LMFDB - Embedded newform 1441.4.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.89777 q^{2} +0.451407 q^{3} +7.19260 q^{4} +9.64232 q^{5} -1.75948 q^{6} -28.6536 q^{7} +3.14706 q^{8} -26.7962 q^{9} +O(q^{10})$	\(q-3.89777 q^{2} +0.451407 q^{3} +7.19260 q^{4} +9.64232 q^{5} -1.75948 q^{6} -28.6536 q^{7} +3.14706 q^{8} -26.7962 q^{9} -37.5835 q^{10} -11.0000 q^{11} +3.24679 q^{12} +61.7908 q^{13} +111.685 q^{14} +4.35261 q^{15} -69.8073 q^{16} +84.0262 q^{17} +104.446 q^{18} +86.5201 q^{19} +69.3534 q^{20} -12.9344 q^{21} +42.8755 q^{22} +18.5564 q^{23} +1.42061 q^{24} -32.0256 q^{25} -240.846 q^{26} -24.2840 q^{27} -206.093 q^{28} -86.0178 q^{29} -16.9655 q^{30} -61.1081 q^{31} +246.916 q^{32} -4.96547 q^{33} -327.515 q^{34} -276.287 q^{35} -192.735 q^{36} -116.066 q^{37} -337.235 q^{38} +27.8928 q^{39} +30.3450 q^{40} -453.556 q^{41} +50.4153 q^{42} +66.9921 q^{43} -79.1186 q^{44} -258.378 q^{45} -72.3284 q^{46} +486.043 q^{47} -31.5115 q^{48} +478.026 q^{49} +124.828 q^{50} +37.9300 q^{51} +444.437 q^{52} -39.5380 q^{53} +94.6533 q^{54} -106.066 q^{55} -90.1746 q^{56} +39.0558 q^{57} +335.277 q^{58} -337.472 q^{59} +31.3066 q^{60} -309.379 q^{61} +238.185 q^{62} +767.807 q^{63} -403.964 q^{64} +595.807 q^{65} +19.3543 q^{66} +892.160 q^{67} +604.366 q^{68} +8.37647 q^{69} +1076.90 q^{70} -452.500 q^{71} -84.3295 q^{72} +14.0733 q^{73} +452.400 q^{74} -14.4566 q^{75} +622.305 q^{76} +315.189 q^{77} -108.720 q^{78} -660.155 q^{79} -673.105 q^{80} +712.536 q^{81} +1767.86 q^{82} -224.638 q^{83} -93.0320 q^{84} +810.207 q^{85} -261.120 q^{86} -38.8290 q^{87} -34.6177 q^{88} +24.6017 q^{89} +1007.10 q^{90} -1770.53 q^{91} +133.469 q^{92} -27.5846 q^{93} -1894.48 q^{94} +834.255 q^{95} +111.460 q^{96} -96.2931 q^{97} -1863.23 q^{98} +294.759 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) $ 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * 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 $

$2$	−3.89777	−1.37807	−0.689035	−	0.724728i	$-0.741965\pi$
$2$	−3.89777	−1.37807	−0.689035	+	0.724728i	$0.741965\pi$
$3$	0.451407	0.0868732	0.0434366	−	0.999056i	$-0.486169\pi$
$3$	0.451407	0.0868732	0.0434366	+	0.999056i	$0.486169\pi$
$4$	7.19260	0.899075
$5$	9.64232	0.862436	0.431218	−	0.902248i	$-0.358084\pi$
$5$	9.64232	0.862436	0.431218	+	0.902248i	$0.358084\pi$
$6$	−1.75948	−0.119717
$7$	−28.6536	−1.54715	−0.773573	−	0.633707i	$-0.781533\pi$
$7$	−28.6536	−1.54715	−0.773573	+	0.633707i	$0.781533\pi$
$8$	3.14706	0.139082
$9$	−26.7962	−0.992453
$10$	−37.5835	−1.18850
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	3.24679	0.0781055
$13$	61.7908	1.31828	0.659142	−	0.752019i	$-0.270920\pi$
$13$	61.7908	1.31828	0.659142	+	0.752019i	$0.270920\pi$
$14$	111.685	2.13207
$15$	4.35261	0.0749226
$16$	−69.8073	−1.09074
$17$	84.0262	1.19878	0.599392	−	0.800455i	$-0.295409\pi$
$17$	84.0262	1.19878	0.599392	+	0.800455i	$0.295409\pi$
$18$	104.446	1.36767
$19$	86.5201	1.04469	0.522344	−	0.852735i	$-0.325058\pi$
$19$	86.5201	1.04469	0.522344	+	0.852735i	$0.325058\pi$
$20$	69.3534	0.775394
$21$	−12.9344	−0.134406
$22$	42.8755	0.415504
$23$	18.5564	0.168229	0.0841146	−	0.996456i	$-0.473194\pi$
$23$	18.5564	0.168229	0.0841146	+	0.996456i	$0.473194\pi$
$24$	1.42061	0.0120825
$25$	−32.0256	−0.256205
$26$	−240.846	−1.81669
$27$	−24.2840	−0.173091
$28$	−206.093	−1.39100
$29$	−86.0178	−0.550797	−0.275398	−	0.961330i	$-0.588810\pi$
$29$	−86.0178	−0.550797	−0.275398	+	0.961330i	$0.588810\pi$
$30$	−16.9655	−0.103248
$31$	−61.1081	−0.354043	−0.177022	−	0.984207i	$-0.556646\pi$
$31$	−61.1081	−0.354043	−0.177022	+	0.984207i	$0.556646\pi$
$32$	246.916	1.36403
$33$	−4.96547	−0.0261933
$34$	−327.515	−1.65201
$35$	−276.287	−1.33431
$36$	−192.735	−0.892290
$37$	−116.066	−0.515708	−0.257854	−	0.966184i	$-0.583015\pi$
$37$	−116.066	−0.515708	−0.257854	+	0.966184i	$0.583015\pi$
$38$	−337.235	−1.43965
$39$	27.8928	0.114524
$40$	30.3450	0.119949
$41$	−453.556	−1.72765	−0.863824	−	0.503793i	$-0.831937\pi$
$41$	−453.556	−1.72765	−0.863824	+	0.503793i	$0.831937\pi$
$42$	50.4153	0.185220
$43$	66.9921	0.237586	0.118793	−	0.992919i	$-0.462098\pi$
$43$	66.9921	0.237586	0.118793	+	0.992919i	$0.462098\pi$
$44$	−79.1186	−0.271081
$45$	−258.378	−0.855927
$46$	−72.3284	−0.231831
$47$	486.043	1.50844	0.754220	−	0.656622i	$-0.228015\pi$
$47$	486.043	1.50844	0.754220	+	0.656622i	$0.228015\pi$
$48$	−31.5115	−0.0947560
$49$	478.026	1.39366
$50$	124.828	0.353068
$51$	37.9300	0.104142
$52$	444.437	1.18524
$53$	−39.5380	−0.102471	−0.0512355	−	0.998687i	$-0.516316\pi$
$53$	−39.5380	−0.102471	−0.0512355	+	0.998687i	$0.516316\pi$
$54$	94.6533	0.238531
$55$	−106.066	−0.260034
$56$	−90.1746	−0.215180
$57$	39.0558	0.0907555
$58$	335.277	0.759036
$59$	−337.472	−0.744664	−0.372332	−	0.928100i	$-0.621442\pi$
$59$	−337.472	−0.744664	−0.372332	+	0.928100i	$0.621442\pi$
$60$	31.3066	0.0673610
$61$	−309.379	−0.649377	−0.324688	−	0.945821i	$-0.605259\pi$
$61$	−309.379	−0.649377	−0.324688	+	0.945821i	$0.605259\pi$
$62$	238.185	0.487896
$63$	767.807	1.53547
$64$	−403.964	−0.788992
$65$	595.807	1.13694
$66$	19.3543	0.0360961
$67$	892.160	1.62679	0.813393	−	0.581714i	$-0.197618\pi$
$67$	892.160	1.62679	0.813393	+	0.581714i	$0.197618\pi$
$68$	604.366	1.07780
$69$	8.37647	0.0146146
$70$	1076.90	1.83878
$71$	−452.500	−0.756364	−0.378182	−	0.925731i	$-0.623451\pi$
$71$	−452.500	−0.756364	−0.378182	+	0.925731i	$0.623451\pi$
$72$	−84.3295	−0.138032
$73$	14.0733	0.0225638	0.0112819	−	0.999936i	$-0.496409\pi$
$73$	14.0733	0.0225638	0.0112819	+	0.999936i	$0.496409\pi$
$74$	452.400	0.710681
$75$	−14.4566	−0.0222573
$76$	622.305	0.939253
$77$	315.189	0.466482
$78$	−108.720	−0.157821
$79$	−660.155	−0.940168	−0.470084	−	0.882622i	$-0.655776\pi$
$79$	−660.155	−0.940168	−0.470084	+	0.882622i	$0.655776\pi$
$80$	−673.105	−0.940692
$81$	712.536	0.977416
$82$	1767.86	2.38082
$83$	−224.638	−0.297074	−0.148537	−	0.988907i	$-0.547456\pi$
$83$	−224.638	−0.297074	−0.148537	+	0.988907i	$0.547456\pi$
$84$	−93.0320	−0.120841
$85$	810.207	1.03387
$86$	−261.120	−0.327410
$87$	−38.8290	−0.0478495
$88$	−34.6177	−0.0419348
$89$	24.6017	0.0293008	0.0146504	−	0.999893i	$-0.495336\pi$
$89$	24.6017	0.0293008	0.0146504	+	0.999893i	$0.495336\pi$
$90$	1007.10	1.17953
$91$	−1770.53	−2.03958
$92$	133.469	0.151251
$93$	−27.5846	−0.0307569
$94$	−1894.48	−2.07873
$95$	834.255	0.900976
$96$	111.460	0.118498
$97$	−96.2931	−0.100795	−0.0503974	−	0.998729i	$-0.516049\pi$
$97$	−96.2931	−0.100795	−0.0503974	+	0.998729i	$0.516049\pi$
$98$	−1863.23	−1.92056
$99$	294.759	0.299236
$100$	−230.347	−0.230347
$101$	−1172.75	−1.15537	−0.577687	−	0.816258i	$-0.696045\pi$
$101$	−1172.75	−1.15537	−0.577687	+	0.816258i	$0.696045\pi$
$102$	−147.842	−0.143515
$103$	−397.753	−0.380502	−0.190251	−	0.981735i	$-0.560930\pi$
$103$	−397.753	−0.380502	−0.190251	+	0.981735i	$0.560930\pi$
$104$	194.460	0.183349
$105$	−124.718	−0.115916
$106$	154.110	0.141212
$107$	−466.289	−0.421288	−0.210644	−	0.977563i	$-0.567556\pi$
$107$	−466.289	−0.421288	−0.210644	+	0.977563i	$0.567556\pi$
$108$	−174.665	−0.155622
$109$	1818.18	1.59771	0.798854	−	0.601526i	$-0.205440\pi$
$109$	1818.18	1.59771	0.798854	+	0.601526i	$0.205440\pi$
$110$	413.419	0.358345
$111$	−52.3931	−0.0448012
$112$	2000.23	1.68753
$113$	1511.22	1.25808	0.629040	−	0.777373i	$-0.283448\pi$
$113$	1511.22	1.25808	0.629040	+	0.777373i	$0.283448\pi$
$114$	−152.230	−0.125067
$115$	178.926	0.145087
$116$	−618.691	−0.495207
$117$	−1655.76	−1.30833
$118$	1315.39	1.02620
$119$	−2407.65	−1.85470
$120$	13.6979	0.0104204
$121$	121.000	0.0909091
$122$	1205.89	0.894886
$123$	−204.738	−0.150086
$124$	−439.526	−0.318311
$125$	−1514.09	−1.08340
$126$	−2992.73	−2.11598
$127$	1407.80	0.983635	0.491818	−	0.870698i	$-0.336333\pi$
$127$	1407.80	0.983635	0.491818	+	0.870698i	$0.336333\pi$
$128$	−400.773	−0.276747
$129$	30.2407	0.0206399
$130$	−2322.32	−1.56678
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	−35.7146	−0.0235497
$133$	−2479.11	−1.61629
$134$	−3477.43	−2.24183
$135$	−234.154	−0.149280
$136$	264.436	0.166729
$137$	−1056.72	−0.658991	−0.329496	−	0.944157i	$-0.606879\pi$
$137$	−1056.72	−0.658991	−0.329496	+	0.944157i	$0.606879\pi$
$138$	−32.6495	−0.0201399
$139$	−1839.36	−1.12239	−0.561196	−	0.827683i	$-0.689659\pi$
$139$	−1839.36	−1.12239	−0.561196	+	0.827683i	$0.689659\pi$
$140$	−1987.22	−1.19965
$141$	219.403	0.131043
$142$	1763.74	1.04232
$143$	−679.699	−0.397478
$144$	1870.57	1.08251
$145$	−829.411	−0.475027
$146$	−54.8545	−0.0310944
$147$	215.784	0.121072
$148$	−834.819	−0.463660
$149$	1418.70	0.780028	0.390014	−	0.920809i	$-0.372470\pi$
$149$	1418.70	0.780028	0.390014	+	0.920809i	$0.372470\pi$
$150$	56.3484	0.0306722
$151$	2303.25	1.24129	0.620647	−	0.784090i	$-0.286870\pi$
$151$	2303.25	1.24129	0.620647	+	0.784090i	$0.286870\pi$
$152$	272.284	0.145297
$153$	−2251.58	−1.18974
$154$	−1228.53	−0.642845
$155$	−589.224	−0.305339
$156$	200.622	0.102965
$157$	2376.84	1.20823	0.604116	−	0.796896i	$-0.293526\pi$
$157$	2376.84	1.20823	0.604116	+	0.796896i	$0.293526\pi$
$158$	2573.13	1.29562
$159$	−17.8477	−0.00890198
$160$	2380.85	1.17639
$161$	−531.706	−0.260275
$162$	−2777.30	−1.34695
$163$	−182.608	−0.0877483	−0.0438742	−	0.999037i	$-0.513970\pi$
$163$	−182.608	−0.0877483	−0.0438742	+	0.999037i	$0.513970\pi$
$164$	−3262.25	−1.55329
$165$	−47.8787	−0.0225900
$166$	875.585	0.409389
$167$	319.152	0.147885	0.0739423	−	0.997263i	$-0.476442\pi$
$167$	319.152	0.147885	0.0739423	+	0.997263i	$0.476442\pi$
$168$	−40.7054	−0.0186934
$169$	1621.11	0.737873
$170$	−3158.00	−1.42475
$171$	−2318.41	−1.03680
$172$	481.847	0.213608
$173$	−2864.68	−1.25895	−0.629474	−	0.777022i	$-0.716730\pi$
$173$	−2864.68	−1.25895	−0.629474	+	0.777022i	$0.716730\pi$
$174$	151.346	0.0659399
$175$	917.647	0.396386
$176$	767.880	0.328870
$177$	−152.337	−0.0646913
$178$	−95.8915	−0.0403785
$179$	3706.56	1.54772	0.773858	−	0.633360i	$-0.218325\pi$
$179$	3706.56	1.54772	0.773858	+	0.633360i	$0.218325\pi$
$180$	−1858.41	−0.769542
$181$	1570.19	0.644812	0.322406	−	0.946601i	$-0.395508\pi$
$181$	1570.19	0.644812	0.322406	+	0.946601i	$0.395508\pi$
$182$	6901.10	2.81068
$183$	−139.656	−0.0564135
$184$	58.3981	0.0233976
$185$	−1119.15	−0.444765
$186$	107.518	0.0423851
$187$	−924.288	−0.361447
$188$	3495.91	1.35620
$189$	695.822	0.267797
$190$	−3251.73	−1.24161
$191$	2514.59	0.952614	0.476307	−	0.879279i	$-0.341975\pi$
$191$	2514.59	0.952614	0.476307	+	0.879279i	$0.341975\pi$
$192$	−182.352	−0.0685423
$193$	−516.666	−0.192697	−0.0963484	−	0.995348i	$-0.530716\pi$
$193$	−516.666	−0.192697	−0.0963484	+	0.995348i	$0.530716\pi$
$194$	375.328	0.138902
$195$	268.951	0.0987692
$196$	3438.25	1.25301
$197$	−1652.15	−0.597518	−0.298759	−	0.954329i	$-0.596573\pi$
$197$	−1652.15	−0.597518	−0.298759	+	0.954329i	$0.596573\pi$
$198$	−1148.90	−0.412368
$199$	3523.32	1.25508	0.627541	−	0.778583i	$-0.284061\pi$
$199$	3523.32	1.25508	0.627541	+	0.778583i	$0.284061\pi$
$200$	−100.787	−0.0356335
$201$	402.727	0.141324
$202$	4571.10	1.59219
$203$	2464.71	0.852163
$204$	272.815	0.0936317
$205$	−4373.34	−1.48999
$206$	1550.35	0.524359
$207$	−497.241	−0.166960
$208$	−4313.45	−1.43790
$209$	−951.721	−0.314985
$210$	486.121	0.159741
$211$	1705.34	0.556401	0.278200	−	0.960523i	$-0.410262\pi$
$211$	1705.34	0.556401	0.278200	+	0.960523i	$0.410262\pi$
$212$	−284.381	−0.0921290
$213$	−204.261	−0.0657078
$214$	1817.48	0.580564
$215$	645.959	0.204903
$216$	−76.4232	−0.0240738
$217$	1750.96	0.547757
$218$	−7086.84	−2.20175
$219$	6.35278	0.00196019
$220$	−762.887	−0.233790
$221$	5192.05	1.58034
$222$	204.216	0.0617392
$223$	3255.57	0.977621	0.488810	−	0.872390i	$-0.337431\pi$
$223$	3255.57	0.977621	0.488810	+	0.872390i	$0.337431\pi$
$224$	−7075.03	−2.11036
$225$	858.166	0.254271
$226$	−5890.37	−1.73372
$227$	−818.124	−0.239211	−0.119605	−	0.992822i	$-0.538163\pi$
$227$	−818.124	−0.239211	−0.119605	+	0.992822i	$0.538163\pi$
$228$	280.912	0.0815959
$229$	−6040.61	−1.74312	−0.871561	−	0.490288i	$-0.836892\pi$
$229$	−6040.61	−1.74312	−0.871561	+	0.490288i	$0.836892\pi$
$230$	−697.414	−0.199940
$231$	142.278	0.0405248
$232$	−270.703	−0.0766058
$233$	2874.05	0.808091	0.404045	−	0.914739i	$-0.367604\pi$
$233$	2874.05	0.808091	0.404045	+	0.914739i	$0.367604\pi$
$234$	6453.77	1.80298
$235$	4686.58	1.30093
$236$	−2427.30	−0.669508
$237$	−297.998	−0.0816754
$238$	9384.45	2.55590
$239$	6998.11	1.89402	0.947009	−	0.321207i	$-0.104089\pi$
$239$	6998.11	1.89402	0.947009	+	0.321207i	$0.104089\pi$
$240$	−303.844	−0.0817210
$241$	−5776.09	−1.54386	−0.771931	−	0.635707i	$-0.780709\pi$
$241$	−5776.09	−1.54386	−0.771931	+	0.635707i	$0.780709\pi$
$242$	−471.630	−0.125279
$243$	977.311	0.258002
$244$	−2225.24	−0.583838
$245$	4609.28	1.20194
$246$	798.022	0.206829
$247$	5346.15	1.37720
$248$	−192.311	−0.0492410
$249$	−101.403	−0.0258078
$250$	5901.58	1.49299
$251$	2463.04	0.619384	0.309692	−	0.950837i	$-0.399774\pi$
$251$	2463.04	0.619384	0.309692	+	0.950837i	$0.399774\pi$
$252$	5522.53	1.38050
$253$	−204.120	−0.0507230
$254$	−5487.26	−1.35552
$255$	365.733	0.0898160
$256$	4793.83	1.17037
$257$	7866.14	1.90925	0.954623	−	0.297817i	$-0.0962584\pi$
$257$	7866.14	1.90925	0.954623	+	0.297817i	$0.0962584\pi$
$258$	−117.871	−0.0284432
$259$	3325.71	0.797876
$260$	4285.40	1.02219
$261$	2304.95	0.546640
$262$	510.608	0.120402
$263$	−4947.69	−1.16003	−0.580014	−	0.814607i	$-0.696953\pi$
$263$	−4947.69	−1.16003	−0.580014	+	0.814607i	$0.696953\pi$
$264$	−15.6267	−0.00364301
$265$	−381.238	−0.0883746
$266$	9662.99	2.22735
$267$	11.1053	0.00254545
$268$	6416.95	1.46260
$269$	430.280	0.0975266	0.0487633	−	0.998810i	$-0.484472\pi$
$269$	430.280	0.0975266	0.0487633	+	0.998810i	$0.484472\pi$
$270$	912.678	0.205718
$271$	302.475	0.0678010	0.0339005	−	0.999425i	$-0.489207\pi$
$271$	302.475	0.0678010	0.0339005	+	0.999425i	$0.489207\pi$
$272$	−5865.64	−1.30756
$273$	−799.227	−0.177185
$274$	4118.86	0.908136
$275$	352.282	0.0772487
$276$	60.2486	0.0131396
$277$	3287.65	0.713126	0.356563	−	0.934271i	$-0.383948\pi$
$277$	3287.65	0.713126	0.356563	+	0.934271i	$0.383948\pi$
$278$	7169.40	1.54673
$279$	1637.47	0.351371
$280$	−869.492	−0.185579
$281$	1590.37	0.337628	0.168814	−	0.985648i	$-0.446006\pi$
$281$	1590.37	0.337628	0.168814	+	0.985648i	$0.446006\pi$
$282$	−855.182	−0.180586
$283$	−1156.29	−0.242878	−0.121439	−	0.992599i	$-0.538751\pi$
$283$	−1156.29	−0.242878	−0.121439	+	0.992599i	$0.538751\pi$
$284$	−3254.65	−0.680028
$285$	376.588	0.0782707
$286$	2649.31	0.547752
$287$	12996.0	2.67292
$288$	−6616.42	−1.35374
$289$	2147.40	0.437084
$290$	3232.85	0.654619
$291$	−43.4674	−0.00875636
$292$	101.224	0.0202865
$293$	−616.675	−0.122957	−0.0614787	−	0.998108i	$-0.519582\pi$
$293$	−616.675	−0.122957	−0.0614787	+	0.998108i	$0.519582\pi$
$294$	−841.076	−0.166845
$295$	−3254.02	−0.642224
$296$	−365.268	−0.0717257
$297$	267.124	0.0521888
$298$	−5529.75	−1.07493
$299$	1146.61	0.221774
$300$	−103.980	−0.0200110
$301$	−1919.56	−0.367580
$302$	−8977.52	−1.71059
$303$	−529.386	−0.100371
$304$	−6039.74	−1.13948
$305$	−2983.14	−0.560046
$306$	8776.15	1.63954
$307$	−3213.48	−0.597404	−0.298702	−	0.954346i	$-0.596554\pi$
$307$	−3213.48	−0.597404	−0.298702	+	0.954346i	$0.596554\pi$
$308$	2267.03	0.419402
$309$	−179.548	−0.0330555
$310$	2296.66	0.420779
$311$	−1551.05	−0.282803	−0.141402	−	0.989952i	$-0.545161\pi$
$311$	−1551.05	−0.282803	−0.141402	+	0.989952i	$0.545161\pi$
$312$	87.7804	0.0159282
$313$	5141.51	0.928483	0.464242	−	0.885709i	$-0.346327\pi$
$313$	5141.51	0.928483	0.464242	+	0.885709i	$0.346327\pi$
$314$	−9264.37	−1.66503
$315$	7403.45	1.32424
$316$	−4748.23	−0.845281
$317$	2893.01	0.512580	0.256290	−	0.966600i	$-0.417500\pi$
$317$	2893.01	0.512580	0.256290	+	0.966600i	$0.417500\pi$
$318$	69.5662	0.0122675
$319$	946.196	0.166071
$320$	−3895.15	−0.680455
$321$	−210.486	−0.0365986
$322$	2072.47	0.358677
$323$	7269.95	1.25236
$324$	5124.99	0.878770
$325$	−1978.89	−0.337751
$326$	711.764	0.120923
$327$	820.738	0.138798
$328$	−1427.37	−0.240285
$329$	−13926.9	−2.33378
$330$	186.620	0.0311306
$331$	1070.59	0.177780	0.0888900	−	0.996041i	$-0.471668\pi$
$331$	1070.59	0.177780	0.0888900	+	0.996041i	$0.471668\pi$
$332$	−1615.73	−0.267092
$333$	3110.14	0.511816
$334$	−1243.98	−0.203795
$335$	8602.50	1.40300
$336$	902.916	0.146601
$337$	3167.51	0.512004	0.256002	−	0.966676i	$-0.417595\pi$
$337$	3167.51	0.512004	0.256002	+	0.966676i	$0.417595\pi$
$338$	−6318.70	−1.01684
$339$	682.172	0.109294
$340$	5827.50	0.929530
$341$	672.189	0.106748
$342$	9036.64	1.42879
$343$	−3868.98	−0.609053
$344$	210.828	0.0330439
$345$	80.7686	0.0126042
$346$	11165.9	1.73492
$347$	7181.72	1.11105	0.555526	−	0.831499i	$-0.312517\pi$
$347$	7181.72	1.11105	0.555526	+	0.831499i	$0.312517\pi$
$348$	−279.281	−0.0430203
$349$	−11958.2	−1.83411	−0.917056	−	0.398758i	$-0.869441\pi$
$349$	−11958.2	−1.83411	−0.917056	+	0.398758i	$0.869441\pi$
$350$	−3576.78	−0.546248
$351$	−1500.53	−0.228183
$352$	−2716.08	−0.411271
$353$	4686.64	0.706642	0.353321	−	0.935502i	$-0.385052\pi$
$353$	4686.64	0.706642	0.353321	+	0.935502i	$0.385052\pi$
$354$	593.775	0.0891491
$355$	−4363.15	−0.652315
$356$	176.950	0.0263436
$357$	−1086.83	−0.161123
$358$	−14447.3	−2.13286
$359$	6270.87	0.921905	0.460953	−	0.887425i	$-0.347508\pi$
$359$	6270.87	0.921905	0.460953	+	0.887425i	$0.347508\pi$
$360$	−813.132	−0.119044
$361$	626.732	0.0913737
$362$	−6120.22	−0.888596
$363$	54.6202	0.00789757
$364$	−12734.7	−1.83373
$365$	135.699	0.0194598
$366$	544.346	0.0777416
$367$	−4476.29	−0.636677	−0.318338	−	0.947977i	$-0.603125\pi$
$367$	−4476.29	−0.636677	−0.318338	+	0.947977i	$0.603125\pi$
$368$	−1295.37	−0.183494
$369$	12153.6	1.71461
$370$	4362.19	0.612917
$371$	1132.90	0.158537
$372$	−198.405	−0.0276527
$373$	2772.66	0.384887	0.192444	−	0.981308i	$-0.438359\pi$
$373$	2772.66	0.384887	0.192444	+	0.981308i	$0.438359\pi$
$374$	3602.66	0.498099
$375$	−683.471	−0.0941181
$376$	1529.61	0.209797
$377$	−5315.11	−0.726106
$378$	−2712.15	−0.369043
$379$	8273.30	1.12130	0.560648	−	0.828054i	$-0.310552\pi$
$379$	8273.30	1.12130	0.560648	+	0.828054i	$0.310552\pi$
$380$	6000.46	0.810045
$381$	635.488	0.0854516
$382$	−9801.29	−1.31277
$383$	13137.5	1.75273	0.876366	−	0.481646i	$-0.159961\pi$
$383$	13137.5	1.75273	0.876366	+	0.481646i	$0.159961\pi$
$384$	−180.911	−0.0240419
$385$	3039.15	0.402311
$386$	2013.85	0.265549
$387$	−1795.14	−0.235793
$388$	−692.598	−0.0906220
$389$	−2115.44	−0.275726	−0.137863	−	0.990451i	$-0.544023\pi$
$389$	−2115.44	−0.275726	−0.137863	+	0.990451i	$0.544023\pi$
$390$	−1048.31	−0.136111
$391$	1559.22	0.201671
$392$	1504.38	0.193833
$393$	−59.1343	−0.00759015
$394$	6439.71	0.823421
$395$	−6365.43	−0.810834
$396$	2120.08	0.269035
$397$	7972.11	1.00783	0.503915	−	0.863753i	$-0.331892\pi$
$397$	7972.11	1.00783	0.503915	+	0.863753i	$0.331892\pi$
$398$	−13733.1	−1.72959
$399$	−1119.09	−0.140412
$400$	2235.62	0.279453
$401$	9694.88	1.20733	0.603665	−	0.797238i	$-0.293707\pi$
$401$	9694.88	1.20733	0.603665	+	0.797238i	$0.293707\pi$
$402$	−1569.74	−0.194755
$403$	−3775.92	−0.466729
$404$	−8435.10	−1.03877
$405$	6870.51	0.842958
$406$	−9606.89	−1.17434
$407$	1276.73	0.155492
$408$	119.368	0.0144843
$409$	11513.2	1.39191	0.695956	−	0.718084i	$-0.254981\pi$
$409$	11513.2	1.39191	0.695956	+	0.718084i	$0.254981\pi$
$410$	17046.2	2.05330
$411$	−477.011	−0.0572487
$412$	−2860.88	−0.342100
$413$	9669.78	1.15210
$414$	1938.13	0.230082
$415$	−2166.03	−0.256208
$416$	15257.2	1.79818
$417$	−830.299	−0.0975058
$418$	3709.59	0.434072
$419$	−12798.4	−1.49223	−0.746113	−	0.665820i	$-0.768082\pi$
$419$	−12798.4	−1.49223	−0.746113	+	0.665820i	$0.768082\pi$
$420$	−897.044	−0.104217
$421$	13717.6	1.58802	0.794010	−	0.607905i	$-0.207990\pi$
$421$	13717.6	1.58802	0.794010	+	0.607905i	$0.207990\pi$
$422$	−6647.02	−0.766758
$423$	−13024.1	−1.49706
$424$	−124.429	−0.0142518
$425$	−2690.99	−0.307134
$426$	796.164	0.0905499
$427$	8864.82	1.00468
$428$	−3353.83	−0.378769
$429$	−306.821	−0.0345302
$430$	−2517.80	−0.282370
$431$	14113.7	1.57734	0.788670	−	0.614817i	$-0.210770\pi$
$431$	14113.7	1.57734	0.788670	+	0.614817i	$0.210770\pi$
$432$	1695.20	0.188797
$433$	−1082.82	−0.120178	−0.0600891	−	0.998193i	$-0.519138\pi$
$433$	−1082.82	−0.120178	−0.0600891	+	0.998193i	$0.519138\pi$
$434$	−6824.85	−0.754846
$435$	−374.402	−0.0412671
$436$	13077.4	1.43646
$437$	1605.50	0.175747
$438$	−24.7617	−0.00270127
$439$	−3328.13	−0.361829	−0.180914	−	0.983499i	$-0.557906\pi$
$439$	−3328.13	−0.361829	−0.180914	+	0.983499i	$0.557906\pi$
$440$	−333.795	−0.0361660
$441$	−12809.3	−1.38314
$442$	−20237.4	−2.17782
$443$	10868.2	1.16561	0.582803	−	0.812613i	$-0.301956\pi$
$443$	10868.2	1.16561	0.582803	+	0.812613i	$0.301956\pi$
$444$	−376.843	−0.0402797
$445$	237.217	0.0252700
$446$	−12689.5	−1.34723
$447$	640.409	0.0677635
$448$	11575.0	1.22069
$449$	4441.57	0.466839	0.233420	−	0.972376i	$-0.425008\pi$
$449$	4441.57	0.466839	0.233420	+	0.972376i	$0.425008\pi$
$450$	−3344.93	−0.350403
$451$	4989.12	0.520906
$452$	10869.6	1.13111
$453$	1039.70	0.107835
$454$	3188.86	0.329649
$455$	−17072.0	−1.75900
$456$	122.911	0.0126224
$457$	−5504.81	−0.563467	−0.281733	−	0.959493i	$-0.590909\pi$
$457$	−5504.81	−0.563467	−0.281733	+	0.959493i	$0.590909\pi$
$458$	23544.9	2.40214
$459$	−2040.49	−0.207499
$460$	1286.95	0.130444
$461$	−5253.22	−0.530730	−0.265365	−	0.964148i	$-0.585493\pi$
$461$	−5253.22	−0.530730	−0.265365	+	0.964148i	$0.585493\pi$
$462$	−554.568	−0.0558460
$463$	15606.0	1.56647	0.783233	−	0.621728i	$-0.213569\pi$
$463$	15606.0	1.56647	0.783233	+	0.621728i	$0.213569\pi$
$464$	6004.67	0.600775
$465$	−265.980	−0.0265258
$466$	−11202.4	−1.11360
$467$	−2384.64	−0.236291	−0.118146	−	0.992996i	$-0.537695\pi$
$467$	−2384.64	−0.236291	−0.118146	+	0.992996i	$0.537695\pi$
$468$	−11909.2	−1.17629
$469$	−25563.6	−2.51688
$470$	−18267.2	−1.79277
$471$	1072.92	0.104963
$472$	−1062.05	−0.103569
$473$	−736.913	−0.0716349
$474$	1161.53	0.112554
$475$	−2770.86	−0.267654
$476$	−17317.2	−1.66751
$477$	1059.47	0.101698
$478$	−27277.0	−2.61009
$479$	4539.23	0.432991	0.216495	−	0.976284i	$-0.430537\pi$
$479$	4539.23	0.432991	0.216495	+	0.976284i	$0.430537\pi$
$480$	1074.73	0.102197
$481$	−7171.84	−0.679850
$482$	22513.9	2.12755
$483$	−240.016	−0.0226109
$484$	870.304	0.0817341
$485$	−928.490	−0.0869290
$486$	−3809.33	−0.355545
$487$	−13778.1	−1.28202	−0.641011	−	0.767532i	$-0.721485\pi$
$487$	−13778.1	−1.28202	−0.641011	+	0.767532i	$0.721485\pi$
$488$	−973.637	−0.0903166
$489$	−82.4305	−0.00762298
$490$	−17965.9	−1.65636
$491$	17756.8	1.63208	0.816042	−	0.577992i	$-0.196164\pi$
$491$	17756.8	1.63208	0.816042	+	0.577992i	$0.196164\pi$
$492$	−1472.60	−0.134939
$493$	−7227.74	−0.660286
$494$	−20838.1	−1.89787
$495$	2842.16	0.258072
$496$	4265.79	0.386169
$497$	12965.7	1.17021
$498$	395.245	0.0355650
$499$	−1380.47	−0.123844	−0.0619222	−	0.998081i	$-0.519723\pi$
$499$	−1380.47	−0.123844	−0.0619222	+	0.998081i	$0.519723\pi$
$500$	−10890.3	−0.974054
$501$	144.067	0.0128472
$502$	−9600.34	−0.853554
$503$	16903.8	1.49842	0.749209	−	0.662334i	$-0.230434\pi$
$503$	16903.8	1.49842	0.749209	+	0.662334i	$0.230434\pi$
$504$	2416.34	0.213556
$505$	−11308.0	−0.996436
$506$	795.613	0.0698998
$507$	731.778	0.0641014
$508$	10125.7	0.884362
$509$	−2099.33	−0.182811	−0.0914057	−	0.995814i	$-0.529136\pi$
$509$	−2099.33	−0.182811	−0.0914057	+	0.995814i	$0.529136\pi$
$510$	−1425.54	−0.123773
$511$	−403.250	−0.0349095
$512$	−15479.1	−1.33610
$513$	−2101.05	−0.180826
$514$	−30660.4	−2.63107
$515$	−3835.26	−0.328159
$516$	217.509	0.0185568
$517$	−5346.47	−0.454812
$518$	−12962.9	−1.09953
$519$	−1293.14	−0.109369
$520$	1875.04	0.158127
$521$	−5321.68	−0.447499	−0.223750	−	0.974647i	$-0.571830\pi$
$521$	−5321.68	−0.447499	−0.223750	+	0.974647i	$0.571830\pi$
$522$	−8984.17	−0.753307
$523$	17207.4	1.43867	0.719336	−	0.694662i	$-0.244446\pi$
$523$	17207.4	1.43867	0.719336	+	0.694662i	$0.244446\pi$
$524$	−942.230	−0.0785525
$525$	414.232	0.0344354
$526$	19284.9	1.59860
$527$	−5134.68	−0.424421
$528$	346.626	0.0285700
$529$	−11822.7	−0.971699
$530$	1485.98	0.121786
$531$	9042.99	0.739044
$532$	−17831.2	−1.45316
$533$	−28025.6	−2.27753
$534$	−43.2861	−0.00350781
$535$	−4496.10	−0.363334
$536$	2807.69	0.226257
$537$	1673.16	0.134455
$538$	−1677.13	−0.134398
$539$	−5258.29	−0.420205
$540$	−1684.17	−0.134214
$541$	−3064.26	−0.243517	−0.121759	−	0.992560i	$-0.538853\pi$
$541$	−3064.26	−0.243517	−0.121759	+	0.992560i	$0.538853\pi$
$542$	−1178.98	−0.0934345
$543$	708.792	0.0560169
$544$	20747.4	1.63518
$545$	17531.5	1.37792
$546$	3115.20	0.244173
$547$	11390.7	0.890371	0.445185	−	0.895438i	$-0.353138\pi$
$547$	11390.7	0.890371	0.445185	+	0.895438i	$0.353138\pi$
$548$	−7600.57	−0.592482
$549$	8290.20	0.644476
$550$	−1373.11	−0.106454
$551$	−7442.27	−0.575411
$552$	26.3613	0.00203263
$553$	18915.8	1.45458
$554$	−12814.5	−0.982737
$555$	−505.192	−0.0386382
$556$	−13229.8	−1.00911
$557$	−14652.2	−1.11460	−0.557300	−	0.830311i	$-0.688163\pi$
$557$	−14652.2	−1.11460	−0.557300	+	0.830311i	$0.688163\pi$
$558$	−6382.47	−0.484214
$559$	4139.50	0.313206
$560$	19286.8	1.45539
$561$	−417.230	−0.0314001
$562$	−6198.89	−0.465275
$563$	−4165.33	−0.311807	−0.155904	−	0.987772i	$-0.549829\pi$
$563$	−4165.33	−0.311807	−0.155904	+	0.987772i	$0.549829\pi$
$564$	1578.08	0.117817
$565$	14571.6	1.08501
$566$	4506.96	0.334703
$567$	−20416.7	−1.51221
$568$	−1424.05	−0.105197
$569$	12744.7	0.938992	0.469496	−	0.882935i	$-0.344436\pi$
$569$	12744.7	0.938992	0.469496	+	0.882935i	$0.344436\pi$
$570$	−1467.85	−0.107862
$571$	9196.53	0.674015	0.337008	−	0.941502i	$-0.390585\pi$
$571$	9196.53	0.674015	0.337008	+	0.941502i	$0.390585\pi$
$572$	−4888.80	−0.357362
$573$	1135.10	0.0827567
$574$	−50655.4	−3.68348
$575$	−594.279	−0.0431011
$576$	10824.7	0.783037
$577$	−8298.79	−0.598757	−0.299379	−	0.954134i	$-0.596779\pi$
$577$	−8298.79	−0.598757	−0.299379	+	0.954134i	$0.596779\pi$
$578$	−8370.05	−0.602333
$579$	−233.227	−0.0167402
$580$	−5965.62	−0.427084
$581$	6436.66	0.459618
$582$	169.426	0.0120669
$583$	434.918	0.0308961
$584$	44.2896	0.00313821
$585$	−15965.4	−1.12835
$586$	2403.66	0.169444
$587$	20308.1	1.42795	0.713973	−	0.700173i	$-0.246894\pi$
$587$	20308.1	1.42795	0.713973	+	0.700173i	$0.246894\pi$
$588$	1552.05	0.108853
$589$	−5287.08	−0.369865
$590$	12683.4	0.885030
$591$	−745.793	−0.0519083
$592$	8102.28	0.562503
$593$	−26530.3	−1.83721	−0.918606	−	0.395174i	$-0.870684\pi$
$593$	−26530.3	−1.83721	−0.918606	+	0.395174i	$0.870684\pi$
$594$	−1041.19	−0.0719198
$595$	−23215.3	−1.59956
$596$	10204.1	0.701303
$597$	1590.45	0.109033
$598$	−4469.23	−0.305620
$599$	1856.52	0.126637	0.0633185	−	0.997993i	$-0.479832\pi$
$599$	1856.52	0.126637	0.0633185	+	0.997993i	$0.479832\pi$
$600$	−45.4958	−0.00309559
$601$	−23376.6	−1.58661	−0.793303	−	0.608827i	$-0.791640\pi$
$601$	−23376.6	−1.58661	−0.793303	+	0.608827i	$0.791640\pi$
$602$	7482.01	0.506551
$603$	−23906.5	−1.61451
$604$	16566.3	1.11602
$605$	1166.72	0.0784032
$606$	2063.42	0.138318
$607$	−25286.0	−1.69082	−0.845410	−	0.534118i	$-0.820644\pi$
$607$	−25286.0	−1.69082	−0.845410	+	0.534118i	$0.820644\pi$
$608$	21363.2	1.42499
$609$	1112.59	0.0740301
$610$	11627.6	0.771782
$611$	30033.0	1.98855
$612$	−16194.7	−1.06966
$613$	−4890.06	−0.322198	−0.161099	−	0.986938i	$-0.551504\pi$
$613$	−4890.06	−0.322198	−0.161099	+	0.986938i	$0.551504\pi$
$614$	12525.4	0.823264
$615$	−1974.15	−0.129440
$616$	991.920	0.0648792
$617$	−2811.14	−0.183423	−0.0917117	−	0.995786i	$-0.529234\pi$
$617$	−2811.14	−0.183423	−0.0917117	+	0.995786i	$0.529234\pi$
$618$	699.837	0.0455527
$619$	−18748.7	−1.21741	−0.608704	−	0.793398i	$-0.708310\pi$
$619$	−18748.7	−1.21741	−0.608704	+	0.793398i	$0.708310\pi$
$620$	−4238.05	−0.274523
$621$	−450.622	−0.0291189
$622$	6045.62	0.389722
$623$	−704.925	−0.0453326
$624$	−1947.12	−0.124915
$625$	−10596.2	−0.678154
$626$	−20040.4	−1.27951
$627$	−429.613	−0.0273638
$628$	17095.7	1.08629
$629$	−9752.61	−0.618223
$630$	−28856.9	−1.82490
$631$	3323.12	0.209653	0.104827	−	0.994491i	$-0.466571\pi$
$631$	3323.12	0.209653	0.104827	+	0.994491i	$0.466571\pi$
$632$	−2077.55	−0.130760
$633$	769.802	0.0483363
$634$	−11276.3	−0.706370
$635$	13574.4	0.848322
$636$	−128.371	−0.00800354
$637$	29537.6	1.83724
$638$	−3688.05	−0.228858
$639$	12125.3	0.750656
$640$	−3864.38	−0.238677
$641$	13240.7	0.815875	0.407938	−	0.913010i	$-0.366248\pi$
$641$	13240.7	0.815875	0.407938	+	0.913010i	$0.366248\pi$
$642$	820.425	0.0504355
$643$	−12583.8	−0.771786	−0.385893	−	0.922543i	$-0.626107\pi$
$643$	−12583.8	−0.771786	−0.385893	+	0.922543i	$0.626107\pi$
$644$	−3824.35	−0.234007
$645$	291.590	0.0178006
$646$	−28336.6	−1.72583
$647$	27598.5	1.67698	0.838491	−	0.544915i	$-0.183438\pi$
$647$	27598.5	1.67698	0.838491	+	0.544915i	$0.183438\pi$
$648$	2242.40	0.135941
$649$	3712.20	0.224525
$650$	7713.25	0.465444
$651$	790.397	0.0475854
$652$	−1313.43	−0.0788923
$653$	17395.4	1.04247	0.521236	−	0.853413i	$-0.325471\pi$
$653$	17395.4	1.04247	0.521236	+	0.853413i	$0.325471\pi$
$654$	−3199.05	−0.191273
$655$	−1263.14	−0.0753513
$656$	31661.5	1.88441
$657$	−377.111	−0.0223935
$658$	54283.7	3.21611
$659$	−21326.2	−1.26063	−0.630313	−	0.776341i	$-0.717073\pi$
$659$	−21326.2	−1.26063	−0.630313	+	0.776341i	$0.717073\pi$
$660$	−344.372	−0.0203101
$661$	−23141.1	−1.36170	−0.680850	−	0.732423i	$-0.738390\pi$
$661$	−23141.1	−1.36170	−0.680850	+	0.732423i	$0.738390\pi$
$662$	−4172.93	−0.244993
$663$	2343.72	0.137289
$664$	−706.949	−0.0413177
$665$	−23904.4	−1.39394
$666$	−12122.6	−0.705318
$667$	−1596.18	−0.0926600
$668$	2295.53	0.132959
$669$	1469.59	0.0849291
$670$	−33530.5	−1.93343
$671$	3403.17	0.195794
$672$	−3193.71	−0.183334
$673$	14843.1	0.850160	0.425080	−	0.905156i	$-0.360246\pi$
$673$	14843.1	0.850160	0.425080	+	0.905156i	$0.360246\pi$
$674$	−12346.2	−0.705577
$675$	777.709	0.0443467
$676$	11660.0	0.663403
$677$	13984.6	0.793900	0.396950	−	0.917840i	$-0.370069\pi$
$677$	13984.6	0.793900	0.396950	+	0.917840i	$0.370069\pi$
$678$	−2658.95	−0.150614
$679$	2759.14	0.155944
$680$	2549.77	0.143793
$681$	−369.306	−0.0207810
$682$	−2620.04	−0.147106
$683$	−4016.42	−0.225013	−0.112507	−	0.993651i	$-0.535888\pi$
$683$	−4016.42	−0.225013	−0.112507	+	0.993651i	$0.535888\pi$
$684$	−16675.4	−0.932164
$685$	−10189.2	−0.568338
$686$	15080.4	0.839317
$687$	−2726.77	−0.151431
$688$	−4676.54	−0.259144
$689$	−2443.08	−0.135086
$690$	−314.817	−0.0173694
$691$	27375.1	1.50709	0.753545	−	0.657396i	$-0.228342\pi$
$691$	27375.1	1.50709	0.753545	+	0.657396i	$0.228342\pi$
$692$	−20604.5	−1.13189
$693$	−8445.88	−0.462962
$694$	−27992.7	−1.53111
$695$	−17735.7	−0.967991
$696$	−122.197	−0.00665500
$697$	−38110.6	−2.07108
$698$	46610.1	2.52753
$699$	1297.36	0.0702015
$700$	6600.27	0.356381
$701$	24857.3	1.33930	0.669648	−	0.742678i	$-0.266445\pi$
$701$	24857.3	1.33930	0.669648	+	0.742678i	$0.266445\pi$
$702$	5848.71	0.314452
$703$	−10042.1	−0.538754
$704$	4443.60	0.237890
$705$	2115.55	0.113016
$706$	−18267.4	−0.973801
$707$	33603.4	1.78753
$708$	−1095.70	−0.0581624
$709$	24751.8	1.31111	0.655553	−	0.755149i	$-0.272436\pi$
$709$	24751.8	1.31111	0.655553	+	0.755149i	$0.272436\pi$
$710$	17006.5	0.898936
$711$	17689.7	0.933072
$712$	77.4230	0.00407521
$713$	−1133.94	−0.0595604
$714$	4236.20	0.222039
$715$	−6553.88	−0.342799
$716$	26659.8	1.39151
$717$	3158.99	0.164539
$718$	−24442.4	−1.27045
$719$	36693.7	1.90326	0.951630	−	0.307247i	$-0.0994077\pi$
$719$	36693.7	1.90326	0.951630	+	0.307247i	$0.0994077\pi$
$720$	18036.7	0.933593
$721$	11397.0	0.588693
$722$	−2442.86	−0.125919
$723$	−2607.36	−0.134120
$724$	11293.7	0.579734
$725$	2754.77	0.141117
$726$	−212.897	−0.0108834
$727$	8812.98	0.449595	0.224797	−	0.974406i	$-0.427828\pi$
$727$	8812.98	0.449595	0.224797	+	0.974406i	$0.427828\pi$
$728$	−5571.96	−0.283668
$729$	−18797.3	−0.955003
$730$	−528.924	−0.0268169
$731$	5629.09	0.284814
$732$	−1004.49	−0.0507199
$733$	14263.3	0.718726	0.359363	−	0.933198i	$-0.382994\pi$
$733$	14263.3	0.718726	0.359363	+	0.933198i	$0.382994\pi$
$734$	17447.5	0.877385
$735$	2080.66	0.104417
$736$	4581.87	0.229470
$737$	−9813.76	−0.490495
$738$	−47371.9	−2.36285
$739$	25351.8	1.26195	0.630975	−	0.775803i	$-0.282655\pi$
$739$	25351.8	1.26195	0.630975	+	0.775803i	$0.282655\pi$
$740$	−8049.59	−0.399877
$741$	2413.29	0.119641
$742$	−4415.79	−0.218476
$743$	−24659.5	−1.21759	−0.608794	−	0.793328i	$-0.708347\pi$
$743$	−24659.5	−1.21759	−0.608794	+	0.793328i	$0.708347\pi$
$744$	−86.8105	−0.00427772
$745$	13679.5	0.672724
$746$	−10807.2	−0.530401
$747$	6019.44	0.294832
$748$	−6648.03	−0.324968
$749$	13360.8	0.651794
$750$	2664.01	0.129701
$751$	−5868.73	−0.285157	−0.142578	−	0.989784i	$-0.545539\pi$
$751$	−5868.73	−0.285157	−0.142578	+	0.989784i	$0.545539\pi$
$752$	−33929.4	−1.64531
$753$	1111.83	0.0538079
$754$	20717.1	1.00062
$755$	22208.6	1.07054
$756$	5004.77	0.240769
$757$	−14821.7	−0.711629	−0.355815	−	0.934557i	$-0.615797\pi$
$757$	−14821.7	−0.711629	−0.355815	+	0.934557i	$0.615797\pi$
$758$	−32247.4	−1.54522
$759$	−92.1411	−0.00440647
$760$	2625.45	0.125310
$761$	10085.5	0.480419	0.240209	−	0.970721i	$-0.422784\pi$
$761$	10085.5	0.480419	0.240209	+	0.970721i	$0.422784\pi$
$762$	−2476.99	−0.117758
$763$	−52097.3	−2.47189
$764$	18086.4	0.856471
$765$	−21710.5	−1.02607
$766$	−51207.0	−2.41539
$767$	−20852.7	−0.981678
$768$	2163.97	0.101674
$769$	−2458.34	−0.115279	−0.0576397	−	0.998337i	$-0.518357\pi$
$769$	−2458.34	−0.115279	−0.0576397	+	0.998337i	$0.518357\pi$
$770$	−11845.9	−0.554412
$771$	3550.83	0.165862
$772$	−3716.17	−0.173249
$773$	−25412.6	−1.18244	−0.591222	−	0.806509i	$-0.701354\pi$
$773$	−25412.6	−1.18244	−0.591222	+	0.806509i	$0.701354\pi$
$774$	6997.02	0.324939
$775$	1957.02	0.0907076
$776$	−303.041	−0.0140187
$777$	1501.25	0.0693141
$778$	8245.51	0.379969
$779$	−39241.7	−1.80485
$780$	1934.46	0.0888009
$781$	4977.50	0.228052
$782$	−6077.48	−0.277916
$783$	2088.85	0.0953378
$784$	−33369.7	−1.52012
$785$	22918.3	1.04202
$786$	230.492	0.0104598
$787$	−31535.3	−1.42835	−0.714174	−	0.699968i	$-0.753198\pi$
$787$	−31535.3	−1.42835	−0.714174	+	0.699968i	$0.753198\pi$
$788$	−11883.3	−0.537213
$789$	−2233.42	−0.100775
$790$	24811.0	1.11739
$791$	−43301.7	−1.94644
$792$	927.624	0.0416183
$793$	−19116.8	−0.856063
$794$	−31073.4	−1.38886
$795$	−172.093	−0.00767738
$796$	25341.8	1.12841
$797$	9385.69	0.417137	0.208569	−	0.978008i	$-0.433120\pi$
$797$	9385.69	0.417137	0.208569	+	0.978008i	$0.433120\pi$
$798$	4361.94	0.193497
$799$	40840.3	1.80829
$800$	−7907.64	−0.349472
$801$	−659.232	−0.0290797
$802$	−37788.4	−1.66378
$803$	−154.806	−0.00680323
$804$	2896.65	0.127061
$805$	−5126.88	−0.224471
$806$	14717.7	0.643185
$807$	194.231	0.00847245
$808$	−3690.71	−0.160692
$809$	7226.60	0.314059	0.157030	−	0.987594i	$-0.449808\pi$
$809$	7226.60	0.314059	0.157030	+	0.987594i	$0.449808\pi$
$810$	−26779.6	−1.16166
$811$	39585.4	1.71397	0.856986	−	0.515340i	$-0.172335\pi$
$811$	39585.4	1.71397	0.856986	+	0.515340i	$0.172335\pi$
$812$	17727.7	0.766158
$813$	136.539	0.00589009
$814$	−4976.40	−0.214279
$815$	−1760.77	−0.0756773
$816$	−2647.79	−0.113592
$817$	5796.16	0.248203
$818$	−44875.9	−1.91815
$819$	47443.4	2.02419
$820$	−31455.6	−1.33961
$821$	−43617.5	−1.85415	−0.927077	−	0.374871i	$-0.877687\pi$
$821$	−43617.5	−1.85415	−0.927077	+	0.374871i	$0.877687\pi$
$822$	1859.28	0.0788927
$823$	−35382.4	−1.49860	−0.749302	−	0.662228i	$-0.769611\pi$
$823$	−35382.4	−1.49860	−0.749302	+	0.662228i	$0.769611\pi$
$824$	−1251.75	−0.0529210
$825$	159.022	0.00671084
$826$	−37690.6	−1.58768
$827$	−36865.9	−1.55012	−0.775062	−	0.631886i	$-0.782281\pi$
$827$	−36865.9	−1.55012	−0.775062	+	0.631886i	$0.782281\pi$
$828$	−3576.45	−0.150109
$829$	−38338.3	−1.60621	−0.803104	−	0.595839i	$-0.796819\pi$
$829$	−38338.3	−1.60621	−0.803104	+	0.595839i	$0.796819\pi$
$830$	8442.67	0.353072
$831$	1484.07	0.0619516
$832$	−24961.3	−1.04012
$833$	40166.7	1.67070
$834$	3236.31	0.134370
$835$	3077.37	0.127541
$836$	−6845.35	−0.283195
$837$	1483.95	0.0612816
$838$	49885.2	2.05639
$839$	−27753.3	−1.14202	−0.571008	−	0.820944i	$-0.693448\pi$
$839$	−27753.3	−1.14202	−0.571008	+	0.820944i	$0.693448\pi$
$840$	−392.495	−0.0161218
$841$	−16989.9	−0.696623
$842$	−53468.1	−2.18840
$843$	717.903	0.0293308
$844$	12265.8	0.500246
$845$	15631.2	0.636368
$846$	50765.0	2.06305
$847$	−3467.08	−0.140650
$848$	2760.04	0.111769
$849$	−521.958	−0.0210996
$850$	10488.9	0.423253
$851$	−2153.77	−0.0867571
$852$	−1469.17	−0.0590762
$853$	20718.7	0.831647	0.415824	−	0.909445i	$-0.363493\pi$
$853$	20718.7	0.831647	0.415824	+	0.909445i	$0.363493\pi$
$854$	−34553.0	−1.38452
$855$	−22354.9	−0.894177
$856$	−1467.44	−0.0585935
$857$	−37611.8	−1.49918	−0.749588	−	0.661905i	$-0.769748\pi$
$857$	−37611.8	−1.49918	−0.749588	+	0.661905i	$0.769748\pi$
$858$	1195.92	0.0475850
$859$	21586.1	0.857400	0.428700	−	0.903447i	$-0.358972\pi$
$859$	21586.1	0.857400	0.428700	+	0.903447i	$0.358972\pi$
$860$	4646.13	0.184223
$861$	5866.48	0.232206
$862$	−55012.0	−2.17368
$863$	−4917.86	−0.193981	−0.0969906	−	0.995285i	$-0.530922\pi$
$863$	−4917.86	−0.193981	−0.0969906	+	0.995285i	$0.530922\pi$
$864$	−5996.11	−0.236101
$865$	−27622.2	−1.08576
$866$	4220.59	0.165614
$867$	969.349	0.0379709
$868$	12594.0	0.492474
$869$	7261.70	0.283471
$870$	1459.33	0.0568689
$871$	55127.3	2.14457
$872$	5721.93	0.222212
$873$	2580.29	0.100034
$874$	−6257.86	−0.242192
$875$	43384.1	1.67617
$876$	45.6930	0.00176236
$877$	21946.1	0.845002	0.422501	−	0.906362i	$-0.361152\pi$
$877$	21946.1	0.845002	0.422501	+	0.906362i	$0.361152\pi$
$878$	12972.3	0.498625
$879$	−278.371	−0.0106817
$880$	7404.15	0.283629
$881$	−2970.54	−0.113598	−0.0567990	−	0.998386i	$-0.518089\pi$
$881$	−2970.54	−0.113598	−0.0567990	+	0.998386i	$0.518089\pi$
$882$	49927.7	1.90607
$883$	−31606.6	−1.20458	−0.602292	−	0.798276i	$-0.705746\pi$
$883$	−31606.6	−1.20458	−0.602292	+	0.798276i	$0.705746\pi$
$884$	37344.3	1.42084
$885$	−1468.88	−0.0557921
$886$	−42361.7	−1.60629
$887$	−3945.52	−0.149355	−0.0746774	−	0.997208i	$-0.523793\pi$
$887$	−3945.52	−0.149355	−0.0746774	+	0.997208i	$0.523793\pi$
$888$	−164.885	−0.00623104
$889$	−40338.4	−1.52183
$890$	−924.617	−0.0348239
$891$	−7837.90	−0.294702
$892$	23416.0	0.878954
$893$	42052.5	1.57585
$894$	−2496.16	−0.0933828
$895$	35739.8	1.33480
$896$	11483.6	0.428168
$897$	517.589	0.0192662
$898$	−17312.2	−0.643337
$899$	5256.38	0.195006
$900$	6172.44	0.228609
$901$	−3322.22	−0.122841
$902$	−19446.4	−0.717844
$903$	−866.503	−0.0319329
$904$	4755.89	0.174976
$905$	15140.2	0.556109
$906$	−4052.51	−0.148604
$907$	39808.6	1.45736	0.728679	−	0.684855i	$-0.240135\pi$
$907$	39808.6	1.45736	0.728679	+	0.684855i	$0.240135\pi$
$908$	−5884.44	−0.215068
$909$	31425.2	1.14665
$910$	66542.7	2.42403
$911$	−12403.9	−0.451107	−0.225554	−	0.974231i	$-0.572419\pi$
$911$	−12403.9	−0.451107	−0.225554	+	0.974231i	$0.572419\pi$
$912$	−2726.38	−0.0989905
$913$	2471.01	0.0895713
$914$	21456.5	0.776496
$915$	−1346.61	−0.0486530
$916$	−43447.7	−1.56720
$917$	3753.62	0.135175
$918$	7953.35	0.285947
$919$	−7676.29	−0.275536	−0.137768	−	0.990465i	$-0.543993\pi$
$919$	−7676.29	−0.275536	−0.137768	+	0.990465i	$0.543993\pi$
$920$	563.093	0.0201789
$921$	−1450.59	−0.0518984
$922$	20475.8	0.731383
$923$	−27960.3	−0.997103
$924$	1023.35	0.0364348
$925$	3717.10	0.132127
$926$	−60828.7	−2.15870
$927$	10658.3	0.377631
$928$	−21239.2	−0.751304
$929$	27835.0	0.983031	0.491516	−	0.870869i	$-0.336443\pi$
$929$	27835.0	0.983031	0.491516	+	0.870869i	$0.336443\pi$
$930$	1036.73	0.0365544
$931$	41358.9	1.45594
$932$	20671.9	0.726534
$933$	−700.153	−0.0245680
$934$	9294.78	0.325626
$935$	−8912.28	−0.311725
$936$	−5210.79	−0.181966
$937$	4581.76	0.159744	0.0798718	−	0.996805i	$-0.474549\pi$
$937$	4581.76	0.159744	0.0798718	+	0.996805i	$0.474549\pi$
$938$	99640.8	3.46843
$939$	2320.91	0.0806603
$940$	33708.7	1.16964
$941$	46887.7	1.62433	0.812165	−	0.583428i	$-0.198289\pi$
$941$	46887.7	1.62433	0.812165	+	0.583428i	$0.198289\pi$
$942$	−4182.00	−0.144646
$943$	−8416.36	−0.290641
$944$	23558.0	0.812234
$945$	6709.34	0.230958
$946$	2872.32	0.0987178
$947$	40467.9	1.38863	0.694314	−	0.719672i	$-0.255708\pi$
$947$	40467.9	1.38863	0.694314	+	0.719672i	$0.255708\pi$
$948$	−2143.38	−0.0734323
$949$	869.601	0.0297455
$950$	10800.2	0.368846
$951$	1305.92	0.0445294
$952$	−7577.02	−0.257955
$953$	−29172.1	−0.991581	−0.495791	−	0.868442i	$-0.665122\pi$
$953$	−29172.1	−0.991581	−0.495791	+	0.868442i	$0.665122\pi$
$954$	−4129.56	−0.140146
$955$	24246.5	0.821568
$956$	50334.6	1.70286
$957$	427.119	0.0144272
$958$	−17692.9	−0.596692
$959$	30278.8	1.01956
$960$	−1758.30	−0.0591133
$961$	−26056.8	−0.874653
$962$	27954.2	0.936880
$963$	12494.8	0.418109
$964$	−41545.1	−1.38805
$965$	−4981.87	−0.166189
$966$	935.525	0.0311594
$967$	−50852.5	−1.69111	−0.845557	−	0.533885i	$-0.820731\pi$
$967$	−50852.5	−1.69111	−0.845557	+	0.533885i	$0.820731\pi$
$968$	380.795	0.0126438
$969$	3281.70	0.108796
$970$	3619.04	0.119794
$971$	−27571.4	−0.911233	−0.455617	−	0.890176i	$-0.650581\pi$
$971$	−27571.4	−0.911233	−0.455617	+	0.890176i	$0.650581\pi$
$972$	7029.40	0.231963
$973$	52704.2	1.73650
$974$	53703.8	1.76671
$975$	−893.283	−0.0293415
$976$	21596.9	0.708301
$977$	22331.8	0.731276	0.365638	−	0.930757i	$-0.380851\pi$
$977$	22331.8	0.731276	0.365638	+	0.930757i	$0.380851\pi$
$978$	321.295	0.0105050
$979$	−270.618	−0.00883452
$980$	33152.7	1.08064
$981$	−48720.4	−1.58565
$982$	−69211.9	−2.24913
$983$	13965.6	0.453137	0.226569	−	0.973995i	$-0.427249\pi$
$983$	13965.6	0.453137	0.226569	+	0.973995i	$0.427249\pi$
$984$	−644.324	−0.0208743
$985$	−15930.6	−0.515321
$986$	28172.1	0.909920
$987$	−6286.68	−0.202743
$988$	38452.7	1.23820
$989$	1243.13	0.0399689
$990$	−11078.1	−0.355641
$991$	−47290.7	−1.51588	−0.757940	−	0.652324i	$-0.773794\pi$
$991$	−47290.7	−1.51588	−0.757940	+	0.652324i	$0.773794\pi$
$992$	−15088.6	−0.482926
$993$	483.273	0.0154443
$994$	−50537.4	−1.61262
$995$	33973.0	1.08243
$996$	−729.350	−0.0232032
$997$	−13887.5	−0.441145	−0.220573	−	0.975371i	$-0.570793\pi$
$997$	−13887.5	−0.441145	−0.220573	+	0.975371i	$0.570793\pi$
$998$	5380.76	0.170666
$999$	2818.55	0.0892643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.16	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.16	✓	84	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-3.89777 q^{2} +0.451407 q^{3} +7.19260 q^{4} +9.64232 q^{5} -1.75948 q^{6} -28.6536 q^{7} +3.14706 q^{8} -26.7962 q^{9} +O(q^{10})\)	\(q-3.89777 q^{2} +0.451407 q^{3} +7.19260 q^{4} +9.64232 q^{5} -1.75948 q^{6} -28.6536 q^{7} +3.14706 q^{8} -26.7962 q^{9} -37.5835 q^{10} -11.0000 q^{11} +3.24679 q^{12} +61.7908 q^{13} +111.685 q^{14} +4.35261 q^{15} -69.8073 q^{16} +84.0262 q^{17} +104.446 q^{18} +86.5201 q^{19} +69.3534 q^{20} -12.9344 q^{21} +42.8755 q^{22} +18.5564 q^{23} +1.42061 q^{24} -32.0256 q^{25} -240.846 q^{26} -24.2840 q^{27} -206.093 q^{28} -86.0178 q^{29} -16.9655 q^{30} -61.1081 q^{31} +246.916 q^{32} -4.96547 q^{33} -327.515 q^{34} -276.287 q^{35} -192.735 q^{36} -116.066 q^{37} -337.235 q^{38} +27.8928 q^{39} +30.3450 q^{40} -453.556 q^{41} +50.4153 q^{42} +66.9921 q^{43} -79.1186 q^{44} -258.378 q^{45} -72.3284 q^{46} +486.043 q^{47} -31.5115 q^{48} +478.026 q^{49} +124.828 q^{50} +37.9300 q^{51} +444.437 q^{52} -39.5380 q^{53} +94.6533 q^{54} -106.066 q^{55} -90.1746 q^{56} +39.0558 q^{57} +335.277 q^{58} -337.472 q^{59} +31.3066 q^{60} -309.379 q^{61} +238.185 q^{62} +767.807 q^{63} -403.964 q^{64} +595.807 q^{65} +19.3543 q^{66} +892.160 q^{67} +604.366 q^{68} +8.37647 q^{69} +1076.90 q^{70} -452.500 q^{71} -84.3295 q^{72} +14.0733 q^{73} +452.400 q^{74} -14.4566 q^{75} +622.305 q^{76} +315.189 q^{77} -108.720 q^{78} -660.155 q^{79} -673.105 q^{80} +712.536 q^{81} +1767.86 q^{82} -224.638 q^{83} -93.0320 q^{84} +810.207 q^{85} -261.120 q^{86} -38.8290 q^{87} -34.6177 q^{88} +24.6017 q^{89} +1007.10 q^{90} -1770.53 q^{91} +133.469 q^{92} -27.5846 q^{93} -1894.48 q^{94} +834.255 q^{95} +111.460 q^{96} -96.2931 q^{97} -1863.23 q^{98} +294.759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * q^99

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