LMFDB - Embedded newform 547.4.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,4,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, 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("547.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	547.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:	$32.2740447731$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.04533 q^{2} -1.70191 q^{3} +17.4553 q^{4} +1.56697 q^{5} +8.58669 q^{6} -17.5256 q^{7} -47.7054 q^{8} -24.1035 q^{9} +O(q^{10})$	\(q-5.04533 q^{2} -1.70191 q^{3} +17.4553 q^{4} +1.56697 q^{5} +8.58669 q^{6} -17.5256 q^{7} -47.7054 q^{8} -24.1035 q^{9} -7.90590 q^{10} -43.0848 q^{11} -29.7074 q^{12} -66.5082 q^{13} +88.4225 q^{14} -2.66685 q^{15} +101.046 q^{16} -131.824 q^{17} +121.610 q^{18} +7.55553 q^{19} +27.3521 q^{20} +29.8270 q^{21} +217.377 q^{22} +157.918 q^{23} +81.1902 q^{24} -122.545 q^{25} +335.556 q^{26} +86.9735 q^{27} -305.916 q^{28} -42.0101 q^{29} +13.4551 q^{30} -283.865 q^{31} -128.170 q^{32} +73.3265 q^{33} +665.095 q^{34} -27.4622 q^{35} -420.735 q^{36} +58.9971 q^{37} -38.1201 q^{38} +113.191 q^{39} -74.7530 q^{40} -381.637 q^{41} -150.487 q^{42} +228.302 q^{43} -752.061 q^{44} -37.7696 q^{45} -796.748 q^{46} +114.884 q^{47} -171.972 q^{48} -35.8529 q^{49} +618.278 q^{50} +224.352 q^{51} -1160.92 q^{52} -27.3791 q^{53} -438.810 q^{54} -67.5128 q^{55} +836.065 q^{56} -12.8588 q^{57} +211.955 q^{58} -11.5364 q^{59} -46.5507 q^{60} -791.189 q^{61} +1432.19 q^{62} +422.429 q^{63} -161.713 q^{64} -104.217 q^{65} -369.956 q^{66} -905.706 q^{67} -2301.03 q^{68} -268.762 q^{69} +138.556 q^{70} -162.771 q^{71} +1149.87 q^{72} +339.863 q^{73} -297.660 q^{74} +208.560 q^{75} +131.884 q^{76} +755.088 q^{77} -571.086 q^{78} +137.914 q^{79} +158.337 q^{80} +502.774 q^{81} +1925.48 q^{82} +450.099 q^{83} +520.641 q^{84} -206.565 q^{85} -1151.86 q^{86} +71.4974 q^{87} +2055.38 q^{88} +300.828 q^{89} +190.560 q^{90} +1165.60 q^{91} +2756.51 q^{92} +483.112 q^{93} -579.630 q^{94} +11.8393 q^{95} +218.133 q^{96} +498.552 q^{97} +180.890 q^{98} +1038.50 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) $ 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9 + 120 * q^10 + 139 * q^11 + 309 * q^12 + 343 * q^13 + 239 * q^14 + 194 * q^15 + 1346 * q^16 + 842 * q^17 + 423 * q^18 + 157 * q^19 + 1292 * q^20 + 434 * q^21 + 436 * q^22 + 1004 * q^23 + 935 * q^24 + 2206 * q^25 + 812 * q^26 + 1282 * q^27 + 584 * q^28 + 1459 * q^29 + 146 * q^30 + 582 * q^31 + 1428 * q^32 + 1080 * q^33 + 393 * q^34 + 1006 * q^35 + 2996 * q^36 + 1477 * q^37 + 1873 * q^38 + 626 * q^39 + 1272 * q^40 + 1112 * q^41 + 1812 * q^42 + 833 * q^43 + 1392 * q^44 + 3841 * q^45 + 782 * q^46 + 2484 * q^47 + 2034 * q^48 + 4727 * q^49 + 1248 * q^50 + 932 * q^51 + 2118 * q^52 + 5077 * q^53 + 1537 * q^54 + 1736 * q^55 + 2281 * q^56 + 1426 * q^57 + 992 * q^58 + 2977 * q^59 + 1418 * q^60 + 3363 * q^61 + 3438 * q^62 + 3194 * q^63 + 6138 * q^64 + 4640 * q^65 + 288 * q^66 + 955 * q^67 + 8553 * q^68 + 4440 * q^69 + 2203 * q^70 + 2458 * q^71 + 4495 * q^72 + 3724 * q^73 + 2099 * q^74 + 4491 * q^75 + 2260 * q^76 + 9774 * q^77 + 1057 * q^78 + 1638 * q^79 + 8221 * q^80 + 10151 * q^81 + 1018 * q^82 + 6121 * q^83 + 4847 * q^84 + 3836 * q^85 + 2305 * q^86 + 3894 * q^87 + 5815 * q^88 + 8110 * q^89 + 4951 * q^90 + 2312 * q^91 + 13138 * q^92 + 9250 * q^93 - 813 * q^94 + 4858 * q^95 + 6882 * q^96 + 4486 * q^97 + 4216 * q^98 + 4969 * 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 $

$2$	−5.04533	−1.78379	−0.891897	−	0.452239i	$-0.850625\pi$
$2$	−5.04533	−1.78379	−0.891897	+	0.452239i	$0.850625\pi$
$3$	−1.70191	−0.327533	−0.163766	−	0.986499i	$-0.552364\pi$
$3$	−1.70191	−0.327533	−0.163766	+	0.986499i	$0.552364\pi$
$4$	17.4553	2.18192
$5$	1.56697	0.140154	0.0700772	−	0.997542i	$-0.477675\pi$
$5$	1.56697	0.140154	0.0700772	+	0.997542i	$0.477675\pi$
$6$	8.58669	0.584250
$7$	−17.5256	−0.946294	−0.473147	−	0.880983i	$-0.656882\pi$
$7$	−17.5256	−0.946294	−0.473147	+	0.880983i	$0.656882\pi$
$8$	−47.7054	−2.10830
$9$	−24.1035	−0.892722
$10$	−7.90590	−0.250006
$11$	−43.0848	−1.18096	−0.590480	−	0.807052i	$-0.701062\pi$
$11$	−43.0848	−1.18096	−0.590480	+	0.807052i	$0.701062\pi$
$12$	−29.7074	−0.714649
$13$	−66.5082	−1.41893	−0.709464	−	0.704742i	$-0.751063\pi$
$13$	−66.5082	−1.41893	−0.709464	+	0.704742i	$0.751063\pi$
$14$	88.4225	1.68799
$15$	−2.66685	−0.0459051
$16$	101.046	1.57885
$17$	−131.824	−1.88071	−0.940353	−	0.340200i	$-0.889505\pi$
$17$	−131.824	−1.88071	−0.940353	+	0.340200i	$0.889505\pi$
$18$	121.610	1.59243
$19$	7.55553	0.0912294	0.0456147	−	0.998959i	$-0.485475\pi$
$19$	7.55553	0.0912294	0.0456147	+	0.998959i	$0.485475\pi$
$20$	27.3521	0.305805
$21$	29.8270	0.309942
$22$	217.377	2.10659
$23$	157.918	1.43166	0.715830	−	0.698275i	$-0.246049\pi$
$23$	157.918	1.43166	0.715830	+	0.698275i	$0.246049\pi$
$24$	81.1902	0.690536
$25$	−122.545	−0.980357
$26$	335.556	2.53107
$27$	86.9735	0.619928
$28$	−305.916	−2.06474
$29$	−42.0101	−0.269003	−0.134501	−	0.990913i	$-0.542943\pi$
$29$	−42.0101	−0.269003	−0.134501	+	0.990913i	$0.542943\pi$
$30$	13.4551	0.0818852
$31$	−283.865	−1.64463	−0.822316	−	0.569030i	$-0.807319\pi$
$31$	−283.865	−1.64463	−0.822316	+	0.569030i	$0.807319\pi$
$32$	−128.170	−0.708044
$33$	73.3265	0.386803
$34$	665.095	3.35479
$35$	−27.4622	−0.132627
$36$	−420.735	−1.94785
$37$	58.9971	0.262137	0.131068	−	0.991373i	$-0.458159\pi$
$37$	58.9971	0.262137	0.131068	+	0.991373i	$0.458159\pi$
$38$	−38.1201	−0.162734
$39$	113.191	0.464745
$40$	−74.7530	−0.295487
$41$	−381.637	−1.45370	−0.726849	−	0.686797i	$-0.759016\pi$
$41$	−381.637	−1.45370	−0.726849	+	0.686797i	$0.759016\pi$
$42$	−150.487	−0.552873
$43$	228.302	0.809669	0.404835	−	0.914390i	$-0.367329\pi$
$43$	228.302	0.809669	0.404835	+	0.914390i	$0.367329\pi$
$44$	−752.061	−2.57676
$45$	−37.7696	−0.125119
$46$	−796.748	−2.55379
$47$	114.884	0.356545	0.178272	−	0.983981i	$-0.442949\pi$
$47$	114.884	0.356545	0.178272	+	0.983981i	$0.442949\pi$
$48$	−171.972	−0.517125
$49$	−35.8529	−0.104527
$50$	618.278	1.74875
$51$	224.352	0.615993
$52$	−1160.92	−3.09598
$53$	−27.3791	−0.0709588	−0.0354794	−	0.999370i	$-0.511296\pi$
$53$	−27.3791	−0.0709588	−0.0354794	+	0.999370i	$0.511296\pi$
$54$	−438.810	−1.10582
$55$	−67.5128	−0.165517
$56$	836.065	1.99507
$57$	−12.8588	−0.0298806
$58$	211.955	0.479846
$59$	−11.5364	−0.0254561	−0.0127280	−	0.999919i	$-0.504052\pi$
$59$	−11.5364	−0.0254561	−0.0127280	+	0.999919i	$0.504052\pi$
$60$	−46.5507	−0.100161
$61$	−791.189	−1.66068	−0.830339	−	0.557258i	$-0.811853\pi$
$61$	−791.189	−1.66068	−0.830339	+	0.557258i	$0.811853\pi$
$62$	1432.19	2.93369
$63$	422.429	0.844778
$64$	−161.713	−0.315846
$65$	−104.217	−0.198869
$66$	−369.956	−0.689977
$67$	−905.706	−1.65149	−0.825743	−	0.564046i	$-0.809244\pi$
$67$	−905.706	−1.65149	−0.825743	+	0.564046i	$0.809244\pi$
$68$	−2301.03	−4.10355
$69$	−268.762	−0.468915
$70$	138.556	0.236580
$71$	−162.771	−0.272075	−0.136037	−	0.990704i	$-0.543437\pi$
$71$	−162.771	−0.272075	−0.136037	+	0.990704i	$0.543437\pi$
$72$	1149.87	1.88213
$73$	339.863	0.544904	0.272452	−	0.962169i	$-0.412165\pi$
$73$	339.863	0.544904	0.272452	+	0.962169i	$0.412165\pi$
$74$	−297.660	−0.467598
$75$	208.560	0.321099
$76$	131.884	0.199055
$77$	755.088	1.11754
$78$	−571.086	−0.829009
$79$	137.914	0.196412	0.0982058	−	0.995166i	$-0.468690\pi$
$79$	137.914	0.196412	0.0982058	+	0.995166i	$0.468690\pi$
$80$	158.337	0.221283
$81$	502.774	0.689676
$82$	1925.48	2.59310
$83$	450.099	0.595238	0.297619	−	0.954685i	$-0.403807\pi$
$83$	450.099	0.595238	0.297619	+	0.954685i	$0.403807\pi$
$84$	520.641	0.676269
$85$	−206.565	−0.263589
$86$	−1151.86	−1.44428
$87$	71.4974	0.0881072
$88$	2055.38	2.48982
$89$	300.828	0.358289	0.179145	−	0.983823i	$-0.442667\pi$
$89$	300.828	0.358289	0.179145	+	0.983823i	$0.442667\pi$
$90$	190.560	0.223186
$91$	1165.60	1.34272
$92$	2756.51	3.12377
$93$	483.112	0.538671
$94$	−579.630	−0.636003
$95$	11.8393	0.0127862
$96$	218.133	0.231908
$97$	498.552	0.521858	0.260929	−	0.965358i	$-0.415971\pi$
$97$	498.552	0.521858	0.260929	+	0.965358i	$0.415971\pi$
$98$	180.890	0.186455
$99$	1038.50	1.05427
$100$	−2139.06	−2.13906
$101$	813.442	0.801391	0.400696	−	0.916211i	$-0.368769\pi$
$101$	813.442	0.801391	0.400696	+	0.916211i	$0.368769\pi$
$102$	−1131.93	−1.09880
$103$	428.048	0.409484	0.204742	−	0.978816i	$-0.434364\pi$
$103$	428.048	0.409484	0.204742	+	0.978816i	$0.434364\pi$
$104$	3172.80	2.99152
$105$	46.7381	0.0434397
$106$	138.137	0.126576
$107$	−227.447	−0.205497	−0.102748	−	0.994707i	$-0.532764\pi$
$107$	−227.447	−0.205497	−0.102748	+	0.994707i	$0.532764\pi$
$108$	1518.15	1.35263
$109$	−1556.69	−1.36793	−0.683963	−	0.729517i	$-0.739745\pi$
$109$	−1556.69	−1.36793	−0.683963	+	0.729517i	$0.739745\pi$
$110$	340.624	0.295248
$111$	−100.408	−0.0858584
$112$	−1770.90	−1.49406
$113$	802.560	0.668128	0.334064	−	0.942550i	$-0.391580\pi$
$113$	802.560	0.668128	0.334064	+	0.942550i	$0.391580\pi$
$114$	64.8770	0.0533008
$115$	247.453	0.200653
$116$	−733.301	−0.586943
$117$	1603.08	1.26671
$118$	58.2048	0.0454084
$119$	2310.30	1.77970
$120$	127.223	0.0967817
$121$	525.304	0.394669
$122$	3991.81	2.96231
$123$	649.511	0.476134
$124$	−4954.96	−3.58846
$125$	−387.896	−0.277556
$126$	−2131.29	−1.50691
$127$	−976.785	−0.682486	−0.341243	−	0.939975i	$-0.610848\pi$
$127$	−976.785	−0.682486	−0.341243	+	0.939975i	$0.610848\pi$
$128$	1841.25	1.27145
$129$	−388.550	−0.265193
$130$	525.807	0.354741
$131$	−2756.16	−1.83822	−0.919108	−	0.394005i	$-0.871089\pi$
$131$	−2756.16	−1.83822	−0.919108	+	0.394005i	$0.871089\pi$
$132$	1279.94	0.843973
$133$	−132.415	−0.0863298
$134$	4569.58	2.94591
$135$	136.285	0.0868857
$136$	6288.71	3.96509
$137$	488.250	0.304482	0.152241	−	0.988343i	$-0.451351\pi$
$137$	488.250	0.304482	0.152241	+	0.988343i	$0.451351\pi$
$138$	1355.99	0.836448
$139$	−657.345	−0.401117	−0.200559	−	0.979682i	$-0.564276\pi$
$139$	−657.345	−0.401117	−0.200559	+	0.979682i	$0.564276\pi$
$140$	−479.362	−0.289382
$141$	−195.523	−0.116780
$142$	821.231	0.485325
$143$	2865.50	1.67570
$144$	−2435.57	−1.40948
$145$	−65.8288	−0.0377019
$146$	−1714.72	−0.971997
$147$	61.0184	0.0342361
$148$	1029.82	0.571962
$149$	2197.05	1.20798	0.603991	−	0.796991i	$-0.293576\pi$
$149$	2197.05	1.20798	0.603991	+	0.796991i	$0.293576\pi$
$150$	−1052.25	−0.572774
$151$	−1284.22	−0.692109	−0.346055	−	0.938214i	$-0.612479\pi$
$151$	−1284.22	−0.692109	−0.346055	+	0.938214i	$0.612479\pi$
$152$	−360.439	−0.192339
$153$	3177.42	1.67895
$154$	−3809.67	−1.99345
$155$	−444.809	−0.230502
$156$	1975.79	1.01404
$157$	−2919.51	−1.48409	−0.742045	−	0.670350i	$-0.766144\pi$
$157$	−2919.51	−1.48409	−0.742045	+	0.670350i	$0.766144\pi$
$158$	−695.821	−0.350358
$159$	46.5968	0.0232413
$160$	−200.838	−0.0992355
$161$	−2767.61	−1.35477
$162$	−2536.66	−1.23024
$163$	−1925.85	−0.925422	−0.462711	−	0.886509i	$-0.653123\pi$
$163$	−1925.85	−0.925422	−0.462711	+	0.886509i	$0.653123\pi$
$164$	−6661.60	−3.17185
$165$	114.901	0.0542122
$166$	−2270.90	−1.06178
$167$	−273.161	−0.126574	−0.0632870	−	0.997995i	$-0.520158\pi$
$167$	−273.161	−0.126574	−0.0632870	+	0.997995i	$0.520158\pi$
$168$	−1422.91	−0.653451
$169$	2226.34	1.01336
$170$	1042.19	0.470189
$171$	−182.115	−0.0814425
$172$	3985.10	1.76663
$173$	754.678	0.331660	0.165830	−	0.986154i	$-0.446970\pi$
$173$	754.678	0.331660	0.165830	+	0.986154i	$0.446970\pi$
$174$	−360.728	−0.157165
$175$	2147.67	0.927706
$176$	−4353.57	−1.86456
$177$	19.6339	0.00833769
$178$	−1517.78	−0.639114
$179$	1682.64	0.702607	0.351304	−	0.936262i	$-0.385739\pi$
$179$	1682.64	0.702607	0.351304	+	0.936262i	$0.385739\pi$
$180$	−659.281	−0.272999
$181$	4762.78	1.95588	0.977941	−	0.208880i	$-0.0669817\pi$
$181$	4762.78	1.95588	0.977941	+	0.208880i	$0.0669817\pi$
$182$	−5880.82	−2.39514
$183$	1346.53	0.543926
$184$	−7533.53	−3.01837
$185$	92.4469	0.0367396
$186$	−2437.46	−0.960878
$187$	5679.61	2.22104
$188$	2005.35	0.777952
$189$	−1524.26	−0.586634
$190$	−59.7333	−0.0228079
$191$	−1838.07	−0.696324	−0.348162	−	0.937434i	$-0.613194\pi$
$191$	−1838.07	−0.696324	−0.348162	+	0.937434i	$0.613194\pi$
$192$	275.221	0.103450
$193$	3656.62	1.36378	0.681889	−	0.731456i	$-0.261159\pi$
$193$	3656.62	1.36378	0.681889	+	0.731456i	$0.261159\pi$
$194$	−2515.36	−0.930887
$195$	177.367	0.0651360
$196$	−625.825	−0.228070
$197$	−4161.77	−1.50515	−0.752573	−	0.658508i	$-0.771188\pi$
$197$	−4161.77	−1.50515	−0.752573	+	0.658508i	$0.771188\pi$
$198$	−5239.55	−1.88060
$199$	416.805	0.148475	0.0742376	−	0.997241i	$-0.476348\pi$
$199$	416.805	0.148475	0.0742376	+	0.997241i	$0.476348\pi$
$200$	5846.03	2.06688
$201$	1541.43	0.540916
$202$	−4104.08	−1.42952
$203$	736.253	0.254556
$204$	3916.15	1.34405
$205$	−598.015	−0.203742
$206$	−2159.65	−0.730435
$207$	−3806.38	−1.27808
$208$	−6720.42	−2.24027
$209$	−325.529	−0.107738
$210$	−235.809	−0.0774875
$211$	−3130.73	−1.02146	−0.510731	−	0.859741i	$-0.670625\pi$
$211$	−3130.73	−1.02146	−0.510731	+	0.859741i	$0.670625\pi$
$212$	−477.913	−0.154826
$213$	277.021	0.0891134
$214$	1147.55	0.366564
$215$	357.744	0.113479
$216$	−4149.10	−1.30699
$217$	4974.90	1.55631
$218$	7854.02	2.44010
$219$	−578.417	−0.178474
$220$	−1178.46	−0.361144
$221$	8767.37	2.66859
$222$	506.590	0.153154
$223$	−4099.20	−1.23095	−0.615476	−	0.788155i	$-0.711036\pi$
$223$	−4099.20	−1.23095	−0.615476	+	0.788155i	$0.711036\pi$
$224$	2246.25	0.670018
$225$	2953.75	0.875186
$226$	−4049.18	−1.19180
$227$	612.656	0.179134	0.0895670	−	0.995981i	$-0.471452\pi$
$227$	612.656	0.179134	0.0895670	+	0.995981i	$0.471452\pi$
$228$	−224.455	−0.0651970
$229$	−3112.45	−0.898151	−0.449075	−	0.893494i	$-0.648247\pi$
$229$	−3112.45	−0.898151	−0.449075	+	0.893494i	$0.648247\pi$
$230$	−1248.48	−0.357924
$231$	−1285.09	−0.366030
$232$	2004.11	0.567139
$233$	5910.23	1.66177	0.830884	−	0.556445i	$-0.187835\pi$
$233$	5910.23	1.66177	0.830884	+	0.556445i	$0.187835\pi$
$234$	−8088.07	−2.25955
$235$	180.021	0.0499713
$236$	−201.372	−0.0555431
$237$	−234.717	−0.0643312
$238$	−11656.2	−3.17462
$239$	−6086.29	−1.64724	−0.823619	−	0.567144i	$-0.808048\pi$
$239$	−6086.29	−1.64724	−0.823619	+	0.567144i	$0.808048\pi$
$240$	−269.475	−0.0724773
$241$	−32.3943	−0.00865851	−0.00432925	−	0.999991i	$-0.501378\pi$
$241$	−32.3943	−0.00865851	−0.00432925	+	0.999991i	$0.501378\pi$
$242$	−2650.33	−0.704007
$243$	−3203.96	−0.845820
$244$	−13810.5	−3.62347
$245$	−56.1806	−0.0146500
$246$	−3277.00	−0.849324
$247$	−502.505	−0.129448
$248$	13541.9	3.46738
$249$	−766.028	−0.194960
$250$	1957.06	0.495102
$251$	3374.31	0.848544	0.424272	−	0.905535i	$-0.360530\pi$
$251$	3374.31	0.848544	0.424272	+	0.905535i	$0.360530\pi$
$252$	7373.64	1.84324
$253$	−6803.87	−1.69073
$254$	4928.20	1.21741
$255$	351.554	0.0863340
$256$	−7996.03	−1.95215
$257$	6041.88	1.46647	0.733234	−	0.679976i	$-0.238010\pi$
$257$	6041.88	1.46647	0.733234	+	0.679976i	$0.238010\pi$
$258$	1960.36	0.473050
$259$	−1033.96	−0.248059
$260$	−1819.14	−0.433916
$261$	1012.59	0.240145
$262$	13905.7	3.27900
$263$	−8042.27	−1.88558	−0.942791	−	0.333385i	$-0.891809\pi$
$263$	−8042.27	−1.88558	−0.942791	+	0.333385i	$0.891809\pi$
$264$	−3498.07	−0.815497
$265$	−42.9024	−0.00994518
$266$	668.079	0.153995
$267$	−511.983	−0.117351
$268$	−15809.4	−3.60341
$269$	8374.18	1.89808	0.949039	−	0.315160i	$-0.102058\pi$
$269$	8374.18	1.89808	0.949039	+	0.315160i	$0.102058\pi$
$270$	−687.604	−0.154986
$271$	−1662.94	−0.372755	−0.186378	−	0.982478i	$-0.559675\pi$
$271$	−1662.94	−0.372755	−0.186378	+	0.982478i	$0.559675\pi$
$272$	−13320.3	−2.96935
$273$	−1983.74	−0.439785
$274$	−2463.38	−0.543133
$275$	5279.82	1.15776
$276$	−4691.34	−1.02314
$277$	−4818.15	−1.04511	−0.522553	−	0.852607i	$-0.675020\pi$
$277$	−4818.15	−1.04511	−0.522553	+	0.852607i	$0.675020\pi$
$278$	3316.52	0.715510
$279$	6842.14	1.46820
$280$	1310.09	0.279618
$281$	−4875.70	−1.03509	−0.517545	−	0.855656i	$-0.673154\pi$
$281$	−4875.70	−1.03509	−0.517545	+	0.855656i	$0.673154\pi$
$282$	986.477	0.208312
$283$	−1016.16	−0.213444	−0.106722	−	0.994289i	$-0.534035\pi$
$283$	−1016.16	−0.213444	−0.106722	+	0.994289i	$0.534035\pi$
$284$	−2841.22	−0.593645
$285$	−20.1494	−0.00418789
$286$	−14457.4	−2.98910
$287$	6688.42	1.37563
$288$	3089.34	0.632087
$289$	12464.6	2.53706
$290$	332.128	0.0672525
$291$	−848.490	−0.170926
$292$	5932.44	1.18894
$293$	4540.25	0.905270	0.452635	−	0.891696i	$-0.350484\pi$
$293$	4540.25	0.905270	0.452635	+	0.891696i	$0.350484\pi$
$294$	−307.858	−0.0610702
$295$	−18.0772	−0.00356778
$296$	−2814.48	−0.552663
$297$	−3747.24	−0.732111
$298$	−11084.8	−2.15479
$299$	−10502.8	−2.03142
$300$	3640.48	0.700611
$301$	−4001.14	−0.766185
$302$	6479.32	1.23458
$303$	−1384.40	−0.262482
$304$	763.459	0.144038
$305$	−1239.77	−0.232751
$306$	−16031.1	−2.99490
$307$	1074.73	0.199799	0.0998995	−	0.994998i	$-0.468148\pi$
$307$	1074.73	0.199799	0.0998995	+	0.994998i	$0.468148\pi$
$308$	13180.3	2.43837
$309$	−728.499	−0.134119
$310$	2244.21	0.411169
$311$	5912.20	1.07797	0.538987	−	0.842314i	$-0.318807\pi$
$311$	5912.20	1.07797	0.538987	+	0.842314i	$0.318807\pi$
$312$	−5399.81	−0.979821
$313$	1066.91	0.192669	0.0963345	−	0.995349i	$-0.469288\pi$
$313$	1066.91	0.192669	0.0963345	+	0.995349i	$0.469288\pi$
$314$	14729.9	2.64731
$315$	661.935	0.118399
$316$	2407.33	0.428554
$317$	−3433.69	−0.608377	−0.304188	−	0.952612i	$-0.598385\pi$
$317$	−3433.69	−0.608377	−0.304188	+	0.952612i	$0.598385\pi$
$318$	−235.096	−0.0414577
$319$	1810.00	0.317682
$320$	−253.400	−0.0442672
$321$	387.094	0.0673069
$322$	13963.5	2.41663
$323$	−996.000	−0.171576
$324$	8776.09	1.50482
$325$	8150.22	1.39106
$326$	9716.52	1.65076
$327$	2649.35	0.448040
$328$	18206.1	3.06483
$329$	−2013.42	−0.337396
$330$	−579.712	−0.0967033
$331$	2437.74	0.404804	0.202402	−	0.979303i	$-0.435125\pi$
$331$	2437.74	0.404804	0.202402	+	0.979303i	$0.435125\pi$
$332$	7856.63	1.29876
$333$	−1422.04	−0.234016
$334$	1378.19	0.225782
$335$	−1419.22	−0.231463
$336$	3013.91	0.489352
$337$	−8902.28	−1.43899	−0.719493	−	0.694500i	$-0.755626\pi$
$337$	−8902.28	−1.43899	−0.719493	+	0.694500i	$0.755626\pi$
$338$	−11232.6	−1.80762
$339$	−1365.88	−0.218834
$340$	−3605.66	−0.575130
$341$	12230.3	1.94225
$342$	918.829	0.145277
$343$	6639.63	1.04521
$344$	−10891.2	−1.70702
$345$	−421.143	−0.0657205
$346$	−3807.60	−0.591612
$347$	−479.317	−0.0741530	−0.0370765	−	0.999312i	$-0.511805\pi$
$347$	−479.317	−0.0741530	−0.0370765	+	0.999312i	$0.511805\pi$
$348$	1248.01	0.192243
$349$	3506.58	0.537831	0.268915	−	0.963164i	$-0.413335\pi$
$349$	3506.58	0.537831	0.268915	+	0.963164i	$0.413335\pi$
$350$	−10835.7	−1.65484
$351$	−5784.45	−0.879633
$352$	5522.17	0.836172
$353$	1970.48	0.297105	0.148553	−	0.988905i	$-0.452539\pi$
$353$	1970.48	0.297105	0.148553	+	0.988905i	$0.452539\pi$
$354$	−99.0593	−0.0148727
$355$	−255.057	−0.0381325
$356$	5251.07	0.781758
$357$	−3931.91	−0.582910
$358$	−8489.49	−1.25331
$359$	10985.3	1.61499	0.807496	−	0.589873i	$-0.200822\pi$
$359$	10985.3	1.61499	0.807496	+	0.589873i	$0.200822\pi$
$360$	1801.81	0.263788
$361$	−6801.91	−0.991677
$362$	−24029.8	−3.48889
$363$	−894.020	−0.129267
$364$	20345.9	2.92971
$365$	532.557	0.0763707
$366$	−6793.70	−0.970252
$367$	5309.60	0.755201	0.377600	−	0.925969i	$-0.376749\pi$
$367$	5309.60	0.755201	0.377600	+	0.925969i	$0.376749\pi$
$368$	15957.1	2.26038
$369$	9198.78	1.29775
$370$	−466.425	−0.0655359
$371$	479.836	0.0671479
$372$	8432.89	1.17534
$373$	−4273.59	−0.593240	−0.296620	−	0.954996i	$-0.595859\pi$
$373$	−4273.59	−0.593240	−0.296620	+	0.954996i	$0.595859\pi$
$374$	−28655.5	−3.96188
$375$	660.163	0.0909085
$376$	−5480.60	−0.751703
$377$	2794.02	0.381696
$378$	7690.42	1.04643
$379$	−1801.03	−0.244097	−0.122049	−	0.992524i	$-0.538946\pi$
$379$	−1801.03	−0.244097	−0.122049	+	0.992524i	$0.538946\pi$
$380$	206.659	0.0278984
$381$	1662.40	0.223536
$382$	9273.65	1.24210
$383$	4525.15	0.603719	0.301859	−	0.953352i	$-0.402393\pi$
$383$	4525.15	0.603719	0.301859	+	0.953352i	$0.402393\pi$
$384$	−3133.65	−0.416441
$385$	1183.20	0.156628
$386$	−18448.8	−2.43270
$387$	−5502.89	−0.722810
$388$	8702.39	1.13865
$389$	−9792.54	−1.27635	−0.638177	−	0.769890i	$-0.720311\pi$
$389$	−9792.54	−1.27635	−0.638177	+	0.769890i	$0.720311\pi$
$390$	−894.876	−0.116189
$391$	−20817.4	−2.69253
$392$	1710.38	0.220375
$393$	4690.73	0.602076
$394$	20997.5	2.68487
$395$	216.107	0.0275279
$396$	18127.3	2.30033
$397$	−9826.90	−1.24231	−0.621156	−	0.783687i	$-0.713337\pi$
$397$	−9826.90	−1.24231	−0.621156	+	0.783687i	$0.713337\pi$
$398$	−2102.92	−0.264849
$399$	225.359	0.0282758
$400$	−12382.7	−1.54784
$401$	−11430.3	−1.42344	−0.711722	−	0.702461i	$-0.752084\pi$
$401$	−11430.3	−1.42344	−0.711722	+	0.702461i	$0.752084\pi$
$402$	−7777.02	−0.964882
$403$	18879.3	2.33361
$404$	14198.9	1.74857
$405$	787.833	0.0966611
$406$	−3714.64	−0.454075
$407$	−2541.88	−0.309574
$408$	−10702.8	−1.29870
$409$	−9091.34	−1.09911	−0.549557	−	0.835456i	$-0.685204\pi$
$409$	−9091.34	−1.09911	−0.549557	+	0.835456i	$0.685204\pi$
$410$	3017.18	0.363434
$411$	−830.957	−0.0997277
$412$	7471.73	0.893461
$413$	202.182	0.0240889
$414$	19204.4	2.27982
$415$	705.293	0.0834252
$416$	8524.33	1.00466
$417$	1118.74	0.131379
$418$	1642.40	0.192183
$419$	5956.01	0.694440	0.347220	−	0.937784i	$-0.387126\pi$
$419$	5956.01	0.694440	0.347220	+	0.937784i	$0.387126\pi$
$420$	815.830	0.0947820
$421$	−11112.7	−1.28646	−0.643228	−	0.765675i	$-0.722405\pi$
$421$	−11112.7	−1.28646	−0.643228	+	0.765675i	$0.722405\pi$
$422$	15795.6	1.82208
$423$	−2769.12	−0.318296
$424$	1306.13	0.149602
$425$	16154.3	1.84376
$426$	−1397.66	−0.158960
$427$	13866.1	1.57149
$428$	−3970.17	−0.448377
$429$	−4876.81	−0.548846
$430$	−1804.93	−0.202422
$431$	−16799.9	−1.87754	−0.938771	−	0.344542i	$-0.888034\pi$
$431$	−16799.9	−1.87754	−0.938771	+	0.344542i	$0.888034\pi$
$432$	8788.36	0.978774
$433$	−3407.84	−0.378223	−0.189111	−	0.981956i	$-0.560561\pi$
$433$	−3407.84	−0.378223	−0.189111	+	0.981956i	$0.560561\pi$
$434$	−25100.0	−2.77613
$435$	112.035	0.0123486
$436$	−27172.6	−2.98470
$437$	1193.15	0.130609
$438$	2918.30	0.318361
$439$	6373.43	0.692909	0.346455	−	0.938067i	$-0.387385\pi$
$439$	6373.43	0.692909	0.346455	+	0.938067i	$0.387385\pi$
$440$	3220.72	0.348959
$441$	864.181	0.0933140
$442$	−44234.3	−4.76021
$443$	−6201.22	−0.665076	−0.332538	−	0.943090i	$-0.607905\pi$
$443$	−6201.22	−0.665076	−0.332538	+	0.943090i	$0.607905\pi$
$444$	−1752.65	−0.187336
$445$	471.390	0.0502158
$446$	20681.8	2.19577
$447$	−3739.18	−0.395654
$448$	2834.12	0.298883
$449$	−3805.70	−0.400005	−0.200002	−	0.979795i	$-0.564095\pi$
$449$	−3805.70	−0.400005	−0.200002	+	0.979795i	$0.564095\pi$
$450$	−14902.7	−1.56115
$451$	16442.8	1.71676
$452$	14009.0	1.45780
$453$	2185.63	0.226688
$454$	−3091.05	−0.319538
$455$	1826.46	0.188188
$456$	613.435	0.0629972
$457$	9689.03	0.991759	0.495879	−	0.868391i	$-0.334846\pi$
$457$	9689.03	0.991759	0.495879	+	0.868391i	$0.334846\pi$
$458$	15703.3	1.60212
$459$	−11465.2	−1.16590
$460$	4319.38	0.437809
$461$	18416.9	1.86065	0.930325	−	0.366736i	$-0.119525\pi$
$461$	18416.9	1.86065	0.930325	+	0.366736i	$0.119525\pi$
$462$	6483.71	0.652921
$463$	−9961.53	−0.999896	−0.499948	−	0.866055i	$-0.666648\pi$
$463$	−9961.53	−0.999896	−0.499948	+	0.866055i	$0.666648\pi$
$464$	−4244.97	−0.424715
$465$	757.024	0.0754971
$466$	−29819.1	−2.96425
$467$	1074.51	0.106472	0.0532361	−	0.998582i	$-0.483046\pi$
$467$	1074.51	0.106472	0.0532361	+	0.998582i	$0.483046\pi$
$468$	27982.3	2.76385
$469$	15873.0	1.56279
$470$	−908.264	−0.0891385
$471$	4968.74	0.486088
$472$	550.347	0.0536690
$473$	−9836.37	−0.956188
$474$	1184.22	0.114754
$475$	−925.890	−0.0894373
$476$	40327.0	3.88316
$477$	659.933	0.0633465
$478$	30707.4	2.93833
$479$	−18896.1	−1.80248	−0.901238	−	0.433325i	$-0.857340\pi$
$479$	−18896.1	−1.80248	−0.901238	+	0.433325i	$0.857340\pi$
$480$	341.809	0.0325029
$481$	−3923.79	−0.371953
$482$	163.440	0.0154450
$483$	4710.22	0.443732
$484$	9169.37	0.861135
$485$	781.217	0.0731407
$486$	16165.0	1.50877
$487$	16048.0	1.49324	0.746618	−	0.665253i	$-0.231677\pi$
$487$	16048.0	1.49324	0.746618	+	0.665253i	$0.231677\pi$
$488$	37744.0	3.50121
$489$	3277.61	0.303106
$490$	283.449	0.0261325
$491$	−5339.92	−0.490809	−0.245405	−	0.969421i	$-0.578921\pi$
$491$	−5339.92	−0.490809	−0.245405	+	0.969421i	$0.578921\pi$
$492$	11337.4	1.03888
$493$	5537.94	0.505915
$494$	2535.30	0.230908
$495$	1627.30	0.147761
$496$	−28683.5	−2.59663
$497$	2852.65	0.257463
$498$	3864.86	0.347768
$499$	7053.43	0.632775	0.316388	−	0.948630i	$-0.397530\pi$
$499$	7053.43	0.632775	0.316388	+	0.948630i	$0.397530\pi$
$500$	−6770.86	−0.605604
$501$	464.895	0.0414571
$502$	−17024.5	−1.51363
$503$	−17334.4	−1.53658	−0.768291	−	0.640101i	$-0.778892\pi$
$503$	−17334.4	−1.53658	−0.768291	+	0.640101i	$0.778892\pi$
$504$	−20152.1	−1.78104
$505$	1274.64	0.112318
$506$	34327.8	3.01592
$507$	−3789.03	−0.331907
$508$	−17050.1	−1.48913
$509$	−19383.0	−1.68789	−0.843944	−	0.536432i	$-0.819772\pi$
$509$	−19383.0	−1.68789	−0.843944	+	0.536432i	$0.819772\pi$
$510$	−1773.71	−0.154002
$511$	−5956.31	−0.515640
$512$	25612.6	2.21079
$513$	657.131	0.0565557
$514$	−30483.3	−2.61588
$515$	670.740	0.0573910
$516$	−6782.27	−0.578630
$517$	−4949.78	−0.421066
$518$	5216.67	0.442485
$519$	−1284.39	−0.108629
$520$	4971.69	0.419275
$521$	−18183.5	−1.52905	−0.764524	−	0.644596i	$-0.777026\pi$
$521$	−18183.5	−1.52905	−0.764524	+	0.644596i	$0.777026\pi$
$522$	−5108.86	−0.428369
$523$	−11767.1	−0.983824	−0.491912	−	0.870645i	$-0.663702\pi$
$523$	−11767.1	−0.983824	−0.491912	+	0.870645i	$0.663702\pi$
$524$	−48109.7	−4.01084
$525$	−3655.14	−0.303854
$526$	40575.9	3.36349
$527$	37420.2	3.09307
$528$	7409.38	0.610704
$529$	12771.1	1.04965
$530$	216.457	0.0177402
$531$	278.067	0.0227252
$532$	−2311.36	−0.188365
$533$	25382.0	2.06269
$534$	2583.12	0.209331
$535$	−356.404	−0.0288013
$536$	43207.0	3.48183
$537$	−2863.71	−0.230127
$538$	−42250.5	−3.38578
$539$	1544.72	0.123443
$540$	2378.91	0.189577
$541$	−9331.44	−0.741571	−0.370785	−	0.928719i	$-0.620911\pi$
$541$	−9331.44	−0.741571	−0.370785	+	0.928719i	$0.620911\pi$
$542$	8390.10	0.664918
$543$	−8105.82	−0.640615
$544$	16895.8	1.33162
$545$	−2439.29	−0.191721
$546$	10008.6	0.784486
$547$	−547.000	−0.0427569
$547$	−547.000	−0.0427569
$548$	8522.57	0.664354
$549$	19070.4	1.48252
$550$	−26638.4	−2.06521
$551$	−317.409	−0.0245410
$552$	12821.4	0.988614
$553$	−2417.02	−0.185863
$554$	24309.1	1.86425
$555$	−157.336	−0.0120334
$556$	−11474.2	−0.875205
$557$	−11823.7	−0.899435	−0.449717	−	0.893171i	$-0.648475\pi$
$557$	−11823.7	−0.899435	−0.449717	+	0.893171i	$0.648475\pi$
$558$	−34520.8	−2.61897
$559$	−15184.0	−1.14886
$560$	−2774.95	−0.209399
$561$	−9666.19	−0.727463
$562$	24599.5	1.84639
$563$	−7654.59	−0.573006	−0.286503	−	0.958079i	$-0.592493\pi$
$563$	−7654.59	−0.573006	−0.286503	+	0.958079i	$0.592493\pi$
$564$	−3412.92	−0.254805
$565$	1257.59	0.0936411
$566$	5126.87	0.380739
$567$	−8811.41	−0.652636
$568$	7765.03	0.573615
$569$	−570.047	−0.0419993	−0.0209997	−	0.999779i	$-0.506685\pi$
$569$	−570.047	−0.0419993	−0.0209997	+	0.999779i	$0.506685\pi$
$570$	101.661	0.00747034
$571$	13636.1	0.999396	0.499698	−	0.866200i	$-0.333444\pi$
$571$	13636.1	0.999396	0.499698	+	0.866200i	$0.333444\pi$
$572$	50018.2	3.65624
$573$	3128.22	0.228069
$574$	−33745.3	−2.45383
$575$	−19352.0	−1.40354
$576$	3897.85	0.281963
$577$	1199.06	0.0865120	0.0432560	−	0.999064i	$-0.486227\pi$
$577$	1199.06	0.0865120	0.0432560	+	0.999064i	$0.486227\pi$
$578$	−62887.8	−4.52558
$579$	−6223.23	−0.446682
$580$	−1149.06	−0.0822626
$581$	−7888.26	−0.563271
$582$	4280.91	0.304896
$583$	1179.63	0.0837995
$584$	−16213.3	−1.14882
$585$	2511.99	0.177535
$586$	−22907.0	−1.61481
$587$	−17600.4	−1.23756	−0.618780	−	0.785564i	$-0.712373\pi$
$587$	−17600.4	−1.23756	−0.618780	+	0.785564i	$0.712373\pi$
$588$	1065.10	0.0747005
$589$	−2144.75	−0.150039
$590$	91.2054	0.00636418
$591$	7082.96	0.492985
$592$	5961.45	0.413875
$593$	7546.35	0.522582	0.261291	−	0.965260i	$-0.415852\pi$
$593$	7546.35	0.522582	0.261291	+	0.965260i	$0.415852\pi$
$594$	18906.1	1.30593
$595$	3620.17	0.249433
$596$	38350.3	2.63572
$597$	−709.365	−0.0486304
$598$	52990.3	3.62364
$599$	−24968.7	−1.70316	−0.851581	−	0.524222i	$-0.824356\pi$
$599$	−24968.7	−1.70316	−0.851581	+	0.524222i	$0.824356\pi$
$600$	−9949.42	−0.676972
$601$	−10521.7	−0.714126	−0.357063	−	0.934080i	$-0.616222\pi$
$601$	−10521.7	−0.714126	−0.357063	+	0.934080i	$0.616222\pi$
$602$	20187.1	1.36672
$603$	21830.7	1.47432
$604$	−22416.5	−1.51013
$605$	823.138	0.0553145
$606$	6984.78	0.468213
$607$	−18150.6	−1.21369	−0.606845	−	0.794820i	$-0.707565\pi$
$607$	−18150.6	−1.21369	−0.606845	+	0.794820i	$0.707565\pi$
$608$	−968.390	−0.0645944
$609$	−1253.04	−0.0833754
$610$	6255.06	0.415180
$611$	−7640.76	−0.505911
$612$	55463.0	3.66333
$613$	3877.48	0.255481	0.127740	−	0.991808i	$-0.459228\pi$
$613$	3877.48	0.255481	0.127740	+	0.991808i	$0.459228\pi$
$614$	−5422.39	−0.356400
$615$	1017.77	0.0667322
$616$	−36021.8	−2.35610
$617$	−18471.8	−1.20526	−0.602630	−	0.798021i	$-0.705880\pi$
$617$	−18471.8	−1.20526	−0.602630	+	0.798021i	$0.705880\pi$
$618$	3675.52	0.239241
$619$	15308.9	0.994050	0.497025	−	0.867736i	$-0.334426\pi$
$619$	15308.9	0.994050	0.497025	+	0.867736i	$0.334426\pi$
$620$	−7764.29	−0.502938
$621$	13734.7	0.887527
$622$	−29829.0	−1.92288
$623$	−5272.20	−0.339047
$624$	11437.5	0.733763
$625$	14710.3	0.941456
$626$	−5382.92	−0.343682
$627$	554.021	0.0352878
$628$	−50961.1	−3.23817
$629$	−7777.24	−0.493003
$630$	−3339.68	−0.211200
$631$	−263.744	−0.0166395	−0.00831973	−	0.999965i	$-0.502648\pi$
$631$	−263.744	−0.0166395	−0.00831973	+	0.999965i	$0.502648\pi$
$632$	−6579.23	−0.414094
$633$	5328.22	0.334562
$634$	17324.1	1.08522
$635$	−1530.60	−0.0956533
$636$	813.364	0.0507107
$637$	2384.51	0.148317
$638$	−9132.05	−0.566679
$639$	3923.34	0.242887
$640$	2885.20	0.178199
$641$	8034.85	0.495098	0.247549	−	0.968875i	$-0.420375\pi$
$641$	8034.85	0.495098	0.247549	+	0.968875i	$0.420375\pi$
$642$	−1953.02	−0.120062
$643$	−26769.5	−1.64181	−0.820906	−	0.571064i	$-0.806531\pi$
$643$	−26769.5	−1.64181	−0.820906	+	0.571064i	$0.806531\pi$
$644$	−48309.6	−2.95600
$645$	−608.847	−0.0371680
$646$	5025.15	0.306055
$647$	3689.72	0.224200	0.112100	−	0.993697i	$-0.464242\pi$
$647$	3689.72	0.224200	0.112100	+	0.993697i	$0.464242\pi$
$648$	−23985.0	−1.45404
$649$	497.043	0.0300626
$650$	−41120.6	−2.48135
$651$	−8466.84	−0.509741
$652$	−33616.3	−2.01920
$653$	−10303.9	−0.617492	−0.308746	−	0.951145i	$-0.599909\pi$
$653$	−10303.9	−0.617492	−0.308746	+	0.951145i	$0.599909\pi$
$654$	−13366.8	−0.799211
$655$	−4318.82	−0.257634
$656$	−38563.0	−2.29517
$657$	−8191.90	−0.486448
$658$	10158.4	0.601846
$659$	−16434.5	−0.971469	−0.485734	−	0.874106i	$-0.661448\pi$
$659$	−16434.5	−0.971469	−0.485734	+	0.874106i	$0.661448\pi$
$660$	2005.63	0.118287
$661$	13518.2	0.795457	0.397729	−	0.917503i	$-0.369799\pi$
$661$	13518.2	0.795457	0.397729	+	0.917503i	$0.369799\pi$
$662$	−12299.2	−0.722087
$663$	−14921.3	−0.874049
$664$	−21472.1	−1.25494
$665$	−207.491	−0.0120995
$666$	7174.65	0.417435
$667$	−6634.16	−0.385121
$668$	−4768.12	−0.276174
$669$	6976.46	0.403177
$670$	7160.42	0.412882
$671$	34088.3	1.96120
$672$	−3822.92	−0.219453
$673$	4185.32	0.239721	0.119860	−	0.992791i	$-0.461755\pi$
$673$	4185.32	0.239721	0.119860	+	0.992791i	$0.461755\pi$
$674$	44914.9	2.56685
$675$	−10658.1	−0.607751
$676$	38861.6	2.21106
$677$	−12486.4	−0.708850	−0.354425	−	0.935085i	$-0.615323\pi$
$677$	−12486.4	−0.708850	−0.354425	+	0.935085i	$0.615323\pi$
$678$	6891.33	0.390354
$679$	−8737.42	−0.493831
$680$	9854.24	0.555725
$681$	−1042.68	−0.0586722
$682$	−61705.7	−3.46457
$683$	19311.0	1.08187	0.540934	−	0.841065i	$-0.318071\pi$
$683$	19311.0	1.08187	0.540934	+	0.841065i	$0.318071\pi$
$684$	−3178.88	−0.177701
$685$	765.075	0.0426744
$686$	−33499.1	−1.86443
$687$	5297.11	0.294174
$688$	23069.1	1.27835
$689$	1820.94	0.100685
$690$	2124.81	0.117232
$691$	−4867.15	−0.267952	−0.133976	−	0.990985i	$-0.542775\pi$
$691$	−4867.15	−0.267952	−0.133976	+	0.990985i	$0.542775\pi$
$692$	13173.2	0.723655
$693$	−18200.3	−0.997650
$694$	2418.31	0.132274
$695$	−1030.04	−0.0562183
$696$	−3410.81	−0.185756
$697$	50308.9	2.73398
$698$	−17691.9	−0.959379
$699$	−10058.7	−0.544283
$700$	37488.3	2.02418
$701$	−23448.0	−1.26337	−0.631684	−	0.775226i	$-0.717636\pi$
$701$	−23448.0	−1.26337	−0.631684	+	0.775226i	$0.717636\pi$
$702$	29184.5	1.56908
$703$	445.755	0.0239146
$704$	6967.39	0.373002
$705$	−306.379	−0.0163672
$706$	−9941.72	−0.529974
$707$	−14256.1	−0.758352
$708$	342.716	0.0181922
$709$	−6688.40	−0.354285	−0.177143	−	0.984185i	$-0.556685\pi$
$709$	−6688.40	−0.354285	−0.177143	+	0.984185i	$0.556685\pi$
$710$	1286.85	0.0680204
$711$	−3324.21	−0.175341
$712$	−14351.1	−0.755381
$713$	−44827.4	−2.35456
$714$	19837.8	1.03979
$715$	4490.16	0.234856
$716$	29371.1	1.53303
$717$	10358.3	0.539524
$718$	−55424.5	−2.88081
$719$	29729.3	1.54203	0.771013	−	0.636819i	$-0.219750\pi$
$719$	29729.3	1.54203	0.771013	+	0.636819i	$0.219750\pi$
$720$	−3816.48	−0.197544
$721$	−7501.81	−0.387492
$722$	34317.9	1.76895
$723$	55.1321	0.00283594
$724$	83136.0	4.26758
$725$	5148.11	0.263719
$726$	4510.62	0.230585
$727$	14217.0	0.725281	0.362641	−	0.931929i	$-0.381875\pi$
$727$	14217.0	0.725281	0.362641	+	0.931929i	$0.381875\pi$
$728$	−55605.2	−2.83086
$729$	−8122.04	−0.412642
$730$	−2686.93	−0.136230
$731$	−30095.7	−1.52275
$732$	23504.2	1.18680
$733$	−16997.9	−0.856526	−0.428263	−	0.903654i	$-0.640874\pi$
$733$	−16997.9	−0.856526	−0.428263	+	0.903654i	$0.640874\pi$
$734$	−26788.7	−1.34712
$735$	95.6142	0.00479835
$736$	−20240.3	−1.01368
$737$	39022.2	1.95034
$738$	−46410.9	−2.31492
$739$	−21767.0	−1.08351	−0.541755	−	0.840536i	$-0.682240\pi$
$739$	−21767.0	−1.08351	−0.541755	+	0.840536i	$0.682240\pi$
$740$	1613.69	0.0801629
$741$	855.218	0.0423984
$742$	−2420.93	−0.119778
$743$	16270.3	0.803366	0.401683	−	0.915779i	$-0.368425\pi$
$743$	16270.3	0.803366	0.401683	+	0.915779i	$0.368425\pi$
$744$	−23047.0	−1.13568
$745$	3442.72	0.169304
$746$	21561.7	1.05822
$747$	−10849.0	−0.531383
$748$	99139.7	4.84613
$749$	3986.15	0.194460
$750$	−3330.74	−0.162162
$751$	−614.520	−0.0298591	−0.0149295	−	0.999889i	$-0.504752\pi$
$751$	−614.520	−0.0298591	−0.0149295	+	0.999889i	$0.504752\pi$
$752$	11608.7	0.562931
$753$	−5742.77	−0.277926
$754$	−14096.7	−0.680866
$755$	−2012.34	−0.0970021
$756$	−26606.6	−1.27999
$757$	24728.6	1.18729	0.593644	−	0.804728i	$-0.297689\pi$
$757$	24728.6	1.18729	0.593644	+	0.804728i	$0.297689\pi$
$758$	9086.81	0.435419
$759$	11579.6	0.553771
$760$	−564.799	−0.0269571
$761$	−24442.2	−1.16430	−0.582148	−	0.813083i	$-0.697787\pi$
$761$	−24442.2	−1.16430	−0.582148	+	0.813083i	$0.697787\pi$
$762$	−8387.36	−0.398743
$763$	27282.0	1.29446
$764$	−32084.1	−1.51932
$765$	4978.93	0.235312
$766$	−22830.9	−1.07691
$767$	767.264	0.0361203
$768$	13608.5	0.639394
$769$	−25940.7	−1.21645	−0.608223	−	0.793767i	$-0.708117\pi$
$769$	−25940.7	−1.21645	−0.608223	+	0.793767i	$0.708117\pi$
$770$	−5969.65	−0.279391
$771$	−10282.7	−0.480316
$772$	63827.5	2.97565
$773$	25048.8	1.16552	0.582758	−	0.812645i	$-0.301973\pi$
$773$	25048.8	1.16552	0.582758	+	0.812645i	$0.301973\pi$
$774$	27763.9	1.28934
$775$	34786.1	1.61233
$776$	−23783.6	−1.10023
$777$	1759.71	0.0812473
$778$	49406.6	2.27675
$779$	−2883.47	−0.132620
$780$	3096.01	0.142122
$781$	7012.94	0.321310
$782$	105031.	4.80292
$783$	−3653.77	−0.166763
$784$	−3622.81	−0.165033
$785$	−4574.79	−0.208002
$786$	−23666.3	−1.07398
$787$	27185.2	1.23132	0.615658	−	0.788013i	$-0.288890\pi$
$787$	27185.2	1.23132	0.615658	+	0.788013i	$0.288890\pi$
$788$	−72645.2	−3.28411
$789$	13687.2	0.617589
$790$	−1090.33	−0.0491042
$791$	−14065.4	−0.632246
$792$	−49541.8	−2.22272
$793$	52620.6	2.35638
$794$	49579.9	2.21603
$795$	73.0160	0.00325737
$796$	7275.48	0.323961
$797$	−16387.9	−0.728345	−0.364172	−	0.931332i	$-0.618648\pi$
$797$	−16387.9	−0.728345	−0.364172	+	0.931332i	$0.618648\pi$
$798$	−1137.01	−0.0504382
$799$	−15144.5	−0.670556
$800$	15706.5	0.694136
$801$	−7251.02	−0.319853
$802$	57669.5	2.53913
$803$	−14643.0	−0.643511
$804$	26906.2	1.18023
$805$	−4336.77	−0.189877
$806$	−95252.5	−4.16269
$807$	−14252.1	−0.621682
$808$	−38805.5	−1.68957
$809$	−18195.2	−0.790740	−0.395370	−	0.918522i	$-0.629384\pi$
$809$	−18195.2	−0.790740	−0.395370	+	0.918522i	$0.629384\pi$
$810$	−3974.88	−0.172423
$811$	−8082.22	−0.349945	−0.174972	−	0.984573i	$-0.555984\pi$
$811$	−8082.22	−0.349945	−0.174972	+	0.984573i	$0.555984\pi$
$812$	12851.6	0.555420
$813$	2830.18	0.122089
$814$	12824.6	0.552215
$815$	−3017.75	−0.129702
$816$	22670.0	0.972560
$817$	1724.95	0.0738656
$818$	45868.8	1.96059
$819$	−28095.0	−1.19868
$820$	−10438.6	−0.444549
$821$	−5989.15	−0.254596	−0.127298	−	0.991865i	$-0.540630\pi$
$821$	−5989.15	−0.254596	−0.127298	+	0.991865i	$0.540630\pi$
$822$	4192.45	0.177894
$823$	2564.47	0.108617	0.0543086	−	0.998524i	$-0.482705\pi$
$823$	2564.47	0.108617	0.0543086	+	0.998524i	$0.482705\pi$
$824$	−20420.2	−0.863315
$825$	−8985.77	−0.379205
$826$	−1020.08	−0.0429697
$827$	30220.7	1.27071	0.635354	−	0.772221i	$-0.280854\pi$
$827$	30220.7	1.27071	0.635354	+	0.772221i	$0.280854\pi$
$828$	−66441.7	−2.78866
$829$	30705.4	1.28642	0.643210	−	0.765690i	$-0.277602\pi$
$829$	30705.4	1.28642	0.643210	+	0.765690i	$0.277602\pi$
$830$	−3558.44	−0.148813
$831$	8200.05	0.342306
$832$	10755.3	0.448163
$833$	4726.27	0.196585
$834$	−5644.42	−0.234353
$835$	−428.036	−0.0177399
$836$	−5682.22	−0.235076
$837$	−24688.7	−1.01955
$838$	−30050.1	−1.23874
$839$	16446.0	0.676732	0.338366	−	0.941015i	$-0.390126\pi$
$839$	16446.0	0.676732	0.338366	+	0.941015i	$0.390126\pi$
$840$	−2229.66	−0.0915840
$841$	−22624.1	−0.927637
$842$	56067.0	2.29477
$843$	8298.00	0.339025
$844$	−54648.0	−2.22875
$845$	3488.62	0.142026
$846$	13971.1	0.567774
$847$	−9206.28	−0.373473
$848$	−2766.57	−0.112033
$849$	1729.41	0.0699097
$850$	−81503.8	−3.28889
$851$	9316.71	0.375291
$852$	4835.49	0.194438
$853$	2581.38	0.103616	0.0518082	−	0.998657i	$-0.483502\pi$
$853$	2581.38	0.103616	0.0518082	+	0.998657i	$0.483502\pi$
$854$	−69958.9	−2.80321
$855$	−285.369	−0.0114145
$856$	10850.4	0.433248
$857$	43404.5	1.73007	0.865034	−	0.501714i	$-0.167297\pi$
$857$	43404.5	1.73007	0.865034	+	0.501714i	$0.167297\pi$
$858$	24605.1	0.979027
$859$	8446.36	0.335490	0.167745	−	0.985830i	$-0.446351\pi$
$859$	8446.36	0.335490	0.167745	+	0.985830i	$0.446351\pi$
$860$	6244.54	0.247601
$861$	−11383.1	−0.450562
$862$	84760.8	3.34915
$863$	13263.9	0.523183	0.261591	−	0.965179i	$-0.415753\pi$
$863$	13263.9	0.523183	0.261591	+	0.965179i	$0.415753\pi$
$864$	−11147.4	−0.438937
$865$	1182.56	0.0464836
$866$	17193.7	0.674671
$867$	−21213.5	−0.830968
$868$	86838.7	3.39573
$869$	−5942.00	−0.231954
$870$	−565.251	−0.0220274
$871$	60236.9	2.34334
$872$	74262.5	2.88400
$873$	−12016.8	−0.465875
$874$	−6019.86	−0.232980
$875$	6798.11	0.262649
$876$	−10096.5	−0.389416
$877$	−9795.56	−0.377164	−0.188582	−	0.982057i	$-0.560389\pi$
$877$	−9795.56	−0.377164	−0.188582	+	0.982057i	$0.560389\pi$
$878$	−32156.0	−1.23601
$879$	−7727.09	−0.296505
$880$	−6821.93	−0.261326
$881$	48139.3	1.84092	0.920462	−	0.390831i	$-0.127812\pi$
$881$	48139.3	1.84092	0.920462	+	0.390831i	$0.127812\pi$
$882$	−4360.08	−0.166453
$883$	−29850.5	−1.13766	−0.568828	−	0.822457i	$-0.692603\pi$
$883$	−29850.5	−1.13766	−0.568828	+	0.822457i	$0.692603\pi$
$884$	153038.	5.82264
$885$	30.7658	0.00116856
$886$	31287.2	1.18636
$887$	26495.4	1.00297	0.501483	−	0.865168i	$-0.332788\pi$
$887$	26495.4	1.00297	0.501483	+	0.865168i	$0.332788\pi$
$888$	4789.99	0.181015
$889$	17118.8	0.645832
$890$	−2378.32	−0.0895746
$891$	−21661.9	−0.814480
$892$	−71552.9	−2.68584
$893$	868.013	0.0325274
$894$	18865.4	0.705765
$895$	2636.66	0.0984734
$896$	−32269.1	−1.20316
$897$	17874.9	0.665357
$898$	19201.0	0.713526
$899$	11925.2	0.442411
$900$	51558.8	1.90959
$901$	3609.23	0.133453
$902$	−82959.1	−3.06235
$903$	6809.57	0.250951
$904$	−38286.4	−1.40861
$905$	7463.15	0.274125
$906$	−11027.2	−0.404365
$907$	18837.1	0.689611	0.344806	−	0.938674i	$-0.387945\pi$
$907$	18837.1	0.689611	0.344806	+	0.938674i	$0.387945\pi$
$908$	10694.1	0.390856
$909$	−19606.8	−0.715420
$910$	−9215.09	−0.335689
$911$	−845.098	−0.0307347	−0.0153674	−	0.999882i	$-0.504892\pi$
$911$	−845.098	−0.0307347	−0.0153674	+	0.999882i	$0.504892\pi$
$912$	−1299.34	−0.0471770
$913$	−19392.4	−0.702953
$914$	−48884.3	−1.76909
$915$	2109.98	0.0762336
$916$	−54328.9	−1.95969
$917$	48303.3	1.73949
$918$	57845.7	2.07973
$919$	29499.9	1.05888	0.529441	−	0.848347i	$-0.322402\pi$
$919$	29499.9	1.05888	0.529441	+	0.848347i	$0.322402\pi$
$920$	−11804.8	−0.423037
$921$	−1829.10	−0.0654407
$922$	−92919.2	−3.31902
$923$	10825.6	0.386054
$924$	−22431.7	−0.798647
$925$	−7229.78	−0.256988
$926$	50259.2	1.78361
$927$	−10317.5	−0.365556
$928$	5384.42	0.190466
$929$	−30933.8	−1.09247	−0.546235	−	0.837632i	$-0.683939\pi$
$929$	−30933.8	−1.09247	−0.546235	+	0.837632i	$0.683939\pi$
$930$	−3819.43	−0.134671
$931$	−270.888	−0.00953597
$932$	103165.	3.62584
$933$	−10062.0	−0.353072
$934$	−5421.27	−0.189924
$935$	8899.81	0.311289
$936$	−76475.5	−2.67060
$937$	28664.5	0.999391	0.499696	−	0.866201i	$-0.333445\pi$
$937$	28664.5	0.999391	0.499696	+	0.866201i	$0.333445\pi$
$938$	−80084.8	−2.78770
$939$	−1815.79	−0.0631054
$940$	3142.33	0.109033
$941$	16621.5	0.575820	0.287910	−	0.957657i	$-0.407040\pi$
$941$	16621.5	0.575820	0.287910	+	0.957657i	$0.407040\pi$
$942$	−25068.9	−0.867081
$943$	−60267.3	−2.08120
$944$	−1165.71	−0.0401913
$945$	−2388.48	−0.0822194
$946$	49627.7	1.70564
$947$	−42527.4	−1.45930	−0.729649	−	0.683822i	$-0.760316\pi$
$947$	−42527.4	−1.45930	−0.729649	+	0.683822i	$0.760316\pi$
$948$	−4097.06	−0.140365
$949$	−22603.7	−0.773180
$950$	4671.42	0.159538
$951$	5843.83	0.199263
$952$	−110213.	−3.75214
$953$	−7787.98	−0.264719	−0.132360	−	0.991202i	$-0.542255\pi$
$953$	−7787.98	−0.264719	−0.132360	+	0.991202i	$0.542255\pi$
$954$	−3329.58	−0.112997
$955$	−2880.20	−0.0975928
$956$	−106238.	−3.59414
$957$	−3080.46	−0.104051
$958$	95337.1	3.21524
$959$	−8556.88	−0.288129
$960$	431.264	0.0144989
$961$	50788.2	1.70482
$962$	19796.8	0.663488
$963$	5482.27	0.183452
$964$	−565.454	−0.0188922
$965$	5729.82	0.191139
$966$	−23764.6	−0.791526
$967$	9599.75	0.319242	0.159621	−	0.987178i	$-0.448973\pi$
$967$	9599.75	0.319242	0.159621	+	0.987178i	$0.448973\pi$
$968$	−25059.8	−0.832080
$969$	1695.10	0.0561966
$970$	−3941.50	−0.130468
$971$	−7776.52	−0.257014	−0.128507	−	0.991709i	$-0.541018\pi$
$971$	−7776.52	−0.257014	−0.128507	+	0.991709i	$0.541018\pi$
$972$	−55926.2	−1.84551
$973$	11520.4	0.379575
$974$	−80967.6	−2.66362
$975$	−13870.9	−0.455616
$976$	−79946.8	−2.62196
$977$	24790.9	0.811802	0.405901	−	0.913917i	$-0.366958\pi$
$977$	24790.9	0.811802	0.405901	+	0.913917i	$0.366958\pi$
$978$	−16536.6	−0.540678
$979$	−12961.1	−0.423126
$980$	−980.651	−0.0319651
$981$	37521.7	1.22118
$982$	26941.7	0.875502
$983$	−53831.6	−1.74666	−0.873328	−	0.487133i	$-0.838043\pi$
$983$	−53831.6	−1.74666	−0.873328	+	0.487133i	$0.838043\pi$
$984$	−30985.2	−1.00383
$985$	−6521.39	−0.210953
$986$	−27940.7	−0.902449
$987$	3426.66	0.110508
$988$	−8771.40	−0.282445
$989$	36053.0	1.15917
$990$	−8210.24	−0.263574
$991$	−39184.2	−1.25603	−0.628015	−	0.778201i	$-0.716132\pi$
$991$	−39184.2	−1.25603	−0.628015	+	0.778201i	$0.716132\pi$
$992$	36382.9	1.16447
$993$	−4148.81	−0.132587
$994$	−14392.6	−0.459260
$995$	653.123	0.0208094
$996$	−13371.3	−0.425387
$997$	49413.4	1.56965	0.784823	−	0.619720i	$-0.212754\pi$
$997$	49413.4	1.56965	0.784823	+	0.619720i	$0.212754\pi$
$998$	−35586.9	−1.12874
$999$	5131.19	0.162506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.b.1.5	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.b.1.5	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-5.04533 q^{2} -1.70191 q^{3} +17.4553 q^{4} +1.56697 q^{5} +8.58669 q^{6} -17.5256 q^{7} -47.7054 q^{8} -24.1035 q^{9} +O(q^{10})\)	\(q-5.04533 q^{2} -1.70191 q^{3} +17.4553 q^{4} +1.56697 q^{5} +8.58669 q^{6} -17.5256 q^{7} -47.7054 q^{8} -24.1035 q^{9} -7.90590 q^{10} -43.0848 q^{11} -29.7074 q^{12} -66.5082 q^{13} +88.4225 q^{14} -2.66685 q^{15} +101.046 q^{16} -131.824 q^{17} +121.610 q^{18} +7.55553 q^{19} +27.3521 q^{20} +29.8270 q^{21} +217.377 q^{22} +157.918 q^{23} +81.1902 q^{24} -122.545 q^{25} +335.556 q^{26} +86.9735 q^{27} -305.916 q^{28} -42.0101 q^{29} +13.4551 q^{30} -283.865 q^{31} -128.170 q^{32} +73.3265 q^{33} +665.095 q^{34} -27.4622 q^{35} -420.735 q^{36} +58.9971 q^{37} -38.1201 q^{38} +113.191 q^{39} -74.7530 q^{40} -381.637 q^{41} -150.487 q^{42} +228.302 q^{43} -752.061 q^{44} -37.7696 q^{45} -796.748 q^{46} +114.884 q^{47} -171.972 q^{48} -35.8529 q^{49} +618.278 q^{50} +224.352 q^{51} -1160.92 q^{52} -27.3791 q^{53} -438.810 q^{54} -67.5128 q^{55} +836.065 q^{56} -12.8588 q^{57} +211.955 q^{58} -11.5364 q^{59} -46.5507 q^{60} -791.189 q^{61} +1432.19 q^{62} +422.429 q^{63} -161.713 q^{64} -104.217 q^{65} -369.956 q^{66} -905.706 q^{67} -2301.03 q^{68} -268.762 q^{69} +138.556 q^{70} -162.771 q^{71} +1149.87 q^{72} +339.863 q^{73} -297.660 q^{74} +208.560 q^{75} +131.884 q^{76} +755.088 q^{77} -571.086 q^{78} +137.914 q^{79} +158.337 q^{80} +502.774 q^{81} +1925.48 q^{82} +450.099 q^{83} +520.641 q^{84} -206.565 q^{85} -1151.86 q^{86} +71.4974 q^{87} +2055.38 q^{88} +300.828 q^{89} +190.560 q^{90} +1165.60 q^{91} +2756.51 q^{92} +483.112 q^{93} -579.630 q^{94} +11.8393 q^{95} +218.133 q^{96} +498.552 q^{97} +180.890 q^{98} +1038.50 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9 + 120 * q^10 + 139 * q^11 + 309 * q^12 + 343 * q^13 + 239 * q^14 + 194 * q^15 + 1346 * q^16 + 842 * q^17 + 423 * q^18 + 157 * q^19 + 1292 * q^20 + 434 * q^21 + 436 * q^22 + 1004 * q^23 + 935 * q^24 + 2206 * q^25 + 812 * q^26 + 1282 * q^27 + 584 * q^28 + 1459 * q^29 + 146 * q^30 + 582 * q^31 + 1428 * q^32 + 1080 * q^33 + 393 * q^34 + 1006 * q^35 + 2996 * q^36 + 1477 * q^37 + 1873 * q^38 + 626 * q^39 + 1272 * q^40 + 1112 * q^41 + 1812 * q^42 + 833 * q^43 + 1392 * q^44 + 3841 * q^45 + 782 * q^46 + 2484 * q^47 + 2034 * q^48 + 4727 * q^49 + 1248 * q^50 + 932 * q^51 + 2118 * q^52 + 5077 * q^53 + 1537 * q^54 + 1736 * q^55 + 2281 * q^56 + 1426 * q^57 + 992 * q^58 + 2977 * q^59 + 1418 * q^60 + 3363 * q^61 + 3438 * q^62 + 3194 * q^63 + 6138 * q^64 + 4640 * q^65 + 288 * q^66 + 955 * q^67 + 8553 * q^68 + 4440 * q^69 + 2203 * q^70 + 2458 * q^71 + 4495 * q^72 + 3724 * q^73 + 2099 * q^74 + 4491 * q^75 + 2260 * q^76 + 9774 * q^77 + 1057 * q^78 + 1638 * q^79 + 8221 * q^80 + 10151 * q^81 + 1018 * q^82 + 6121 * q^83 + 4847 * q^84 + 3836 * q^85 + 2305 * q^86 + 3894 * q^87 + 5815 * q^88 + 8110 * q^89 + 4951 * q^90 + 2312 * q^91 + 13138 * q^92 + 9250 * q^93 - 813 * q^94 + 4858 * q^95 + 6882 * q^96 + 4486 * q^97 + 4216 * q^98 + 4969 * q^99

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