LMFDB - Embedded newform 547.4.a.b.1.8

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			1.8
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)

$f(q)$	$=$	$q-4.68521 q^{2} +2.05946 q^{3} +13.9512 q^{4} +16.8174 q^{5} -9.64900 q^{6} +3.12603 q^{7} -27.8825 q^{8} -22.7586 q^{9} +O(q^{10})$	\(q-4.68521 q^{2} +2.05946 q^{3} +13.9512 q^{4} +16.8174 q^{5} -9.64900 q^{6} +3.12603 q^{7} -27.8825 q^{8} -22.7586 q^{9} -78.7929 q^{10} +9.04318 q^{11} +28.7319 q^{12} +53.3444 q^{13} -14.6461 q^{14} +34.6347 q^{15} +19.0258 q^{16} -98.4932 q^{17} +106.629 q^{18} -8.00668 q^{19} +234.622 q^{20} +6.43793 q^{21} -42.3692 q^{22} +186.527 q^{23} -57.4228 q^{24} +157.824 q^{25} -249.930 q^{26} -102.476 q^{27} +43.6118 q^{28} +234.773 q^{29} -162.271 q^{30} +206.288 q^{31} +133.920 q^{32} +18.6241 q^{33} +461.461 q^{34} +52.5716 q^{35} -317.509 q^{36} +225.743 q^{37} +37.5129 q^{38} +109.861 q^{39} -468.910 q^{40} -133.351 q^{41} -30.1631 q^{42} -385.829 q^{43} +126.163 q^{44} -382.740 q^{45} -873.919 q^{46} -405.323 q^{47} +39.1829 q^{48} -333.228 q^{49} -739.438 q^{50} -202.843 q^{51} +744.218 q^{52} -60.5540 q^{53} +480.121 q^{54} +152.083 q^{55} -87.1615 q^{56} -16.4894 q^{57} -1099.96 q^{58} +379.335 q^{59} +483.195 q^{60} +647.920 q^{61} -966.502 q^{62} -71.1442 q^{63} -779.649 q^{64} +897.113 q^{65} -87.2576 q^{66} +575.939 q^{67} -1374.10 q^{68} +384.145 q^{69} -246.309 q^{70} +453.382 q^{71} +634.567 q^{72} -609.113 q^{73} -1057.65 q^{74} +325.032 q^{75} -111.702 q^{76} +28.2693 q^{77} -514.720 q^{78} +494.638 q^{79} +319.964 q^{80} +403.438 q^{81} +624.777 q^{82} +272.053 q^{83} +89.8167 q^{84} -1656.40 q^{85} +1807.69 q^{86} +483.506 q^{87} -252.146 q^{88} +38.0718 q^{89} +1793.22 q^{90} +166.756 q^{91} +2602.27 q^{92} +424.842 q^{93} +1899.02 q^{94} -134.651 q^{95} +275.803 q^{96} +1304.54 q^{97} +1561.24 q^{98} -205.810 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.68521	−1.65647	−0.828236	−	0.560380i	$-0.810655\pi$
$2$	−4.68521	−1.65647	−0.828236	+	0.560380i	$0.810655\pi$
$3$	2.05946	0.396343	0.198172	−	0.980167i	$-0.436500\pi$
$3$	2.05946	0.396343	0.198172	+	0.980167i	$0.436500\pi$
$4$	13.9512	1.74390
$5$	16.8174	1.50419	0.752096	−	0.659054i	$-0.229043\pi$
$5$	16.8174	1.50419	0.752096	+	0.659054i	$0.229043\pi$
$6$	−9.64900	−0.656531
$7$	3.12603	0.168790	0.0843949	−	0.996432i	$-0.473104\pi$
$7$	3.12603	0.168790	0.0843949	+	0.996432i	$0.473104\pi$
$8$	−27.8825	−1.23224
$9$	−22.7586	−0.842912
$10$	−78.7929	−2.49165
$11$	9.04318	0.247875	0.123937	−	0.992290i	$-0.460448\pi$
$11$	9.04318	0.247875	0.123937	+	0.992290i	$0.460448\pi$
$12$	28.7319	0.691182
$13$	53.3444	1.13808	0.569042	−	0.822309i	$-0.307314\pi$
$13$	53.3444	1.13808	0.569042	+	0.822309i	$0.307314\pi$
$14$	−14.6461	−0.279595
$15$	34.6347	0.596176
$16$	19.0258	0.297278
$17$	−98.4932	−1.40518	−0.702591	−	0.711594i	$-0.747974\pi$
$17$	−98.4932	−1.40518	−0.702591	+	0.711594i	$0.747974\pi$
$18$	106.629	1.39626
$19$	−8.00668	−0.0966767	−0.0483383	−	0.998831i	$-0.515393\pi$
$19$	−8.00668	−0.0966767	−0.0483383	+	0.998831i	$0.515393\pi$
$20$	234.622	2.62315
$21$	6.43793	0.0668987
$22$	−42.3692	−0.410597
$23$	186.527	1.69103	0.845513	−	0.533954i	$-0.179295\pi$
$23$	186.527	1.69103	0.845513	+	0.533954i	$0.179295\pi$
$24$	−57.4228	−0.488391
$25$	157.824	1.26259
$26$	−249.930	−1.88520
$27$	−102.476	−0.730426
$28$	43.6118	0.294352
$29$	234.773	1.50332	0.751660	−	0.659551i	$-0.229253\pi$
$29$	234.773	1.50332	0.751660	+	0.659551i	$0.229253\pi$
$30$	−162.271	−0.987548
$31$	206.288	1.19517	0.597587	−	0.801804i	$-0.296126\pi$
$31$	206.288	1.19517	0.597587	+	0.801804i	$0.296126\pi$
$32$	133.920	0.739810
$33$	18.6241	0.0982435
$34$	461.461	2.32764
$35$	52.5716	0.253892
$36$	−317.509	−1.46995
$37$	225.743	1.00303	0.501513	−	0.865150i	$-0.332777\pi$
$37$	225.743	1.00303	0.501513	+	0.865150i	$0.332777\pi$
$38$	37.5129	0.160142
$39$	109.861	0.451072
$40$	−468.910	−1.85353
$41$	−133.351	−0.507949	−0.253975	−	0.967211i	$-0.581738\pi$
$41$	−133.351	−0.507949	−0.253975	+	0.967211i	$0.581738\pi$
$42$	−30.1631	−0.110816
$43$	−385.829	−1.36833	−0.684167	−	0.729325i	$-0.739834\pi$
$43$	−385.829	−1.36833	−0.684167	+	0.729325i	$0.739834\pi$
$44$	126.163	0.432268
$45$	−382.740	−1.26790
$46$	−873.919	−2.80114
$47$	−405.323	−1.25792	−0.628962	−	0.777436i	$-0.716520\pi$
$47$	−405.323	−1.25792	−0.628962	+	0.777436i	$0.716520\pi$
$48$	39.1829	0.117824
$49$	−333.228	−0.971510
$50$	−739.438	−2.09145
$51$	−202.843	−0.556935
$52$	744.218	1.98470
$53$	−60.5540	−0.156938	−0.0784691	−	0.996917i	$-0.525003\pi$
$53$	−60.5540	−0.156938	−0.0784691	+	0.996917i	$0.525003\pi$
$54$	480.121	1.20993
$55$	152.083	0.372851
$56$	−87.1615	−0.207990
$57$	−16.4894	−0.0383172
$58$	−1099.96	−2.49021
$59$	379.335	0.837038	0.418519	−	0.908208i	$-0.362549\pi$
$59$	379.335	0.837038	0.418519	+	0.908208i	$0.362549\pi$
$60$	483.195	1.03967
$61$	647.920	1.35996	0.679981	−	0.733230i	$-0.261988\pi$
$61$	647.920	1.35996	0.679981	+	0.733230i	$0.261988\pi$
$62$	−966.502	−1.97977
$63$	−71.1442	−0.142275
$64$	−779.649	−1.52275
$65$	897.113	1.71190
$66$	−87.2576	−0.162737
$67$	575.939	1.05018	0.525091	−	0.851046i	$-0.324031\pi$
$67$	575.939	1.05018	0.525091	+	0.851046i	$0.324031\pi$
$68$	−1374.10	−2.45049
$69$	384.145	0.670227
$70$	−246.309	−0.420565
$71$	453.382	0.757839	0.378919	−	0.925430i	$-0.376296\pi$
$71$	453.382	0.757839	0.378919	+	0.925430i	$0.376296\pi$
$72$	634.567	1.03867
$73$	−609.113	−0.976592	−0.488296	−	0.872678i	$-0.662381\pi$
$73$	−609.113	−0.976592	−0.488296	+	0.872678i	$0.662381\pi$
$74$	−1057.65	−1.66148
$75$	325.032	0.500419
$76$	−111.702	−0.168594
$77$	28.2693	0.0418387
$78$	−514.720	−0.747187
$79$	494.638	0.704444	0.352222	−	0.935916i	$-0.385426\pi$
$79$	494.638	0.704444	0.352222	+	0.935916i	$0.385426\pi$
$80$	319.964	0.447164
$81$	403.438	0.553413
$82$	624.777	0.841403
$83$	272.053	0.359779	0.179890	−	0.983687i	$-0.442426\pi$
$83$	272.053	0.359779	0.179890	+	0.983687i	$0.442426\pi$
$84$	89.8167	0.116664
$85$	−1656.40	−2.11366
$86$	1807.69	2.26661
$87$	483.506	0.595831
$88$	−252.146	−0.305442
$89$	38.0718	0.0453439	0.0226720	−	0.999743i	$-0.492783\pi$
$89$	38.0718	0.0453439	0.0226720	+	0.999743i	$0.492783\pi$
$90$	1793.22	2.10024
$91$	166.756	0.192097
$92$	2602.27	2.94898
$93$	424.842	0.473699
$94$	1899.02	2.08371
$95$	−134.651	−0.145420
$96$	275.803	0.293219
$97$	1304.54	1.36552	0.682761	−	0.730642i	$-0.260779\pi$
$97$	1304.54	1.36552	0.682761	+	0.730642i	$0.260779\pi$
$98$	1561.24	1.60928
$99$	−205.810	−0.208937
$100$	2201.83	2.20183
$101$	−1316.67	−1.29717	−0.648584	−	0.761143i	$-0.724639\pi$
$101$	−1316.67	−1.29717	−0.648584	+	0.761143i	$0.724639\pi$
$102$	950.360	0.922546
$103$	−1886.00	−1.80420	−0.902101	−	0.431524i	$-0.857976\pi$
$103$	−1886.00	−1.80420	−0.902101	+	0.431524i	$0.857976\pi$
$104$	−1487.38	−1.40240
$105$	108.269	0.100628
$106$	283.708	0.259964
$107$	1423.23	1.28588	0.642938	−	0.765919i	$-0.277715\pi$
$107$	1423.23	1.28588	0.642938	+	0.765919i	$0.277715\pi$
$108$	−1429.66	−1.27379
$109$	1028.82	0.904064	0.452032	−	0.892002i	$-0.350699\pi$
$109$	1028.82	0.904064	0.452032	+	0.892002i	$0.350699\pi$
$110$	−712.538	−0.617617
$111$	464.909	0.397542
$112$	59.4753	0.0501776
$113$	1695.12	1.41118	0.705591	−	0.708620i	$-0.250682\pi$
$113$	1695.12	1.41118	0.705591	+	0.708620i	$0.250682\pi$
$114$	77.2564	0.0634713
$115$	3136.90	2.54363
$116$	3275.36	2.62163
$117$	−1214.05	−0.959304
$118$	−1777.26	−1.38653
$119$	−307.893	−0.237180
$120$	−965.701	−0.734634
$121$	−1249.22	−0.938558
$122$	−3035.64	−2.25274
$123$	−274.631	−0.201322
$124$	2877.96	2.08426
$125$	552.011	0.394987
$126$	333.325	0.235674
$127$	−657.897	−0.459677	−0.229838	−	0.973229i	$-0.573820\pi$
$127$	−657.897	−0.459677	−0.229838	+	0.973229i	$0.573820\pi$
$128$	2581.46	1.78258
$129$	−794.599	−0.542330
$130$	−4203.16	−2.83571
$131$	1727.36	1.15206	0.576030	−	0.817428i	$-0.304601\pi$
$131$	1727.36	1.15206	0.576030	+	0.817428i	$0.304601\pi$
$132$	259.828	0.171326
$133$	−25.0291	−0.0163180
$134$	−2698.39	−1.73960
$135$	−1723.37	−1.09870
$136$	2746.23	1.73153
$137$	2053.49	1.28059	0.640297	−	0.768127i	$-0.278811\pi$
$137$	2053.49	1.28059	0.640297	+	0.768127i	$0.278811\pi$
$138$	−1799.80	−1.11021
$139$	−219.493	−0.133936	−0.0669680	−	0.997755i	$-0.521333\pi$
$139$	−219.493	−0.133936	−0.0669680	+	0.997755i	$0.521333\pi$
$140$	733.436	0.442762
$141$	−834.746	−0.498569
$142$	−2124.19	−1.25534
$143$	482.403	0.282102
$144$	−433.001	−0.250580
$145$	3948.27	2.26128
$146$	2853.82	1.61770
$147$	−686.270	−0.385051
$148$	3149.38	1.74917
$149$	850.599	0.467677	0.233838	−	0.972275i	$-0.424871\pi$
$149$	850.599	0.467677	0.233838	+	0.972275i	$0.424871\pi$
$150$	−1522.84	−0.828930
$151$	−3100.77	−1.67111	−0.835554	−	0.549409i	$-0.814853\pi$
$151$	−3100.77	−1.67111	−0.835554	+	0.549409i	$0.814853\pi$
$152$	223.246	0.119129
$153$	2241.57	1.18445
$154$	−132.447	−0.0693046
$155$	3469.22	1.79777
$156$	1532.69	0.786622
$157$	−1907.45	−0.969627	−0.484814	−	0.874618i	$-0.661113\pi$
$157$	−1907.45	−0.969627	−0.484814	+	0.874618i	$0.661113\pi$
$158$	−2317.48	−1.16689
$159$	−124.708	−0.0622014
$160$	2252.18	1.11282
$161$	583.090	0.285428
$162$	−1890.19	−0.916712
$163$	2759.70	1.32611	0.663057	−	0.748569i	$-0.269259\pi$
$163$	2759.70	1.32611	0.663057	+	0.748569i	$0.269259\pi$
$164$	−1860.40	−0.885811
$165$	313.208	0.147777
$166$	−1274.62	−0.595964
$167$	2177.08	1.00879	0.504394	−	0.863473i	$-0.331716\pi$
$167$	2177.08	1.00879	0.504394	+	0.863473i	$0.331716\pi$
$168$	−179.506	−0.0824354
$169$	648.630	0.295234
$170$	7760.56	3.50122
$171$	182.221	0.0814900
$172$	−5382.77	−2.38623
$173$	−250.414	−0.110050	−0.0550249	−	0.998485i	$-0.517524\pi$
$173$	−250.414	−0.110050	−0.0550249	+	0.998485i	$0.517524\pi$
$174$	−2265.33	−0.986976
$175$	493.362	0.213112
$176$	172.054	0.0736878
$177$	781.226	0.331754
$178$	−178.375	−0.0751109
$179$	−1404.21	−0.586346	−0.293173	−	0.956059i	$-0.594711\pi$
$179$	−1404.21	−0.586346	−0.293173	+	0.956059i	$0.594711\pi$
$180$	−5339.67	−2.21109
$181$	−40.6048	−0.0166748	−0.00833739	−	0.999965i	$-0.502654\pi$
$181$	−40.6048	−0.0166748	−0.00833739	+	0.999965i	$0.502654\pi$
$182$	−781.288	−0.318203
$183$	1334.36	0.539011
$184$	−5200.84	−2.08376
$185$	3796.41	1.50874
$186$	−1990.47	−0.784669
$187$	−890.692	−0.348309
$188$	−5654.73	−2.19369
$189$	−320.343	−0.123288
$190$	630.869	0.240884
$191$	−1754.09	−0.664512	−0.332256	−	0.943189i	$-0.607810\pi$
$191$	−1754.09	−0.664512	−0.332256	+	0.943189i	$0.607810\pi$
$192$	−1605.66	−0.603533
$193$	−3995.04	−1.49000	−0.744999	−	0.667066i	$-0.767550\pi$
$193$	−3995.04	−1.49000	−0.744999	+	0.667066i	$0.767550\pi$
$194$	−6112.03	−2.26195
$195$	1847.57	0.678498
$196$	−4648.92	−1.69421
$197$	4190.23	1.51544	0.757719	−	0.652581i	$-0.226314\pi$
$197$	4190.23	1.51544	0.757719	+	0.652581i	$0.226314\pi$
$198$	964.264	0.346097
$199$	3123.21	1.11255	0.556277	−	0.830997i	$-0.312229\pi$
$199$	3123.21	1.11255	0.556277	+	0.830997i	$0.312229\pi$
$200$	−4400.52	−1.55582
$201$	1186.12	0.416232
$202$	6168.89	2.14872
$203$	733.908	0.253745
$204$	−2829.89	−0.971236
$205$	−2242.61	−0.764053
$206$	8836.29	2.98861
$207$	−4245.10	−1.42539
$208$	1014.92	0.338328
$209$	−72.4058	−0.0239637
$210$	−507.263	−0.166688
$211$	−4425.42	−1.44388	−0.721940	−	0.691956i	$-0.756749\pi$
$211$	−4425.42	−1.44388	−0.721940	+	0.691956i	$0.756749\pi$
$212$	−844.799	−0.273684
$213$	933.722	0.300364
$214$	−6668.12	−2.13002
$215$	−6488.63	−2.05824
$216$	2857.28	0.900062
$217$	644.863	0.201733
$218$	−4820.23	−1.49756
$219$	−1254.44	−0.387066
$220$	2121.73	0.650213
$221$	−5254.06	−1.59922
$222$	−2178.20	−0.658518
$223$	3197.22	0.960097	0.480049	−	0.877242i	$-0.340619\pi$
$223$	3197.22	0.960097	0.480049	+	0.877242i	$0.340619\pi$
$224$	418.638	0.124872
$225$	−3591.85	−1.06425
$226$	−7941.99	−2.33758
$227$	6133.40	1.79334	0.896670	−	0.442699i	$-0.145979\pi$
$227$	6133.40	1.79334	0.896670	+	0.442699i	$0.145979\pi$
$228$	−230.047	−0.0668212
$229$	4669.19	1.34738	0.673688	−	0.739016i	$-0.264709\pi$
$229$	4669.19	1.34738	0.673688	+	0.739016i	$0.264709\pi$
$230$	−14697.0	−4.21345
$231$	58.2194	0.0165825
$232$	−6546.06	−1.85246
$233$	3772.62	1.06074	0.530370	−	0.847766i	$-0.322053\pi$
$233$	3772.62	1.06074	0.530370	+	0.847766i	$0.322053\pi$
$234$	5688.06	1.58906
$235$	−6816.46	−1.89216
$236$	5292.17	1.45971
$237$	1018.69	0.279202
$238$	1442.54	0.392883
$239$	−2695.19	−0.729446	−0.364723	−	0.931116i	$-0.618836\pi$
$239$	−2695.19	−0.729446	−0.364723	+	0.931116i	$0.618836\pi$
$240$	658.953	0.177230
$241$	1924.75	0.514456	0.257228	−	0.966351i	$-0.417191\pi$
$241$	1924.75	0.514456	0.257228	+	0.966351i	$0.417191\pi$
$242$	5852.86	1.55469
$243$	3597.71	0.949767
$244$	9039.24	2.37163
$245$	−5604.02	−1.46134
$246$	1286.70	0.333484
$247$	−427.112	−0.110026
$248$	−5751.82	−1.47275
$249$	560.282	0.142596
$250$	−2586.29	−0.654285
$251$	−6144.11	−1.54507	−0.772536	−	0.634971i	$-0.781012\pi$
$251$	−6144.11	−1.54507	−0.772536	+	0.634971i	$0.781012\pi$
$252$	−992.544	−0.248113
$253$	1686.80	0.419163
$254$	3082.39	0.761441
$255$	−3411.28	−0.837736
$256$	−5857.48	−1.43005
$257$	651.547	0.158141	0.0790707	−	0.996869i	$-0.474805\pi$
$257$	651.547	0.158141	0.0790707	+	0.996869i	$0.474805\pi$
$258$	3722.86	0.898354
$259$	705.680	0.169301
$260$	12515.8	2.98537
$261$	−5343.11	−1.26717
$262$	−8093.03	−1.90836
$263$	3459.29	0.811060	0.405530	−	0.914082i	$-0.367087\pi$
$263$	3459.29	0.811060	0.405530	+	0.914082i	$0.367087\pi$
$264$	−519.285	−0.121060
$265$	−1018.36	−0.236065
$266$	117.267	0.0270304
$267$	78.4074	0.0179718
$268$	8035.03	1.83141
$269$	7686.20	1.74214	0.871070	−	0.491158i	$-0.163426\pi$
$269$	7686.20	1.74214	0.871070	+	0.491158i	$0.163426\pi$
$270$	8074.37	1.81996
$271$	−3194.21	−0.715994	−0.357997	−	0.933723i	$-0.616540\pi$
$271$	−3194.21	−0.715994	−0.357997	+	0.933723i	$0.616540\pi$
$272$	−1873.91	−0.417730
$273$	343.428	0.0761363
$274$	−9621.03	−2.12127
$275$	1427.23	0.312964
$276$	5359.28	1.16881
$277$	−5491.58	−1.19118	−0.595591	−	0.803288i	$-0.703082\pi$
$277$	−5491.58	−1.19118	−0.595591	+	0.803288i	$0.703082\pi$
$278$	1028.37	0.221861
$279$	−4694.83	−1.00743
$280$	−1465.83	−0.312857
$281$	1628.94	0.345816	0.172908	−	0.984938i	$-0.444684\pi$
$281$	1628.94	0.345816	0.172908	+	0.984938i	$0.444684\pi$
$282$	3910.96	0.825866
$283$	−4496.51	−0.944487	−0.472244	−	0.881468i	$-0.656556\pi$
$283$	−4496.51	−0.944487	−0.472244	+	0.881468i	$0.656556\pi$
$284$	6325.21	1.32159
$285$	−277.309	−0.0576363
$286$	−2260.16	−0.467294
$287$	−416.859	−0.0857366
$288$	−3047.83	−0.623595
$289$	4787.91	0.974538
$290$	−18498.5	−3.74575
$291$	2686.64	0.541216
$292$	−8497.83	−1.70308
$293$	2310.06	0.460597	0.230299	−	0.973120i	$-0.426030\pi$
$293$	2310.06	0.460597	0.230299	+	0.973120i	$0.426030\pi$
$294$	3215.32	0.637827
$295$	6379.42	1.25906
$296$	−6294.28	−1.23597
$297$	−926.708	−0.181054
$298$	−3985.23	−0.774693
$299$	9950.19	1.92453
$300$	4534.58	0.872680
$301$	−1206.11	−0.230961
$302$	14527.8	2.76814
$303$	−2711.64	−0.514124
$304$	−152.334	−0.0287399
$305$	10896.3	2.04564
$306$	−10502.2	−1.96200
$307$	−3707.58	−0.689259	−0.344630	−	0.938739i	$-0.611995\pi$
$307$	−3707.58	−0.689259	−0.344630	+	0.938739i	$0.611995\pi$
$308$	394.389	0.0729624
$309$	−3884.14	−0.715083
$310$	−16254.0	−2.97796
$311$	−509.285	−0.0928582	−0.0464291	−	0.998922i	$-0.514784\pi$
$311$	−509.285	−0.0928582	−0.0464291	+	0.998922i	$0.514784\pi$
$312$	−3063.19	−0.555830
$313$	−4120.75	−0.744148	−0.372074	−	0.928203i	$-0.621353\pi$
$313$	−4120.75	−0.744148	−0.372074	+	0.928203i	$0.621353\pi$
$314$	8936.82	1.60616
$315$	−1196.46	−0.214009
$316$	6900.77	1.22848
$317$	10159.2	1.79999	0.899997	−	0.435897i	$-0.143569\pi$
$317$	10159.2	1.79999	0.899997	+	0.435897i	$0.143569\pi$
$318$	584.285	0.103035
$319$	2123.10	0.372635
$320$	−13111.6	−2.29051
$321$	2931.08	0.509648
$322$	−2731.90	−0.472803
$323$	788.603	0.135848
$324$	5628.43	0.965095
$325$	8419.03	1.43693
$326$	−12929.8	−2.19667
$327$	2118.81	0.358320
$328$	3718.15	0.625917
$329$	−1267.05	−0.212325
$330$	−1467.44	−0.244788
$331$	−4186.96	−0.695276	−0.347638	−	0.937629i	$-0.613016\pi$
$331$	−4186.96	−0.695276	−0.347638	+	0.937629i	$0.613016\pi$
$332$	3795.46	0.627418
$333$	−5137.60	−0.845462
$334$	−10200.1	−1.67103
$335$	9685.78	1.57967
$336$	122.487	0.0198875
$337$	465.667	0.0752715	0.0376358	−	0.999292i	$-0.488017\pi$
$337$	465.667	0.0752715	0.0376358	+	0.999292i	$0.488017\pi$
$338$	−3038.97	−0.489047
$339$	3491.03	0.559312
$340$	−23108.7	−3.68601
$341$	1865.50	0.296254
$342$	−853.743	−0.134986
$343$	−2113.91	−0.332771
$344$	10757.9	1.68612
$345$	6460.31	1.00815
$346$	1173.24	0.182294
$347$	−10579.9	−1.63677	−0.818384	−	0.574672i	$-0.805130\pi$
$347$	−10579.9	−1.63677	−0.818384	+	0.574672i	$0.805130\pi$
$348$	6745.47	1.03907
$349$	4255.56	0.652707	0.326354	−	0.945248i	$-0.394180\pi$
$349$	4255.56	0.652707	0.326354	+	0.945248i	$0.394180\pi$
$350$	−2311.50	−0.353015
$351$	−5466.52	−0.831286
$352$	1211.06	0.183380
$353$	10264.8	1.54771	0.773853	−	0.633365i	$-0.218327\pi$
$353$	10264.8	1.54771	0.773853	+	0.633365i	$0.218327\pi$
$354$	−3660.20	−0.549541
$355$	7624.69	1.13993
$356$	531.147	0.0790751
$357$	−634.093	−0.0940049
$358$	6579.03	0.971265
$359$	−2939.03	−0.432078	−0.216039	−	0.976385i	$-0.569314\pi$
$359$	−2939.03	−0.432078	−0.216039	+	0.976385i	$0.569314\pi$
$360$	10671.7	1.56236
$361$	−6794.89	−0.990654
$362$	190.242	0.0276213
$363$	−2572.72	−0.371991
$364$	2326.45	0.334997
$365$	−10243.7	−1.46898
$366$	−6251.78	−0.892857
$367$	6643.51	0.944928	0.472464	−	0.881350i	$-0.343365\pi$
$367$	6643.51	0.944928	0.472464	+	0.881350i	$0.343365\pi$
$368$	3548.83	0.502706
$369$	3034.88	0.428156
$370$	−17787.0	−2.49919
$371$	−189.294	−0.0264896
$372$	5927.04	0.826083
$373$	−5191.02	−0.720592	−0.360296	−	0.932838i	$-0.617324\pi$
$373$	−5191.02	−0.720592	−0.360296	+	0.932838i	$0.617324\pi$
$374$	4173.08	0.576964
$375$	1136.85	0.156550
$376$	11301.4	1.55007
$377$	12523.8	1.71090
$378$	1500.87	0.204224
$379$	−1096.62	−0.148627	−0.0743136	−	0.997235i	$-0.523677\pi$
$379$	−1096.62	−0.148627	−0.0743136	+	0.997235i	$0.523677\pi$
$380$	−1878.54	−0.253598
$381$	−1354.91	−0.182190
$382$	8218.30	1.10074
$383$	−3200.15	−0.426945	−0.213472	−	0.976949i	$-0.568477\pi$
$383$	−3200.15	−0.426945	−0.213472	+	0.976949i	$0.568477\pi$
$384$	5316.41	0.706515
$385$	475.415	0.0629334
$386$	18717.6	2.46814
$387$	8780.94	1.15339
$388$	18199.8	2.38133
$389$	2193.91	0.285953	0.142977	−	0.989726i	$-0.454333\pi$
$389$	2193.91	0.285953	0.142977	+	0.989726i	$0.454333\pi$
$390$	−8656.24	−1.12391
$391$	−18371.7	−2.37620
$392$	9291.22	1.19714
$393$	3557.42	0.456612
$394$	−19632.1	−2.51028
$395$	8318.50	1.05962
$396$	−2871.30	−0.364364
$397$	−2088.63	−0.264043	−0.132022	−	0.991247i	$-0.542147\pi$
$397$	−2088.63	−0.264043	−0.132022	+	0.991247i	$0.542147\pi$
$398$	−14632.9	−1.84292
$399$	−51.5465	−0.00646754
$400$	3002.73	0.375341
$401$	−2923.75	−0.364102	−0.182051	−	0.983289i	$-0.558274\pi$
$401$	−2923.75	−0.364102	−0.182051	+	0.983289i	$0.558274\pi$
$402$	−5557.24	−0.689477
$403$	11004.3	1.36021
$404$	−18369.1	−2.26213
$405$	6784.76	0.832439
$406$	−3438.51	−0.420321
$407$	2041.44	0.248625
$408$	5655.76	0.686279
$409$	2060.58	0.249118	0.124559	−	0.992212i	$-0.460248\pi$
$409$	2060.58	0.249118	0.124559	+	0.992212i	$0.460248\pi$
$410$	10507.1	1.26563
$411$	4229.08	0.507555
$412$	−26311.9	−3.14634
$413$	1185.81	0.141283
$414$	19889.2	2.36111
$415$	4575.21	0.541177
$416$	7143.88	0.841966
$417$	−452.036	−0.0530847
$418$	339.236	0.0396952
$419$	−5147.06	−0.600120	−0.300060	−	0.953920i	$-0.597007\pi$
$419$	−5147.06	−0.600120	−0.300060	+	0.953920i	$0.597007\pi$
$420$	1510.48	0.175486
$421$	−15839.8	−1.83369	−0.916847	−	0.399239i	$-0.869274\pi$
$421$	−15839.8	−1.83369	−0.916847	+	0.399239i	$0.869274\pi$
$422$	20734.0	2.39174
$423$	9224.59	1.06032
$424$	1688.39	0.193386
$425$	−15544.6	−1.77417
$426$	−4374.68	−0.497545
$427$	2025.42	0.229548
$428$	19855.7	2.24243
$429$	993.491	0.111809
$430$	30400.6	3.40941
$431$	4719.70	0.527471	0.263736	−	0.964595i	$-0.415045\pi$
$431$	4719.70	0.527471	0.263736	+	0.964595i	$0.415045\pi$
$432$	−1949.69	−0.217140
$433$	6040.28	0.670386	0.335193	−	0.942149i	$-0.391198\pi$
$433$	6040.28	0.670386	0.335193	+	0.942149i	$0.391198\pi$
$434$	−3021.32	−0.334165
$435$	8131.30	0.896243
$436$	14353.2	1.57659
$437$	−1493.46	−0.163483
$438$	5877.33	0.641163
$439$	−10810.5	−1.17530	−0.587649	−	0.809116i	$-0.699946\pi$
$439$	−10810.5	−1.17530	−0.587649	+	0.809116i	$0.699946\pi$
$440$	−4240.44	−0.459443
$441$	7583.81	0.818897
$442$	24616.4	2.64905
$443$	−12183.4	−1.30666	−0.653330	−	0.757073i	$-0.726628\pi$
$443$	−12183.4	−1.30666	−0.653330	+	0.757073i	$0.726628\pi$
$444$	6486.03	0.693273
$445$	640.268	0.0682059
$446$	−14979.6	−1.59037
$447$	1751.78	0.185360
$448$	−2437.21	−0.257025
$449$	−12823.9	−1.34788	−0.673941	−	0.738785i	$-0.735400\pi$
$449$	−12823.9	−1.34788	−0.673941	+	0.738785i	$0.735400\pi$
$450$	16828.6	1.76290
$451$	−1205.92	−0.125908
$452$	23648.9	2.46095
$453$	−6385.91	−0.662332
$454$	−28736.3	−2.97062
$455$	2804.40	0.288950
$456$	459.766	0.0472160
$457$	−5877.22	−0.601586	−0.300793	−	0.953689i	$-0.597251\pi$
$457$	−5877.22	−0.601586	−0.300793	+	0.953689i	$0.597251\pi$
$458$	−21876.1	−2.23189
$459$	10093.2	1.02638
$460$	43763.4	4.43582
$461$	−17628.4	−1.78099	−0.890493	−	0.454998i	$-0.849640\pi$
$461$	−17628.4	−1.78099	−0.890493	+	0.454998i	$0.849640\pi$
$462$	−272.770	−0.0274684
$463$	13993.0	1.40456	0.702280	−	0.711901i	$-0.252165\pi$
$463$	13993.0	1.40456	0.702280	+	0.711901i	$0.252165\pi$
$464$	4466.75	0.446905
$465$	7144.72	0.712535
$466$	−17675.5	−1.75708
$467$	−12944.8	−1.28269	−0.641344	−	0.767254i	$-0.721623\pi$
$467$	−12944.8	−1.28269	−0.641344	+	0.767254i	$0.721623\pi$
$468$	−16937.4	−1.67293
$469$	1800.40	0.177260
$470$	31936.5	3.13430
$471$	−3928.33	−0.384305
$472$	−10576.8	−1.03143
$473$	−3489.12	−0.339175
$474$	−4772.76	−0.462489
$475$	−1263.64	−0.122063
$476$	−4295.46	−0.413618
$477$	1378.12	0.132285
$478$	12627.5	1.20831
$479$	1691.65	0.161364	0.0806822	−	0.996740i	$-0.474290\pi$
$479$	1691.65	0.161364	0.0806822	+	0.996740i	$0.474290\pi$
$480$	4638.27	0.441057
$481$	12042.1	1.14153
$482$	−9017.84	−0.852181
$483$	1200.85	0.113127
$484$	−17428.1	−1.63675
$485$	21938.9	2.05401
$486$	−16856.0	−1.57326
$487$	16488.8	1.53425	0.767123	−	0.641500i	$-0.221687\pi$
$487$	16488.8	1.53425	0.767123	+	0.641500i	$0.221687\pi$
$488$	−18065.6	−1.67580
$489$	5683.49	0.525596
$490$	26256.0	2.42066
$491$	−8302.34	−0.763094	−0.381547	−	0.924349i	$-0.624609\pi$
$491$	−8302.34	−0.763094	−0.381547	+	0.924349i	$0.624609\pi$
$492$	−3831.42	−0.351085
$493$	−23123.6	−2.11244
$494$	2001.11	0.182255
$495$	−3461.19	−0.314281
$496$	3924.80	0.355300
$497$	1417.29	0.127915
$498$	−2625.04	−0.236206
$499$	−10418.9	−0.934697	−0.467348	−	0.884073i	$-0.654791\pi$
$499$	−10418.9	−0.934697	−0.467348	+	0.884073i	$0.654791\pi$
$500$	7701.20	0.688817
$501$	4483.61	0.399827
$502$	28786.4	2.55937
$503$	−14318.5	−1.26924	−0.634622	−	0.772823i	$-0.718844\pi$
$503$	−14318.5	−1.26924	−0.634622	+	0.772823i	$0.718844\pi$
$504$	1983.68	0.175317
$505$	−22143.0	−1.95119
$506$	−7903.01	−0.694331
$507$	1335.83	0.117014
$508$	−9178.44	−0.801629
$509$	−6833.49	−0.595067	−0.297533	−	0.954711i	$-0.596164\pi$
$509$	−6833.49	−0.595067	−0.297533	+	0.954711i	$0.596164\pi$
$510$	15982.6	1.38769
$511$	−1904.10	−0.164839
$512$	6791.83	0.586249
$513$	820.491	0.0706151
$514$	−3052.63	−0.261957
$515$	−31717.5	−2.71387
$516$	−11085.6	−0.945767
$517$	−3665.41	−0.311807
$518$	−3306.26	−0.280441
$519$	−515.717	−0.0436175
$520$	−25013.7	−2.10947
$521$	21480.0	1.80625	0.903124	−	0.429380i	$-0.141268\pi$
$521$	21480.0	1.80625	0.903124	+	0.429380i	$0.141268\pi$
$522$	25033.6	2.09902
$523$	9682.45	0.809530	0.404765	−	0.914421i	$-0.367353\pi$
$523$	9682.45	0.809530	0.404765	+	0.914421i	$0.367353\pi$
$524$	24098.7	2.00907
$525$	1016.06	0.0844657
$526$	−16207.5	−1.34350
$527$	−20318.0	−1.67944
$528$	354.338	0.0292057
$529$	22625.4	1.85957
$530$	4771.22	0.391035
$531$	−8633.15	−0.705549
$532$	−349.185	−0.0284570
$533$	−7113.53	−0.578089
$534$	−367.355	−0.0297697
$535$	23934.9	1.93420
$536$	−16058.6	−1.29408
$537$	−2891.92	−0.232394
$538$	−36011.4	−2.88581
$539$	−3013.44	−0.240813
$540$	−24043.1	−1.91602
$541$	20557.8	1.63373	0.816866	−	0.576827i	$-0.195709\pi$
$541$	20557.8	1.63373	0.816866	+	0.576827i	$0.195709\pi$
$542$	14965.5	1.18602
$543$	−83.6240	−0.00660893
$544$	−13190.2	−1.03957
$545$	17302.0	1.35989
$546$	−1609.03	−0.126118
$547$	−547.000	−0.0427569
$547$	−547.000	−0.0427569
$548$	28648.6	2.23323
$549$	−14745.8	−1.14633
$550$	−6686.87	−0.518416
$551$	−1879.75	−0.145336
$552$	−10710.9	−0.825883
$553$	1546.25	0.118903
$554$	25729.2	1.97316
$555$	7818.55	0.597980
$556$	−3062.18	−0.233571
$557$	−3465.83	−0.263648	−0.131824	−	0.991273i	$-0.542083\pi$
$557$	−3465.83	−0.263648	−0.131824	+	0.991273i	$0.542083\pi$
$558$	21996.3	1.66877
$559$	−20581.8	−1.55728
$560$	1000.22	0.0754766
$561$	−1834.34	−0.138050
$562$	−7631.92	−0.572835
$563$	−17181.7	−1.28618	−0.643092	−	0.765789i	$-0.722349\pi$
$563$	−17181.7	−1.28618	−0.643092	+	0.765789i	$0.722349\pi$
$564$	−11645.7	−0.869453
$565$	28507.5	2.12269
$566$	21067.1	1.56452
$567$	1261.16	0.0934104
$568$	−12641.4	−0.933842
$569$	−5855.33	−0.431403	−0.215701	−	0.976459i	$-0.569204\pi$
$569$	−5855.33	−0.431403	−0.215701	+	0.976459i	$0.569204\pi$
$570$	1299.25	0.0954729
$571$	−13605.8	−0.997171	−0.498586	−	0.866840i	$-0.666147\pi$
$571$	−13605.8	−0.997171	−0.498586	+	0.866840i	$0.666147\pi$
$572$	6730.09	0.491957
$573$	−3612.49	−0.263375
$574$	1953.07	0.142020
$575$	29438.4	2.13508
$576$	17743.7	1.28355
$577$	2406.40	0.173622	0.0868110	−	0.996225i	$-0.472332\pi$
$577$	2406.40	0.173622	0.0868110	+	0.996225i	$0.472332\pi$
$578$	−22432.3	−1.61429
$579$	−8227.63	−0.590551
$580$	55083.0	3.94344
$581$	850.446	0.0607271
$582$	−12587.5	−0.896508
$583$	−547.600	−0.0389010
$584$	16983.6	1.20340
$585$	−20417.1	−1.44298
$586$	−10823.1	−0.762966
$587$	4380.89	0.308039	0.154019	−	0.988068i	$-0.450778\pi$
$587$	4380.89	0.308039	0.154019	+	0.988068i	$0.450778\pi$
$588$	−9574.26	−0.671490
$589$	−1651.68	−0.115546
$590$	−29888.9	−2.08560
$591$	8629.60	0.600633
$592$	4294.95	0.298178
$593$	20951.0	1.45085	0.725424	−	0.688302i	$-0.241644\pi$
$593$	20951.0	1.45085	0.725424	+	0.688302i	$0.241644\pi$
$594$	4341.82	0.299911
$595$	−5177.94	−0.356765
$596$	11866.9	0.815580
$597$	6432.12	0.440954
$598$	−46618.7	−3.18793
$599$	4862.58	0.331686	0.165843	−	0.986152i	$-0.446966\pi$
$599$	4862.58	0.331686	0.165843	+	0.986152i	$0.446966\pi$
$600$	−9062.70	−0.616638
$601$	−7480.34	−0.507703	−0.253852	−	0.967243i	$-0.581697\pi$
$601$	−7480.34	−0.507703	−0.253852	+	0.967243i	$0.581697\pi$
$602$	5650.89	0.382580
$603$	−13107.6	−0.885211
$604$	−43259.4	−2.91424
$605$	−21008.6	−1.41177
$606$	12704.6	0.851631
$607$	−3596.52	−0.240491	−0.120246	−	0.992744i	$-0.538368\pi$
$607$	−3596.52	−0.240491	−0.120246	+	0.992744i	$0.538368\pi$
$608$	−1072.25	−0.0715224
$609$	1511.45	0.100570
$610$	−51051.5	−3.38855
$611$	−21621.7	−1.43162
$612$	31272.5	2.06555
$613$	−23291.5	−1.53464	−0.767320	−	0.641264i	$-0.778410\pi$
$613$	−23291.5	−1.53464	−0.767320	+	0.641264i	$0.778410\pi$
$614$	17370.8	1.14174
$615$	−4618.57	−0.302827
$616$	−788.217	−0.0515555
$617$	1007.65	0.0657479	0.0328739	−	0.999460i	$-0.489534\pi$
$617$	1007.65	0.0657479	0.0328739	+	0.999460i	$0.489534\pi$
$618$	18198.0	1.18452
$619$	12262.3	0.796225	0.398112	−	0.917337i	$-0.369665\pi$
$619$	12262.3	0.796225	0.398112	+	0.917337i	$0.369665\pi$
$620$	48399.7	3.13513
$621$	−19114.5	−1.23517
$622$	2386.11	0.153817
$623$	119.014	0.00765359
$624$	2090.19	0.134094
$625$	−10444.6	−0.668455
$626$	19306.6	1.23266
$627$	−149.117	−0.00949785
$628$	−26611.2	−1.69093
$629$	−22234.2	−1.40943
$630$	5605.65	0.354499
$631$	3337.92	0.210587	0.105294	−	0.994441i	$-0.466422\pi$
$631$	3337.92	0.210587	0.105294	+	0.994441i	$0.466422\pi$
$632$	−13791.7	−0.868046
$633$	−9113.98	−0.572272
$634$	−47598.0	−2.98164
$635$	−11064.1	−0.691442
$636$	−1739.83	−0.108473
$637$	−17775.9	−1.10566
$638$	−9947.15	−0.617259
$639$	−10318.4	−0.638791
$640$	43413.3	2.68135
$641$	8111.33	0.499810	0.249905	−	0.968270i	$-0.419601\pi$
$641$	8111.33	0.499810	0.249905	+	0.968270i	$0.419601\pi$
$642$	−13732.7	−0.844217
$643$	−1796.68	−0.110193	−0.0550966	−	0.998481i	$-0.517547\pi$
$643$	−1796.68	−0.110193	−0.0550966	+	0.998481i	$0.517547\pi$
$644$	8134.79	0.497757
$645$	−13363.1	−0.815768
$646$	−3694.77	−0.225029
$647$	−19943.0	−1.21181	−0.605903	−	0.795538i	$-0.707188\pi$
$647$	−19943.0	−1.21181	−0.605903	+	0.795538i	$0.707188\pi$
$648$	−11248.8	−0.681939
$649$	3430.40	0.207481
$650$	−39444.9	−2.38024
$651$	1328.07	0.0799556
$652$	38501.1	2.31260
$653$	−5746.74	−0.344391	−0.172196	−	0.985063i	$-0.555086\pi$
$653$	−5746.74	−0.344391	−0.172196	+	0.985063i	$0.555086\pi$
$654$	−9927.08	−0.593546
$655$	29049.6	1.73292
$656$	−2537.11	−0.151002
$657$	13862.6	0.823181
$658$	5936.40	0.351710
$659$	−30759.2	−1.81822	−0.909110	−	0.416557i	$-0.863237\pi$
$659$	−30759.2	−1.81822	−0.909110	+	0.416557i	$0.863237\pi$
$660$	4369.62	0.257708
$661$	−16059.1	−0.944973	−0.472487	−	0.881338i	$-0.656643\pi$
$661$	−16059.1	−0.944973	−0.472487	+	0.881338i	$0.656643\pi$
$662$	19616.8	1.15170
$663$	−10820.5	−0.633838
$664$	−7585.51	−0.443335
$665$	−420.924	−0.0245454
$666$	24070.7	1.40048
$667$	43791.6	2.54215
$668$	30372.9	1.75922
$669$	6584.55	0.380528
$670$	−45379.9	−2.61668
$671$	5859.26	0.337100
$672$	862.168	0.0494923
$673$	1119.37	0.0641140	0.0320570	−	0.999486i	$-0.489794\pi$
$673$	1119.37	0.0641140	0.0320570	+	0.999486i	$0.489794\pi$
$674$	−2181.75	−0.124685
$675$	−16173.1	−0.922229
$676$	9049.15	0.514858
$677$	19502.8	1.10717	0.553584	−	0.832793i	$-0.313260\pi$
$677$	19502.8	1.10717	0.553584	+	0.832793i	$0.313260\pi$
$678$	−16356.2	−0.926484
$679$	4078.02	0.230486
$680$	46184.4	2.60455
$681$	12631.5	0.710778
$682$	−8740.25	−0.490736
$683$	25228.9	1.41341	0.706703	−	0.707510i	$-0.250182\pi$
$683$	25228.9	1.41341	0.706703	+	0.707510i	$0.250182\pi$
$684$	2542.20	0.142110
$685$	34534.3	1.92626
$686$	9904.10	0.551225
$687$	9616.02	0.534023
$688$	−7340.71	−0.406776
$689$	−3230.22	−0.178609
$690$	−30267.9	−1.66997
$691$	−2999.33	−0.165123	−0.0825614	−	0.996586i	$-0.526310\pi$
$691$	−2999.33	−0.165123	−0.0825614	+	0.996586i	$0.526310\pi$
$692$	−3493.56	−0.191915
$693$	−643.369	−0.0352664
$694$	49569.0	2.71126
$695$	−3691.29	−0.201465
$696$	−13481.3	−0.734208
$697$	13134.2	0.713761
$698$	−19938.2	−1.08119
$699$	7769.55	0.420417
$700$	6882.98	0.371646
$701$	−31828.0	−1.71487	−0.857436	−	0.514590i	$-0.827944\pi$
$701$	−31828.0	−1.71487	−0.857436	+	0.514590i	$0.827944\pi$
$702$	25611.8	1.37700
$703$	−1807.45	−0.0969692
$704$	−7050.51	−0.377452
$705$	−14038.2	−0.749944
$706$	−48092.7	−2.56373
$707$	−4115.96	−0.218949
$708$	10899.0	0.578545
$709$	−830.924	−0.0440141	−0.0220071	−	0.999758i	$-0.507006\pi$
$709$	−830.924	−0.0440141	−0.0220071	+	0.999758i	$0.507006\pi$
$710$	−35723.3	−1.88827
$711$	−11257.3	−0.593784
$712$	−1061.54	−0.0558747
$713$	38478.3	2.02107
$714$	2970.86	0.155716
$715$	8112.76	0.424336
$716$	−19590.4	−1.02253
$717$	−5550.64	−0.289111
$718$	13770.0	0.715725
$719$	2043.76	0.106007	0.0530037	−	0.998594i	$-0.483120\pi$
$719$	2043.76	0.106007	0.0530037	+	0.998594i	$0.483120\pi$
$720$	−7281.95	−0.376920
$721$	−5895.69	−0.304531
$722$	31835.5	1.64099
$723$	3963.94	0.203901
$724$	−566.485	−0.0290791
$725$	37052.8	1.89808
$726$	12053.7	0.616193
$727$	6701.65	0.341885	0.170943	−	0.985281i	$-0.445319\pi$
$727$	6701.65	0.341885	0.170943	+	0.985281i	$0.445319\pi$
$728$	−4649.58	−0.236710
$729$	−3483.48	−0.176979
$730$	47993.7	2.43333
$731$	38001.5	1.92276
$732$	18616.0	0.939980
$733$	−1003.77	−0.0505801	−0.0252901	−	0.999680i	$-0.508051\pi$
$733$	−1003.77	−0.0505801	−0.0252901	+	0.999680i	$0.508051\pi$
$734$	−31126.2	−1.56525
$735$	−11541.2	−0.579191
$736$	24979.7	1.25104
$737$	5208.32	0.260313
$738$	−14219.1	−0.709229
$739$	−36091.9	−1.79657	−0.898283	−	0.439418i	$-0.855185\pi$
$739$	−36091.9	−1.79657	−0.898283	+	0.439418i	$0.855185\pi$
$740$	52964.3	2.63109
$741$	−879.619	−0.0436081
$742$	886.879	0.0438792
$743$	−30898.7	−1.52566	−0.762829	−	0.646601i	$-0.776190\pi$
$743$	−30898.7	−1.52566	−0.762829	+	0.646601i	$0.776190\pi$
$744$	−11845.6	−0.583713
$745$	14304.8	0.703475
$746$	24321.0	1.19364
$747$	−6191.55	−0.303262
$748$	−12426.2	−0.607415
$749$	4449.05	0.217043
$750$	−5326.36	−0.259321
$751$	−22302.3	−1.08365	−0.541827	−	0.840490i	$-0.682267\pi$
$751$	−22302.3	−1.08365	−0.541827	+	0.840490i	$0.682267\pi$
$752$	−7711.60	−0.373953
$753$	−12653.6	−0.612379
$754$	−58676.8	−2.83406
$755$	−52146.8	−2.51366
$756$	−4469.16	−0.215002
$757$	−36709.3	−1.76251	−0.881255	−	0.472641i	$-0.843301\pi$
$757$	−36709.3	−1.76251	−0.881255	+	0.472641i	$0.843301\pi$
$758$	5137.90	0.246197
$759$	3473.90	0.166132
$760$	3754.41	0.179193
$761$	4758.65	0.226677	0.113338	−	0.993556i	$-0.463846\pi$
$761$	4758.65	0.226677	0.113338	+	0.993556i	$0.463846\pi$
$762$	6348.05	0.301792
$763$	3216.12	0.152597
$764$	−24471.7	−1.15884
$765$	37697.3	1.78163
$766$	14993.3	0.707221
$767$	20235.4	0.952619
$768$	−12063.2	−0.566790
$769$	12558.2	0.588895	0.294448	−	0.955668i	$-0.404864\pi$
$769$	12558.2	0.588895	0.294448	+	0.955668i	$0.404864\pi$
$770$	−2227.42	−0.104247
$771$	1341.83	0.0626783
$772$	−55735.5	−2.59840
$773$	−18989.7	−0.883586	−0.441793	−	0.897117i	$-0.645658\pi$
$773$	−18989.7	−0.883586	−0.441793	+	0.897117i	$0.645658\pi$
$774$	−41140.5	−1.91055
$775$	32557.2	1.50902
$776$	−36373.7	−1.68266
$777$	1453.32	0.0671011
$778$	−10278.9	−0.473673
$779$	1067.70	0.0491068
$780$	25775.7	1.18323
$781$	4100.02	0.187849
$782$	86075.0	3.93611
$783$	−24058.6	−1.09806
$784$	−6339.93	−0.288809
$785$	−32078.4	−1.45850
$786$	−16667.3	−0.756364
$787$	−24451.4	−1.10750	−0.553748	−	0.832685i	$-0.686803\pi$
$787$	−24451.4	−1.10750	−0.553748	+	0.832685i	$0.686803\pi$
$788$	58458.6	2.64277
$789$	7124.26	0.321458
$790$	−38973.9	−1.75523
$791$	5299.00	0.238193
$792$	5738.50	0.257461
$793$	34562.9	1.54775
$794$	9785.66	0.437380
$795$	−2097.27	−0.0935628
$796$	43572.4	1.94018
$797$	16184.7	0.719311	0.359655	−	0.933085i	$-0.382894\pi$
$797$	16184.7	0.719311	0.359655	+	0.933085i	$0.382894\pi$
$798$	241.506	0.0107133
$799$	39921.5	1.76761
$800$	21135.8	0.934077
$801$	−866.463	−0.0382209
$802$	13698.4	0.603125
$803$	−5508.32	−0.242073
$804$	16547.8	0.725866
$805$	9806.04	0.429338
$806$	−51557.5	−2.25315
$807$	15829.4	0.690486
$808$	36712.1	1.59843
$809$	−36484.2	−1.58556	−0.792779	−	0.609510i	$-0.791366\pi$
$809$	−36484.2	−1.58556	−0.792779	+	0.609510i	$0.791366\pi$
$810$	−31788.0	−1.37891
$811$	−9503.55	−0.411485	−0.205743	−	0.978606i	$-0.565961\pi$
$811$	−9503.55	−0.411485	−0.205743	+	0.978606i	$0.565961\pi$
$812$	10238.9	0.442505
$813$	−6578.35	−0.283780
$814$	−9564.55	−0.411840
$815$	46410.9	1.99473
$816$	−3859.25	−0.165565
$817$	3089.21	0.132286
$818$	−9654.27	−0.412657
$819$	−3795.15	−0.161921
$820$	−31287.1	−1.33243
$821$	34665.9	1.47363	0.736815	−	0.676095i	$-0.236329\pi$
$821$	34665.9	1.47363	0.736815	+	0.676095i	$0.236329\pi$
$822$	−19814.1	−0.840750
$823$	−20557.0	−0.870684	−0.435342	−	0.900265i	$-0.643373\pi$
$823$	−20557.0	−0.870684	−0.435342	+	0.900265i	$0.643373\pi$
$824$	52586.3	2.22322
$825$	2939.32	0.124041
$826$	−5555.78	−0.234032
$827$	−1346.30	−0.0566087	−0.0283044	−	0.999599i	$-0.509011\pi$
$827$	−1346.30	−0.0566087	−0.0283044	+	0.999599i	$0.509011\pi$
$828$	−59224.2	−2.48573
$829$	11259.3	0.471716	0.235858	−	0.971788i	$-0.424210\pi$
$829$	11259.3	0.471716	0.235858	+	0.971788i	$0.424210\pi$
$830$	−21435.8	−0.896444
$831$	−11309.7	−0.472117
$832$	−41589.9	−1.73302
$833$	32820.7	1.36515
$834$	2117.88	0.0879332
$835$	36612.8	1.51741
$836$	−1010.15	−0.0417902
$837$	−21139.5	−0.872986
$838$	24115.0	0.994081
$839$	−18349.0	−0.755038	−0.377519	−	0.926002i	$-0.623223\pi$
$839$	−18349.0	−0.755038	−0.377519	+	0.926002i	$0.623223\pi$
$840$	−3018.81	−0.123999
$841$	30729.4	1.25997
$842$	74212.8	3.03746
$843$	3354.74	0.137062
$844$	−61739.8	−2.51798
$845$	10908.3	0.444089
$846$	−43219.1	−1.75639
$847$	−3905.10	−0.158419
$848$	−1152.09	−0.0466543
$849$	−9260.39	−0.374341
$850$	72829.6	2.93886
$851$	42107.3	1.69614
$852$	13026.5	0.523804
$853$	−10376.0	−0.416492	−0.208246	−	0.978076i	$-0.566775\pi$
$853$	−10376.0	−0.416492	−0.208246	+	0.978076i	$0.566775\pi$
$854$	−9489.50	−0.380239
$855$	3064.48	0.122576
$856$	−39683.1	−1.58451
$857$	−41354.7	−1.64837	−0.824183	−	0.566324i	$-0.808365\pi$
$857$	−41354.7	−1.64837	−0.824183	+	0.566324i	$0.808365\pi$
$858$	−4654.71	−0.185209
$859$	24854.2	0.987212	0.493606	−	0.869686i	$-0.335678\pi$
$859$	24854.2	0.987212	0.493606	+	0.869686i	$0.335678\pi$
$860$	−90524.0	−3.58935
$861$	−858.504	−0.0339811
$862$	−22112.8	−0.873740
$863$	−14064.0	−0.554743	−0.277371	−	0.960763i	$-0.589463\pi$
$863$	−14064.0	−0.554743	−0.277371	+	0.960763i	$0.589463\pi$
$864$	−13723.6	−0.540376
$865$	−4211.30	−0.165536
$866$	−28300.0	−1.11048
$867$	9860.50	0.386252
$868$	8996.59	0.351802
$869$	4473.10	0.174614
$870$	−38096.8	−1.48460
$871$	30723.2	1.19519
$872$	−28686.0	−1.11403
$873$	−29689.5	−1.15102
$874$	6997.18	0.270805
$875$	1725.60	0.0666698
$876$	−17500.9	−0.675003
$877$	7002.89	0.269636	0.134818	−	0.990870i	$-0.456955\pi$
$877$	7002.89	0.269636	0.134818	+	0.990870i	$0.456955\pi$
$878$	50649.3	1.94685
$879$	4757.47	0.182555
$880$	2893.49	0.110841
$881$	−38276.2	−1.46374	−0.731872	−	0.681442i	$-0.761353\pi$
$881$	−38276.2	−1.46374	−0.731872	+	0.681442i	$0.761353\pi$
$882$	−35531.7	−1.35648
$883$	29667.8	1.13069	0.565346	−	0.824854i	$-0.308743\pi$
$883$	29667.8	1.13069	0.565346	+	0.824854i	$0.308743\pi$
$884$	−73300.4	−2.78887
$885$	13138.2	0.499022
$886$	57081.7	2.16444
$887$	−16548.6	−0.626433	−0.313217	−	0.949682i	$-0.601407\pi$
$887$	−16548.6	−0.626433	−0.313217	+	0.949682i	$0.601407\pi$
$888$	−12962.8	−0.489869
$889$	−2056.61	−0.0775887
$890$	−2999.79	−0.112981
$891$	3648.36	0.137177
$892$	44605.0	1.67431
$893$	3245.29	0.121612
$894$	−8207.43	−0.307044
$895$	−23615.2	−0.881976
$896$	8069.72	0.300882
$897$	20492.0	0.762774
$898$	60082.8	2.23273
$899$	48430.9	1.79673
$900$	−50110.6	−1.85595
$901$	5964.15	0.220527
$902$	5649.97	0.208563
$903$	−2483.94	−0.0915398
$904$	−47264.1	−1.73892
$905$	−682.866	−0.0250820
$906$	29919.3	1.09713
$907$	21044.8	0.770432	0.385216	−	0.922827i	$-0.374127\pi$
$907$	21044.8	0.770432	0.385216	+	0.922827i	$0.374127\pi$
$908$	85568.2	3.12740
$909$	29965.7	1.09340
$910$	−13139.2	−0.478638
$911$	−22210.6	−0.807760	−0.403880	−	0.914812i	$-0.632339\pi$
$911$	−22210.6	−0.807760	−0.403880	+	0.914812i	$0.632339\pi$
$912$	−313.725	−0.0113909
$913$	2460.22	0.0891802
$914$	27536.0	0.996510
$915$	22440.5	0.810776
$916$	65140.7	2.34968
$917$	5399.77	0.194456
$918$	−47288.6	−1.70017
$919$	17578.9	0.630984	0.315492	−	0.948928i	$-0.397830\pi$
$919$	17578.9	0.630984	0.315492	+	0.948928i	$0.397830\pi$
$920$	−87464.5	−3.13437
$921$	−7635.60	−0.273183
$922$	82592.5	2.95015
$923$	24185.4	0.862484
$924$	812.229	0.0289182
$925$	35627.7	1.26641
$926$	−65560.2	−2.32661
$927$	42922.7	1.52078
$928$	31440.8	1.11217
$929$	16689.2	0.589404	0.294702	−	0.955589i	$-0.404780\pi$
$929$	16689.2	0.589404	0.294702	+	0.955589i	$0.404780\pi$
$930$	−33474.5	−1.18029
$931$	2668.05	0.0939224
$932$	52632.4	1.84982
$933$	−1048.85	−0.0368037
$934$	60649.2	2.12473
$935$	−14979.1	−0.523924
$936$	33850.6	1.18210
$937$	−8936.14	−0.311559	−0.155780	−	0.987792i	$-0.549789\pi$
$937$	−8936.14	−0.311559	−0.155780	+	0.987792i	$0.549789\pi$
$938$	−8435.27	−0.293626
$939$	−8486.52	−0.294938
$940$	−95097.6	−3.29973
$941$	−35212.8	−1.21988	−0.609939	−	0.792448i	$-0.708806\pi$
$941$	−35212.8	−1.21988	−0.609939	+	0.792448i	$0.708806\pi$
$942$	18405.0	0.636590
$943$	−24873.6	−0.858955
$944$	7217.16	0.248833
$945$	−5387.32	−0.185449
$946$	16347.3	0.561834
$947$	1621.93	0.0556554	0.0278277	−	0.999613i	$-0.491141\pi$
$947$	1621.93	0.0556554	0.0278277	+	0.999613i	$0.491141\pi$
$948$	14211.9	0.486899
$949$	−32492.8	−1.11144
$950$	5920.44	0.202194
$951$	20922.5	0.713415
$952$	8584.81	0.292264
$953$	12564.7	0.427085	0.213542	−	0.976934i	$-0.431500\pi$
$953$	12564.7	0.427085	0.213542	+	0.976934i	$0.431500\pi$
$954$	−6456.80	−0.219126
$955$	−29499.2	−0.999553
$956$	−37601.1	−1.27208
$957$	4372.43	0.147691
$958$	−7925.74	−0.267296
$959$	6419.27	0.216151
$960$	−27002.9	−0.907828
$961$	12763.7	0.428443
$962$	−56420.0	−1.89091
$963$	−32390.7	−1.08388
$964$	26852.5	0.897157
$965$	−67186.1	−2.24124
$966$	−5626.23	−0.187392
$967$	3333.97	0.110872	0.0554361	−	0.998462i	$-0.482345\pi$
$967$	3333.97	0.110872	0.0554361	+	0.998462i	$0.482345\pi$
$968$	34831.4	1.15653
$969$	1624.10	0.0538426
$970$	−102788.	−3.40240
$971$	−23237.6	−0.768001	−0.384000	−	0.923333i	$-0.625454\pi$
$971$	−23237.6	−0.768001	−0.384000	+	0.923333i	$0.625454\pi$
$972$	50192.3	1.65630
$973$	−686.140	−0.0226070
$974$	−77253.4	−2.54144
$975$	17338.7	0.569519
$976$	12327.2	0.404287
$977$	42237.6	1.38311	0.691556	−	0.722322i	$-0.256925\pi$
$977$	42237.6	1.38311	0.691556	+	0.722322i	$0.256925\pi$
$978$	−26628.3	−0.870635
$979$	344.291	0.0112396
$980$	−78182.6	−2.54842
$981$	−23414.5	−0.762047
$982$	38898.2	1.26404
$983$	−23654.8	−0.767517	−0.383759	−	0.923433i	$-0.625371\pi$
$983$	−23654.8	−0.767517	−0.383759	+	0.923433i	$0.625371\pi$
$984$	7657.39	0.248078
$985$	70468.6	2.27951
$986$	108339.	3.49919
$987$	−2609.44	−0.0841534
$988$	−5958.71	−0.191874
$989$	−71967.6	−2.31389
$990$	16216.4	0.520597
$991$	32044.6	1.02718	0.513588	−	0.858037i	$-0.328316\pi$
$991$	32044.6	1.02718	0.513588	+	0.858037i	$0.328316\pi$
$992$	27626.1	0.884202
$993$	−8622.88	−0.275568
$994$	−6640.28	−0.211888
$995$	52524.2	1.67350
$996$	7816.59	0.248673
$997$	45105.7	1.43281	0.716406	−	0.697684i	$-0.245786\pi$
$997$	45105.7	1.43281	0.716406	+	0.697684i	$0.245786\pi$
$998$	48814.7	1.54830
$999$	−23133.2	−0.732636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.b.1.8	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.b.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-4.68521 q^{2} +2.05946 q^{3} +13.9512 q^{4} +16.8174 q^{5} -9.64900 q^{6} +3.12603 q^{7} -27.8825 q^{8} -22.7586 q^{9} +O(q^{10})\)	\(q-4.68521 q^{2} +2.05946 q^{3} +13.9512 q^{4} +16.8174 q^{5} -9.64900 q^{6} +3.12603 q^{7} -27.8825 q^{8} -22.7586 q^{9} -78.7929 q^{10} +9.04318 q^{11} +28.7319 q^{12} +53.3444 q^{13} -14.6461 q^{14} +34.6347 q^{15} +19.0258 q^{16} -98.4932 q^{17} +106.629 q^{18} -8.00668 q^{19} +234.622 q^{20} +6.43793 q^{21} -42.3692 q^{22} +186.527 q^{23} -57.4228 q^{24} +157.824 q^{25} -249.930 q^{26} -102.476 q^{27} +43.6118 q^{28} +234.773 q^{29} -162.271 q^{30} +206.288 q^{31} +133.920 q^{32} +18.6241 q^{33} +461.461 q^{34} +52.5716 q^{35} -317.509 q^{36} +225.743 q^{37} +37.5129 q^{38} +109.861 q^{39} -468.910 q^{40} -133.351 q^{41} -30.1631 q^{42} -385.829 q^{43} +126.163 q^{44} -382.740 q^{45} -873.919 q^{46} -405.323 q^{47} +39.1829 q^{48} -333.228 q^{49} -739.438 q^{50} -202.843 q^{51} +744.218 q^{52} -60.5540 q^{53} +480.121 q^{54} +152.083 q^{55} -87.1615 q^{56} -16.4894 q^{57} -1099.96 q^{58} +379.335 q^{59} +483.195 q^{60} +647.920 q^{61} -966.502 q^{62} -71.1442 q^{63} -779.649 q^{64} +897.113 q^{65} -87.2576 q^{66} +575.939 q^{67} -1374.10 q^{68} +384.145 q^{69} -246.309 q^{70} +453.382 q^{71} +634.567 q^{72} -609.113 q^{73} -1057.65 q^{74} +325.032 q^{75} -111.702 q^{76} +28.2693 q^{77} -514.720 q^{78} +494.638 q^{79} +319.964 q^{80} +403.438 q^{81} +624.777 q^{82} +272.053 q^{83} +89.8167 q^{84} -1656.40 q^{85} +1807.69 q^{86} +483.506 q^{87} -252.146 q^{88} +38.0718 q^{89} +1793.22 q^{90} +166.756 q^{91} +2602.27 q^{92} +424.842 q^{93} +1899.02 q^{94} -134.651 q^{95} +275.803 q^{96} +1304.54 q^{97} +1561.24 q^{98} -205.810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) 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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