243
$680$	−6949.37	−0.391906
$681$	2450.32	0.137880
$682$	−10603.6	−0.595355
$683$	29295.8	1.64125	0.820624	−	0.571468i	$-0.193626\pi$
$683$	29295.8	1.64125	0.820624	+	0.571468i	$0.193626\pi$
$684$	−4708.50	−0.263208
$685$	−37843.9	−2.11086
$686$	−15181.4	−0.844938
$687$	10055.9	0.558455
$688$	−4628.32	−0.256472
$689$	25431.5	1.40619
$690$	10049.3	0.554452
$691$	−32759.8	−1.80353	−0.901766	−	0.432225i	$-0.857729\pi$
$691$	−32759.8	−1.80353	−0.901766	+	0.432225i	$0.857729\pi$
$692$	910.998	0.0500447
$693$	−20865.0	−1.14372
$694$	19145.4	1.04719
$695$	11094.4	0.605518
$696$	0	0
$697$	−290.260	−0.0157739
$698$	2227.40	0.120786
$699$	1089.67	0.0589629
$700$	10595.5	0.572102
$701$	27958.5	1.50639	0.753195	−	0.657797i	$-0.228512\pi$
$701$	27958.5	1.50639	0.753195	+	0.657797i	$0.228512\pi$
$702$	18304.0	0.984104
$703$	745.532	0.0399975
$704$	−28020.8	−1.50010
$705$	712.939	0.0380863
$706$	−18358.3	−0.978644
$707$	−4145.77	−0.220534
$708$	−1851.03	−0.0982572
$709$	−31863.5	−1.68781	−0.843906	−	0.536492i	$-0.819749\pi$
$709$	−31863.5	−1.68781	−0.843906	+	0.536492i	$0.819749\pi$
$710$	−20234.0	−1.06953
$711$	−23278.9	−1.22789
$712$	−34123.6	−1.79612
$713$	−11970.6	−0.628753
$714$	1073.04	0.0562432
$715$	84178.6	4.40294
$716$	1425.29	0.0743931
$717$	−12803.4	−0.666879
$718$	−10542.2	−0.547953
$719$	7944.76	0.412085	0.206043	−	0.978543i	$-0.433941\pi$
$719$	7944.76	0.412085	0.206043	+	0.978543i	$0.433941\pi$
$720$	13554.7	0.701601
$721$	8956.76	0.462645
$722$	5307.06	0.273557
$723$	−13097.6	−0.673729
$724$	1424.21	0.0731080
$725$	0	0
$726$	5861.39	0.299637
$727$	−28640.3	−1.46109	−0.730543	−	0.682866i	$-0.760733\pi$
$727$	−28640.3	−1.46109	−0.730543	+	0.682866i	$0.760733\pi$
$728$	36314.1	1.84875
$729$	−6340.84	−0.322148
$730$	−14260.7	−0.723031
$731$	−2276.51	−0.115184
$732$	−460.996	−0.0232772
$733$	−11852.7	−0.597258	−0.298629	−	0.954369i	$-0.596529\pi$
$733$	−11852.7	−0.597258	−0.298629	+	0.954369i	$0.596529\pi$
$734$	21139.2	1.06303
$735$	1987.06	0.0997194
$736$	−16798.3	−0.841297
$737$	−17347.8	−0.867047
$738$	996.570	0.0497076
$739$	24052.5	1.19727	0.598636	−	0.801021i	$-0.295710\pi$
$739$	24052.5	1.19727	0.598636	+	0.801021i	$0.295710\pi$
$740$	607.151	0.0301612
$741$	−10815.9	−0.536210
$742$	−10974.4	−0.542968
$743$	12530.4	0.618704	0.309352	−	0.950948i	$-0.399888\pi$
$743$	12530.4	0.618704	0.309352	+	0.950948i	$0.399888\pi$
$744$	4091.37	0.201609
$745$	−14214.7	−0.699042
$746$	18560.8	0.910937
$747$	−14028.8	−0.687132
$748$	−2405.06	−0.117564
$749$	7232.71	0.352840
$750$	6523.85	0.317623
$751$	−30921.6	−1.50246	−0.751229	−	0.660042i	$-0.770539\pi$
$751$	−30921.6	−1.50246	−0.751229	+	0.660042i	$0.770539\pi$
$752$	660.823	0.0320449
$753$	−8985.11	−0.434841
$754$	0	0
$755$	7845.54	0.378184
$756$	4680.86	0.225187
$757$	6257.40	0.300435	0.150217	−	0.988653i	$-0.452003\pi$
$757$	6257.40	0.300435	0.150217	+	0.988653i	$0.452003\pi$
$758$	15409.7	0.738397
$759$	12824.6	0.613310
$760$	−30227.2	−1.44270
$761$	−20094.8	−0.957211	−0.478605	−	0.878030i	$-0.658858\pi$
$761$	−20094.8	−0.957211	−0.478605	+	0.878030i	$0.658858\pi$
$762$	11031.6	0.524450
$763$	16306.4	0.773697
$764$	2480.00	0.117439
$765$	6667.06	0.315095
$766$	10817.6	0.510257
$767$	29537.1	1.39051
$768$	7116.46	0.334366
$769$	26647.8	1.24960	0.624801	−	0.780784i	$-0.285180\pi$
$769$	26647.8	1.24960	0.624801	+	0.780784i	$0.285180\pi$
$770$	−36325.3	−1.70009
$771$	−4586.48	−0.214239
$772$	−4316.03	−0.201214
$773$	18513.2	0.861414	0.430707	−	0.902492i	$-0.358264\pi$
$773$	18513.2	0.861414	0.430707	+	0.902492i	$0.358264\pi$
$774$	7816.09	0.362976
$775$	−19048.8	−0.882909
$776$	8217.05	0.380122
$777$	−345.696	−0.0159611
$778$	11140.3	0.513365
$779$	−1262.52	−0.0580675
$780$	−8808.32	−0.404344
$781$	−25821.8	−1.18307
$782$	4581.58	0.209510
$783$	0	0
$784$	1841.80	0.0839014
$785$	30818.0	1.40120
$786$	−3635.46	−0.164978
$787$	−29524.5	−1.33727	−0.668636	−	0.743590i	$-0.733122\pi$
$787$	−29524.5	−1.33727	−0.668636	+	0.743590i	$0.733122\pi$
$788$	5933.59	0.268243
$789$	−5184.25	−0.233921
$790$	−40527.8	−1.82521
$791$	−28747.2	−1.29220
$792$	30448.9	1.36610
$793$	7356.16	0.329413
$794$	27542.3	1.23103
$795$	9815.74	0.437897
$796$	1060.81	0.0472356
$797$	−38789.4	−1.72395	−0.861976	−	0.506949i	$-0.830773\pi$
$797$	−38789.4	−1.72395	−0.861976	+	0.506949i	$0.830773\pi$
$798$	4667.34	0.207045
$799$	325.035	0.0143916
$800$	−26731.3	−1.18137
$801$	32737.3	1.44409
$802$	26831.5	1.18136
$803$	−18199.0	−0.799785
$804$	1815.25	0.0796254
$805$	−41008.2	−1.79546
$806$	−17705.1	−0.773741
$807$	−10238.7	−0.446617
$808$	6050.04	0.263415
$809$	11552.0	0.502037	0.251018	−	0.967982i	$-0.419235\pi$
$809$	11552.0	0.502037	0.251018	+	0.967982i	$0.419235\pi$
$810$	−19120.9	−0.829433
$811$	26939.1	1.16641	0.583205	−	0.812325i	$-0.301798\pi$
$811$	26939.1	1.16641	0.583205	+	0.812325i	$0.301798\pi$
$812$	0	0
$813$	−5840.25	−0.251939
$814$	−1307.47	−0.0562981
$815$	−37377.1	−1.60646
$816$	−889.596	−0.0381643
$817$	−9901.96	−0.424022
$818$	24984.8	1.06794
$819$	−34838.9	−1.48641
$820$	−1028.18	−0.0437874
$821$	−7558.67	−0.321315	−0.160657	−	0.987010i	$-0.551361\pi$
$821$	−7558.67	−0.321315	−0.160657	+	0.987010i	$0.551361\pi$
$822$	−8527.48	−0.361837
$823$	3201.90	0.135615	0.0678076	−	0.997698i	$-0.478400\pi$
$823$	3201.90	0.135615	0.0678076	+	0.997698i	$0.478400\pi$
$824$	−13070.8	−0.552603
$825$	20407.8	0.861223
$826$	−12746.0	−0.536915
$827$	11479.1	0.482670	0.241335	−	0.970442i	$-0.422415\pi$
$827$	11479.1	0.482670	0.241335	+	0.970442i	$0.422415\pi$
$828$	9321.98	0.391257
$829$	1667.94	0.0698794	0.0349397	−	0.999389i	$-0.488876\pi$
$829$	1667.94	0.0698794	0.0349397	+	0.999389i	$0.488876\pi$
$830$	−24423.7	−1.02140
$831$	−7309.78	−0.305142
$832$	−46787.0	−1.94958
$833$	905.917	0.0376809
$834$	2499.94	0.103796
$835$	46625.3	1.93238
$836$	−10461.1	−0.432781
$837$	−8415.38	−0.347525
$838$	−25902.8	−1.06778
$839$	−15210.3	−0.625884	−0.312942	−	0.949772i	$-0.601315\pi$
$839$	−15210.3	−0.625884	−0.312942	+	0.949772i	$0.601315\pi$
$840$	14016.0	0.575713
$841$	0	0
$842$	−28854.7	−1.18100
$843$	−3050.92	−0.124649
$844$	12299.2	0.501606
$845$	100276.	4.08235
$846$	−1115.97	−0.0453519
$847$	−23918.5	−0.970306
$848$	9098.20	0.368436
$849$	−14351.9	−0.580161
$850$	7290.70	0.294199
$851$	−1476.02	−0.0594563
$852$	2701.95	0.108647
$853$	18281.2	0.733805	0.366902	−	0.930259i	$-0.380418\pi$
$853$	18281.2	0.733805	0.366902	+	0.930259i	$0.380418\pi$
$854$	−3174.38	−0.127195
$855$	28999.2	1.15994
$856$	−10554.9	−0.421447
$857$	585.415	0.0233342	0.0116671	−	0.999932i	$-0.496286\pi$
$857$	585.415	0.0233342	0.0116671	+	0.999932i	$0.496286\pi$
$858$	18968.2	0.754737
$859$	935.611	0.0371626	0.0185813	−	0.999827i	$-0.494085\pi$
$859$	935.611	0.0371626	0.0185813	+	0.999827i	$0.494085\pi$
$860$	−8064.02	−0.319745
$861$	585.419	0.0231719
$862$	9162.92	0.362054
$863$	−12110.7	−0.477696	−0.238848	−	0.971057i	$-0.576770\pi$
$863$	−12110.7	−0.477696	−0.238848	+	0.971057i	$0.576770\pi$
$864$	−11809.3	−0.465002
$865$	−5610.75	−0.220545
$866$	−8664.43	−0.339988
$867$	8618.46	0.337599
$868$	−4527.70	−0.177051
$869$	−51720.0	−2.01896
$870$	0	0
$871$	−28966.1	−1.12684
$872$	−23796.4	−0.924136
$873$	−7883.24	−0.305621
$874$	19928.2	0.771260
$875$	−26621.8	−1.02855
$876$	1904.31	0.0734483
$877$	5841.41	0.224915	0.112458	−	0.993657i	$-0.464128\pi$
$877$	5841.41	0.224915	0.112458	+	0.993657i	$0.464128\pi$
$878$	−23897.1	−0.918551
$879$	14913.6	0.572267
$880$	30115.1	1.15361
$881$	47826.2	1.82895	0.914476	−	0.404641i	$-0.132603\pi$
$881$	47826.2	1.82895	0.914476	+	0.404641i	$0.132603\pi$
$882$	−3110.35	−0.118743
$883$	17337.5	0.660761	0.330381	−	0.943848i	$-0.392823\pi$
$883$	17337.5	0.660761	0.330381	+	0.943848i	$0.392823\pi$
$884$	−4015.79	−0.152789
$885$	11400.4	0.433015
$886$	23059.9	0.874392
$887$	−35181.5	−1.33177	−0.665885	−	0.746055i	$-0.731946\pi$
$887$	−35181.5	−1.33177	−0.665885	+	0.746055i	$0.731946\pi$
$888$	504.483	0.0190646
$889$	−45016.3	−1.69831
$890$	56994.6	2.14659
$891$	−24401.4	−0.917482
$892$	−3966.08	−0.148872
$893$	1413.78	0.0529792
$894$	−3203.04	−0.119827
$895$	−8778.22	−0.327848
$896$	3114.56	0.116127
$897$	21413.5	0.797075
$898$	27850.3	1.03494
$899$	0	0
$900$	14834.1	0.549412
$901$	4475.08	0.165468
$902$	2214.13	0.0817322
$903$	4591.44	0.169207
$904$	41951.6	1.54346
$905$	−8771.56	−0.322184
$906$	1767.86	0.0648270
$907$	28184.4	1.03180	0.515902	−	0.856648i	$-0.327457\pi$
$907$	28184.4	1.03180	0.515902	+	0.856648i	$0.327457\pi$
$908$	3957.15	0.144629
$909$	−5804.26	−0.211788
$910$	−60653.3	−2.20949
$911$	34136.6	1.24149	0.620745	−	0.784013i	$-0.286830\pi$
$911$	34136.6	1.24149	0.620745	+	0.784013i	$0.286830\pi$
$912$	−3869.41	−0.140492
$913$	−31168.5	−1.12982
$914$	23886.8	0.864448
$915$	2839.23	0.102582
$916$	16239.9	0.585788
$917$	14835.2	0.534242
$918$	3220.88	0.115801
$919$	15512.0	0.556794	0.278397	−	0.960466i	$-0.410197\pi$
$919$	15512.0	0.556794	0.278397	+	0.960466i	$0.410197\pi$
$920$	59844.4	2.14458
$921$	−11298.3	−0.404227
$922$	22007.3	0.786086
$923$	−43115.3	−1.53755
$924$	4850.71	0.172702
$925$	−2348.80	−0.0834897
$926$	43055.5	1.52796
$927$	12539.9	0.444297
$928$	0	0
$929$	−3100.72	−0.109506	−0.0547531	−	0.998500i	$-0.517437\pi$
$929$	−3100.72	−0.109506	−0.0547531	+	0.998500i	$0.517437\pi$
$930$	−6833.58	−0.240948
$931$	3940.40	0.138713
$932$	1759.77	0.0618488
$933$	−15055.8	−0.528299
$934$	−774.498	−0.0271331
$935$	14812.5	0.518098
$936$	50841.3	1.77543
$937$	−19638.8	−0.684708	−0.342354	−	0.939571i	$-0.611224\pi$
$937$	−19638.8	−0.684708	−0.342354	+	0.939571i	$0.611224\pi$
$938$	12499.6	0.435103
$939$	−3460.29	−0.120258
$940$	1151.37	0.0399504
$941$	−50033.6	−1.73332	−0.866658	−	0.498903i	$-0.833736\pi$
$941$	−50033.6	−1.73332	−0.866658	+	0.498903i	$0.833736\pi$
$942$	6944.30	0.240189
$943$	2499.57	0.0863172
$944$	10567.0	0.364328
$945$	−28829.0	−0.992389
$946$	17365.4	0.596827
$947$	−19758.4	−0.677994	−0.338997	−	0.940787i	$-0.610088\pi$
$947$	−19758.4	−0.677994	−0.338997	+	0.940787i	$0.610088\pi$
$948$	5411.90	0.185412
$949$	−30387.3	−1.03942
$950$	31711.8	1.08302
$951$	2254.20	0.0768636
$952$	6390.03	0.217544
$953$	33843.4	1.15036	0.575180	−	0.818027i	$-0.304932\pi$
$953$	33843.4	1.15036	0.575180	+	0.818027i	$0.304932\pi$
$954$	−15364.6	−0.521434
$955$	−15274.1	−0.517548
$956$	−20677.0	−0.699520
$957$	0	0
$958$	−568.624	−0.0191768
$959$	34798.0	1.17173
$960$	−18058.2	−0.607112
$961$	−21651.0	−0.726762
$962$	−2183.11	−0.0731666
$963$	10126.1	0.338846
$964$	−21152.1	−0.706705
$965$	26582.1	0.886743
$966$	−9240.50	−0.307772
$967$	−35236.9	−1.17181	−0.585906	−	0.810379i	$-0.699261\pi$
$967$	−35236.9	−1.17181	−0.585906	+	0.810379i	$0.699261\pi$
$968$	34904.9	1.15897
$969$	−1903.23	−0.0630964
$970$	−13724.5	−0.454294
$971$	4505.40	0.148903	0.0744517	−	0.997225i	$-0.476279\pi$
$971$	4505.40	0.148903	0.0744517	+	0.997225i	$0.476279\pi$
$972$	10050.1	0.331644
$973$	−10201.5	−0.336119
$974$	29708.0	0.977314
$975$	34075.5	1.11927
$976$	2631.69	0.0863096
$977$	−15167.4	−0.496671	−0.248336	−	0.968674i	$-0.579884\pi$
$977$	−15167.4	−0.496671	−0.248336	+	0.968674i	$0.579884\pi$
$978$	−8422.29	−0.275373
$979$	72734.2	2.37446
$980$	3209.01	0.104600
$981$	22829.7	0.743012
$982$	−14466.3	−0.470099
$983$	−25342.5	−0.822278	−0.411139	−	0.911573i	$-0.634869\pi$
$983$	−25342.5	−0.822278	−0.411139	+	0.911573i	$0.634869\pi$
$984$	−854.318	−0.0276775
$985$	−36544.4	−1.18213
$986$	0	0
$987$	−655.557	−0.0211414
$988$	−17467.2	−0.562455
$989$	19604.1	0.630307
$990$	−50857.0	−1.63267
$991$	40576.1	1.30065	0.650324	−	0.759657i	$-0.274633\pi$
$991$	40576.1	1.30065	0.650324	+	0.759657i	$0.274633\pi$
$992$	11422.9	0.365603
$993$	6947.37	0.222022
$994$	18605.4	0.593689
$995$	−6533.46	−0.208166
$996$	3261.43	0.103757
$997$	−7442.49	−0.236415	−0.118208	−	0.992989i	$-0.537715\pi$
$997$	−7442.49	−0.236415	−0.118208	+	0.992989i	$0.537715\pi$
$998$	−18132.6	−0.575128
$999$	−1037.65	−0.0328627

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.4.a.b.1.2		5
29.28	even	2		29.4.a.b.1.4	✓	5
87.86	odd	2		261.4.a.f.1.2		5
116.115	odd	2		464.4.a.l.1.3		5
145.144	even	2		725.4.a.c.1.2		5
203.202	odd	2		1421.4.a.e.1.4		5
232.115	odd	2		1856.4.a.bb.1.3		5
232.173	even	2		1856.4.a.y.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.b.1.4	✓	5	29.28	even	2
261.4.a.f.1.2		5	87.86	odd	2
464.4.a.l.1.3		5	116.115	odd	2
725.4.a.c.1.2		5	145.144	even	2
841.4.a.b.1.2		5	1.1	even	1	trivial
1421.4.a.e.1.4		5	203.202	odd	2
1856.4.a.y.1.3		5	232.173	even	2
1856.4.a.bb.1.3		5	232.115	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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24125 q^{2} -1.84328 q^{3} -2.97681 q^{4} +18.3339 q^{5} +4.13124 q^{6} -16.8583 q^{7} +24.6017 q^{8} -23.6023 q^{9} +O(q^{10})\)	\(q-2.24125 q^{2} -1.84328 q^{3} -2.97681 q^{4} +18.3339 q^{5} +4.13124 q^{6} -16.8583 q^{7} +24.6017 q^{8} -23.6023 q^{9} -41.0908 q^{10} -52.4385 q^{11} +5.48709 q^{12} -87.5580 q^{13} +37.7836 q^{14} -33.7945 q^{15} -31.3241 q^{16} -15.4072 q^{17} +52.8987 q^{18} -67.0156 q^{19} -54.5766 q^{20} +31.0745 q^{21} +117.528 q^{22} +132.679 q^{23} -45.3478 q^{24} +211.133 q^{25} +196.239 q^{26} +93.2741 q^{27} +50.1839 q^{28} +75.7418 q^{30} -90.2221 q^{31} -126.609 q^{32} +96.6587 q^{33} +34.5314 q^{34} -309.078 q^{35} +70.2597 q^{36} -11.1247 q^{37} +150.199 q^{38} +161.394 q^{39} +451.047 q^{40} +18.8392 q^{41} -69.6456 q^{42} +147.756 q^{43} +156.100 q^{44} -432.723 q^{45} -297.366 q^{46} -21.0963 q^{47} +57.7390 q^{48} -58.7983 q^{49} -473.201 q^{50} +28.3997 q^{51} +260.644 q^{52} -290.454 q^{53} -209.050 q^{54} -961.404 q^{55} -414.743 q^{56} +123.528 q^{57} -337.343 q^{59} +100.600 q^{60} -84.0147 q^{61} +202.210 q^{62} +397.895 q^{63} +534.355 q^{64} -1605.28 q^{65} -216.636 q^{66} +330.821 q^{67} +45.8644 q^{68} -244.564 q^{69} +692.721 q^{70} +492.420 q^{71} -580.659 q^{72} +347.053 q^{73} +24.9333 q^{74} -389.176 q^{75} +199.493 q^{76} +884.023 q^{77} -361.723 q^{78} +986.297 q^{79} -574.294 q^{80} +465.333 q^{81} -42.2234 q^{82} +594.382 q^{83} -92.5029 q^{84} -282.475 q^{85} -331.157 q^{86} -1290.08 q^{88} -1387.04 q^{89} +969.840 q^{90} +1476.08 q^{91} -394.960 q^{92} +166.304 q^{93} +47.2820 q^{94} -1228.66 q^{95} +233.375 q^{96} +334.003 q^{97} +131.781 q^{98} +1237.67 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9} + 64 q^{10} - 12 q^{11} + 224 q^{12} + 14 q^{13} + 192 q^{14} + 74 q^{15} + 146 q^{16} - 66 q^{17} + 108 q^{18} - 214 q^{19} + 6 q^{20} - 98 q^{22} + 164 q^{23} + 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} + 540 q^{28} - 234 q^{30} - 420 q^{31} + 652 q^{32} - 576 q^{33} + 204 q^{34} - 52 q^{35} - 260 q^{36} - 378 q^{37} - 496 q^{38} + 374 q^{39} + 80 q^{40} + 1158 q^{41} + 348 q^{42} + 204 q^{43} - 784 q^{44} - 1506 q^{45} - 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} - 908 q^{50} + 228 q^{51} + 1482 q^{52} - 554 q^{53} + 918 q^{54} - 546 q^{55} + 608 q^{56} + 44 q^{57} + 440 q^{59} - 636 q^{60} - 618 q^{61} + 1250 q^{62} + 804 q^{63} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} + 2184 q^{70} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} + 1616 q^{77} - 1302 q^{78} - 272 q^{79} - 890 q^{80} + 1801 q^{81} + 92 q^{82} + 512 q^{83} + 3208 q^{84} + 1628 q^{85} + 2446 q^{86} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 2580 q^{91} + 3468 q^{92} - 40 q^{93} - 5942 q^{94} - 2244 q^{95} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} + 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9 + 64 * q^10 - 12 * q^11 + 224 * q^12 + 14 * q^13 + 192 * q^14 + 74 * q^15 + 146 * q^16 - 66 * q^17 + 108 * q^18 - 214 * q^19 + 6 * q^20 - 98 * q^22 + 164 * q^23 + 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 + 540 * q^28 - 234 * q^30 - 420 * q^31 + 652 * q^32 - 576 * q^33 + 204 * q^34 - 52 * q^35 - 260 * q^36 - 378 * q^37 - 496 * q^38 + 374 * q^39 + 80 * q^40 + 1158 * q^41 + 348 * q^42 + 204 * q^43 - 784 * q^44 - 1506 * q^45 - 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 - 908 * q^50 + 228 * q^51 + 1482 * q^52 - 554 * q^53 + 918 * q^54 - 546 * q^55 + 608 * q^56 + 44 * q^57 + 440 * q^59 - 636 * q^60 - 618 * q^61 + 1250 * q^62 + 804 * q^63 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 + 2184 * q^70 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 + 1616 * q^77 - 1302 * q^78 - 272 * q^79 - 890 * q^80 + 1801 * q^81 + 92 * q^82 + 512 * q^83 + 3208 * q^84 + 1628 * q^85 + 2446 * q^86 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 2580 * q^91 + 3468 * q^92 - 40 * q^93 - 5942 * q^94 - 2244 * q^95 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 + 238 * q^99

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