LMFDB - Embedded newform 547.4.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-3.45260 q^{2} -9.18913 q^{3} +3.92046 q^{4} -10.5912 q^{5} +31.7264 q^{6} +24.4389 q^{7} +14.0850 q^{8} +57.4401 q^{9} +O(q^{10})$	\(q-3.45260 q^{2} -9.18913 q^{3} +3.92046 q^{4} -10.5912 q^{5} +31.7264 q^{6} +24.4389 q^{7} +14.0850 q^{8} +57.4401 q^{9} +36.5672 q^{10} +53.8612 q^{11} -36.0256 q^{12} +20.5683 q^{13} -84.3778 q^{14} +97.3239 q^{15} -79.9937 q^{16} +89.6360 q^{17} -198.318 q^{18} +114.256 q^{19} -41.5224 q^{20} -224.572 q^{21} -185.961 q^{22} +58.3622 q^{23} -129.429 q^{24} -12.8266 q^{25} -71.0143 q^{26} -279.718 q^{27} +95.8118 q^{28} +162.264 q^{29} -336.021 q^{30} +88.0853 q^{31} +163.506 q^{32} -494.937 q^{33} -309.477 q^{34} -258.837 q^{35} +225.192 q^{36} +171.187 q^{37} -394.480 q^{38} -189.005 q^{39} -149.177 q^{40} -148.329 q^{41} +775.359 q^{42} +406.693 q^{43} +211.161 q^{44} -608.360 q^{45} -201.502 q^{46} +271.444 q^{47} +735.072 q^{48} +254.260 q^{49} +44.2852 q^{50} -823.677 q^{51} +80.6373 q^{52} +260.148 q^{53} +965.756 q^{54} -570.454 q^{55} +344.222 q^{56} -1049.91 q^{57} -560.233 q^{58} +803.105 q^{59} +381.554 q^{60} +64.9987 q^{61} -304.123 q^{62} +1403.77 q^{63} +75.4277 q^{64} -217.843 q^{65} +1708.82 q^{66} -790.651 q^{67} +351.414 q^{68} -536.298 q^{69} +893.662 q^{70} -520.742 q^{71} +809.046 q^{72} -43.4131 q^{73} -591.040 q^{74} +117.866 q^{75} +447.936 q^{76} +1316.31 q^{77} +652.559 q^{78} +205.063 q^{79} +847.228 q^{80} +1019.49 q^{81} +512.121 q^{82} +72.3656 q^{83} -880.427 q^{84} -949.352 q^{85} -1404.15 q^{86} -1491.06 q^{87} +758.636 q^{88} +148.320 q^{89} +2100.42 q^{90} +502.667 q^{91} +228.807 q^{92} -809.427 q^{93} -937.187 q^{94} -1210.11 q^{95} -1502.48 q^{96} -1243.32 q^{97} -877.858 q^{98} +3093.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.45260	−1.22068	−0.610340	−	0.792140i	$-0.708967\pi$
$2$	−3.45260	−1.22068	−0.610340	+	0.792140i	$0.708967\pi$
$3$	−9.18913	−1.76845	−0.884225	−	0.467062i	$-0.845312\pi$
$3$	−9.18913	−1.76845	−0.884225	+	0.467062i	$0.845312\pi$
$4$	3.92046	0.490058
$5$	−10.5912	−0.947305	−0.473653	−	0.880712i	$-0.657065\pi$
$5$	−10.5912	−0.947305	−0.473653	+	0.880712i	$0.657065\pi$
$6$	31.7264	2.15871
$7$	24.4389	1.31958	0.659788	−	0.751452i	$-0.270646\pi$
$7$	24.4389	1.31958	0.659788	+	0.751452i	$0.270646\pi$
$8$	14.0850	0.622476
$9$	57.4401	2.12741
$10$	36.5672	1.15636
$11$	53.8612	1.47634	0.738171	−	0.674614i	$-0.235690\pi$
$11$	53.8612	1.47634	0.738171	+	0.674614i	$0.235690\pi$
$12$	−36.0256	−0.866642
$13$	20.5683	0.438818	0.219409	−	0.975633i	$-0.429587\pi$
$13$	20.5683	0.438818	0.219409	+	0.975633i	$0.429587\pi$
$14$	−84.3778	−1.61078
$15$	97.3239	1.67526
$16$	−79.9937	−1.24990
$17$	89.6360	1.27882	0.639409	−	0.768867i	$-0.279179\pi$
$17$	89.6360	1.27882	0.639409	+	0.768867i	$0.279179\pi$
$18$	−198.318	−2.59689
$19$	114.256	1.37958	0.689792	−	0.724008i	$-0.257702\pi$
$19$	114.256	1.37958	0.689792	+	0.724008i	$0.257702\pi$
$20$	−41.5224	−0.464234
$21$	−224.572	−2.33360
$22$	−185.961	−1.80214
$23$	58.3622	0.529103	0.264551	−	0.964372i	$-0.414776\pi$
$23$	58.3622	0.529103	0.264551	+	0.964372i	$0.414776\pi$
$24$	−129.429	−1.10082
$25$	−12.8266	−0.102613
$26$	−71.0143	−0.535655
$27$	−279.718	−1.99377
$28$	95.8118	0.646669
$29$	162.264	1.03902	0.519511	−	0.854464i	$-0.326114\pi$
$29$	162.264	1.03902	0.519511	+	0.854464i	$0.326114\pi$
$30$	−336.021	−2.04496
$31$	88.0853	0.510341	0.255171	−	0.966896i	$-0.417868\pi$
$31$	88.0853	0.510341	0.255171	+	0.966896i	$0.417868\pi$
$32$	163.506	0.903252
$33$	−494.937	−2.61083
$34$	−309.477	−1.56103
$35$	−258.837	−1.25004
$36$	225.192	1.04255
$37$	171.187	0.760620	0.380310	−	0.924859i	$-0.375817\pi$
$37$	171.187	0.760620	0.380310	+	0.924859i	$0.375817\pi$
$38$	−394.480	−1.68403
$39$	−189.005	−0.776026
$40$	−149.177	−0.589675
$41$	−148.329	−0.565002	−0.282501	−	0.959267i	$-0.591164\pi$
$41$	−148.329	−0.565002	−0.282501	+	0.959267i	$0.591164\pi$
$42$	775.359	2.84858
$43$	406.693	1.44233	0.721164	−	0.692765i	$-0.243608\pi$
$43$	406.693	1.44233	0.721164	+	0.692765i	$0.243608\pi$
$44$	211.161	0.723492
$45$	−608.360	−2.01531
$46$	−201.502	−0.645865
$47$	271.444	0.842429	0.421214	−	0.906961i	$-0.361604\pi$
$47$	271.444	0.842429	0.421214	+	0.906961i	$0.361604\pi$
$48$	735.072	2.21039
$49$	254.260	0.741282
$50$	44.2852	0.125258
$51$	−823.677	−2.26153
$52$	80.6373	0.215046
$53$	260.148	0.674227	0.337114	−	0.941464i	$-0.390549\pi$
$53$	260.148	0.674227	0.337114	+	0.941464i	$0.390549\pi$
$54$	965.756	2.43375
$55$	−570.454	−1.39855
$56$	344.222	0.821405
$57$	−1049.91	−2.43972
$58$	−560.233	−1.26831
$59$	803.105	1.77213	0.886063	−	0.463566i	$-0.153430\pi$
$59$	803.105	1.77213	0.886063	+	0.463566i	$0.153430\pi$
$60$	381.554	0.820975
$61$	64.9987	0.136430	0.0682150	−	0.997671i	$-0.478270\pi$
$61$	64.9987	0.136430	0.0682150	+	0.997671i	$0.478270\pi$
$62$	−304.123	−0.622963
$63$	1403.77	2.80728
$64$	75.4277	0.147320
$65$	−217.843	−0.415694
$66$	1708.82	3.18699
$67$	−790.651	−1.44169	−0.720846	−	0.693095i	$-0.756246\pi$
$67$	−790.651	−1.44169	−0.720846	+	0.693095i	$0.756246\pi$
$68$	351.414	0.626695
$69$	−536.298	−0.935692
$70$	893.662	1.52590
$71$	−520.742	−0.870433	−0.435216	−	0.900326i	$-0.643328\pi$
$71$	−520.742	−0.870433	−0.435216	+	0.900326i	$0.643328\pi$
$72$	809.046	1.32426
$73$	−43.4131	−0.0696044	−0.0348022	−	0.999394i	$-0.511080\pi$
$73$	−43.4131	−0.0696044	−0.0348022	+	0.999394i	$0.511080\pi$
$74$	−591.040	−0.928474
$75$	117.866	0.181466
$76$	447.936	0.676075
$77$	1316.31	1.94815
$78$	652.559	0.947279
$79$	205.063	0.292043	0.146022	−	0.989281i	$-0.453353\pi$
$79$	205.063	0.292043	0.146022	+	0.989281i	$0.453353\pi$
$80$	847.228	1.18404
$81$	1019.49	1.39847
$82$	512.121	0.689686
$83$	72.3656	0.0957007	0.0478504	−	0.998855i	$-0.484763\pi$
$83$	72.3656	0.0957007	0.0478504	+	0.998855i	$0.484763\pi$
$84$	−880.427	−1.14360
$85$	−949.352	−1.21143
$86$	−1404.15	−1.76062
$87$	−1491.06	−1.83746
$88$	758.636	0.918987
$89$	148.320	0.176650	0.0883249	−	0.996092i	$-0.471849\pi$
$89$	148.320	0.176650	0.0883249	+	0.996092i	$0.471849\pi$
$90$	2100.42	2.46005
$91$	502.667	0.579053
$92$	228.807	0.259291
$93$	−809.427	−0.902513
$94$	−937.187	−1.02834
$95$	−1210.11	−1.30689
$96$	−1502.48	−1.59736
$97$	−1243.32	−1.30144	−0.650722	−	0.759316i	$-0.725534\pi$
$97$	−1243.32	−1.30144	−0.650722	+	0.759316i	$0.725534\pi$
$98$	−877.858	−0.904868
$99$	3093.79	3.14079
$100$	−50.2863	−0.0502863
$101$	−161.485	−0.159093	−0.0795465	−	0.996831i	$-0.525347\pi$
$101$	−161.485	−0.159093	−0.0795465	+	0.996831i	$0.525347\pi$
$102$	2843.83	2.76060
$103$	722.218	0.690896	0.345448	−	0.938438i	$-0.387727\pi$
$103$	722.218	0.690896	0.345448	+	0.938438i	$0.387727\pi$
$104$	289.705	0.273153
$105$	2378.49	2.21064
$106$	−898.187	−0.823015
$107$	1093.97	0.988393	0.494196	−	0.869350i	$-0.335462\pi$
$107$	1093.97	0.988393	0.494196	+	0.869350i	$0.335462\pi$
$108$	−1096.63	−0.977063
$109$	−2245.65	−1.97335	−0.986673	−	0.162717i	$-0.947974\pi$
$109$	−2245.65	−1.97335	−0.986673	+	0.162717i	$0.947974\pi$
$110$	1969.55	1.70718
$111$	−1573.06	−1.34512
$112$	−1954.96	−1.64934
$113$	1981.18	1.64933	0.824663	−	0.565624i	$-0.191364\pi$
$113$	1981.18	1.64933	0.824663	+	0.565624i	$0.191364\pi$
$114$	3624.93	2.97812
$115$	−618.126	−0.501222
$116$	636.150	0.509181
$117$	1181.45	0.933546
$118$	−2772.80	−2.16320
$119$	2190.60	1.68750
$120$	1370.81	1.04281
$121$	1570.03	1.17958
$122$	−224.415	−0.166537
$123$	1363.01	0.999177
$124$	345.335	0.250097
$125$	1459.75	1.04451
$126$	−4846.67	−3.42679
$127$	−1291.60	−0.902449	−0.451224	−	0.892411i	$-0.649013\pi$
$127$	−1291.60	−0.902449	−0.451224	+	0.892411i	$0.649013\pi$
$128$	−1568.47	−1.08308
$129$	−3737.15	−2.55068
$130$	752.126	0.507429
$131$	1822.75	1.21568	0.607840	−	0.794059i	$-0.292036\pi$
$131$	1822.75	1.21568	0.607840	+	0.794059i	$0.292036\pi$
$132$	−1940.38	−1.27946
$133$	2792.29	1.82047
$134$	2729.80	1.75984
$135$	2962.55	1.88871
$136$	1262.52	0.796034
$137$	508.753	0.317268	0.158634	−	0.987337i	$-0.449291\pi$
$137$	508.753	0.317268	0.158634	+	0.987337i	$0.449291\pi$
$138$	1851.62	1.14218
$139$	−55.6432	−0.0339539	−0.0169770	−	0.999856i	$-0.505404\pi$
$139$	−55.6432	−0.0339539	−0.0169770	+	0.999856i	$0.505404\pi$
$140$	−1014.76	−0.612593
$141$	−2494.33	−1.48979
$142$	1797.92	1.06252
$143$	1107.83	0.647844
$144$	−4594.85	−2.65905
$145$	−1718.57	−0.984271
$146$	149.888	0.0849646
$147$	−2336.43	−1.31092
$148$	671.132	0.372748
$149$	−2945.03	−1.61923	−0.809617	−	0.586958i	$-0.800325\pi$
$149$	−2945.03	−1.61923	−0.809617	+	0.586958i	$0.800325\pi$
$150$	−406.943	−0.221512
$151$	−2137.42	−1.15193	−0.575964	−	0.817475i	$-0.695373\pi$
$151$	−2137.42	−1.15193	−0.575964	+	0.817475i	$0.695373\pi$
$152$	1609.30	0.858757
$153$	5148.70	2.72057
$154$	−4544.69	−2.37806
$155$	−932.928	−0.483449
$156$	−740.987	−0.380298
$157$	3774.62	1.91877	0.959387	−	0.282092i	$-0.0910284\pi$
$157$	3774.62	1.91877	0.959387	+	0.282092i	$0.0910284\pi$
$158$	−708.002	−0.356491
$159$	−2390.53	−1.19234
$160$	−1731.73	−0.855656
$161$	1426.31	0.698192
$162$	−3519.88	−1.70708
$163$	−1910.66	−0.918125	−0.459063	−	0.888404i	$-0.651815\pi$
$163$	−1910.66	−0.918125	−0.459063	+	0.888404i	$0.651815\pi$
$164$	−581.518	−0.276884
$165$	5241.98	2.47326
$166$	−249.850	−0.116820
$167$	3055.42	1.41578	0.707890	−	0.706323i	$-0.249647\pi$
$167$	3055.42	1.41578	0.707890	+	0.706323i	$0.249647\pi$
$168$	−3163.11	−1.45261
$169$	−1773.94	−0.807439
$170$	3277.73	1.47877
$171$	6562.87	2.93494
$172$	1594.42	0.706824
$173$	−2988.48	−1.31335	−0.656675	−	0.754174i	$-0.728038\pi$
$173$	−2988.48	−1.31335	−0.656675	+	0.754174i	$0.728038\pi$
$174$	5148.05	2.24295
$175$	−313.469	−0.135406
$176$	−4308.55	−1.84528
$177$	−7379.84	−3.13391
$178$	−512.088	−0.215633
$179$	−4506.13	−1.88158	−0.940792	−	0.338983i	$-0.889917\pi$
$179$	−4506.13	−1.88158	−0.940792	+	0.338983i	$0.889917\pi$
$180$	−2385.05	−0.987617
$181$	2516.70	1.03351	0.516754	−	0.856134i	$-0.327140\pi$
$181$	2516.70	1.03351	0.516754	+	0.856134i	$0.327140\pi$
$182$	−1735.51	−0.706838
$183$	−597.282	−0.241270
$184$	822.033	0.329354
$185$	−1813.07	−0.720540
$186$	2794.63	1.10168
$187$	4827.90	1.88797
$188$	1064.18	0.412839
$189$	−6836.01	−2.63093
$190$	4178.01	1.59529
$191$	−2620.37	−0.992687	−0.496343	−	0.868126i	$-0.665324\pi$
$191$	−2620.37	−0.992687	−0.496343	+	0.868126i	$0.665324\pi$
$192$	−693.115	−0.260527
$193$	−522.589	−0.194906	−0.0974529	−	0.995240i	$-0.531070\pi$
$193$	−522.589	−0.194906	−0.0974529	+	0.995240i	$0.531070\pi$
$194$	4292.69	1.58865
$195$	2001.79	0.735134
$196$	996.816	0.363271
$197$	54.8011	0.0198194	0.00990969	−	0.999951i	$-0.496846\pi$
$197$	54.8011	0.0198194	0.00990969	+	0.999951i	$0.496846\pi$
$198$	−10681.6	−3.83389
$199$	−4495.89	−1.60153	−0.800766	−	0.598977i	$-0.795574\pi$
$199$	−4495.89	−1.60153	−0.800766	+	0.598977i	$0.795574\pi$
$200$	−180.663	−0.0638741
$201$	7265.39	2.54956
$202$	557.545	0.194202
$203$	3965.55	1.37107
$204$	−3229.19	−1.10828
$205$	1570.98	0.535229
$206$	−2493.53	−0.843362
$207$	3352.33	1.12562
$208$	−1645.34	−0.548479
$209$	6153.95	2.03674
$210$	−8211.97	−2.69848
$211$	−993.185	−0.324046	−0.162023	−	0.986787i	$-0.551802\pi$
$211$	−993.185	−0.324046	−0.162023	+	0.986787i	$0.551802\pi$
$212$	1019.90	0.330410
$213$	4785.17	1.53932
$214$	−3777.04	−1.20651
$215$	−4307.36	−1.36632
$216$	−3939.84	−1.24107
$217$	2152.71	0.673435
$218$	7753.35	2.40882
$219$	398.929	0.123092
$220$	−2236.44	−0.685368
$221$	1843.66	0.561168
$222$	5431.15	1.64196
$223$	−3188.57	−0.957499	−0.478749	−	0.877952i	$-0.658910\pi$
$223$	−3188.57	−0.957499	−0.478749	+	0.877952i	$0.658910\pi$
$224$	3995.91	1.19191
$225$	−736.763	−0.218300
$226$	−6840.23	−2.01330
$227$	18.1162	0.00529697	0.00264848	−	0.999996i	$-0.499157\pi$
$227$	18.1162	0.00529697	0.00264848	+	0.999996i	$0.499157\pi$
$228$	−4116.14	−1.19561
$229$	4098.61	1.18272	0.591361	−	0.806407i	$-0.298591\pi$
$229$	4098.61	1.18272	0.591361	+	0.806407i	$0.298591\pi$
$230$	2134.14	0.611831
$231$	−12095.7	−3.44520
$232$	2285.49	0.646767
$233$	3738.45	1.05113	0.525567	−	0.850752i	$-0.323853\pi$
$233$	3738.45	1.05113	0.525567	+	0.850752i	$0.323853\pi$
$234$	−4079.07	−1.13956
$235$	−2874.91	−0.798037
$236$	3148.54	0.868444
$237$	−1884.35	−0.516463
$238$	−7563.29	−2.05989
$239$	463.824	0.125533	0.0627663	−	0.998028i	$-0.480008\pi$
$239$	463.824	0.125533	0.0627663	+	0.998028i	$0.480008\pi$
$240$	−7785.29	−2.09391
$241$	−1142.95	−0.305493	−0.152746	−	0.988265i	$-0.548812\pi$
$241$	−1142.95	−0.305493	−0.152746	+	0.988265i	$0.548812\pi$
$242$	−5420.68	−1.43989
$243$	−1815.79	−0.479353
$244$	254.825	0.0668586
$245$	−2692.92	−0.702221
$246$	−4705.94	−1.21967
$247$	2350.05	0.605385
$248$	1240.68	0.317675
$249$	−664.977	−0.169242
$250$	−5039.93	−1.27501
$251$	−4385.44	−1.10282	−0.551408	−	0.834236i	$-0.685909\pi$
$251$	−4385.44	−1.10282	−0.551408	+	0.834236i	$0.685909\pi$
$252$	5503.44	1.37573
$253$	3143.46	0.781137
$254$	4459.38	1.10160
$255$	8723.72	2.14235
$256$	4811.88	1.17478
$257$	−729.523	−0.177068	−0.0885339	−	0.996073i	$-0.528218\pi$
$257$	−729.523	−0.177068	−0.0885339	+	0.996073i	$0.528218\pi$
$258$	12902.9	3.11356
$259$	4183.62	1.00370
$260$	−854.046	−0.203714
$261$	9320.46	2.21043
$262$	−6293.22	−1.48396
$263$	1879.07	0.440565	0.220283	−	0.975436i	$-0.429302\pi$
$263$	1879.07	0.440565	0.220283	+	0.975436i	$0.429302\pi$
$264$	−6971.20	−1.62518
$265$	−2755.28	−0.638699
$266$	−9640.66	−2.22221
$267$	−1362.93	−0.312396
$268$	−3099.72	−0.706512
$269$	−1600.96	−0.362871	−0.181436	−	0.983403i	$-0.558074\pi$
$269$	−1600.96	−0.362871	−0.181436	+	0.983403i	$0.558074\pi$
$270$	−10228.5	−2.30551
$271$	−3068.83	−0.687889	−0.343945	−	0.938990i	$-0.611763\pi$
$271$	−3068.83	−0.687889	−0.343945	+	0.938990i	$0.611763\pi$
$272$	−7170.31	−1.59840
$273$	−4619.08	−1.02403
$274$	−1756.52	−0.387282
$275$	−690.857	−0.151492
$276$	−2102.54	−0.458543
$277$	−5158.26	−1.11888	−0.559440	−	0.828871i	$-0.688984\pi$
$277$	−5158.26	−1.11888	−0.559440	+	0.828871i	$0.688984\pi$
$278$	192.114	0.0414468
$279$	5059.63	1.08571
$280$	−3645.73	−0.778121
$281$	−4286.54	−0.910013	−0.455007	−	0.890488i	$-0.650363\pi$
$281$	−4286.54	−0.910013	−0.455007	+	0.890488i	$0.650363\pi$
$282$	8611.94	1.81856
$283$	−1266.89	−0.266108	−0.133054	−	0.991109i	$-0.542478\pi$
$283$	−1266.89	−0.266108	−0.133054	+	0.991109i	$0.542478\pi$
$284$	−2041.55	−0.426562
$285$	11119.8	2.31116
$286$	−3824.91	−0.790810
$287$	−3624.99	−0.745563
$288$	9391.81	1.92159
$289$	3121.61	0.635377
$290$	5933.53	1.20148
$291$	11425.0	2.30154
$292$	−170.199	−0.0341102
$293$	7779.80	1.55120	0.775599	−	0.631226i	$-0.217448\pi$
$293$	7779.80	1.55120	0.775599	+	0.631226i	$0.217448\pi$
$294$	8066.75	1.60021
$295$	−8505.84	−1.67874
$296$	2411.17	0.473468
$297$	−15066.0	−2.94349
$298$	10168.0	1.97657
$299$	1200.41	0.232180
$300$	462.087	0.0889287
$301$	9939.12	1.90326
$302$	7379.67	1.40613
$303$	1483.91	0.281348
$304$	−9139.74	−1.72434
$305$	−688.414	−0.129241
$306$	−17776.4	−3.32095
$307$	−1595.63	−0.296637	−0.148319	−	0.988940i	$-0.547386\pi$
$307$	−1595.63	−0.296637	−0.148319	+	0.988940i	$0.547386\pi$
$308$	5160.53	0.954704
$309$	−6636.55	−1.22181
$310$	3221.03	0.590136
$311$	5381.62	0.981234	0.490617	−	0.871375i	$-0.336771\pi$
$311$	5381.62	0.981234	0.490617	+	0.871375i	$0.336771\pi$
$312$	−2662.14	−0.483058
$313$	2529.70	0.456827	0.228414	−	0.973564i	$-0.426646\pi$
$313$	2529.70	0.456827	0.228414	+	0.973564i	$0.426646\pi$
$314$	−13032.3	−2.34221
$315$	−14867.6	−2.65935
$316$	803.942	0.143118
$317$	10900.3	1.93131	0.965653	−	0.259837i	$-0.0836687\pi$
$317$	10900.3	1.93131	0.965653	+	0.259837i	$0.0836687\pi$
$318$	8253.56	1.45546
$319$	8739.73	1.53395
$320$	−798.869	−0.139557
$321$	−10052.6	−1.74792
$322$	−4924.48	−0.852268
$323$	10241.4	1.76424
$324$	3996.85	0.685331
$325$	−263.822	−0.0450284
$326$	6596.75	1.12074
$327$	20635.6	3.48976
$328$	−2089.22	−0.351700
$329$	6633.79	1.11165
$330$	−18098.5	−3.01905
$331$	4629.53	0.768767	0.384384	−	0.923173i	$-0.374414\pi$
$331$	4629.53	0.768767	0.384384	+	0.923173i	$0.374414\pi$
$332$	283.707	0.0468989
$333$	9833.00	1.61815
$334$	−10549.1	−1.72821
$335$	8373.93	1.36572
$336$	17964.4	2.91677
$337$	−3116.64	−0.503781	−0.251891	−	0.967756i	$-0.581052\pi$
$337$	−3116.64	−0.503781	−0.251891	+	0.967756i	$0.581052\pi$
$338$	6124.72	0.985624
$339$	−18205.3	−2.91675
$340$	−3721.90	−0.593671
$341$	4744.38	0.753438
$342$	−22659.0	−3.58262
$343$	−2168.71	−0.341398
$344$	5728.28	0.897814
$345$	5680.04	0.886385
$346$	10318.0	1.60318
$347$	−7541.15	−1.16666	−0.583329	−	0.812236i	$-0.698250\pi$
$347$	−7541.15	−1.16666	−0.583329	+	0.812236i	$0.698250\pi$
$348$	−5845.66	−0.900461
$349$	9585.90	1.47026	0.735131	−	0.677925i	$-0.237121\pi$
$349$	9585.90	1.47026	0.735131	+	0.677925i	$0.237121\pi$
$350$	1082.28	0.165287
$351$	−5753.34	−0.874902
$352$	8806.63	1.33351
$353$	−3025.39	−0.456162	−0.228081	−	0.973642i	$-0.573245\pi$
$353$	−3025.39	−0.456162	−0.228081	+	0.973642i	$0.573245\pi$
$354$	25479.6	3.82550
$355$	5515.28	0.824565
$356$	581.481	0.0865686
$357$	−20129.8	−2.98426
$358$	15557.9	2.29681
$359$	−6317.31	−0.928733	−0.464366	−	0.885643i	$-0.653718\pi$
$359$	−6317.31	−0.928733	−0.464366	+	0.885643i	$0.653718\pi$
$360$	−8568.76	−1.25448
$361$	6195.39	0.903250
$362$	−8689.17	−1.26158
$363$	−14427.2	−2.08603
$364$	1970.69	0.283770
$365$	459.797	0.0659366
$366$	2062.18	0.294513
$367$	5837.99	0.830356	0.415178	−	0.909740i	$-0.363719\pi$
$367$	5837.99	0.830356	0.415178	+	0.909740i	$0.363719\pi$
$368$	−4668.61	−0.661326
$369$	−8520.03	−1.20199
$370$	6259.82	0.879548
$371$	6357.73	0.889695
$372$	−3173.33	−0.442283
$373$	10994.0	1.52613	0.763066	−	0.646321i	$-0.223693\pi$
$373$	10994.0	1.52613	0.763066	+	0.646321i	$0.223693\pi$
$374$	−16668.8	−2.30461
$375$	−13413.8	−1.84716
$376$	3823.29	0.524392
$377$	3337.50	0.455941
$378$	23602.0	3.21153
$379$	−14238.0	−1.92970	−0.964852	−	0.262793i	$-0.915356\pi$
$379$	−14238.0	−1.92970	−0.964852	+	0.262793i	$0.915356\pi$
$380$	−4744.17	−0.640450
$381$	11868.7	1.59593
$382$	9047.09	1.21175
$383$	−4068.71	−0.542823	−0.271411	−	0.962463i	$-0.587490\pi$
$383$	−4068.71	−0.542823	−0.271411	+	0.962463i	$0.587490\pi$
$384$	14412.9	1.91538
$385$	−13941.3	−1.84549
$386$	1804.29	0.237917
$387$	23360.5	3.06842
$388$	−4874.39	−0.637783
$389$	5040.85	0.657021	0.328510	−	0.944500i	$-0.393453\pi$
$389$	5040.85	0.657021	0.328510	+	0.944500i	$0.393453\pi$
$390$	−6911.38	−0.897363
$391$	5231.36	0.676627
$392$	3581.26	0.461431
$393$	−16749.5	−2.14987
$394$	−189.207	−0.0241931
$395$	−2171.86	−0.276654
$396$	12129.1	1.53917
$397$	−13025.9	−1.64672	−0.823362	−	0.567517i	$-0.807904\pi$
$397$	−13025.9	−1.64672	−0.823362	+	0.567517i	$0.807904\pi$
$398$	15522.5	1.95496
$399$	−25658.7	−3.21940
$400$	1026.05	0.128256
$401$	−12459.1	−1.55157	−0.775784	−	0.630998i	$-0.782646\pi$
$401$	−12459.1	−1.55157	−0.775784	+	0.630998i	$0.782646\pi$
$402$	−25084.5	−3.11219
$403$	1811.77	0.223947
$404$	−633.097	−0.0779648
$405$	−10797.6	−1.32478
$406$	−13691.5	−1.67364
$407$	9220.33	1.12294
$408$	−11601.5	−1.40775
$409$	−14141.3	−1.70964	−0.854818	−	0.518928i	$-0.826331\pi$
$409$	−14141.3	−1.70964	−0.854818	+	0.518928i	$0.826331\pi$
$410$	−5423.97	−0.653343
$411$	−4675.00	−0.561072
$412$	2831.43	0.338579
$413$	19627.0	2.33846
$414$	−11574.3	−1.37402
$415$	−766.439	−0.0906578
$416$	3363.05	0.396363
$417$	511.312	0.0600458
$418$	−21247.2	−2.48620
$419$	3144.49	0.366631	0.183315	−	0.983054i	$-0.441317\pi$
$419$	3144.49	0.366631	0.183315	+	0.983054i	$0.441317\pi$
$420$	9324.77	1.08334
$421$	2838.03	0.328544	0.164272	−	0.986415i	$-0.447472\pi$
$421$	2838.03	0.328544	0.164272	+	0.986415i	$0.447472\pi$
$422$	3429.07	0.395556
$423$	15591.8	1.79219
$424$	3664.19	0.419690
$425$	−1149.73	−0.131223
$426$	−16521.3	−1.87901
$427$	1588.50	0.180030
$428$	4288.86	0.484369
$429$	−10180.0	−1.14568
$430$	14871.6	1.66784
$431$	−8565.30	−0.957253	−0.478627	−	0.878019i	$-0.658865\pi$
$431$	−8565.30	−0.957253	−0.478627	+	0.878019i	$0.658865\pi$
$432$	22375.7	2.49202
$433$	9483.17	1.05250	0.526250	−	0.850330i	$-0.323598\pi$
$433$	9483.17	1.05250	0.526250	+	0.850330i	$0.323598\pi$
$434$	−7432.44	−0.822048
$435$	15792.2	1.74063
$436$	−8804.00	−0.967053
$437$	6668.23	0.729942
$438$	−1377.34	−0.150256
$439$	−4904.86	−0.533249	−0.266625	−	0.963800i	$-0.585908\pi$
$439$	−4904.86	−0.533249	−0.266625	+	0.963800i	$0.585908\pi$
$440$	−8034.86	−0.870561
$441$	14604.7	1.57701
$442$	−6365.43	−0.685006
$443$	13381.3	1.43513	0.717565	−	0.696491i	$-0.245257\pi$
$443$	13381.3	1.43513	0.717565	+	0.696491i	$0.245257\pi$
$444$	−6167.12	−0.659186
$445$	−1570.88	−0.167341
$446$	11008.9	1.16880
$447$	27062.2	2.86353
$448$	1843.37	0.194400
$449$	2037.72	0.214178	0.107089	−	0.994249i	$-0.465847\pi$
$449$	2037.72	0.214178	0.107089	+	0.994249i	$0.465847\pi$
$450$	2543.75	0.266474
$451$	−7989.17	−0.834136
$452$	7767.15	0.808265
$453$	19641.1	2.03713
$454$	−62.5479	−0.00646590
$455$	−5323.85	−0.548540
$456$	−14788.0	−1.51867
$457$	518.796	0.0531034	0.0265517	−	0.999647i	$-0.491547\pi$
$457$	518.796	0.0531034	0.0265517	+	0.999647i	$0.491547\pi$
$458$	−14150.9	−1.44373
$459$	−25072.8	−2.54967
$460$	−2423.34	−0.245628
$461$	−2133.37	−0.215534	−0.107767	−	0.994176i	$-0.534370\pi$
$461$	−2133.37	−0.215534	−0.107767	+	0.994176i	$0.534370\pi$
$462$	41761.7	4.20548
$463$	2254.81	0.226328	0.113164	−	0.993576i	$-0.463901\pi$
$463$	2254.81	0.226328	0.113164	+	0.993576i	$0.463901\pi$
$464$	−12980.1	−1.29868
$465$	8572.80	0.854955
$466$	−12907.4	−1.28310
$467$	−2568.26	−0.254486	−0.127243	−	0.991872i	$-0.540613\pi$
$467$	−2568.26	−0.254486	−0.127243	+	0.991872i	$0.540613\pi$
$468$	4631.82	0.457491
$469$	−19322.6	−1.90242
$470$	9925.93	0.974147
$471$	−34685.5	−3.39326
$472$	11311.8	1.10311
$473$	21904.9	2.12937
$474$	6505.92	0.630436
$475$	−1465.52	−0.141563
$476$	8588.18	0.826972
$477$	14942.9	1.43436
$478$	−1601.40	−0.153235
$479$	11464.7	1.09361	0.546803	−	0.837261i	$-0.315845\pi$
$479$	11464.7	1.09361	0.546803	+	0.837261i	$0.315845\pi$
$480$	15913.1	1.51318
$481$	3521.03	0.333774
$482$	3946.15	0.372909
$483$	−13106.5	−1.23472
$484$	6155.23	0.578064
$485$	13168.3	1.23287
$486$	6269.19	0.585136
$487$	−16689.2	−1.55289	−0.776446	−	0.630183i	$-0.782980\pi$
$487$	−16689.2	−1.55289	−0.776446	+	0.630183i	$0.782980\pi$
$488$	915.508	0.0849244
$489$	17557.3	1.62366
$490$	9297.57	0.857186
$491$	11285.4	1.03728	0.518638	−	0.854994i	$-0.326439\pi$
$491$	11285.4	1.03728	0.518638	+	0.854994i	$0.326439\pi$
$492$	5343.64	0.489654
$493$	14544.7	1.32872
$494$	−8113.79	−0.738981
$495$	−32767.0	−2.97528
$496$	−7046.27	−0.637876
$497$	−12726.4	−1.14860
$498$	2295.90	0.206590
$499$	17418.7	1.56267	0.781333	−	0.624115i	$-0.214540\pi$
$499$	17418.7	1.56267	0.781333	+	0.624115i	$0.214540\pi$
$500$	5722.89	0.511871
$501$	−28076.6	−2.50373
$502$	15141.2	1.34618
$503$	−11442.6	−1.01431	−0.507157	−	0.861854i	$-0.669304\pi$
$503$	−11442.6	−1.01431	−0.507157	+	0.861854i	$0.669304\pi$
$504$	19772.2	1.74747
$505$	1710.32	0.150710
$506$	−10853.1	−0.953517
$507$	16301.0	1.42792
$508$	−5063.67	−0.442252
$509$	−10131.8	−0.882284	−0.441142	−	0.897437i	$-0.645427\pi$
$509$	−10131.8	−0.882284	−0.441142	+	0.897437i	$0.645427\pi$
$510$	−30119.5	−2.61513
$511$	−1060.97	−0.0918483
$512$	−4065.76	−0.350943
$513$	−31959.5	−2.75057
$514$	2518.75	0.216143
$515$	−7649.15	−0.654489
$516$	−14651.4	−1.24998
$517$	14620.3	1.24371
$518$	−14444.4	−1.22519
$519$	27461.5	2.32259
$520$	−3068.33	−0.258760
$521$	−1382.19	−0.116228	−0.0581141	−	0.998310i	$-0.518509\pi$
$521$	−1382.19	−0.116228	−0.0581141	+	0.998310i	$0.518509\pi$
$522$	−32179.8	−2.69823
$523$	13960.2	1.16718	0.583592	−	0.812047i	$-0.301647\pi$
$523$	13960.2	1.16718	0.583592	+	0.812047i	$0.301647\pi$
$524$	7146.01	0.595754
$525$	2880.50	0.239458
$526$	−6487.69	−0.537789
$527$	7895.61	0.652634
$528$	39591.9	3.26329
$529$	−8760.85	−0.720050
$530$	9512.87	0.779647
$531$	46130.5	3.77004
$532$	10947.1	0.892133
$533$	−3050.88	−0.247933
$534$	4705.65	0.381336
$535$	−11586.4	−0.936309
$536$	−11136.3	−0.897418
$537$	41407.4	3.32749
$538$	5527.49	0.442950
$539$	13694.7	1.09439
$540$	11614.6	0.925577
$541$	21595.2	1.71617	0.858086	−	0.513506i	$-0.171654\pi$
$541$	21595.2	1.71617	0.858086	+	0.513506i	$0.171654\pi$
$542$	10595.4	0.839692
$543$	−23126.3	−1.82771
$544$	14656.0	1.15510
$545$	23784.2	1.86936
$546$	15947.8	1.25001
$547$	−547.000	−0.0427569
$547$	−547.000	−0.0427569
$548$	1994.55	0.155480
$549$	3733.53	0.290243
$550$	2385.25	0.184923
$551$	18539.6	1.43342
$552$	−7553.77	−0.582446
$553$	5011.52	0.385373
$554$	17809.4	1.36579
$555$	16660.6	1.27424
$556$	−218.147	−0.0166394
$557$	1595.92	0.121403	0.0607015	−	0.998156i	$-0.480666\pi$
$557$	1595.92	0.121403	0.0607015	+	0.998156i	$0.480666\pi$
$558$	−17468.9	−1.32530
$559$	8364.99	0.632918
$560$	20705.3	1.56243
$561$	−44364.2	−3.33878
$562$	14799.7	1.11083
$563$	−18617.9	−1.39370	−0.696848	−	0.717219i	$-0.745415\pi$
$563$	−18617.9	−1.39370	−0.696848	+	0.717219i	$0.745415\pi$
$564$	−9778.93	−0.730084
$565$	−20983.1	−1.56242
$566$	4374.05	0.324832
$567$	24915.1	1.84539
$568$	−7334.67	−0.541823
$569$	1842.95	0.135783	0.0678913	−	0.997693i	$-0.478373\pi$
$569$	1842.95	0.135783	0.0678913	+	0.997693i	$0.478373\pi$
$570$	−38392.3	−2.82119
$571$	−6922.59	−0.507358	−0.253679	−	0.967288i	$-0.581641\pi$
$571$	−6922.59	−0.507358	−0.253679	+	0.967288i	$0.581641\pi$
$572$	4343.22	0.317481
$573$	24078.9	1.75552
$574$	12515.7	0.910094
$575$	−748.590	−0.0542928
$576$	4332.58	0.313410
$577$	−2.52426	−0.000182125 0	−9.10626e−5	−	1.00000i	$-0.500029\pi$
$577$	−2.52426	−0.000182125 0	−9.10626e−5		1.00000i	$0.500029\pi$
$578$	−10777.7	−0.775591
$579$	4802.14	0.344681
$580$	−6737.58	−0.482350
$581$	1768.54	0.126284
$582$	−39446.1	−2.80944
$583$	14011.9	0.995390
$584$	−611.475	−0.0433270
$585$	−12512.9	−0.884353
$586$	−26860.6	−1.89351
$587$	−1374.02	−0.0966132	−0.0483066	−	0.998833i	$-0.515382\pi$
$587$	−1374.02	−0.0966132	−0.0483066	+	0.998833i	$0.515382\pi$
$588$	−9159.87	−0.642427
$589$	10064.3	0.704059
$590$	29367.3	2.04921
$591$	−503.575	−0.0350496
$592$	−13693.9	−0.950700
$593$	−19500.9	−1.35043	−0.675217	−	0.737619i	$-0.735950\pi$
$593$	−19500.9	−1.35043	−0.675217	+	0.737619i	$0.735950\pi$
$594$	52016.8	3.59305
$595$	−23201.1	−1.59858
$596$	−11545.9	−0.793518
$597$	41313.3	2.83223
$598$	−4144.55	−0.283417
$599$	−24961.0	−1.70264	−0.851318	−	0.524651i	$-0.824196\pi$
$599$	−24961.0	−1.70264	−0.851318	+	0.524651i	$0.824196\pi$
$600$	1660.14	0.112958
$601$	17269.5	1.17211	0.586054	−	0.810272i	$-0.300681\pi$
$601$	17269.5	1.17211	0.586054	+	0.810272i	$0.300681\pi$
$602$	−34315.8	−2.32327
$603$	−45415.1	−3.06707
$604$	−8379.69	−0.564511
$605$	−16628.4	−1.11743
$606$	−5123.35	−0.343436
$607$	−26010.7	−1.73928	−0.869639	−	0.493689i	$-0.835648\pi$
$607$	−26010.7	−1.73928	−0.869639	+	0.493689i	$0.835648\pi$
$608$	18681.5	1.24611
$609$	−36440.0	−2.42467
$610$	2376.82	0.157762
$611$	5583.14	0.369672
$612$	20185.3	1.33324
$613$	−10233.4	−0.674265	−0.337133	−	0.941457i	$-0.609457\pi$
$613$	−10233.4	−0.674265	−0.337133	+	0.941457i	$0.609457\pi$
$614$	5509.08	0.362099
$615$	−14435.9	−0.946526
$616$	18540.2	1.21267
$617$	7697.61	0.502260	0.251130	−	0.967953i	$-0.419198\pi$
$617$	7697.61	0.502260	0.251130	+	0.967953i	$0.419198\pi$
$618$	22913.4	1.49144
$619$	−9321.54	−0.605274	−0.302637	−	0.953106i	$-0.597867\pi$
$619$	−9321.54	−0.605274	−0.302637	+	0.953106i	$0.597867\pi$
$620$	−3657.51	−0.236918
$621$	−16325.0	−1.05491
$622$	−18580.6	−1.19777
$623$	3624.77	0.233103
$624$	15119.2	0.969956
$625$	−13857.1	−0.886858
$626$	−8734.04	−0.557640
$627$	−56549.5	−3.60186
$628$	14798.3	0.940310
$629$	15344.5	0.972695
$630$	51332.0	3.24622
$631$	−3960.51	−0.249866	−0.124933	−	0.992165i	$-0.539872\pi$
$631$	−3960.51	−0.249866	−0.124933	+	0.992165i	$0.539872\pi$
$632$	2888.32	0.181790
$633$	9126.51	0.573059
$634$	−37634.5	−2.35750
$635$	13679.6	0.854894
$636$	−9371.99	−0.584314
$637$	5229.70	0.325288
$638$	−30174.8	−1.87246
$639$	−29911.5	−1.85177
$640$	16612.0	1.02601
$641$	19023.7	1.17222	0.586110	−	0.810232i	$-0.300659\pi$
$641$	19023.7	1.17222	0.586110	+	0.810232i	$0.300659\pi$
$642$	34707.7	2.13365
$643$	−17649.4	−1.08246	−0.541232	−	0.840873i	$-0.682042\pi$
$643$	−17649.4	−1.08246	−0.541232	+	0.840873i	$0.682042\pi$
$644$	5591.79	0.342154
$645$	39580.9	2.41627
$646$	−35359.6	−2.15357
$647$	−31060.0	−1.88732	−0.943659	−	0.330921i	$-0.892641\pi$
$647$	−31060.0	−1.88732	−0.943659	+	0.330921i	$0.892641\pi$
$648$	14359.5	0.870514
$649$	43256.2	2.61626
$650$	910.873	0.0549652
$651$	−19781.5	−1.19093
$652$	−7490.67	−0.449934
$653$	13680.8	0.819865	0.409932	−	0.912116i	$-0.365552\pi$
$653$	13680.8	0.819865	0.409932	+	0.912116i	$0.365552\pi$
$654$	−71246.6	−4.25988
$655$	−19305.1	−1.15162
$656$	11865.4	0.706197
$657$	−2493.65	−0.148077
$658$	−22903.8	−1.35697
$659$	−19837.0	−1.17259	−0.586296	−	0.810097i	$-0.699415\pi$
$659$	−19837.0	−1.17259	−0.586296	+	0.810097i	$0.699415\pi$
$660$	20551.0	1.21204
$661$	−10542.9	−0.620382	−0.310191	−	0.950674i	$-0.600393\pi$
$661$	−10542.9	−0.620382	−0.310191	+	0.950674i	$0.600393\pi$
$662$	−15983.9	−0.938418
$663$	−16941.7	−0.992397
$664$	1019.27	0.0595714
$665$	−29573.7	−1.72454
$666$	−33949.4	−1.97525
$667$	9470.09	0.549750
$668$	11978.6	0.693814
$669$	29300.2	1.69329
$670$	−28911.9	−1.66711
$671$	3500.91	0.201417
$672$	−36718.9	−2.10783
$673$	−19623.4	−1.12396	−0.561981	−	0.827150i	$-0.689960\pi$
$673$	−19623.4	−1.12396	−0.561981	+	0.827150i	$0.689960\pi$
$674$	10760.5	0.614955
$675$	3587.84	0.204587
$676$	−6954.68	−0.395692
$677$	−7559.18	−0.429133	−0.214566	−	0.976709i	$-0.568834\pi$
$677$	−7559.18	−0.429133	−0.214566	+	0.976709i	$0.568834\pi$
$678$	62855.8	3.56042
$679$	−30385.4	−1.71736
$680$	−13371.6	−0.754087
$681$	−166.472	−0.00936742
$682$	−16380.4	−0.919706
$683$	−4051.73	−0.226992	−0.113496	−	0.993538i	$-0.536205\pi$
$683$	−4051.73	−0.226992	−0.113496	+	0.993538i	$0.536205\pi$
$684$	25729.5	1.43829
$685$	−5388.30	−0.300549
$686$	7487.70	0.416737
$687$	−37662.6	−2.09159
$688$	−32532.8	−1.80277
$689$	5350.81	0.295863
$690$	−19610.9	−1.08199
$691$	−22157.4	−1.21983	−0.609917	−	0.792465i	$-0.708797\pi$
$691$	−22157.4	−1.21983	−0.609917	+	0.792465i	$0.708797\pi$
$692$	−11716.2	−0.643617
$693$	75608.9	4.14451
$694$	26036.6	1.42411
$695$	589.328	0.0321647
$696$	−21001.7	−1.14377
$697$	−13295.6	−0.722535
$698$	−33096.3	−1.79472
$699$	−34353.1	−1.85888
$700$	−1228.94	−0.0663566
$701$	−4739.38	−0.255355	−0.127678	−	0.991816i	$-0.540752\pi$
$701$	−4739.38	−0.255355	−0.127678	+	0.991816i	$0.540752\pi$
$702$	19864.0	1.06797
$703$	19559.1	1.04934
$704$	4062.62	0.217494
$705$	26418.0	1.41129
$706$	10445.5	0.556827
$707$	−3946.53	−0.209935
$708$	−28932.4	−1.53580
$709$	1457.73	0.0772158	0.0386079	−	0.999254i	$-0.487708\pi$
$709$	1457.73	0.0772158	0.0386079	+	0.999254i	$0.487708\pi$
$710$	−19042.1	−1.00653
$711$	11778.9	0.621296
$712$	2089.08	0.109960
$713$	5140.85	0.270023
$714$	69500.0	3.64282
$715$	−11733.3	−0.613706
$716$	−17666.1	−0.922085
$717$	−4262.14	−0.221998
$718$	21811.2	1.13368
$719$	19874.9	1.03089	0.515445	−	0.856923i	$-0.327627\pi$
$719$	19874.9	1.03089	0.515445	+	0.856923i	$0.327627\pi$
$720$	48664.9	2.51894
$721$	17650.2	0.911690
$722$	−21390.2	−1.10258
$723$	10502.7	0.540249
$724$	9866.63	0.506478
$725$	−2081.30	−0.106617
$726$	49811.3	2.54638
$727$	483.890	0.0246857	0.0123428	−	0.999924i	$-0.496071\pi$
$727$	483.890	0.0246857	0.0123428	+	0.999924i	$0.496071\pi$
$728$	7080.08	0.360447
$729$	−10840.6	−0.550759
$730$	−1587.49	−0.0804874
$731$	36454.3	1.84447
$732$	−2341.62	−0.118236
$733$	−4193.55	−0.211313	−0.105656	−	0.994403i	$-0.533694\pi$
$733$	−4193.55	−0.211313	−0.105656	+	0.994403i	$0.533694\pi$
$734$	−20156.3	−1.01360
$735$	24745.6	1.24184
$736$	9542.58	0.477913
$737$	−42585.4	−2.12843
$738$	29416.3	1.46725
$739$	−34243.2	−1.70454	−0.852272	−	0.523099i	$-0.824776\pi$
$739$	−34243.2	−1.70454	−0.852272	+	0.523099i	$0.824776\pi$
$740$	−7108.09	−0.353106
$741$	−21594.9	−1.07059
$742$	−21950.7	−1.08603
$743$	29014.8	1.43264	0.716320	−	0.697772i	$-0.245825\pi$
$743$	29014.8	1.43264	0.716320	+	0.697772i	$0.245825\pi$
$744$	−11400.8	−0.561793
$745$	31191.3	1.53391
$746$	−37957.9	−1.86292
$747$	4156.69	0.203595
$748$	18927.6	0.925216
$749$	26735.4	1.30426
$750$	46312.6	2.25480
$751$	−18959.5	−0.921226	−0.460613	−	0.887601i	$-0.652370\pi$
$751$	−18959.5	−0.921226	−0.460613	+	0.887601i	$0.652370\pi$
$752$	−21713.8	−1.05295
$753$	40298.4	1.95027
$754$	−11523.1	−0.556558
$755$	22637.9	1.09123
$756$	−26800.3	−1.28931
$757$	−28440.7	−1.36552	−0.682758	−	0.730645i	$-0.739219\pi$
$757$	−28440.7	−1.36552	−0.682758	+	0.730645i	$0.739219\pi$
$758$	49158.2	2.35555
$759$	−28885.7	−1.38140
$760$	−17044.4	−0.813505
$761$	−33770.3	−1.60864	−0.804318	−	0.594200i	$-0.797469\pi$
$761$	−33770.3	−1.60864	−0.804318	+	0.594200i	$0.797469\pi$
$762$	−40977.9	−1.94812
$763$	−54881.3	−2.60398
$764$	−10273.1	−0.486474
$765$	−54530.9	−2.57721
$766$	14047.6	0.662613
$767$	16518.5	0.777640
$768$	−44217.0	−2.07753
$769$	26654.7	1.24992	0.624962	−	0.780655i	$-0.285114\pi$
$769$	26654.7	1.24992	0.624962	+	0.780655i	$0.285114\pi$
$770$	48133.7	2.25275
$771$	6703.69	0.313135
$772$	−2048.79	−0.0955151
$773$	13000.9	0.604931	0.302465	−	0.953160i	$-0.402190\pi$
$773$	13000.9	0.604931	0.302465	+	0.953160i	$0.402190\pi$
$774$	−80654.5	−3.74556
$775$	−1129.84	−0.0523677
$776$	−17512.2	−0.810118
$777$	−38443.8	−1.77499
$778$	−17404.0	−0.802012
$779$	−16947.4	−0.779467
$780$	7847.94	0.360258
$781$	−28047.8	−1.28506
$782$	−18061.8	−0.825944
$783$	−45388.2	−2.07157
$784$	−20339.2	−0.926530
$785$	−39977.7	−1.81767
$786$	57829.2	2.62430
$787$	−17911.8	−0.811292	−0.405646	−	0.914030i	$-0.632953\pi$
$787$	−17911.8	−0.811292	−0.405646	+	0.914030i	$0.632953\pi$
$788$	214.846	0.00971264
$789$	−17267.0	−0.779117
$790$	7498.58	0.337706
$791$	48417.9	2.17641
$792$	43576.1	1.95506
$793$	1336.91	0.0598679
$794$	44973.1	2.01012
$795$	25318.6	1.12951
$796$	−17626.0	−0.784843
$797$	−10694.5	−0.475308	−0.237654	−	0.971350i	$-0.576378\pi$
$797$	−10694.5	−0.475308	−0.237654	+	0.971350i	$0.576378\pi$
$798$	88589.2	3.92986
$799$	24331.1	1.07731
$800$	−2097.23	−0.0926854
$801$	8519.49	0.375807
$802$	43016.4	1.89397
$803$	−2338.28	−0.102760
$804$	28483.7	1.24943
$805$	−15106.3	−0.661401
$806$	−6255.31	−0.273367
$807$	14711.5	0.641720
$808$	−2274.53	−0.0990316
$809$	−22849.8	−0.993022	−0.496511	−	0.868030i	$-0.665386\pi$
$809$	−22849.8	−0.993022	−0.496511	+	0.868030i	$0.665386\pi$
$810$	37279.7	1.61713
$811$	26045.0	1.12770	0.563850	−	0.825877i	$-0.309320\pi$
$811$	26045.0	1.12770	0.563850	+	0.825877i	$0.309320\pi$
$812$	15546.8	0.671903
$813$	28199.9	1.21650
$814$	−31834.1	−1.37074
$815$	20236.2	0.869745
$816$	65888.9	2.82668
$817$	46467.0	1.98981
$818$	48824.2	2.08692
$819$	28873.3	1.23189
$820$	6158.97	0.262293
$821$	−3338.26	−0.141908	−0.0709538	−	0.997480i	$-0.522604\pi$
$821$	−3338.26	−0.141908	−0.0709538	+	0.997480i	$0.522604\pi$
$822$	16140.9	0.684889
$823$	14416.2	0.610592	0.305296	−	0.952258i	$-0.401245\pi$
$823$	14416.2	0.610592	0.305296	+	0.952258i	$0.401245\pi$
$824$	10172.5	0.430066
$825$	6348.38	0.267906
$826$	−67764.3	−2.85450
$827$	−1771.31	−0.0744793	−0.0372396	−	0.999306i	$-0.511856\pi$
$827$	−1771.31	−0.0744793	−0.0372396	+	0.999306i	$0.511856\pi$
$828$	13142.7	0.551619
$829$	−36617.3	−1.53410	−0.767052	−	0.641585i	$-0.778277\pi$
$829$	−36617.3	−1.53410	−0.767052	+	0.641585i	$0.778277\pi$
$830$	2646.21	0.110664
$831$	47399.9	1.97868
$832$	1551.42	0.0646465
$833$	22790.8	0.947966
$834$	−1765.36	−0.0732966
$835$	−32360.5	−1.34118
$836$	24126.3	0.998118
$837$	−24639.1	−1.01750
$838$	−10856.7	−0.447539
$839$	−34347.3	−1.41335	−0.706674	−	0.707539i	$-0.749805\pi$
$839$	−34347.3	−1.41335	−0.706674	+	0.707539i	$0.749805\pi$
$840$	33501.1	1.37607
$841$	1940.58	0.0795680
$842$	−9798.59	−0.401047
$843$	39389.6	1.60931
$844$	−3893.75	−0.158801
$845$	18788.2	0.764891
$846$	−53832.2	−2.18769
$847$	38369.7	1.55655
$848$	−20810.2	−0.842718
$849$	11641.6	0.470598
$850$	3969.55	0.160182
$851$	9990.85	0.402446
$852$	18760.1	0.754354
$853$	25274.5	1.01452	0.507258	−	0.861794i	$-0.330659\pi$
$853$	25274.5	1.01452	0.507258	+	0.861794i	$0.330659\pi$
$854$	−5484.45	−0.219759
$855$	−69508.6	−2.78029
$856$	15408.6	0.615251
$857$	636.270	0.0253612	0.0126806	−	0.999920i	$-0.495964\pi$
$857$	636.270	0.0253612	0.0126806	+	0.999920i	$0.495964\pi$
$858$	35147.6	1.39851
$859$	40045.5	1.59061	0.795305	−	0.606209i	$-0.207311\pi$
$859$	40045.5	1.59061	0.795305	+	0.606209i	$0.207311\pi$
$860$	−16886.8	−0.669578
$861$	33310.6	1.31849
$862$	29572.6	1.16850
$863$	23703.3	0.934959	0.467480	−	0.884004i	$-0.345162\pi$
$863$	23703.3	0.934959	0.467480	+	0.884004i	$0.345162\pi$
$864$	−45735.7	−1.80088
$865$	31651.5	1.24414
$866$	−32741.6	−1.28476
$867$	−28684.8	−1.12363
$868$	8439.61	0.330022
$869$	11044.9	0.431155
$870$	−54524.0	−2.12476
$871$	−16262.4	−0.632640
$872$	−31630.1	−1.22836
$873$	−71416.5	−2.76871
$874$	−23022.7	−0.891025
$875$	35674.6	1.37831
$876$	1563.98	0.0603221
$877$	−7327.77	−0.282145	−0.141073	−	0.989999i	$-0.545055\pi$
$877$	−7327.77	−0.282145	−0.141073	+	0.989999i	$0.545055\pi$
$878$	16934.5	0.650926
$879$	−71489.6	−2.74321
$880$	45632.7	1.74804
$881$	44046.9	1.68442	0.842212	−	0.539146i	$-0.181253\pi$
$881$	44046.9	1.68442	0.842212	+	0.539146i	$0.181253\pi$
$882$	−50424.3	−1.92503
$883$	−51420.4	−1.95972	−0.979861	−	0.199678i	$-0.936010\pi$
$883$	−51420.4	−1.95972	−0.979861	+	0.199678i	$0.936010\pi$
$884$	7228.01	0.275005
$885$	78161.3	2.96877
$886$	−46200.2	−1.75183
$887$	−28304.6	−1.07145	−0.535725	−	0.844393i	$-0.679962\pi$
$887$	−28304.6	−1.07145	−0.535725	+	0.844393i	$0.679962\pi$
$888$	−22156.6	−0.837304
$889$	−31565.3	−1.19085
$890$	5423.63	0.204270
$891$	54910.7	2.06462
$892$	−12500.7	−0.469230
$893$	31014.0	1.16220
$894$	−93435.1	−3.49546
$895$	47725.3	1.78243
$896$	−38331.7	−1.42921
$897$	−11030.8	−0.410598
$898$	−7035.44	−0.261443
$899$	14293.1	0.530256
$900$	−2888.45	−0.106980
$901$	23318.6	0.862214
$902$	27583.4	1.01821
$903$	−91331.9	−3.36582
$904$	27905.0	1.02667
$905$	−26654.9	−0.979047
$906$	−67812.8	−2.48668
$907$	11531.6	0.422161	0.211080	−	0.977469i	$-0.432302\pi$
$907$	11531.6	0.422161	0.211080	+	0.977469i	$0.432302\pi$
$908$	71.0237	0.00259582
$909$	−9275.74	−0.338456
$910$	18381.1	0.669592
$911$	−44466.3	−1.61716	−0.808580	−	0.588386i	$-0.799764\pi$
$911$	−44466.3	−1.61716	−0.808580	+	0.588386i	$0.799764\pi$
$912$	83986.3	3.04941
$913$	3897.70	0.141287
$914$	−1791.20	−0.0648223
$915$	6325.93	0.228556
$916$	16068.4	0.579602
$917$	44546.0	1.60418
$918$	86566.5	3.11233
$919$	14648.3	0.525791	0.262895	−	0.964824i	$-0.415323\pi$
$919$	14648.3	0.525791	0.262895	+	0.964824i	$0.415323\pi$
$920$	−8706.32	−0.311999
$921$	14662.5	0.524587
$922$	7365.68	0.263097
$923$	−10710.8	−0.381961
$924$	−47420.8	−1.68835
$925$	−2195.75	−0.0780495
$926$	−7784.96	−0.276274
$927$	41484.3	1.46982
$928$	26531.2	0.938500
$929$	−7958.49	−0.281065	−0.140533	−	0.990076i	$-0.544881\pi$
$929$	−7958.49	−0.281065	−0.140533	+	0.990076i	$0.544881\pi$
$930$	−29598.5	−1.04363
$931$	29050.7	1.02266
$932$	14656.5	0.515116
$933$	−49452.4	−1.73526
$934$	8867.18	0.310646
$935$	−51133.2	−1.78849
$936$	16640.7	0.581110
$937$	40305.5	1.40525	0.702627	−	0.711559i	$-0.252010\pi$
$937$	40305.5	1.40525	0.702627	+	0.711559i	$0.252010\pi$
$938$	66713.4	2.32225
$939$	−23245.7	−0.807876
$940$	−11271.0	−0.391084
$941$	−5416.49	−0.187643	−0.0938217	−	0.995589i	$-0.529908\pi$
$941$	−5416.49	−0.187643	−0.0938217	+	0.995589i	$0.529908\pi$
$942$	119755.	4.14208
$943$	−8656.81	−0.298944
$944$	−64243.3	−2.21498
$945$	72401.5	2.49230
$946$	−75629.1	−2.59927
$947$	34268.5	1.17590	0.587950	−	0.808897i	$-0.299935\pi$
$947$	34268.5	1.17590	0.587950	+	0.808897i	$0.299935\pi$
$948$	−7387.53	−0.253097
$949$	−892.935	−0.0305436
$950$	5059.85	0.172803
$951$	−100165.	−3.41541
$952$	30854.7	1.05043
$953$	−17728.2	−0.602596	−0.301298	−	0.953530i	$-0.597420\pi$
$953$	−17728.2	−0.602596	−0.301298	+	0.953530i	$0.597420\pi$
$954$	−51592.0	−1.75089
$955$	27752.8	0.940377
$956$	1818.40	0.0615182
$957$	−80310.5	−2.71272
$958$	−39583.2	−1.33494
$959$	12433.4	0.418659
$960$	7340.92	0.246799
$961$	−22032.0	−0.739552
$962$	−12156.7	−0.407430
$963$	62837.7	2.10272
$964$	−4480.89	−0.149709
$965$	5534.85	0.184635
$966$	45251.7	1.50719
$967$	10645.0	0.354004	0.177002	−	0.984211i	$-0.443360\pi$
$967$	10645.0	0.354004	0.177002	+	0.984211i	$0.443360\pi$
$968$	22113.9	0.734263
$969$	−94109.9	−3.11996
$970$	−45464.8	−1.50493
$971$	−11963.2	−0.395384	−0.197692	−	0.980264i	$-0.563345\pi$
$971$	−11963.2	−0.395384	−0.197692	+	0.980264i	$0.563345\pi$
$972$	−7118.72	−0.234911
$973$	−1359.86	−0.0448048
$974$	57621.1	1.89558
$975$	2424.30	0.0796304
$976$	−5199.49	−0.170524
$977$	51985.9	1.70233	0.851165	−	0.524899i	$-0.175897\pi$
$977$	51985.9	1.70233	0.851165	+	0.524899i	$0.175897\pi$
$978$	−60618.4	−1.98197
$979$	7988.66	0.260796
$980$	−10557.5	−0.344129
$981$	−128991.	−4.19812
$982$	−38964.0	−1.26618
$983$	−1617.17	−0.0524718	−0.0262359	−	0.999656i	$-0.508352\pi$
$983$	−1617.17	−0.0524718	−0.0262359	+	0.999656i	$0.508352\pi$
$984$	19198.1	0.621964
$985$	−580.409	−0.0187750
$986$	−50217.0	−1.62194
$987$	−60958.7	−1.96589
$988$	9213.29	0.296674
$989$	23735.5	0.763140
$990$	113131.	3.63187
$991$	−55946.0	−1.79332	−0.896661	−	0.442718i	$-0.854014\pi$
$991$	−55946.0	−1.79332	−0.896661	+	0.442718i	$0.854014\pi$
$992$	14402.5	0.460967
$993$	−42541.3	−1.35953
$994$	43939.1	1.40208
$995$	47616.8	1.51714
$996$	−2607.02	−0.0829383
$997$	32028.2	1.01740	0.508698	−	0.860945i	$-0.330127\pi$
$997$	32028.2	1.01740	0.508698	+	0.860945i	$0.330127\pi$
$998$	−60140.0	−1.90751
$999$	−47884.1	−1.51650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.b.1.15	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-3.45260 q^{2} -9.18913 q^{3} +3.92046 q^{4} -10.5912 q^{5} +31.7264 q^{6} +24.4389 q^{7} +14.0850 q^{8} +57.4401 q^{9} +O(q^{10})\)	\(q-3.45260 q^{2} -9.18913 q^{3} +3.92046 q^{4} -10.5912 q^{5} +31.7264 q^{6} +24.4389 q^{7} +14.0850 q^{8} +57.4401 q^{9} +36.5672 q^{10} +53.8612 q^{11} -36.0256 q^{12} +20.5683 q^{13} -84.3778 q^{14} +97.3239 q^{15} -79.9937 q^{16} +89.6360 q^{17} -198.318 q^{18} +114.256 q^{19} -41.5224 q^{20} -224.572 q^{21} -185.961 q^{22} +58.3622 q^{23} -129.429 q^{24} -12.8266 q^{25} -71.0143 q^{26} -279.718 q^{27} +95.8118 q^{28} +162.264 q^{29} -336.021 q^{30} +88.0853 q^{31} +163.506 q^{32} -494.937 q^{33} -309.477 q^{34} -258.837 q^{35} +225.192 q^{36} +171.187 q^{37} -394.480 q^{38} -189.005 q^{39} -149.177 q^{40} -148.329 q^{41} +775.359 q^{42} +406.693 q^{43} +211.161 q^{44} -608.360 q^{45} -201.502 q^{46} +271.444 q^{47} +735.072 q^{48} +254.260 q^{49} +44.2852 q^{50} -823.677 q^{51} +80.6373 q^{52} +260.148 q^{53} +965.756 q^{54} -570.454 q^{55} +344.222 q^{56} -1049.91 q^{57} -560.233 q^{58} +803.105 q^{59} +381.554 q^{60} +64.9987 q^{61} -304.123 q^{62} +1403.77 q^{63} +75.4277 q^{64} -217.843 q^{65} +1708.82 q^{66} -790.651 q^{67} +351.414 q^{68} -536.298 q^{69} +893.662 q^{70} -520.742 q^{71} +809.046 q^{72} -43.4131 q^{73} -591.040 q^{74} +117.866 q^{75} +447.936 q^{76} +1316.31 q^{77} +652.559 q^{78} +205.063 q^{79} +847.228 q^{80} +1019.49 q^{81} +512.121 q^{82} +72.3656 q^{83} -880.427 q^{84} -949.352 q^{85} -1404.15 q^{86} -1491.06 q^{87} +758.636 q^{88} +148.320 q^{89} +2100.42 q^{90} +502.667 q^{91} +228.807 q^{92} -809.427 q^{93} -937.187 q^{94} -1210.11 q^{95} -1502.48 q^{96} -1243.32 q^{97} -877.858 q^{98} +3093.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) 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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