LMFDB - Embedded newform 547.4.a.a.1.18

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:	$1$
Dimension:	$65$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-3.32782 q^{2} +9.69808 q^{3} +3.07435 q^{4} -12.4114 q^{5} -32.2734 q^{6} +29.0135 q^{7} +16.3916 q^{8} +67.0527 q^{9} +O(q^{10})$	\(q-3.32782 q^{2} +9.69808 q^{3} +3.07435 q^{4} -12.4114 q^{5} -32.2734 q^{6} +29.0135 q^{7} +16.3916 q^{8} +67.0527 q^{9} +41.3030 q^{10} -68.2990 q^{11} +29.8153 q^{12} -12.2732 q^{13} -96.5517 q^{14} -120.367 q^{15} -79.1432 q^{16} -125.409 q^{17} -223.139 q^{18} -33.0724 q^{19} -38.1572 q^{20} +281.376 q^{21} +227.286 q^{22} -192.726 q^{23} +158.967 q^{24} +29.0439 q^{25} +40.8428 q^{26} +388.435 q^{27} +89.1979 q^{28} +206.049 q^{29} +400.560 q^{30} -15.9955 q^{31} +132.241 q^{32} -662.369 q^{33} +417.337 q^{34} -360.100 q^{35} +206.144 q^{36} +82.7933 q^{37} +110.059 q^{38} -119.026 q^{39} -203.444 q^{40} -240.659 q^{41} -936.366 q^{42} +140.348 q^{43} -209.975 q^{44} -832.221 q^{45} +641.358 q^{46} -64.9401 q^{47} -767.537 q^{48} +498.786 q^{49} -96.6527 q^{50} -1216.22 q^{51} -37.7320 q^{52} -413.287 q^{53} -1292.64 q^{54} +847.689 q^{55} +475.580 q^{56} -320.739 q^{57} -685.693 q^{58} +288.772 q^{59} -370.051 q^{60} -292.999 q^{61} +53.2300 q^{62} +1945.44 q^{63} +193.073 q^{64} +152.328 q^{65} +2204.24 q^{66} -212.030 q^{67} -385.551 q^{68} -1869.08 q^{69} +1198.35 q^{70} +758.626 q^{71} +1099.10 q^{72} -489.364 q^{73} -275.521 q^{74} +281.670 q^{75} -101.676 q^{76} -1981.60 q^{77} +396.097 q^{78} -435.768 q^{79} +982.281 q^{80} +1956.65 q^{81} +800.869 q^{82} -1073.75 q^{83} +865.048 q^{84} +1556.50 q^{85} -467.051 q^{86} +1998.28 q^{87} -1119.53 q^{88} -635.290 q^{89} +2769.48 q^{90} -356.088 q^{91} -592.509 q^{92} -155.125 q^{93} +216.109 q^{94} +410.476 q^{95} +1282.48 q^{96} -1434.02 q^{97} -1659.87 q^{98} -4579.64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) $ 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * 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 $

$2$	−3.32782	−1.17656	−0.588280	−	0.808657i	$-0.700195\pi$
$2$	−3.32782	−1.17656	−0.588280	+	0.808657i	$0.700195\pi$
$3$	9.69808	1.86640	0.933198	−	0.359362i	$-0.117006\pi$
$3$	9.69808	1.86640	0.933198	+	0.359362i	$0.117006\pi$
$4$	3.07435	0.384294
$5$	−12.4114	−1.11011	−0.555057	−	0.831813i	$-0.687303\pi$
$5$	−12.4114	−1.11011	−0.555057	+	0.831813i	$0.687303\pi$
$6$	−32.2734	−2.19593
$7$	29.0135	1.56658	0.783292	−	0.621654i	$-0.213539\pi$
$7$	29.0135	1.56658	0.783292	+	0.621654i	$0.213539\pi$
$8$	16.3916	0.724415
$9$	67.0527	2.48343
$10$	41.3030	1.30611
$11$	−68.2990	−1.87208	−0.936042	−	0.351888i	$-0.885540\pi$
$11$	−68.2990	−1.87208	−0.936042	+	0.351888i	$0.885540\pi$
$12$	29.8153	0.717245
$13$	−12.2732	−0.261843	−0.130922	−	0.991393i	$-0.541794\pi$
$13$	−12.2732	−0.261843	−0.130922	+	0.991393i	$0.541794\pi$
$14$	−96.5517	−1.84318
$15$	−120.367	−2.07191
$16$	−79.1432	−1.23661
$17$	−125.409	−1.78918	−0.894591	−	0.446886i	$-0.852533\pi$
$17$	−125.409	−1.78918	−0.894591	+	0.446886i	$0.852533\pi$
$18$	−223.139	−2.92191
$19$	−33.0724	−0.399333	−0.199666	−	0.979864i	$-0.563986\pi$
$19$	−33.0724	−0.399333	−0.199666	+	0.979864i	$0.563986\pi$
$20$	−38.1572	−0.426610
$21$	281.376	2.92387
$22$	227.286	2.20262
$23$	−192.726	−1.74723	−0.873614	−	0.486619i	$-0.838230\pi$
$23$	−192.726	−1.74723	−0.873614	+	0.486619i	$0.838230\pi$
$24$	158.967	1.35205
$25$	29.0439	0.232351
$26$	40.8428	0.308074
$27$	388.435	2.76868
$28$	89.1979	0.602029
$29$	206.049	1.31939	0.659695	−	0.751533i	$-0.270685\pi$
$29$	206.049	1.31939	0.659695	+	0.751533i	$0.270685\pi$
$30$	400.560	2.43773
$31$	−15.9955	−0.0926733	−0.0463367	−	0.998926i	$-0.514755\pi$
$31$	−15.9955	−0.0926733	−0.0463367	+	0.998926i	$0.514755\pi$
$32$	132.241	0.730534
$33$	−662.369	−3.49405
$34$	417.337	2.10508
$35$	−360.100	−1.73909
$36$	206.144	0.954370
$37$	82.7933	0.367869	0.183934	−	0.982939i	$-0.441117\pi$
$37$	82.7933	0.367869	0.183934	+	0.982939i	$0.441117\pi$
$38$	110.059	0.469839
$39$	−119.026	−0.488703
$40$	−203.444	−0.804183
$41$	−240.659	−0.916698	−0.458349	−	0.888772i	$-0.651559\pi$
$41$	−240.659	−0.916698	−0.458349	+	0.888772i	$0.651559\pi$
$42$	−936.366	−3.44011
$43$	140.348	0.497740	0.248870	−	0.968537i	$-0.419941\pi$
$43$	140.348	0.497740	0.248870	+	0.968537i	$0.419941\pi$
$44$	−209.975	−0.719431
$45$	−832.221	−2.75689
$46$	641.358	2.05572
$47$	−64.9401	−0.201542	−0.100771	−	0.994910i	$-0.532131\pi$
$47$	−64.9401	−0.201542	−0.100771	+	0.994910i	$0.532131\pi$
$48$	−767.537	−2.30801
$49$	498.786	1.45419
$50$	−96.6527	−0.273375
$51$	−1216.22	−3.33932
$52$	−37.7320	−0.100625
$53$	−413.287	−1.07112	−0.535560	−	0.844497i	$-0.679899\pi$
$53$	−413.287	−1.07112	−0.535560	+	0.844497i	$0.679899\pi$
$54$	−1292.64	−3.25752
$55$	847.689	2.07823
$56$	475.580	1.13486
$57$	−320.739	−0.745313
$58$	−685.693	−1.55234
$59$	288.772	0.637203	0.318601	−	0.947889i	$-0.396787\pi$
$59$	288.772	0.637203	0.318601	+	0.947889i	$0.396787\pi$
$60$	−370.051	−0.796223
$61$	−292.999	−0.614995	−0.307498	−	0.951549i	$-0.599492\pi$
$61$	−292.999	−0.614995	−0.307498	+	0.951549i	$0.599492\pi$
$62$	53.2300	0.109036
$63$	1945.44	3.89051
$64$	193.073	0.377095
$65$	152.328	0.290676
$66$	2204.24	4.11096
$67$	−212.030	−0.386620	−0.193310	−	0.981138i	$-0.561922\pi$
$67$	−212.030	−0.386620	−0.193310	+	0.981138i	$0.561922\pi$
$68$	−385.551	−0.687572
$69$	−1869.08	−3.26102
$70$	1198.35	2.04614
$71$	758.626	1.26806	0.634031	−	0.773308i	$-0.281399\pi$
$71$	758.626	1.26806	0.634031	+	0.773308i	$0.281399\pi$
$72$	1099.10	1.79904
$73$	−489.364	−0.784599	−0.392299	−	0.919838i	$-0.628320\pi$
$73$	−489.364	−0.784599	−0.392299	+	0.919838i	$0.628320\pi$
$74$	−275.521	−0.432820
$75$	281.670	0.433659
$76$	−101.676	−0.153461
$77$	−1981.60	−2.93278
$78$	396.097	0.574989
$79$	−435.768	−0.620603	−0.310302	−	0.950638i	$-0.600430\pi$
$79$	−435.768	−0.620603	−0.310302	+	0.950638i	$0.600430\pi$
$80$	982.281	1.37278
$81$	1956.65	2.68401
$82$	800.869	1.07855
$83$	−1073.75	−1.41999	−0.709994	−	0.704208i	$-0.751302\pi$
$83$	−1073.75	−1.41999	−0.709994	+	0.704208i	$0.751302\pi$
$84$	865.048	1.12363
$85$	1556.50	1.98619
$86$	−467.051	−0.585621
$87$	1998.28	2.46251
$88$	−1119.53	−1.35617
$89$	−635.290	−0.756636	−0.378318	−	0.925676i	$-0.623497\pi$
$89$	−635.290	−0.756636	−0.378318	+	0.925676i	$0.623497\pi$
$90$	2769.48	3.24365
$91$	−356.088	−0.410200
$92$	−592.509	−0.671450
$93$	−155.125	−0.172965
$94$	216.109	0.237127
$95$	410.476	0.443305
$96$	1282.48	1.36347
$97$	−1434.02	−1.50105	−0.750527	−	0.660839i	$-0.770200\pi$
$97$	−1434.02	−1.50105	−0.750527	+	0.660839i	$0.770200\pi$
$98$	−1659.87	−1.71094
$99$	−4579.64	−4.64920
$100$	89.2911	0.0892911
$101$	−1090.10	−1.07395	−0.536975	−	0.843598i	$-0.680433\pi$
$101$	−1090.10	−1.07395	−0.536975	+	0.843598i	$0.680433\pi$
$102$	4047.37	3.92891
$103$	−952.610	−0.911296	−0.455648	−	0.890160i	$-0.650592\pi$
$103$	−952.610	−0.911296	−0.455648	+	0.890160i	$0.650592\pi$
$104$	−201.177	−0.189683
$105$	−3492.28	−3.24582
$106$	1375.34	1.26024
$107$	1104.17	0.997605	0.498803	−	0.866716i	$-0.333773\pi$
$107$	1104.17	0.997605	0.498803	+	0.866716i	$0.333773\pi$
$108$	1194.19	1.06399
$109$	660.746	0.580624	0.290312	−	0.956932i	$-0.406241\pi$
$109$	660.746	0.580624	0.290312	+	0.956932i	$0.406241\pi$
$110$	−2820.95	−2.44516
$111$	802.936	0.686589
$112$	−2296.22	−1.93726
$113$	934.891	0.778293	0.389147	−	0.921176i	$-0.372770\pi$
$113$	934.891	0.778293	0.389147	+	0.921176i	$0.372770\pi$
$114$	1067.36	0.876906
$115$	2392.01	1.93962
$116$	633.467	0.507034
$117$	−822.949	−0.650271
$118$	−960.981	−0.749707
$119$	−3638.55	−2.80290
$120$	−1973.01	−1.50092
$121$	3333.75	2.50470
$122$	975.047	0.723579
$123$	−2333.93	−1.71092
$124$	−49.1758	−0.0356138
$125$	1190.95	0.852177
$126$	−6474.06	−4.57742
$127$	2424.22	1.69382	0.846908	−	0.531739i	$-0.178461\pi$
$127$	2424.22	1.69382	0.846908	+	0.531739i	$0.178461\pi$
$128$	−1700.44	−1.17421
$129$	1361.10	0.928980
$130$	−506.918	−0.341998
$131$	−436.549	−0.291156	−0.145578	−	0.989347i	$-0.546504\pi$
$131$	−436.549	−0.291156	−0.145578	+	0.989347i	$0.546504\pi$
$132$	−2036.36	−1.34274
$133$	−959.547	−0.625589
$134$	705.595	0.454882
$135$	−4821.03	−3.07354
$136$	−2055.65	−1.29611
$137$	1126.65	0.702602	0.351301	−	0.936263i	$-0.385739\pi$
$137$	1126.65	0.702602	0.351301	+	0.936263i	$0.385739\pi$
$138$	6219.94	3.83679
$139$	−2125.74	−1.29715	−0.648573	−	0.761153i	$-0.724634\pi$
$139$	−2125.74	−1.29715	−0.648573	+	0.761153i	$0.724634\pi$
$140$	−1107.07	−0.668321
$141$	−629.794	−0.376158
$142$	−2524.57	−1.49195
$143$	838.245	0.490193
$144$	−5306.77	−3.07105
$145$	−2557.36	−1.46467
$146$	1628.51	0.923128
$147$	4837.27	2.71409
$148$	254.536	0.141370
$149$	2073.12	1.13985	0.569923	−	0.821698i	$-0.306973\pi$
$149$	2073.12	1.13985	0.569923	+	0.821698i	$0.306973\pi$
$150$	−937.345	−0.510226
$151$	−1983.13	−1.06877	−0.534386	−	0.845240i	$-0.679457\pi$
$151$	−1983.13	−1.06877	−0.534386	+	0.845240i	$0.679457\pi$
$152$	−542.111	−0.289283
$153$	−8409.00	−4.44332
$154$	6594.39	3.45059
$155$	198.527	0.102878
$156$	−365.928	−0.187806
$157$	−2138.22	−1.08693	−0.543467	−	0.839431i	$-0.682889\pi$
$157$	−2138.22	−1.08693	−0.543467	+	0.839431i	$0.682889\pi$
$158$	1450.15	0.730177
$159$	−4008.09	−1.99913
$160$	−1641.30	−0.810975
$161$	−5591.68	−2.73718
$162$	−6511.36	−3.15790
$163$	1551.29	0.745439	0.372720	−	0.927944i	$-0.378425\pi$
$163$	1551.29	0.745439	0.372720	+	0.927944i	$0.378425\pi$
$164$	−739.871	−0.352282
$165$	8220.96	3.87879
$166$	3573.23	1.67070
$167$	1734.36	0.803647	0.401823	−	0.915717i	$-0.368377\pi$
$167$	1734.36	0.803647	0.401823	+	0.915717i	$0.368377\pi$
$168$	4612.21	2.11809
$169$	−2046.37	−0.931438
$170$	−5179.75	−2.33688
$171$	−2217.59	−0.991717
$172$	431.478	0.191278
$173$	−2688.13	−1.18136	−0.590678	−	0.806907i	$-0.701140\pi$
$173$	−2688.13	−1.18136	−0.590678	+	0.806907i	$0.701140\pi$
$174$	−6649.90	−2.89729
$175$	842.666	0.363997
$176$	5405.40	2.31504
$177$	2800.54	1.18927
$178$	2114.13	0.890228
$179$	1810.60	0.756036	0.378018	−	0.925798i	$-0.376606\pi$
$179$	1810.60	0.756036	0.378018	+	0.925798i	$0.376606\pi$
$180$	−2558.54	−1.05946
$181$	1284.34	0.527425	0.263713	−	0.964601i	$-0.415053\pi$
$181$	1284.34	0.527425	0.263713	+	0.964601i	$0.415053\pi$
$182$	1185.00	0.482625
$183$	−2841.53	−1.14782
$184$	−3159.10	−1.26572
$185$	−1027.58	−0.408376
$186$	516.229	0.203504
$187$	8565.29	3.34950
$188$	−199.649	−0.0774515
$189$	11269.9	4.33737
$190$	−1365.99	−0.521575
$191$	−204.127	−0.0773303	−0.0386652	−	0.999252i	$-0.512311\pi$
$191$	−204.127	−0.0773303	−0.0386652	+	0.999252i	$0.512311\pi$
$192$	1872.43	0.703809
$193$	1867.75	0.696597	0.348299	−	0.937384i	$-0.386759\pi$
$193$	1867.75	0.696597	0.348299	+	0.937384i	$0.386759\pi$
$194$	4772.14	1.76608
$195$	1477.29	0.542516
$196$	1533.44	0.558835
$197$	−1615.00	−0.584081	−0.292041	−	0.956406i	$-0.594334\pi$
$197$	−1615.00	−0.584081	−0.292041	+	0.956406i	$0.594334\pi$
$198$	15240.2	5.47006
$199$	−2157.44	−0.768527	−0.384263	−	0.923224i	$-0.625545\pi$
$199$	−2157.44	−0.768527	−0.384263	+	0.923224i	$0.625545\pi$
$200$	476.077	0.168319
$201$	−2056.28	−0.721586
$202$	3627.65	1.26357
$203$	5978.21	2.06694
$204$	−3739.10	−1.28328
$205$	2986.93	1.01764
$206$	3170.11	1.07219
$207$	−12922.8	−4.33913
$208$	971.337	0.323799
$209$	2258.81	0.747585
$210$	11621.7	3.81891
$211$	−2523.37	−0.823299	−0.411649	−	0.911342i	$-0.635047\pi$
$211$	−2523.37	−0.823299	−0.411649	+	0.911342i	$0.635047\pi$
$212$	−1270.59	−0.411625
$213$	7357.22	2.36671
$214$	−3674.46	−1.17374
$215$	−1741.92	−0.552547
$216$	6367.08	2.00567
$217$	−464.086	−0.145181
$218$	−2198.84	−0.683139
$219$	−4745.89	−1.46437
$220$	2606.10	0.798650
$221$	1539.16	0.468485
$222$	−2672.02	−0.807813
$223$	3504.53	1.05238	0.526191	−	0.850367i	$-0.323620\pi$
$223$	3504.53	1.05238	0.526191	+	0.850367i	$0.323620\pi$
$224$	3836.77	1.14444
$225$	1947.47	0.577029
$226$	−3111.14	−0.915709
$227$	−294.921	−0.0862317	−0.0431159	−	0.999070i	$-0.513728\pi$
$227$	−294.921	−0.0862317	−0.0431159	+	0.999070i	$0.513728\pi$
$228$	−986.064	−0.286420
$229$	−3477.77	−1.00357	−0.501785	−	0.864992i	$-0.667323\pi$
$229$	−3477.77	−1.00357	−0.501785	+	0.864992i	$0.667323\pi$
$230$	−7960.18	−2.28208
$231$	−19217.7	−5.47373
$232$	3377.48	0.955786
$233$	−860.588	−0.241970	−0.120985	−	0.992654i	$-0.538605\pi$
$233$	−860.588	−0.241970	−0.120985	+	0.992654i	$0.538605\pi$
$234$	2738.62	0.765083
$235$	806.000	0.223735
$236$	887.788	0.244873
$237$	−4226.11	−1.15829
$238$	12108.4	3.29779
$239$	−603.852	−0.163431	−0.0817154	−	0.996656i	$-0.526040\pi$
$239$	−603.852	−0.163431	−0.0817154	+	0.996656i	$0.526040\pi$
$240$	9526.24	2.56215
$241$	652.688	0.174454	0.0872269	−	0.996188i	$-0.472199\pi$
$241$	652.688	0.174454	0.0872269	+	0.996188i	$0.472199\pi$
$242$	−11094.1	−2.94693
$243$	8487.97	2.24076
$244$	−900.783	−0.236339
$245$	−6190.65	−1.61431
$246$	7766.89	2.01300
$247$	405.903	0.104563
$248$	−262.192	−0.0671339
$249$	−10413.3	−2.65026
$250$	−3963.27	−1.00264
$251$	−4571.49	−1.14960	−0.574801	−	0.818293i	$-0.694920\pi$
$251$	−4571.49	−1.14960	−0.574801	+	0.818293i	$0.694920\pi$
$252$	5980.96	1.49510
$253$	13163.0	3.27096
$254$	−8067.35	−1.99288
$255$	15095.1	3.70702
$256$	4114.16	1.00443
$257$	4269.69	1.03633	0.518164	−	0.855281i	$-0.326616\pi$
$257$	4269.69	1.03633	0.518164	+	0.855281i	$0.326616\pi$
$258$	−4529.50	−1.09300
$259$	2402.13	0.576297
$260$	468.309	0.111705
$261$	13816.1	3.27662
$262$	1452.75	0.342563
$263$	976.496	0.228948	0.114474	−	0.993426i	$-0.463482\pi$
$263$	976.496	0.228948	0.114474	+	0.993426i	$0.463482\pi$
$264$	−10857.3	−2.53114
$265$	5129.49	1.18906
$266$	3193.20	0.736043
$267$	−6161.09	−1.41218
$268$	−651.854	−0.148576
$269$	8323.01	1.88648	0.943240	−	0.332112i	$-0.107761\pi$
$269$	8323.01	1.88648	0.943240	+	0.332112i	$0.107761\pi$
$270$	16043.5	3.61621
$271$	1716.64	0.384791	0.192395	−	0.981317i	$-0.438374\pi$
$271$	1716.64	0.384791	0.192395	+	0.981317i	$0.438374\pi$
$272$	9925.25	2.21252
$273$	−3453.37	−0.765595
$274$	−3749.29	−0.826653
$275$	−1983.67	−0.434981
$276$	−5746.20	−1.25319
$277$	−7171.38	−1.55555	−0.777773	−	0.628545i	$-0.783651\pi$
$277$	−7171.38	−1.55555	−0.777773	+	0.628545i	$0.783651\pi$
$278$	7074.08	1.52617
$279$	−1072.54	−0.230148
$280$	−5902.63	−1.25982
$281$	3911.75	0.830447	0.415224	−	0.909719i	$-0.363703\pi$
$281$	3911.75	0.830447	0.415224	+	0.909719i	$0.363703\pi$
$282$	2095.84	0.442572
$283$	−5248.88	−1.10252	−0.551260	−	0.834333i	$-0.685853\pi$
$283$	−5248.88	−1.10252	−0.551260	+	0.834333i	$0.685853\pi$
$284$	2332.29	0.487309
$285$	3980.83	0.827382
$286$	−2789.52	−0.576741
$287$	−6982.37	−1.43608
$288$	8867.10	1.81423
$289$	10814.4	2.20117
$290$	8510.44	1.72328
$291$	−13907.2	−2.80156
$292$	−1504.48	−0.301517
$293$	−393.110	−0.0783814	−0.0391907	−	0.999232i	$-0.512478\pi$
$293$	−393.110	−0.0783814	−0.0391907	+	0.999232i	$0.512478\pi$
$294$	−16097.5	−3.19329
$295$	−3584.08	−0.707367
$296$	1357.12	0.266490
$297$	−26529.7	−5.18320
$298$	−6898.98	−1.34110
$299$	2365.36	0.457500
$300$	865.953	0.166653
$301$	4071.98	0.779751
$302$	6599.48	1.25748
$303$	−10571.9	−2.00441
$304$	2617.45	0.493820
$305$	3636.54	0.682714
$306$	27983.6	5.22783
$307$	6641.34	1.23466	0.617332	−	0.786703i	$-0.288214\pi$
$307$	6641.34	1.23466	0.617332	+	0.786703i	$0.288214\pi$
$308$	−6092.13	−1.12705
$309$	−9238.49	−1.70084
$310$	−660.661	−0.121042
$311$	−5279.02	−0.962527	−0.481264	−	0.876576i	$-0.659822\pi$
$311$	−5279.02	−0.962527	−0.481264	+	0.876576i	$0.659822\pi$
$312$	−1951.03	−0.354024
$313$	3449.83	0.622991	0.311495	−	0.950248i	$-0.399170\pi$
$313$	3449.83	0.622991	0.311495	+	0.950248i	$0.399170\pi$
$314$	7115.60	1.27884
$315$	−24145.7	−4.31891
$316$	−1339.70	−0.238494
$317$	5823.45	1.03179	0.515895	−	0.856652i	$-0.327460\pi$
$317$	5823.45	1.03179	0.515895	+	0.856652i	$0.327460\pi$
$318$	13338.2	2.35210
$319$	−14072.9	−2.47001
$320$	−2396.31	−0.418618
$321$	10708.3	1.86193
$322$	18608.1	3.22046
$323$	4147.57	0.714479
$324$	6015.42	1.03145
$325$	−356.460	−0.0608396
$326$	−5162.41	−0.877054
$327$	6407.97	1.08367
$328$	−3944.80	−0.664070
$329$	−1884.14	−0.315733
$330$	−27357.8	−4.56363
$331$	6749.93	1.12088	0.560438	−	0.828197i	$-0.310633\pi$
$331$	6749.93	1.12088	0.560438	+	0.828197i	$0.310633\pi$
$332$	−3301.08	−0.545693
$333$	5551.52	0.913578
$334$	−5771.64	−0.945539
$335$	2631.59	0.429192
$336$	−22269.0	−3.61569
$337$	5058.69	0.817699	0.408849	−	0.912602i	$-0.365930\pi$
$337$	5058.69	0.817699	0.408849	+	0.912602i	$0.365930\pi$
$338$	6809.94	1.09589
$339$	9066.64	1.45260
$340$	4785.24	0.763283
$341$	1092.48	0.173492
$342$	7379.74	1.16682
$343$	4519.90	0.711522
$344$	2300.53	0.360570
$345$	23197.9	3.62010
$346$	8945.59	1.38994
$347$	−11337.6	−1.75398	−0.876991	−	0.480507i	$-0.840453\pi$
$347$	−11337.6	−1.75398	−0.876991	+	0.480507i	$0.840453\pi$
$348$	6143.42	0.946327
$349$	54.6308	0.00837914	0.00418957	−	0.999991i	$-0.498666\pi$
$349$	54.6308	0.00837914	0.00418957	+	0.999991i	$0.498666\pi$
$350$	−2804.24	−0.428265
$351$	−4767.32	−0.724960
$352$	−9031.91	−1.36762
$353$	763.903	0.115180	0.0575898	−	0.998340i	$-0.481658\pi$
$353$	763.903	0.115180	0.0575898	+	0.998340i	$0.481658\pi$
$354$	−9319.67	−1.39925
$355$	−9415.64	−1.40769
$356$	−1953.11	−0.290771
$357$	−35287.0	−5.23133
$358$	−6025.34	−0.889522
$359$	781.700	0.114921	0.0574604	−	0.998348i	$-0.481700\pi$
$359$	781.700	0.114921	0.0574604	+	0.998348i	$0.481700\pi$
$360$	−13641.5	−1.99713
$361$	−5765.22	−0.840533
$362$	−4274.03	−0.620548
$363$	32331.0	4.67476
$364$	−1094.74	−0.157637
$365$	6073.71	0.870993
$366$	9456.08	1.35048
$367$	−650.880	−0.0925767	−0.0462884	−	0.998928i	$-0.514739\pi$
$367$	−650.880	−0.0925767	−0.0462884	+	0.998928i	$0.514739\pi$
$368$	15253.0	2.16064
$369$	−16136.8	−2.27656
$370$	3419.61	0.480479
$371$	−11990.9	−1.67800
$372$	−476.910	−0.0664695
$373$	9128.62	1.26719	0.633595	−	0.773665i	$-0.281578\pi$
$373$	9128.62	1.26719	0.633595	+	0.773665i	$0.281578\pi$
$374$	−28503.7	−3.94089
$375$	11550.0	1.59050
$376$	−1064.47	−0.146000
$377$	−2528.87	−0.345474
$378$	−37504.0	−5.10317
$379$	9270.26	1.25642	0.628208	−	0.778046i	$-0.283789\pi$
$379$	9270.26	1.25642	0.628208	+	0.778046i	$0.283789\pi$
$380$	1261.95	0.170359
$381$	23510.3	3.16133
$382$	679.296	0.0909838
$383$	−13585.3	−1.81247	−0.906235	−	0.422775i	$-0.861056\pi$
$383$	−13585.3	−1.81247	−0.906235	+	0.422775i	$0.861056\pi$
$384$	−16491.0	−2.19154
$385$	24594.5	3.25571
$386$	−6215.51	−0.819589
$387$	9410.69	1.23610
$388$	−4408.67	−0.576847
$389$	−3717.10	−0.484484	−0.242242	−	0.970216i	$-0.577883\pi$
$389$	−3717.10	−0.484484	−0.242242	+	0.970216i	$0.577883\pi$
$390$	−4916.13	−0.638303
$391$	24169.6	3.12611
$392$	8175.92	1.05343
$393$	−4233.68	−0.543412
$394$	5374.42	0.687207
$395$	5408.50	0.688940
$396$	−14079.4	−1.78666
$397$	−8804.54	−1.11307	−0.556533	−	0.830825i	$-0.687869\pi$
$397$	−8804.54	−1.11307	−0.556533	+	0.830825i	$0.687869\pi$
$398$	7179.56	0.904218
$399$	−9305.77	−1.16760
$400$	−2298.62	−0.287328
$401$	−1970.93	−0.245446	−0.122723	−	0.992441i	$-0.539163\pi$
$401$	−1970.93	−0.245446	−0.122723	+	0.992441i	$0.539163\pi$
$402$	6842.92	0.848989
$403$	196.315	0.0242659
$404$	−3351.35	−0.412713
$405$	−24284.8	−2.97956
$406$	−19894.4	−2.43188
$407$	−5654.70	−0.688681
$408$	−19935.9	−2.41905
$409$	620.781	0.0750504	0.0375252	−	0.999296i	$-0.488053\pi$
$409$	620.781	0.0750504	0.0375252	+	0.999296i	$0.488053\pi$
$410$	−9939.94	−1.19731
$411$	10926.4	1.31133
$412$	−2928.66	−0.350206
$413$	8378.31	0.998232
$414$	43004.8	5.10525
$415$	13326.7	1.57635
$416$	−1623.01	−0.191285
$417$	−20615.6	−2.42099
$418$	−7516.91	−0.879579
$419$	−9685.71	−1.12930	−0.564652	−	0.825329i	$-0.690989\pi$
$419$	−9685.71	−1.12930	−0.564652	+	0.825329i	$0.690989\pi$
$420$	−10736.5	−1.24735
$421$	−12385.9	−1.43386	−0.716928	−	0.697147i	$-0.754453\pi$
$421$	−12385.9	−1.43386	−0.716928	+	0.697147i	$0.754453\pi$
$422$	8397.31	0.968661
$423$	−4354.41	−0.500517
$424$	−6774.45	−0.775935
$425$	−3642.36	−0.415718
$426$	−24483.5	−2.78457
$427$	−8500.94	−0.963442
$428$	3394.60	0.383374
$429$	8129.37	0.914894
$430$	5796.77	0.650105
$431$	−1327.38	−0.148347	−0.0741735	−	0.997245i	$-0.523632\pi$
$431$	−1327.38	−0.148347	−0.0741735	+	0.997245i	$0.523632\pi$
$432$	−30742.0	−3.42378
$433$	5521.03	0.612757	0.306379	−	0.951910i	$-0.400883\pi$
$433$	5521.03	0.612757	0.306379	+	0.951910i	$0.400883\pi$
$434$	1544.39	0.170814
$435$	−24801.5	−2.73366
$436$	2031.37	0.223130
$437$	6373.93	0.697726
$438$	15793.4	1.72292
$439$	6110.63	0.664338	0.332169	−	0.943220i	$-0.392220\pi$
$439$	6110.63	0.664338	0.332169	+	0.943220i	$0.392220\pi$
$440$	13895.0	1.50550
$441$	33445.0	3.61138
$442$	−5122.05	−0.551201
$443$	7976.04	0.855424	0.427712	−	0.903915i	$-0.359320\pi$
$443$	7976.04	0.855424	0.427712	+	0.903915i	$0.359320\pi$
$444$	2468.51	0.263852
$445$	7884.86	0.839951
$446$	−11662.4	−1.23819
$447$	20105.3	2.12740
$448$	5601.72	0.590751
$449$	14285.4	1.50149	0.750747	−	0.660590i	$-0.229694\pi$
$449$	14285.4	1.50149	0.750747	+	0.660590i	$0.229694\pi$
$450$	−6480.82	−0.678909
$451$	16436.8	1.71614
$452$	2874.18	0.299094
$453$	−19232.5	−1.99475
$454$	981.443	0.101457
$455$	4419.57	0.455368
$456$	−5257.43	−0.539916
$457$	11702.0	1.19781	0.598903	−	0.800822i	$-0.295603\pi$
$457$	11702.0	1.19781	0.598903	+	0.800822i	$0.295603\pi$
$458$	11573.4	1.18076
$459$	−48713.1	−4.95367
$460$	7353.90	0.745385
$461$	−7039.67	−0.711215	−0.355607	−	0.934635i	$-0.615726\pi$
$461$	−7039.67	−0.711215	−0.355607	+	0.934635i	$0.615726\pi$
$462$	63952.9	6.44017
$463$	12382.5	1.24290	0.621452	−	0.783452i	$-0.286543\pi$
$463$	12382.5	1.24290	0.621452	+	0.783452i	$0.286543\pi$
$464$	−16307.4	−1.63157
$465$	1925.33	0.192011
$466$	2863.88	0.284692
$467$	−6732.04	−0.667070	−0.333535	−	0.942738i	$-0.608241\pi$
$467$	−6732.04	−0.667070	−0.333535	+	0.942738i	$0.608241\pi$
$468$	−2530.04	−0.249895
$469$	−6151.73	−0.605673
$470$	−2682.22	−0.263237
$471$	−20736.6	−2.02865
$472$	4733.45	0.461599
$473$	−9585.60	−0.931811
$474$	14063.7	1.36280
$475$	−960.550	−0.0927854
$476$	−11186.2	−1.07714
$477$	−27712.0	−2.66005
$478$	2009.51	0.192286
$479$	−9522.31	−0.908321	−0.454160	−	0.890920i	$-0.650061\pi$
$479$	−9522.31	−0.908321	−0.454160	+	0.890920i	$0.650061\pi$
$480$	−15917.4	−1.51360
$481$	−1016.14	−0.0963239
$482$	−2172.03	−0.205255
$483$	−54228.6	−5.10866
$484$	10249.1	0.962541
$485$	17798.2	1.66634
$486$	−28246.4	−2.63638
$487$	−10583.0	−0.984729	−0.492365	−	0.870389i	$-0.663867\pi$
$487$	−10583.0	−0.984729	−0.492365	+	0.870389i	$0.663867\pi$
$488$	−4802.74	−0.445512
$489$	15044.6	1.39128
$490$	20601.3	1.89933
$491$	5444.22	0.500396	0.250198	−	0.968195i	$-0.419504\pi$
$491$	5444.22	0.500396	0.250198	+	0.968195i	$0.419504\pi$
$492$	−7175.33	−0.657497
$493$	−25840.3	−2.36063
$494$	−1350.77	−0.123024
$495$	56839.9	5.16114
$496$	1265.93	0.114601
$497$	22010.4	1.98653
$498$	34653.5	3.11819
$499$	1395.79	0.125219	0.0626094	−	0.998038i	$-0.480058\pi$
$499$	1395.79	0.125219	0.0626094	+	0.998038i	$0.480058\pi$
$500$	3661.41	0.327487
$501$	16820.0	1.49992
$502$	15213.1	1.35258
$503$	−4136.60	−0.366683	−0.183342	−	0.983049i	$-0.558691\pi$
$503$	−4136.60	−0.366683	−0.183342	+	0.983049i	$0.558691\pi$
$504$	31888.9	2.81834
$505$	13529.7	1.19221
$506$	−43804.1	−3.84848
$507$	−19845.9	−1.73843
$508$	7452.91	0.650924
$509$	5675.90	0.494263	0.247131	−	0.968982i	$-0.420512\pi$
$509$	5675.90	0.494263	0.247131	+	0.968982i	$0.420512\pi$
$510$	−50233.7	−4.36154
$511$	−14198.2	−1.22914
$512$	−87.6610	−0.00756661
$513$	−12846.5	−1.10562
$514$	−14208.7	−1.21930
$515$	11823.3	1.01164
$516$	4184.51	0.357001
$517$	4435.34	0.377304
$518$	−7993.84	−0.678048
$519$	−26069.7	−2.20488
$520$	2496.90	0.210570
$521$	−2529.65	−0.212718	−0.106359	−	0.994328i	$-0.533919\pi$
$521$	−2529.65	−0.212718	−0.106359	+	0.994328i	$0.533919\pi$
$522$	−45977.6	−3.85514
$523$	−10088.5	−0.843476	−0.421738	−	0.906718i	$-0.638580\pi$
$523$	−10088.5	−0.843476	−0.421738	+	0.906718i	$0.638580\pi$
$524$	−1342.11	−0.111890
$525$	8172.24	0.679363
$526$	−3249.60	−0.269371
$527$	2005.97	0.165809
$528$	52422.0	4.32079
$529$	24976.5	2.05281
$530$	−17070.0	−1.39900
$531$	19363.0	1.58245
$532$	−2949.99	−0.240410
$533$	2953.65	0.240031
$534$	20503.0	1.66152
$535$	−13704.3	−1.10745
$536$	−3475.51	−0.280073
$537$	17559.3	1.41106
$538$	−27697.4	−2.21956
$539$	−34066.6	−2.72236
$540$	−14821.6	−1.18115
$541$	−7515.88	−0.597288	−0.298644	−	0.954365i	$-0.596534\pi$
$541$	−7515.88	−0.597288	−0.298644	+	0.954365i	$0.596534\pi$
$542$	−5712.65	−0.452730
$543$	12455.6	0.984384
$544$	−16584.1	−1.30706
$545$	−8200.81	−0.644558
$546$	11492.2	0.900769
$547$	547.000	0.0427569
$547$	547.000	0.0427569
$548$	3463.73	0.270006
$549$	−19646.4	−1.52730
$550$	6601.28	0.511781
$551$	−6814.53	−0.526876
$552$	−30637.2	−2.36233
$553$	−12643.2	−0.972228
$554$	23865.0	1.83019
$555$	−9965.59	−0.762191
$556$	−6535.29	−0.498486
$557$	15761.2	1.19897	0.599483	−	0.800388i	$-0.295373\pi$
$557$	15761.2	1.19897	0.599483	+	0.800388i	$0.295373\pi$
$558$	3569.22	0.270783
$559$	−1722.51	−0.130330
$560$	28499.5	2.15057
$561$	83066.9	6.25149
$562$	−13017.6	−0.977071
$563$	10309.0	0.771712	0.385856	−	0.922559i	$-0.373906\pi$
$563$	10309.0	0.771712	0.385856	+	0.922559i	$0.373906\pi$
$564$	−1936.21	−0.144555
$565$	−11603.3	−0.863993
$566$	17467.3	1.29718
$567$	56769.2	4.20473
$568$	12435.1	0.918603
$569$	10691.8	0.787736	0.393868	−	0.919167i	$-0.371137\pi$
$569$	10691.8	0.787736	0.393868	+	0.919167i	$0.371137\pi$
$570$	−13247.5	−0.973465
$571$	20605.1	1.51015	0.755077	−	0.655636i	$-0.227599\pi$
$571$	20605.1	1.51015	0.755077	+	0.655636i	$0.227599\pi$
$572$	2577.06	0.188378
$573$	−1979.64	−0.144329
$574$	23236.0	1.68964
$575$	−5597.52	−0.405970
$576$	12946.1	0.936491
$577$	−1527.38	−0.110200	−0.0551002	−	0.998481i	$-0.517548\pi$
$577$	−1527.38	−0.110200	−0.0551002	+	0.998481i	$0.517548\pi$
$578$	−35988.2	−2.58981
$579$	18113.5	1.30013
$580$	−7862.24	−0.562865
$581$	−31153.2	−2.22453
$582$	46280.6	3.29621
$583$	28227.1	2.00523
$584$	−8021.48	−0.568375
$585$	10214.0	0.721874
$586$	1308.20	0.0922204
$587$	7069.92	0.497116	0.248558	−	0.968617i	$-0.420043\pi$
$587$	7069.92	0.497116	0.248558	+	0.968617i	$0.420043\pi$
$588$	14871.5	1.04301
$589$	529.009	0.0370075
$590$	11927.2	0.832260
$591$	−15662.4	−1.09013
$592$	−6552.53	−0.454911
$593$	28030.1	1.94108	0.970539	−	0.240946i	$-0.0774576\pi$
$593$	28030.1	1.94108	0.970539	+	0.240946i	$0.0774576\pi$
$594$	88285.9	6.09834
$595$	45159.7	3.11154
$596$	6373.52	0.438036
$597$	−20923.0	−1.43438
$598$	−7871.49	−0.538276
$599$	−8548.55	−0.583113	−0.291556	−	0.956554i	$-0.594173\pi$
$599$	−8548.55	−0.583113	−0.291556	+	0.956554i	$0.594173\pi$
$600$	4617.03	0.314149
$601$	−18559.0	−1.25963	−0.629815	−	0.776745i	$-0.716869\pi$
$601$	−18559.0	−1.25963	−0.629815	+	0.776745i	$0.716869\pi$
$602$	−13550.8	−0.917424
$603$	−14217.2	−0.960145
$604$	−6096.84	−0.410723
$605$	−41376.7	−2.78050
$606$	35181.2	2.35832
$607$	−12447.0	−0.832303	−0.416151	−	0.909295i	$-0.636621\pi$
$607$	−12447.0	−0.832303	−0.416151	+	0.909295i	$0.636621\pi$
$608$	−4373.52	−0.291726
$609$	57977.2	3.85772
$610$	−12101.7	−0.803254
$611$	797.020	0.0527725
$612$	−25852.2	−1.70754
$613$	8658.90	0.570521	0.285261	−	0.958450i	$-0.407920\pi$
$613$	8658.90	0.570521	0.285261	+	0.958450i	$0.407920\pi$
$614$	−22101.2	−1.45266
$615$	28967.4	1.89932
$616$	−32481.6	−2.12455
$617$	−4888.06	−0.318940	−0.159470	−	0.987203i	$-0.550978\pi$
$617$	−4888.06	−0.318940	−0.159470	+	0.987203i	$0.550978\pi$
$618$	30744.0	2.00114
$619$	−4994.00	−0.324274	−0.162137	−	0.986768i	$-0.551839\pi$
$619$	−4994.00	−0.324274	−0.162137	+	0.986768i	$0.551839\pi$
$620$	610.342	0.0395354
$621$	−74861.6	−4.83751
$622$	17567.6	1.13247
$623$	−18432.0	−1.18533
$624$	9420.11	0.604337
$625$	−18411.9	−1.17836
$626$	−11480.4	−0.732986
$627$	21906.1	1.39529
$628$	−6573.65	−0.417702
$629$	−10383.0	−0.658184
$630$	80352.4	5.08145
$631$	18954.4	1.19582	0.597909	−	0.801564i	$-0.295998\pi$
$631$	18954.4	1.19582	0.597909	+	0.801564i	$0.295998\pi$
$632$	−7142.94	−0.449574
$633$	−24471.9	−1.53660
$634$	−19379.4	−1.21396
$635$	−30088.1	−1.88033
$636$	−12322.3	−0.768255
$637$	−6121.68	−0.380769
$638$	46832.1	2.90612
$639$	50868.0	3.14915
$640$	21104.9	1.30350
$641$	−3134.78	−0.193161	−0.0965806	−	0.995325i	$-0.530791\pi$
$641$	−3134.78	−0.193161	−0.0965806	+	0.995325i	$0.530791\pi$
$642$	−35635.2	−2.19067
$643$	−31413.0	−1.92660	−0.963302	−	0.268419i	$-0.913499\pi$
$643$	−31413.0	−1.92660	−0.963302	+	0.268419i	$0.913499\pi$
$644$	−17190.8	−1.05188
$645$	−16893.2	−1.03127
$646$	−13802.3	−0.840628
$647$	−13328.4	−0.809882	−0.404941	−	0.914343i	$-0.632708\pi$
$647$	−13328.4	−0.809882	−0.404941	+	0.914343i	$0.632708\pi$
$648$	32072.6	1.94434
$649$	−19722.9	−1.19290
$650$	1186.23	0.0715814
$651$	−4500.74	−0.270964
$652$	4769.22	0.286468
$653$	−7913.27	−0.474227	−0.237113	−	0.971482i	$-0.576201\pi$
$653$	−7913.27	−0.474227	−0.237113	+	0.971482i	$0.576201\pi$
$654$	−21324.5	−1.27501
$655$	5418.20	0.323216
$656$	19046.5	1.13360
$657$	−32813.2	−1.94850
$658$	6270.08	0.371479
$659$	17474.1	1.03292	0.516460	−	0.856311i	$-0.327249\pi$
$659$	17474.1	1.03292	0.516460	+	0.856311i	$0.327249\pi$
$660$	25274.1	1.49060
$661$	−2440.19	−0.143589	−0.0717945	−	0.997419i	$-0.522873\pi$
$661$	−2440.19	−0.143589	−0.0717945	+	0.997419i	$0.522873\pi$
$662$	−22462.5	−1.31878
$663$	14926.9	0.874379
$664$	−17600.5	−1.02866
$665$	11909.4	0.694474
$666$	−18474.4	−1.07488
$667$	−39711.1	−2.30528
$668$	5332.05	0.308837
$669$	33987.3	1.96416
$670$	−8757.45	−0.504970
$671$	20011.6	1.15132
$672$	37209.3	2.13598
$673$	−16252.4	−0.930883	−0.465441	−	0.885079i	$-0.654104\pi$
$673$	−16252.4	−0.930883	−0.465441	+	0.885079i	$0.654104\pi$
$674$	−16834.4	−0.962072
$675$	11281.6	0.643305
$676$	−6291.26	−0.357946
$677$	−8120.90	−0.461021	−0.230511	−	0.973070i	$-0.574040\pi$
$677$	−8120.90	−0.461021	−0.230511	+	0.973070i	$0.574040\pi$
$678$	−30172.1	−1.70908
$679$	−41605.9	−2.35153
$680$	25513.6	1.43883
$681$	−2860.17	−0.160943
$682$	−3635.56	−0.204124
$683$	−16912.3	−0.947482	−0.473741	−	0.880664i	$-0.657097\pi$
$683$	−16912.3	−0.947482	−0.473741	+	0.880664i	$0.657097\pi$
$684$	−6817.67	−0.381111
$685$	−13983.4	−0.779967
$686$	−15041.4	−0.837148
$687$	−33727.7	−1.87306
$688$	−11107.6	−0.615511
$689$	5072.34	0.280465
$690$	−77198.4	−4.25927
$691$	23031.2	1.26794	0.633970	−	0.773358i	$-0.281424\pi$
$691$	23031.2	1.26794	0.633970	+	0.773358i	$0.281424\pi$
$692$	−8264.26	−0.453988
$693$	−132871.	−7.28336
$694$	37729.3	2.06367
$695$	26383.5	1.43998
$696$	32755.1	1.78388
$697$	30180.7	1.64014
$698$	−181.801	−0.00985857
$699$	−8346.05	−0.451612
$700$	2590.65	0.139882
$701$	−30580.1	−1.64764	−0.823819	−	0.566853i	$-0.808161\pi$
$701$	−30580.1	−1.64764	−0.823819	+	0.566853i	$0.808161\pi$
$702$	15864.8	0.852959
$703$	−2738.17	−0.146902
$704$	−13186.7	−0.705954
$705$	7816.65	0.417577
$706$	−2542.13	−0.135516
$707$	−31627.6	−1.68243
$708$	8609.84	0.457031
$709$	26494.4	1.40341	0.701704	−	0.712468i	$-0.252423\pi$
$709$	26494.4	1.40341	0.701704	+	0.712468i	$0.252423\pi$
$710$	31333.5	1.65623
$711$	−29219.4	−1.54123
$712$	−10413.4	−0.548118
$713$	3082.75	0.161921
$714$	117429.	6.15497
$715$	−10403.8	−0.544169
$716$	5566.42	0.290540
$717$	−5856.21	−0.305027
$718$	−2601.35	−0.135211
$719$	25598.7	1.32778	0.663888	−	0.747832i	$-0.268905\pi$
$719$	25598.7	1.32778	0.663888	+	0.747832i	$0.268905\pi$
$720$	65864.6	3.40921
$721$	−27638.6	−1.42762
$722$	19185.6	0.988938
$723$	6329.82	0.325600
$724$	3948.50	0.202686
$725$	5984.46	0.306562
$726$	−107592.	−5.50014
$727$	−11785.2	−0.601225	−0.300613	−	0.953746i	$-0.597191\pi$
$727$	−11785.2	−0.601225	−0.300613	+	0.953746i	$0.597191\pi$
$728$	−5836.87	−0.297155
$729$	29487.6	1.49812
$730$	−20212.2	−1.02478
$731$	−17600.8	−0.890547
$732$	−8735.86	−0.441102
$733$	35757.9	1.80184	0.900919	−	0.433988i	$-0.142894\pi$
$733$	35757.9	1.80184	0.900919	+	0.433988i	$0.142894\pi$
$734$	2166.01	0.108922
$735$	−60037.4	−3.01294
$736$	−25486.3	−1.27641
$737$	14481.4	0.723785
$738$	53700.4	2.67851
$739$	13367.2	0.665384	0.332692	−	0.943036i	$-0.392043\pi$
$739$	13367.2	0.665384	0.332692	+	0.943036i	$0.392043\pi$
$740$	−3159.16	−0.156936
$741$	3936.48	0.195155
$742$	39903.6	1.97427
$743$	15161.4	0.748613	0.374307	−	0.927305i	$-0.377881\pi$
$743$	15161.4	0.748613	0.374307	+	0.927305i	$0.377881\pi$
$744$	−2542.76	−0.125299
$745$	−25730.5	−1.26536
$746$	−30378.4	−1.49093
$747$	−71997.7	−3.52645
$748$	26332.7	1.28719
$749$	32035.8	1.56283
$750$	−38436.1	−1.87132
$751$	−33553.7	−1.63035	−0.815173	−	0.579217i	$-0.803358\pi$
$751$	−33553.7	−1.63035	−0.815173	+	0.579217i	$0.803358\pi$
$752$	5139.56	0.249230
$753$	−44334.7	−2.14561
$754$	8415.62	0.406471
$755$	24613.5	1.18646
$756$	34647.6	1.66682
$757$	−36730.0	−1.76351	−0.881754	−	0.471709i	$-0.843637\pi$
$757$	−36730.0	−1.76351	−0.881754	+	0.471709i	$0.843637\pi$
$758$	−30849.7	−1.47825
$759$	127656.	6.10490
$760$	6728.37	0.321137
$761$	−33670.8	−1.60389	−0.801947	−	0.597395i	$-0.796203\pi$
$761$	−33670.8	−1.60389	−0.801947	+	0.597395i	$0.796203\pi$
$762$	−78237.8	−3.71950
$763$	19170.6	0.909596
$764$	−627.558	−0.0297176
$765$	104368.	4.93258
$766$	45209.3	2.13248
$767$	−3544.15	−0.166847
$768$	39899.4	1.87467
$769$	−1079.87	−0.0506385	−0.0253192	−	0.999679i	$-0.508060\pi$
$769$	−1079.87	−0.0506385	−0.0253192	+	0.999679i	$0.508060\pi$
$770$	−81845.9	−3.83055
$771$	41407.8	1.93420
$772$	5742.11	0.267698
$773$	−4524.07	−0.210504	−0.105252	−	0.994446i	$-0.533565\pi$
$773$	−4524.07	−0.210504	−0.105252	+	0.994446i	$0.533565\pi$
$774$	−31317.0	−1.45435
$775$	−464.571	−0.0215327
$776$	−23505.9	−1.08739
$777$	23296.0	1.07560
$778$	12369.8	0.570025
$779$	7959.17	0.366068
$780$	4541.70	0.208486
$781$	−51813.4	−2.37392
$782$	−80431.9	−3.67806
$783$	80036.5	3.65297
$784$	−39475.5	−1.79826
$785$	26538.4	1.20662
$786$	14088.9	0.639358
$787$	15243.3	0.690425	0.345212	−	0.938525i	$-0.387807\pi$
$787$	15243.3	0.690425	0.345212	+	0.938525i	$0.387807\pi$
$788$	−4965.08	−0.224459
$789$	9470.13	0.427308
$790$	−17998.5	−0.810580
$791$	27124.5	1.21926
$792$	−75067.7	−3.36795
$793$	3596.03	0.161032
$794$	29299.9	1.30959
$795$	49746.2	2.21926
$796$	−6632.73	−0.295340
$797$	−28252.5	−1.25565	−0.627827	−	0.778353i	$-0.716055\pi$
$797$	−28252.5	−1.25565	−0.627827	+	0.778353i	$0.716055\pi$
$798$	30967.9	1.37375
$799$	8144.05	0.360596
$800$	3840.78	0.169740
$801$	−42597.9	−1.87906
$802$	6558.90	0.288782
$803$	33423.1	1.46884
$804$	−6321.73	−0.277301
$805$	69400.8	3.03858
$806$	−653.301	−0.0285503
$807$	80717.2	3.52092
$808$	−17868.5	−0.777985
$809$	599.204	0.0260407	0.0130203	−	0.999915i	$-0.495855\pi$
$809$	599.204	0.0260407	0.0130203	+	0.999915i	$0.495855\pi$
$810$	80815.3	3.50563
$811$	23836.7	1.03208	0.516041	−	0.856564i	$-0.327405\pi$
$811$	23836.7	1.03208	0.516041	+	0.856564i	$0.327405\pi$
$812$	18379.1	0.794312
$813$	16648.1	0.718172
$814$	18817.8	0.810275
$815$	−19253.8	−0.827522
$816$	96255.8	4.12945
$817$	−4641.63	−0.198764
$818$	−2065.84	−0.0883014
$819$	−23876.7	−1.01870
$820$	9182.86	0.391073
$821$	−29735.1	−1.26402	−0.632011	−	0.774960i	$-0.717770\pi$
$821$	−29735.1	−1.26402	−0.632011	+	0.774960i	$0.717770\pi$
$822$	−36360.9	−1.54286
$823$	39052.9	1.65407	0.827033	−	0.562153i	$-0.190027\pi$
$823$	39052.9	1.65407	0.827033	+	0.562153i	$0.190027\pi$
$824$	−15614.8	−0.660156
$825$	−19237.8	−0.811846
$826$	−27881.5	−1.17448
$827$	−20353.5	−0.855818	−0.427909	−	0.903822i	$-0.640750\pi$
$827$	−20353.5	−0.855818	−0.427909	+	0.903822i	$0.640750\pi$
$828$	−39729.4	−1.66750
$829$	−4757.07	−0.199300	−0.0996502	−	0.995023i	$-0.531772\pi$
$829$	−4757.07	−0.199300	−0.0996502	+	0.995023i	$0.531772\pi$
$830$	−44348.9	−1.85467
$831$	−69548.6	−2.90327
$832$	−2369.61	−0.0987398
$833$	−62552.1	−2.60180
$834$	68605.0	2.84844
$835$	−21525.9	−0.892139
$836$	6944.38	0.287293
$837$	−6213.20	−0.256582
$838$	32232.3	1.32869
$839$	−33705.1	−1.38692	−0.693461	−	0.720494i	$-0.743915\pi$
$839$	−33705.1	−1.38692	−0.693461	+	0.720494i	$0.743915\pi$
$840$	−57244.2	−2.35132
$841$	18067.2	0.740792
$842$	41218.1	1.68702
$843$	37936.5	1.54994
$844$	−7757.74	−0.316389
$845$	25398.4	1.03400
$846$	14490.7	0.588888
$847$	96724.1	3.92382
$848$	32708.8	1.32456
$849$	−50904.0	−2.05774
$850$	12121.1	0.489117
$851$	−15956.5	−0.642750
$852$	22618.7	0.909511
$853$	2987.64	0.119924	0.0599618	−	0.998201i	$-0.480902\pi$
$853$	2987.64	0.119924	0.0599618	+	0.998201i	$0.480902\pi$
$854$	28289.6	1.13355
$855$	27523.5	1.10092
$856$	18099.1	0.722680
$857$	10484.2	0.417890	0.208945	−	0.977927i	$-0.432997\pi$
$857$	10484.2	0.417890	0.208945	+	0.977927i	$0.432997\pi$
$858$	−27053.0	−1.07643
$859$	−12609.9	−0.500866	−0.250433	−	0.968134i	$-0.580573\pi$
$859$	−12609.9	−0.500866	−0.250433	+	0.968134i	$0.580573\pi$
$860$	−5355.27	−0.212341
$861$	−67715.6	−2.68030
$862$	4417.27	0.174539
$863$	−29186.3	−1.15123	−0.575616	−	0.817720i	$-0.695238\pi$
$863$	−29186.3	−1.15123	−0.575616	+	0.817720i	$0.695238\pi$
$864$	51366.9	2.02261
$865$	33363.5	1.31144
$866$	−18373.0	−0.720946
$867$	104878.	4.10826
$868$	−1426.76	−0.0557921
$869$	29762.5	1.16182
$870$	82534.9	3.21632
$871$	2602.27	0.101234
$872$	10830.7	0.420612
$873$	−96154.7	−3.72777
$874$	−21211.2	−0.820917
$875$	34553.8	1.33501
$876$	−14590.5	−0.562750
$877$	6372.80	0.245375	0.122688	−	0.992445i	$-0.460849\pi$
$877$	6372.80	0.245375	0.122688	+	0.992445i	$0.460849\pi$
$878$	−20335.0	−0.781633
$879$	−3812.41	−0.146291
$880$	−67088.8	−2.56996
$881$	46766.4	1.78842	0.894212	−	0.447644i	$-0.147737\pi$
$881$	46766.4	1.78842	0.894212	+	0.447644i	$0.147737\pi$
$882$	−111299.	−4.24900
$883$	−37387.3	−1.42490	−0.712448	−	0.701725i	$-0.752414\pi$
$883$	−37387.3	−1.42490	−0.712448	+	0.701725i	$0.752414\pi$
$884$	4731.93	0.180036
$885$	−34758.7	−1.32023
$886$	−26542.8	−1.00646
$887$	−661.992	−0.0250592	−0.0125296	−	0.999922i	$-0.503988\pi$
$887$	−661.992	−0.0250592	−0.0125296	+	0.999922i	$0.503988\pi$
$888$	13161.4	0.497375
$889$	70335.2	2.65351
$890$	−26239.4	−0.988253
$891$	−133637.	−5.02470
$892$	10774.2	0.404424
$893$	2147.72	0.0804824
$894$	−66906.8	−2.50302
$895$	−22472.1	−0.839286
$896$	−49335.7	−1.83950
$897$	22939.5	0.853876
$898$	−47539.3	−1.76660
$899$	−3295.85	−0.122272
$900$	5987.22	0.221749
$901$	51829.8	1.91643
$902$	−54698.5	−2.01914
$903$	39490.4	1.45532
$904$	15324.4	0.563807
$905$	−15940.5	−0.585502
$906$	64002.3	2.34695
$907$	35433.5	1.29719	0.648595	−	0.761134i	$-0.275357\pi$
$907$	35433.5	1.29719	0.648595	+	0.761134i	$0.275357\pi$
$908$	−906.692	−0.0331384
$909$	−73094.1	−2.66708
$910$	−14707.5	−0.535768
$911$	49108.9	1.78600	0.893002	−	0.450052i	$-0.148594\pi$
$911$	49108.9	1.78600	0.893002	+	0.450052i	$0.148594\pi$
$912$	25384.3	0.921664
$913$	73335.8	2.65834
$914$	−38942.2	−1.40929
$915$	35267.5	1.27421
$916$	−10691.9	−0.385666
$917$	−12665.8	−0.456120
$918$	162108.	5.82829
$919$	−22507.3	−0.807884	−0.403942	−	0.914785i	$-0.632360\pi$
$919$	−22507.3	−0.807884	−0.403942	+	0.914785i	$0.632360\pi$
$920$	39209.0	1.40509
$921$	64408.3	2.30437
$922$	23426.7	0.836787
$923$	−9310.74	−0.332033
$924$	−59081.9	−2.10352
$925$	2404.64	0.0854746
$926$	−41206.8	−1.46235
$927$	−63875.1	−2.26314
$928$	27248.1	0.963860
$929$	−51571.6	−1.82132	−0.910662	−	0.413152i	$-0.864428\pi$
$929$	−51571.6	−1.82132	−0.910662	+	0.413152i	$0.864428\pi$
$930$	−6407.14	−0.225912
$931$	−16496.0	−0.580705
$932$	−2645.75	−0.0929877
$933$	−51196.4	−1.79646
$934$	22403.0	0.784848
$935$	−106308.	−3.71832
$936$	−13489.5	−0.471066
$937$	33655.7	1.17341	0.586705	−	0.809801i	$-0.300425\pi$
$937$	33655.7	1.17341	0.586705	+	0.809801i	$0.300425\pi$
$938$	20471.8	0.712610
$939$	33456.7	1.16275
$940$	2477.93	0.0859799
$941$	−1529.18	−0.0529755	−0.0264877	−	0.999649i	$-0.508432\pi$
$941$	−1529.18	−0.0529755	−0.0264877	+	0.999649i	$0.508432\pi$
$942$	69007.7	2.38683
$943$	46381.4	1.60168
$944$	−22854.4	−0.787973
$945$	−139875.	−4.81497
$946$	31899.1	1.09633
$947$	48117.3	1.65111	0.825555	−	0.564321i	$-0.190862\pi$
$947$	48117.3	1.65111	0.825555	+	0.564321i	$0.190862\pi$
$948$	−12992.6	−0.445125
$949$	6006.04	0.205442
$950$	3196.53	0.109168
$951$	56476.2	1.92573
$952$	−59641.8	−2.03047
$953$	−5248.75	−0.178409	−0.0892044	−	0.996013i	$-0.528432\pi$
$953$	−5248.75	−0.178409	−0.0892044	+	0.996013i	$0.528432\pi$
$954$	92220.5	3.12971
$955$	2533.51	0.0858454
$956$	−1856.46	−0.0628055
$957$	−136480.	−4.61002
$958$	31688.5	1.06869
$959$	32688.2	1.10068
$960$	−23239.6	−0.781307
$961$	−29535.1	−0.991412
$962$	3381.51	0.113331
$963$	74037.4	2.47749
$964$	2006.60	0.0670416
$965$	−23181.4	−0.773302
$966$	180463.	6.01065
$967$	−45097.1	−1.49972	−0.749858	−	0.661599i	$-0.769878\pi$
$967$	−45097.1	−1.49972	−0.749858	+	0.661599i	$0.769878\pi$
$968$	54645.7	1.81444
$969$	40223.4	1.33350
$970$	−59229.2	−1.96055
$971$	3906.16	0.129098	0.0645492	−	0.997915i	$-0.479439\pi$
$971$	3906.16	0.129098	0.0645492	+	0.997915i	$0.479439\pi$
$972$	26095.0	0.861109
$973$	−61675.4	−2.03209
$974$	35218.4	1.15859
$975$	−3456.98	−0.113551
$976$	23188.9	0.760510
$977$	8217.56	0.269092	0.134546	−	0.990907i	$-0.457042\pi$
$977$	8217.56	0.269092	0.134546	+	0.990907i	$0.457042\pi$
$978$	−50065.5	−1.63693
$979$	43389.7	1.41649
$980$	−19032.3	−0.620371
$981$	44304.8	1.44194
$982$	−18117.4	−0.588746
$983$	48340.4	1.56848	0.784242	−	0.620456i	$-0.213052\pi$
$983$	48340.4	1.56848	0.784242	+	0.620456i	$0.213052\pi$
$984$	−38256.9	−1.23942
$985$	20044.5	0.648396
$986$	85991.9	2.77742
$987$	−18272.6	−0.589283
$988$	1247.89	0.0401828
$989$	−27048.7	−0.869665
$990$	−189153.	−6.07239
$991$	−21747.4	−0.697102	−0.348551	−	0.937290i	$-0.613326\pi$
$991$	−21747.4	−0.697102	−0.348551	+	0.937290i	$0.613326\pi$
$992$	−2115.25	−0.0677010
$993$	65461.4	2.09200
$994$	−73246.7	−2.33727
$995$	26776.9	0.853151
$996$	−32014.1	−1.01848
$997$	560.651	0.0178094	0.00890471	−	0.999960i	$-0.497166\pi$
$997$	560.651	0.0178094	0.00890471	+	0.999960i	$0.497166\pi$
$998$	−4644.93	−0.147327
$999$	32159.8	1.01851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.a.1.18	✓	65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.a.1.18	✓	65	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)

\(f(q)\)	\(=\)	\(q-3.32782 q^{2} +9.69808 q^{3} +3.07435 q^{4} -12.4114 q^{5} -32.2734 q^{6} +29.0135 q^{7} +16.3916 q^{8} +67.0527 q^{9} +O(q^{10})\)	\(q-3.32782 q^{2} +9.69808 q^{3} +3.07435 q^{4} -12.4114 q^{5} -32.2734 q^{6} +29.0135 q^{7} +16.3916 q^{8} +67.0527 q^{9} +41.3030 q^{10} -68.2990 q^{11} +29.8153 q^{12} -12.2732 q^{13} -96.5517 q^{14} -120.367 q^{15} -79.1432 q^{16} -125.409 q^{17} -223.139 q^{18} -33.0724 q^{19} -38.1572 q^{20} +281.376 q^{21} +227.286 q^{22} -192.726 q^{23} +158.967 q^{24} +29.0439 q^{25} +40.8428 q^{26} +388.435 q^{27} +89.1979 q^{28} +206.049 q^{29} +400.560 q^{30} -15.9955 q^{31} +132.241 q^{32} -662.369 q^{33} +417.337 q^{34} -360.100 q^{35} +206.144 q^{36} +82.7933 q^{37} +110.059 q^{38} -119.026 q^{39} -203.444 q^{40} -240.659 q^{41} -936.366 q^{42} +140.348 q^{43} -209.975 q^{44} -832.221 q^{45} +641.358 q^{46} -64.9401 q^{47} -767.537 q^{48} +498.786 q^{49} -96.6527 q^{50} -1216.22 q^{51} -37.7320 q^{52} -413.287 q^{53} -1292.64 q^{54} +847.689 q^{55} +475.580 q^{56} -320.739 q^{57} -685.693 q^{58} +288.772 q^{59} -370.051 q^{60} -292.999 q^{61} +53.2300 q^{62} +1945.44 q^{63} +193.073 q^{64} +152.328 q^{65} +2204.24 q^{66} -212.030 q^{67} -385.551 q^{68} -1869.08 q^{69} +1198.35 q^{70} +758.626 q^{71} +1099.10 q^{72} -489.364 q^{73} -275.521 q^{74} +281.670 q^{75} -101.676 q^{76} -1981.60 q^{77} +396.097 q^{78} -435.768 q^{79} +982.281 q^{80} +1956.65 q^{81} +800.869 q^{82} -1073.75 q^{83} +865.048 q^{84} +1556.50 q^{85} -467.051 q^{86} +1998.28 q^{87} -1119.53 q^{88} -635.290 q^{89} +2769.48 q^{90} -356.088 q^{91} -592.509 q^{92} -155.125 q^{93} +216.109 q^{94} +410.476 q^{95} +1282.48 q^{96} -1434.02 q^{97} -1659.87 q^{98} -4579.64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * q^99

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