LMFDB - Embedded newform 289.6.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,6,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	289.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:	$46.3509239260$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.95189 q^{2} +29.0894 q^{3} +48.1363 q^{4} +65.2984 q^{5} -260.405 q^{6} +113.506 q^{7} -144.450 q^{8} +603.192 q^{9} +O(q^{10})$	\(q-8.95189 q^{2} +29.0894 q^{3} +48.1363 q^{4} +65.2984 q^{5} -260.405 q^{6} +113.506 q^{7} -144.450 q^{8} +603.192 q^{9} -584.544 q^{10} -71.3393 q^{11} +1400.26 q^{12} +7.95633 q^{13} -1016.09 q^{14} +1899.49 q^{15} -247.258 q^{16} -5399.71 q^{18} +1048.49 q^{19} +3143.22 q^{20} +3301.82 q^{21} +638.622 q^{22} -458.936 q^{23} -4201.97 q^{24} +1138.88 q^{25} -71.2242 q^{26} +10477.8 q^{27} +5463.77 q^{28} +4797.26 q^{29} -17004.0 q^{30} +4803.38 q^{31} +6835.84 q^{32} -2075.22 q^{33} +7411.77 q^{35} +29035.4 q^{36} +2980.88 q^{37} -9385.96 q^{38} +231.445 q^{39} -9432.38 q^{40} -752.362 q^{41} -29557.6 q^{42} -19883.0 q^{43} -3434.01 q^{44} +39387.5 q^{45} +4108.35 q^{46} -11155.7 q^{47} -7192.57 q^{48} -3923.35 q^{49} -10195.1 q^{50} +382.989 q^{52} -31142.8 q^{53} -93795.8 q^{54} -4658.34 q^{55} -16396.0 q^{56} +30499.9 q^{57} -42944.5 q^{58} +29228.5 q^{59} +91434.4 q^{60} +3929.09 q^{61} -42999.3 q^{62} +68466.0 q^{63} -53281.4 q^{64} +519.536 q^{65} +18577.1 q^{66} -23881.2 q^{67} -13350.2 q^{69} -66349.3 q^{70} -41696.4 q^{71} -87131.4 q^{72} +24549.8 q^{73} -26684.5 q^{74} +33129.3 q^{75} +50470.4 q^{76} -8097.46 q^{77} -2071.87 q^{78} -74466.3 q^{79} -16145.5 q^{80} +158216. q^{81} +6735.06 q^{82} +41757.5 q^{83} +158938. q^{84} +177991. q^{86} +139549. q^{87} +10305.0 q^{88} -88747.9 q^{89} -352592. q^{90} +903.093 q^{91} -22091.5 q^{92} +139727. q^{93} +99864.7 q^{94} +68464.7 q^{95} +198850. q^{96} +84804.4 q^{97} +35121.4 q^{98} -43031.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9}+O(q^{10}) $ 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9	$ 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9} + 304 q^{13} + 4392 q^{15} + 7176 q^{16} + 1896 q^{18} + 9288 q^{19} + 12032 q^{21} + 17692 q^{25} + 29600 q^{26} - 17784 q^{30} + 19032 q^{32} + 38800 q^{33} + 26056 q^{35} + 77816 q^{36} + 36384 q^{38} + 123904 q^{42} + 46520 q^{43} + 71808 q^{47} + 38748 q^{49} + 241632 q^{50} + 6008 q^{52} + 61360 q^{53} + 46680 q^{55} + 256920 q^{59} + 330504 q^{60} - 72496 q^{64} + 10736 q^{66} + 250608 q^{67} - 107696 q^{69} + 273320 q^{70} + 463640 q^{72} + 974048 q^{76} + 482672 q^{77} + 242060 q^{81} + 458584 q^{83} + 1605472 q^{84} + 718272 q^{86} + 1009400 q^{87} + 501088 q^{89} + 903248 q^{93} + 1315264 q^{94} - 156256 q^{98}+O(q^{100}) $ 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9 + 304 * q^13 + 4392 * q^15 + 7176 * q^16 + 1896 * q^18 + 9288 * q^19 + 12032 * q^21 + 17692 * q^25 + 29600 * q^26 - 17784 * q^30 + 19032 * q^32 + 38800 * q^33 + 26056 * q^35 + 77816 * q^36 + 36384 * q^38 + 123904 * q^42 + 46520 * q^43 + 71808 * q^47 + 38748 * q^49 + 241632 * q^50 + 6008 * q^52 + 61360 * q^53 + 46680 * q^55 + 256920 * q^59 + 330504 * q^60 - 72496 * q^64 + 10736 * q^66 + 250608 * q^67 - 107696 * q^69 + 273320 * q^70 + 463640 * q^72 + 974048 * q^76 + 482672 * q^77 + 242060 * q^81 + 458584 * q^83 + 1605472 * q^84 + 718272 * q^86 + 1009400 * q^87 + 501088 * q^89 + 903248 * q^93 + 1315264 * q^94 - 156256 * q^98

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 $

$2$	−8.95189	−1.58249	−0.791243	−	0.611502i	$-0.790565\pi$
$2$	−8.95189	−1.58249	−0.791243	+	0.611502i	$0.790565\pi$
$3$	29.0894	1.86608	0.933042	−	0.359766i	$-0.117144\pi$
$3$	29.0894	1.86608	0.933042	+	0.359766i	$0.117144\pi$
$4$	48.1363	1.50426
$5$	65.2984	1.16809	0.584047	−	0.811720i	$-0.301469\pi$
$5$	65.2984	1.16809	0.584047	+	0.811720i	$0.301469\pi$
$6$	−260.405	−2.95305
$7$	113.506	0.875537	0.437768	−	0.899088i	$-0.355769\pi$
$7$	113.506	0.875537	0.437768	+	0.899088i	$0.355769\pi$
$8$	−144.450	−0.797983
$9$	603.192	2.48227
$10$	−584.544	−1.84849
$11$	−71.3393	−0.177765	−0.0888827	−	0.996042i	$-0.528330\pi$
$11$	−71.3393	−0.177765	−0.0888827	+	0.996042i	$0.528330\pi$
$12$	1400.26	2.80708
$13$	7.95633	0.0130573	0.00652867	−	0.999979i	$-0.497922\pi$
$13$	7.95633	0.0130573	0.00652867	+	0.999979i	$0.497922\pi$
$14$	−1016.09	−1.38552
$15$	1899.49	2.17976
$16$	−247.258	−0.241463
$17$	0	0
$17$	0	0
$18$	−5399.71	−3.92816
$19$	1048.49	0.666316	0.333158	−	0.942871i	$-0.391886\pi$
$19$	1048.49	0.666316	0.333158	+	0.942871i	$0.391886\pi$
$20$	3143.22	1.75712
$21$	3301.82	1.63383
$22$	638.622	0.281311
$23$	−458.936	−0.180898	−0.0904488	−	0.995901i	$-0.528830\pi$
$23$	−458.936	−0.180898	−0.0904488	+	0.995901i	$0.528830\pi$
$24$	−4201.97	−1.48910
$25$	1138.88	0.364442
$26$	−71.2242	−0.0206630
$27$	10477.8	2.76605
$28$	5463.77	1.31703
$29$	4797.26	1.05925	0.529624	−	0.848232i	$-0.322333\pi$
$29$	4797.26	1.05925	0.529624	+	0.848232i	$0.322333\pi$
$30$	−17004.0	−3.44944
$31$	4803.38	0.897724	0.448862	−	0.893601i	$-0.351829\pi$
$31$	4803.38	0.897724	0.448862	+	0.893601i	$0.351829\pi$
$32$	6835.84	1.18009
$33$	−2075.22	−0.331725
$34$	0	0
$35$	7411.77	1.02271
$36$	29035.4	3.73398
$37$	2980.88	0.357965	0.178982	−	0.983852i	$-0.442719\pi$
$37$	2980.88	0.357965	0.178982	+	0.983852i	$0.442719\pi$
$38$	−9385.96	−1.05443
$39$	231.445	0.0243661
$40$	−9432.38	−0.932119
$41$	−752.362	−0.0698984	−0.0349492	−	0.999389i	$-0.511127\pi$
$41$	−752.362	−0.0698984	−0.0349492	+	0.999389i	$0.511127\pi$
$42$	−29557.6	−2.58551
$43$	−19883.0	−1.63988	−0.819939	−	0.572450i	$-0.805993\pi$
$43$	−19883.0	−1.63988	−0.819939	+	0.572450i	$0.805993\pi$
$44$	−3434.01	−0.267405
$45$	39387.5	2.89953
$46$	4108.35	0.286268
$47$	−11155.7	−0.736636	−0.368318	−	0.929700i	$-0.620066\pi$
$47$	−11155.7	−0.736636	−0.368318	+	0.929700i	$0.620066\pi$
$48$	−7192.57	−0.450590
$49$	−3923.35	−0.233435
$50$	−10195.1	−0.576724
$51$	0	0
$52$	382.989	0.0196416
$53$	−31142.8	−1.52289	−0.761444	−	0.648230i	$-0.775509\pi$
$53$	−31142.8	−1.52289	−0.761444	+	0.648230i	$0.775509\pi$
$54$	−93795.8	−4.37723
$55$	−4658.34	−0.207647
$56$	−16396.0	−0.698664
$57$	30499.9	1.24340
$58$	−42944.5	−1.67625
$59$	29228.5	1.09314	0.546571	−	0.837413i	$-0.315933\pi$
$59$	29228.5	1.09314	0.546571	+	0.837413i	$0.315933\pi$
$60$	91434.4	3.27893
$61$	3929.09	0.135197	0.0675986	−	0.997713i	$-0.478466\pi$
$61$	3929.09	0.135197	0.0675986	+	0.997713i	$0.478466\pi$
$62$	−42999.3	−1.42064
$63$	68466.0	2.17332
$64$	−53281.4	−1.62602
$65$	519.536	0.0152522
$66$	18577.1	0.524951
$67$	−23881.2	−0.649933	−0.324966	−	0.945726i	$-0.605353\pi$
$67$	−23881.2	−0.649933	−0.324966	+	0.945726i	$0.605353\pi$
$68$	0	0
$69$	−13350.2	−0.337570
$70$	−66349.3	−1.61842
$71$	−41696.4	−0.981642	−0.490821	−	0.871260i	$-0.663303\pi$
$71$	−41696.4	−0.981642	−0.490821	+	0.871260i	$0.663303\pi$
$72$	−87131.4	−1.98081
$73$	24549.8	0.539189	0.269595	−	0.962974i	$-0.413110\pi$
$73$	24549.8	0.539189	0.269595	+	0.962974i	$0.413110\pi$
$74$	−26684.5	−0.566474
$75$	33129.3	0.680079
$76$	50470.4	1.00231
$77$	−8097.46	−0.155640
$78$	−2071.87	−0.0385590
$79$	−74466.3	−1.34243	−0.671216	−	0.741262i	$-0.734228\pi$
$79$	−74466.3	−1.34243	−0.671216	+	0.741262i	$0.734228\pi$
$80$	−16145.5	−0.282051
$81$	158216.	2.67940
$82$	6735.06	0.110613
$83$	41757.5	0.665334	0.332667	−	0.943044i	$-0.392052\pi$
$83$	41757.5	0.665334	0.332667	+	0.943044i	$0.392052\pi$
$84$	158938.	2.45770
$85$	0	0
$86$	177991.	2.59508
$87$	139549.	1.97665
$88$	10305.0	0.141854
$89$	−88747.9	−1.18764	−0.593818	−	0.804600i	$-0.702380\pi$
$89$	−88747.9	−1.18764	−0.593818	+	0.804600i	$0.702380\pi$
$90$	−352592.	−4.58846
$91$	903.093	0.0114322
$92$	−22091.5	−0.272117
$93$	139727.	1.67523
$94$	99864.7	1.16572
$95$	68464.7	0.778319
$96$	198850.	2.20216
$97$	84804.4	0.915143	0.457572	−	0.889173i	$-0.348719\pi$
$97$	84804.4	0.915143	0.457572	+	0.889173i	$0.348719\pi$
$98$	35121.4	0.369408
$99$	−43031.3	−0.441262
$100$	54821.5	0.548215
$101$	60993.1	0.594946	0.297473	−	0.954730i	$-0.403856\pi$
$101$	60993.1	0.594946	0.297473	+	0.954730i	$0.403856\pi$
$102$	0	0
$103$	17591.3	0.163382	0.0816911	−	0.996658i	$-0.473968\pi$
$103$	17591.3	0.163382	0.0816911	+	0.996658i	$0.473968\pi$
$104$	−1149.30	−0.0104195
$105$	215604.	1.90846
$106$	278787.	2.40995
$107$	205594.	1.73600	0.868001	−	0.496563i	$-0.165405\pi$
$107$	205594.	1.73600	0.868001	+	0.496563i	$0.165405\pi$
$108$	504361.	4.16085
$109$	154313.	1.24405	0.622023	−	0.782999i	$-0.286311\pi$
$109$	154313.	1.24405	0.622023	+	0.782999i	$0.286311\pi$
$110$	41701.0	0.328598
$111$	86712.0	0.667993
$112$	−28065.3	−0.211409
$113$	−148236.	−1.09209	−0.546045	−	0.837756i	$-0.683867\pi$
$113$	−148236.	−1.09209	−0.546045	+	0.837756i	$0.683867\pi$
$114$	−273032.	−1.96766
$115$	−29967.8	−0.211305
$116$	230922.	1.59338
$117$	4799.20	0.0324119
$118$	−261650.	−1.72988
$119$	0	0
$120$	−274382.	−1.73941
$121$	−155962.	−0.968399
$122$	−35172.8	−0.213948
$123$	−21885.7	−0.130436
$124$	231217.	1.35041
$125$	−129690.	−0.742391
$126$	−612900.	−3.43925
$127$	−282128.	−1.55216	−0.776082	−	0.630633i	$-0.782796\pi$
$127$	−282128.	−1.55216	−0.776082	+	0.630633i	$0.782796\pi$
$128$	258222.	1.39306
$129$	−578386.	−3.06015
$130$	−4650.83	−0.0241364
$131$	300176.	1.52826	0.764130	−	0.645062i	$-0.223168\pi$
$131$	300176.	1.52826	0.764130	+	0.645062i	$0.223168\pi$
$132$	−99893.3	−0.499001
$133$	119010.	0.583384
$134$	213781.	1.02851
$135$	684182.	3.23100
$136$	0	0
$137$	−70714.1	−0.321888	−0.160944	−	0.986964i	$-0.551454\pi$
$137$	−70714.1	−0.321888	−0.160944	+	0.986964i	$0.551454\pi$
$138$	119509.	0.534200
$139$	−44998.6	−0.197543	−0.0987717	−	0.995110i	$-0.531491\pi$
$139$	−44998.6	−0.197543	−0.0987717	+	0.995110i	$0.531491\pi$
$140$	356775.	1.53842
$141$	−324513.	−1.37462
$142$	373262.	1.55343
$143$	−567.600	−0.00232114
$144$	−149144.	−0.599376
$145$	313253.	1.23730
$146$	−219767.	−0.853259
$147$	−114128.	−0.435610
$148$	143489.	0.538472
$149$	50562.6	0.186579	0.0932896	−	0.995639i	$-0.470262\pi$
$149$	50562.6	0.186579	0.0932896	+	0.995639i	$0.470262\pi$
$150$	−296570.	−1.07621
$151$	−249560.	−0.890702	−0.445351	−	0.895356i	$-0.646921\pi$
$151$	−249560.	−0.890702	−0.445351	+	0.895356i	$0.646921\pi$
$152$	−151455.	−0.531709
$153$	0	0
$154$	72487.5	0.246298
$155$	313653.	1.04863
$156$	11140.9	0.0366529
$157$	−304669.	−0.986459	−0.493229	−	0.869899i	$-0.664184\pi$
$157$	−304669.	−0.986459	−0.493229	+	0.869899i	$0.664184\pi$
$158$	666614.	2.12438
$159$	−905925.	−2.84184
$160$	446369.	1.37846
$161$	−52092.1	−0.158382
$162$	−1.41633e6	−4.24012
$163$	311916.	0.919537	0.459768	−	0.888039i	$-0.347932\pi$
$163$	311916.	0.919537	0.459768	+	0.888039i	$0.347932\pi$
$164$	−36215.9	−0.105145
$165$	−135508.	−0.387486
$166$	−373809.	−1.05288
$167$	138381.	0.383959	0.191979	−	0.981399i	$-0.438509\pi$
$167$	138381.	0.383959	0.191979	+	0.981399i	$0.438509\pi$
$168$	−476950.	−1.30377
$169$	−371230.	−0.999830
$170$	0	0
$171$	632441.	1.65398
$172$	−957096.	−2.46680
$173$	−28900.9	−0.0734170	−0.0367085	−	0.999326i	$-0.511687\pi$
$173$	−28900.9	−0.0734170	−0.0367085	+	0.999326i	$0.511687\pi$
$174$	−1.24923e6	−3.12802
$175$	129270.	0.319082
$176$	17639.2	0.0429237
$177$	850240.	2.03990
$178$	794462.	1.87942
$179$	305697.	0.713113	0.356557	−	0.934274i	$-0.383951\pi$
$179$	305697.	0.713113	0.356557	+	0.934274i	$0.383951\pi$
$180$	1.89597e6	4.36164
$181$	743725.	1.68739	0.843696	−	0.536821i	$-0.180375\pi$
$181$	743725.	1.68739	0.843696	+	0.536821i	$0.180375\pi$
$182$	−8084.39	−0.0180913
$183$	114295.	0.252290
$184$	66293.5	0.144353
$185$	194647.	0.418136
$186$	−1.25082e6	−2.65103
$187$	0	0
$188$	−536995.	−1.10809
$189$	1.18929e6	2.42178
$190$	−612888.	−1.23168
$191$	704162.	1.39666	0.698328	−	0.715778i	$-0.253928\pi$
$191$	704162.	1.39666	0.698328	+	0.715778i	$0.253928\pi$
$192$	−1.54992e6	−3.03429
$193$	−301707.	−0.583032	−0.291516	−	0.956566i	$-0.594160\pi$
$193$	−301707.	−0.583032	−0.291516	+	0.956566i	$0.594160\pi$
$194$	−759160.	−1.44820
$195$	15113.0	0.0284619
$196$	−188856.	−0.351148
$197$	746710.	1.37084	0.685419	−	0.728149i	$-0.259619\pi$
$197$	746710.	1.37084	0.685419	+	0.728149i	$0.259619\pi$
$198$	385212.	0.698291
$199$	−281738.	−0.504328	−0.252164	−	0.967684i	$-0.581142\pi$
$199$	−281738.	−0.504328	−0.252164	+	0.967684i	$0.581142\pi$
$200$	−164512.	−0.290818
$201$	−694688.	−1.21283
$202$	−546003.	−0.941493
$203$	544518.	0.927411
$204$	0	0
$205$	−49128.0	−0.0816478
$206$	−157475.	−0.258550
$207$	−276827.	−0.449037
$208$	−1967.26	−0.00315286
$209$	−74798.5	−0.118448
$210$	−1.93006e6	−3.02011
$211$	39934.9	0.0617514	0.0308757	−	0.999523i	$-0.490170\pi$
$211$	39934.9	0.0617514	0.0308757	+	0.999523i	$0.490170\pi$
$212$	−1.49910e6	−2.29082
$213$	−1.21292e6	−1.83183
$214$	−1.84045e6	−2.74720
$215$	−1.29833e6	−1.91553
$216$	−1.51352e6	−2.20726
$217$	545213.	0.785990
$218$	−1.38139e6	−1.96868
$219$	714140.	1.00617
$220$	−224236.	−0.312354
$221$	0	0
$222$	−776236.	−1.05709
$223$	−885892.	−1.19294	−0.596470	−	0.802635i	$-0.703431\pi$
$223$	−885892.	−1.19294	−0.596470	+	0.802635i	$0.703431\pi$
$224$	775910.	1.03322
$225$	686964.	0.904643
$226$	1.32700e6	1.72822
$227$	−360960.	−0.464937	−0.232468	−	0.972604i	$-0.574680\pi$
$227$	−360960.	−0.464937	−0.232468	+	0.972604i	$0.574680\pi$
$228$	1.46815e6	1.87040
$229$	−312552.	−0.393852	−0.196926	−	0.980418i	$-0.563096\pi$
$229$	−312552.	−0.393852	−0.196926	+	0.980418i	$0.563096\pi$
$230$	268268.	0.334387
$231$	−235550.	−0.290438
$232$	−692966.	−0.845263
$233$	1.35303e6	1.63274	0.816369	−	0.577530i	$-0.195983\pi$
$233$	1.35303e6	1.63274	0.816369	+	0.577530i	$0.195983\pi$
$234$	−42961.9	−0.0512913
$235$	−728450.	−0.860459
$236$	1.40695e6	1.64437
$237$	−2.16618e6	−2.50509
$238$	0	0
$239$	658792.	0.746025	0.373013	−	0.927826i	$-0.378325\pi$
$239$	658792.	0.746025	0.373013	+	0.927826i	$0.378325\pi$
$240$	−469664.	−0.526331
$241$	−1.30199e6	−1.44399	−0.721997	−	0.691897i	$-0.756775\pi$
$241$	−1.30199e6	−1.44399	−0.721997	+	0.691897i	$0.756775\pi$
$242$	1.39615e6	1.53248
$243$	2.05631e6	2.23395
$244$	189132.	0.203372
$245$	−256188.	−0.272674
$246$	195919.	0.206414
$247$	8342.13	0.00870031
$248$	−693851.	−0.716369
$249$	1.21470e6	1.24157
$250$	1.16097e6	1.17482
$251$	−190860.	−0.191219	−0.0956096	−	0.995419i	$-0.530480\pi$
$251$	−190860.	−0.191219	−0.0956096	+	0.995419i	$0.530480\pi$
$252$	3.29570e6	3.26924
$253$	32740.2	0.0321573
$254$	2.52558e6	2.45628
$255$	0	0
$256$	−606573.	−0.578473
$257$	−222335.	−0.209979	−0.104989	−	0.994473i	$-0.533481\pi$
$257$	−222335.	−0.209979	−0.104989	+	0.994473i	$0.533481\pi$
$258$	5.17764e6	4.84265
$259$	338349.	0.313411
$260$	25008.5	0.0229432
$261$	2.89367e6	2.62934
$262$	−2.68714e6	−2.41845
$263$	1.04754e6	0.933859	0.466930	−	0.884295i	$-0.345360\pi$
$263$	1.04754e6	0.933859	0.466930	+	0.884295i	$0.345360\pi$
$264$	299766.	0.264711
$265$	−2.03358e6	−1.77888
$266$	−1.06536e6	−0.923196
$267$	−2.58162e6	−2.21623
$268$	−1.14955e6	−0.977667
$269$	887946.	0.748179	0.374090	−	0.927393i	$-0.377955\pi$
$269$	887946.	0.748179	0.374090	+	0.927393i	$0.377955\pi$
$270$	−6.12472e6	−5.11301
$271$	−465708.	−0.385204	−0.192602	−	0.981277i	$-0.561693\pi$
$271$	−465708.	−0.385204	−0.192602	+	0.981277i	$0.561693\pi$
$272$	0	0
$273$	26270.4	0.0213334
$274$	633025.	0.509383
$275$	−81247.0	−0.0647851
$276$	−642628.	−0.507793
$277$	−282055.	−0.220869	−0.110434	−	0.993883i	$-0.535224\pi$
$277$	−282055.	−0.220869	−0.110434	+	0.993883i	$0.535224\pi$
$278$	402823.	0.312609
$279$	2.89736e6	2.22840
$280$	−1.07063e6	−0.816104
$281$	−1.96318e6	−1.48318	−0.741591	−	0.670852i	$-0.765928\pi$
$281$	−1.96318e6	−1.48318	−0.741591	+	0.670852i	$0.765928\pi$
$282$	2.90500e6	2.17532
$283$	47015.7	0.0348961	0.0174481	−	0.999848i	$-0.494446\pi$
$283$	47015.7	0.0348961	0.0174481	+	0.999848i	$0.494446\pi$
$284$	−2.00711e6	−1.47664
$285$	1.99159e6	1.45241
$286$	5081.09	0.00367318
$287$	−85397.7	−0.0611986
$288$	4.12332e6	2.92932
$289$	0	0
$290$	−2.80421e6	−1.95801
$291$	2.46691e6	1.70773
$292$	1.18174e6	0.811081
$293$	−383997.	−0.261312	−0.130656	−	0.991428i	$-0.541708\pi$
$293$	−383997.	−0.261312	−0.130656	+	0.991428i	$0.541708\pi$
$294$	1.02166e6	0.689347
$295$	1.90858e6	1.27689
$296$	−430590.	−0.285650
$297$	−747477.	−0.491708
$298$	−452630.	−0.295259
$299$	−3651.45	−0.00236204
$300$	1.59472e6	1.02302
$301$	−2.25685e6	−1.43577
$302$	2.23403e6	1.40952
$303$	1.77425e6	1.11022
$304$	−259247.	−0.160890
$305$	256564.	0.157923
$306$	0	0
$307$	639793.	0.387430	0.193715	−	0.981058i	$-0.437946\pi$
$307$	639793.	0.387430	0.193715	+	0.981058i	$0.437946\pi$
$308$	−389782.	−0.234123
$309$	511720.	0.304885
$310$	−2.80779e6	−1.65943
$311$	−2.00047e6	−1.17282	−0.586408	−	0.810016i	$-0.699459\pi$
$311$	−2.00047e6	−1.17282	−0.586408	+	0.810016i	$0.699459\pi$
$312$	−33432.3	−0.0194437
$313$	−907474.	−0.523568	−0.261784	−	0.965126i	$-0.584311\pi$
$313$	−907474.	−0.523568	−0.261784	+	0.965126i	$0.584311\pi$
$314$	2.72736e6	1.56106
$315$	4.47072e6	2.53864
$316$	−3.58453e6	−2.01937
$317$	−1.87330e6	−1.04703	−0.523514	−	0.852017i	$-0.675379\pi$
$317$	−1.87330e6	−1.04703	−0.523514	+	0.852017i	$0.675379\pi$
$318$	8.10974e6	4.49717
$319$	−342233.	−0.188298
$320$	−3.47919e6	−1.89934
$321$	5.98059e6	3.23953
$322$	466323.	0.250638
$323$	0	0
$324$	7.61594e6	4.03052
$325$	9061.31	0.00475864
$326$	−2.79224e6	−1.45515
$327$	4.48887e6	2.32149
$328$	108679.	0.0557778
$329$	−1.26624e6	−0.644952
$330$	1.21306e6	0.613191
$331$	−2.70040e6	−1.35475	−0.677374	−	0.735639i	$-0.736882\pi$
$331$	−2.70040e6	−1.35475	−0.677374	+	0.735639i	$0.736882\pi$
$332$	2.01005e6	1.00083
$333$	1.79805e6	0.888567
$334$	−1.23877e6	−0.607609
$335$	−1.55940e6	−0.759182
$336$	−816402.	−0.394508
$337$	3.07468e6	1.47477	0.737385	−	0.675472i	$-0.236060\pi$
$337$	3.07468e6	1.47477	0.737385	+	0.675472i	$0.236060\pi$
$338$	3.32321e6	1.58222
$339$	−4.31210e6	−2.03793
$340$	0	0
$341$	−342670.	−0.159584
$342$	−5.66154e6	−2.61739
$343$	−2.35302e6	−1.07992
$344$	2.87211e6	1.30860
$345$	−871745.	−0.394314
$346$	258718.	0.116181
$347$	−4871.84	−0.00217205	−0.00108602	−	0.999999i	$-0.500346\pi$
$347$	−4871.84	−0.00217205	−0.00108602	+	0.999999i	$0.500346\pi$
$348$	6.71738e6	2.97339
$349$	120795.	0.0530867	0.0265434	−	0.999648i	$-0.491550\pi$
$349$	120795.	0.0530867	0.0265434	+	0.999648i	$0.491550\pi$
$350$	−1.15721e6	−0.504943
$351$	83364.6	0.0361172
$352$	−487664.	−0.209780
$353$	4.38961e6	1.87495	0.937474	−	0.348055i	$-0.113158\pi$
$353$	4.38961e6	1.87495	0.937474	+	0.348055i	$0.113158\pi$
$354$	−7.61125e6	−3.22811
$355$	−2.72271e6	−1.14665
$356$	−4.27200e6	−1.78651
$357$	0	0
$358$	−2.73657e6	−1.12849
$359$	−2.46955e6	−1.01130	−0.505651	−	0.862738i	$-0.668748\pi$
$359$	−2.46955e6	−1.01130	−0.505651	+	0.862738i	$0.668748\pi$
$360$	−5.68954e6	−2.31377
$361$	−1.37677e6	−0.556024
$362$	−6.65774e6	−2.67027
$363$	−4.53683e6	−1.80712
$364$	43471.6	0.0171970
$365$	1.60306e6	0.629824
$366$	−1.02316e6	−0.399244
$367$	−1.05071e6	−0.407209	−0.203605	−	0.979053i	$-0.565266\pi$
$367$	−1.05071e6	−0.407209	−0.203605	+	0.979053i	$0.565266\pi$
$368$	113476.	0.0436800
$369$	−453819.	−0.173507
$370$	−1.74246e6	−0.661695
$371$	−3.53490e6	−1.33334
$372$	6.72596e6	2.51998
$373$	4.31189e6	1.60471	0.802354	−	0.596849i	$-0.203581\pi$
$373$	4.31189e6	1.60471	0.802354	+	0.596849i	$0.203581\pi$
$374$	0	0
$375$	−3.77261e6	−1.38537
$376$	1.61145e6	0.587823
$377$	38168.6	0.0138310
$378$	−1.06464e7	−3.83242
$379$	−2.81208e6	−1.00561	−0.502805	−	0.864400i	$-0.667698\pi$
$379$	−2.81208e6	−1.00561	−0.502805	+	0.864400i	$0.667698\pi$
$380$	3.29564e6	1.17079
$381$	−8.20694e6	−2.89647
$382$	−6.30358e6	−2.21019
$383$	5.08183e6	1.77021	0.885103	−	0.465396i	$-0.154088\pi$
$383$	5.08183e6	1.77021	0.885103	+	0.465396i	$0.154088\pi$
$384$	7.51153e6	2.59956
$385$	−528751.	−0.181802
$386$	2.70085e6	0.922640
$387$	−1.19933e7	−4.07063
$388$	4.08217e6	1.37661
$389$	−979118.	−0.328066	−0.164033	−	0.986455i	$-0.552450\pi$
$389$	−979118.	−0.328066	−0.164033	+	0.986455i	$0.552450\pi$
$390$	−135290.	−0.0450405
$391$	0	0
$392$	566730.	0.186278
$393$	8.73193e6	2.85186
$394$	−6.68446e6	−2.16933
$395$	−4.86253e6	−1.56809
$396$	−2.07137e6	−0.663773
$397$	1.20612e6	0.384075	0.192037	−	0.981388i	$-0.438491\pi$
$397$	1.20612e6	0.384075	0.192037	+	0.981388i	$0.438491\pi$
$398$	2.52209e6	0.798092
$399$	3.46193e6	1.08864
$400$	−281597.	−0.0879990
$401$	779260.	0.242003	0.121002	−	0.992652i	$-0.461389\pi$
$401$	779260.	0.242003	0.121002	+	0.992652i	$0.461389\pi$
$402$	6.21877e6	1.91928
$403$	38217.3	0.0117219
$404$	2.93598e6	0.894953
$405$	1.03313e7	3.12979
$406$	−4.87447e6	−1.46761
$407$	−212654.	−0.0636338
$408$	0	0
$409$	3.47943e6	1.02849	0.514244	−	0.857644i	$-0.328072\pi$
$409$	3.47943e6	1.02849	0.514244	+	0.857644i	$0.328072\pi$
$410$	439789.	0.129207
$411$	−2.05703e6	−0.600670
$412$	846780.	0.245769
$413$	3.31762e6	0.957086
$414$	2.47812e6	0.710595
$415$	2.72670e6	0.777172
$416$	54388.2	0.0154089
$417$	−1.30898e6	−0.368633
$418$	669588.	0.187442
$419$	3.00281e6	0.835589	0.417795	−	0.908542i	$-0.362803\pi$
$419$	3.00281e6	0.835589	0.417795	+	0.908542i	$0.362803\pi$
$420$	1.03784e7	2.87082
$421$	221923.	0.0610234	0.0305117	−	0.999534i	$-0.490286\pi$
$421$	221923.	0.0610234	0.0305117	+	0.999534i	$0.490286\pi$
$422$	−357493.	−0.0977206
$423$	−6.72904e6	−1.82853
$424$	4.49859e6	1.21524
$425$	0	0
$426$	1.08580e7	2.89884
$427$	445976.	0.118370
$428$	9.89652e6	2.61140
$429$	−16511.1	−0.00433145
$430$	1.16225e7	3.03130
$431$	−3.67967e6	−0.954148	−0.477074	−	0.878863i	$-0.658303\pi$
$431$	−3.67967e6	−0.954148	−0.477074	+	0.878863i	$0.658303\pi$
$432$	−2.59071e6	−0.667897
$433$	−5.01473e6	−1.28537	−0.642684	−	0.766131i	$-0.722179\pi$
$433$	−5.01473e6	−1.28537	−0.642684	+	0.766131i	$0.722179\pi$
$434$	−4.88069e6	−1.24382
$435$	9.11234e6	2.30891
$436$	7.42806e6	1.87137
$437$	−481190.	−0.120535
$438$	−6.39290e6	−1.59225
$439$	−1.56473e6	−0.387506	−0.193753	−	0.981050i	$-0.562066\pi$
$439$	−1.56473e6	−0.387506	−0.193753	+	0.981050i	$0.562066\pi$
$440$	672900.	0.165699
$441$	−2.36653e6	−0.579451
$442$	0	0
$443$	−5.63694e6	−1.36469	−0.682345	−	0.731030i	$-0.739040\pi$
$443$	−5.63694e6	−1.36469	−0.682345	+	0.731030i	$0.739040\pi$
$444$	4.17400e6	1.00483
$445$	−5.79510e6	−1.38727
$446$	7.93041e6	1.88781
$447$	1.47083e6	0.348173
$448$	−6.04777e6	−1.42364
$449$	7.54467e6	1.76614	0.883069	−	0.469244i	$-0.155474\pi$
$449$	7.54467e6	1.76614	0.883069	+	0.469244i	$0.155474\pi$
$450$	−6.14962e6	−1.43158
$451$	53673.0	0.0124255
$452$	−7.13555e6	−1.64279
$453$	−7.25954e6	−1.66213
$454$	3.23127e6	0.735756
$455$	58970.5	0.0133538
$456$	−4.40572e6	−0.992214
$457$	−198935.	−0.0445575	−0.0222788	−	0.999752i	$-0.507092\pi$
$457$	−198935.	−0.0445575	−0.0222788	+	0.999752i	$0.507092\pi$
$458$	2.79793e6	0.623265
$459$	0	0
$460$	−1.44254e6	−0.317858
$461$	2.46469e6	0.540145	0.270072	−	0.962840i	$-0.412952\pi$
$461$	2.46469e6	0.540145	0.270072	+	0.962840i	$0.412952\pi$
$462$	2.10862e6	0.459614
$463$	−3.64498e6	−0.790210	−0.395105	−	0.918636i	$-0.629292\pi$
$463$	−3.64498e6	−0.790210	−0.395105	+	0.918636i	$0.629292\pi$
$464$	−1.18616e6	−0.255769
$465$	9.12398e6	1.95682
$466$	−1.21121e7	−2.58378
$467$	7.07889e6	1.50201	0.751005	−	0.660296i	$-0.229569\pi$
$467$	7.07889e6	1.50201	0.751005	+	0.660296i	$0.229569\pi$
$468$	231016.	0.0487559
$469$	−2.71066e6	−0.569040
$470$	6.52100e6	1.36166
$471$	−8.86263e6	−1.84082
$472$	−4.22207e6	−0.872310
$473$	1.41844e6	0.291514
$474$	1.93914e7	3.96427
$475$	1.19410e6	0.242833
$476$	0	0
$477$	−1.87851e7	−3.78022
$478$	−5.89743e6	−1.18057
$479$	4.91772e6	0.979321	0.489660	−	0.871913i	$-0.337121\pi$
$479$	4.91772e6	0.979321	0.489660	+	0.871913i	$0.337121\pi$
$480$	1.29846e7	2.57232
$481$	23716.9	0.00467407
$482$	1.16553e7	2.28510
$483$	−1.51533e6	−0.295555
$484$	−7.50742e6	−1.45672
$485$	5.53759e6	1.06897
$486$	−1.84079e7	−3.53519
$487$	−8.52348e6	−1.62852	−0.814262	−	0.580497i	$-0.802858\pi$
$487$	−8.52348e6	−1.62852	−0.814262	+	0.580497i	$0.802858\pi$
$488$	−567559.	−0.107885
$489$	9.07345e6	1.71593
$490$	2.29337e6	0.431503
$491$	−578682.	−0.108327	−0.0541634	−	0.998532i	$-0.517249\pi$
$491$	−578682.	−0.108327	−0.0541634	+	0.998532i	$0.517249\pi$
$492$	−1.05350e6	−0.196210
$493$	0	0
$494$	−74677.8	−0.0137681
$495$	−2.80988e6	−0.515436
$496$	−1.18767e6	−0.216767
$497$	−4.73280e6	−0.859464
$498$	−1.08739e7	−1.96476
$499$	3.73689e6	0.671828	0.335914	−	0.941893i	$-0.390955\pi$
$499$	3.73689e6	0.671828	0.335914	+	0.941893i	$0.390955\pi$
$500$	−6.24282e6	−1.11675
$501$	4.02541e6	0.716500
$502$	1.70856e6	0.302602
$503$	382631.	0.0674311	0.0337155	−	0.999431i	$-0.489266\pi$
$503$	382631.	0.0674311	0.0337155	+	0.999431i	$0.489266\pi$
$504$	−9.88995e6	−1.73427
$505$	3.98275e6	0.694952
$506$	−293087.	−0.0508885
$507$	−1.07988e7	−1.86577
$508$	−1.35806e7	−2.33486
$509$	−1.11151e7	−1.90159	−0.950797	−	0.309816i	$-0.899733\pi$
$509$	−1.11151e7	−1.90159	−0.950797	+	0.309816i	$0.899733\pi$
$510$	0	0
$511$	2.78656e6	0.472080
$512$	−2.83314e6	−0.477632
$513$	1.09858e7	1.84306
$514$	1.99032e6	0.332288
$515$	1.14868e6	0.190846
$516$	−2.78413e7	−4.60327
$517$	795841.	0.130948
$518$	−3.02886e6	−0.495969
$519$	−840711.	−0.137002
$520$	−75047.2	−0.0121710
$521$	−132807.	−0.0214352	−0.0107176	−	0.999943i	$-0.503412\pi$
$521$	−132807.	−0.0214352	−0.0107176	+	0.999943i	$0.503412\pi$
$522$	−2.59038e7	−4.16090
$523$	−6.11506e6	−0.977567	−0.488784	−	0.872405i	$-0.662559\pi$
$523$	−6.11506e6	−0.977567	−0.488784	+	0.872405i	$0.662559\pi$
$524$	1.44494e7	2.29890
$525$	3.76038e6	0.595434
$526$	−9.37746e6	−1.47782
$527$	0	0
$528$	513114.	0.0800993
$529$	−6.22572e6	−0.967276
$530$	1.82043e7	2.81504
$531$	1.76304e7	2.71348
$532$	5.72870e6	0.877561
$533$	−5986.04	−0.000912687 0
$534$	2.31104e7	3.50715
$535$	1.34249e7	2.02781
$536$	3.44964e6	0.518635
$537$	8.89254e6	1.33073
$538$	−7.94879e6	−1.18398
$539$	279889.	0.0414968
$540$	3.29340e7	4.86026
$541$	5.61147e6	0.824296	0.412148	−	0.911117i	$-0.364779\pi$
$541$	5.61147e6	0.824296	0.412148	+	0.911117i	$0.364779\pi$
$542$	4.16897e6	0.609579
$543$	2.16345e7	3.14882
$544$	0	0
$545$	1.00764e7	1.45316
$546$	−235170.	−0.0337598
$547$	−4.62251e6	−0.660556	−0.330278	−	0.943884i	$-0.607143\pi$
$547$	−4.62251e6	−0.660556	−0.330278	+	0.943884i	$0.607143\pi$
$548$	−3.40392e6	−0.484203
$549$	2.37000e6	0.335596
$550$	727314.	0.102522
$551$	5.02987e6	0.705794
$552$	1.92844e6	0.269375
$553$	−8.45239e6	−1.17535
$554$	2.52492e6	0.349521
$555$	5.66216e6	0.780278
$556$	−2.16607e6	−0.297157
$557$	−659682.	−0.0900942	−0.0450471	−	0.998985i	$-0.514344\pi$
$557$	−659682.	−0.0900942	−0.0450471	+	0.998985i	$0.514344\pi$
$558$	−2.59369e7	−3.52640
$559$	−158196.	−0.0214125
$560$	−1.83262e6	−0.246946
$561$	0	0
$562$	1.75742e7	2.34711
$563$	−6.91606e6	−0.919576	−0.459788	−	0.888029i	$-0.652075\pi$
$563$	−6.91606e6	−0.919576	−0.459788	+	0.888029i	$0.652075\pi$
$564$	−1.56209e7	−2.06779
$565$	−9.67960e6	−1.27566
$566$	−420880.	−0.0552226
$567$	1.79585e7	2.34592
$568$	6.02307e6	0.783334
$569$	2.47136e6	0.320004	0.160002	−	0.987117i	$-0.448850\pi$
$569$	2.47136e6	0.320004	0.160002	+	0.987117i	$0.448850\pi$
$570$	−1.78285e7	−2.29842
$571$	1.34798e7	1.73019	0.865094	−	0.501610i	$-0.167259\pi$
$571$	1.34798e7	1.73019	0.865094	+	0.501610i	$0.167259\pi$
$572$	−27322.1	−0.00349160
$573$	2.04836e7	2.60628
$574$	764471.	0.0968459
$575$	−522673.	−0.0659266
$576$	−3.21389e7	−4.03622
$577$	4.35284e6	0.544294	0.272147	−	0.962256i	$-0.412266\pi$
$577$	4.35284e6	0.544294	0.272147	+	0.962256i	$0.412266\pi$
$578$	0	0
$579$	−8.77648e6	−1.08799
$580$	1.50788e7	1.86122
$581$	4.73974e6	0.582524
$582$	−2.20835e7	−2.70247
$583$	2.22171e6	0.270717
$584$	−3.54623e6	−0.430264
$585$	313380.	0.0378601
$586$	3.43750e6	0.413522
$587$	−450987.	−0.0540218	−0.0270109	−	0.999635i	$-0.508599\pi$
$587$	−450987.	−0.0540218	−0.0270109	+	0.999635i	$0.508599\pi$
$588$	−5.49369e6	−0.655271
$589$	5.03629e6	0.598168
$590$	−1.70854e7	−2.02066
$591$	2.17213e7	2.55810
$592$	−737046.	−0.0864352
$593$	−5.28445e6	−0.617110	−0.308555	−	0.951206i	$-0.599845\pi$
$593$	−5.28445e6	−0.617110	−0.308555	+	0.951206i	$0.599845\pi$
$594$	6.69133e6	0.778120
$595$	0	0
$596$	2.43390e6	0.280664
$597$	−8.19560e6	−0.941120
$598$	32687.4	0.00373789
$599$	7.13658e6	0.812687	0.406343	−	0.913720i	$-0.366804\pi$
$599$	7.13658e6	0.812687	0.406343	+	0.913720i	$0.366804\pi$
$600$	−4.78554e6	−0.542692
$601$	−7.53985e6	−0.851484	−0.425742	−	0.904845i	$-0.639987\pi$
$601$	−7.53985e6	−0.851484	−0.425742	+	0.904845i	$0.639987\pi$
$602$	2.02031e7	2.27209
$603$	−1.44049e7	−1.61331
$604$	−1.20129e7	−1.33985
$605$	−1.01840e7	−1.13118
$606$	−1.58829e7	−1.75691
$607$	−1.40296e7	−1.54551	−0.772757	−	0.634701i	$-0.781123\pi$
$607$	−1.40296e7	−1.54551	−0.772757	+	0.634701i	$0.781123\pi$
$608$	7.16730e6	0.786315
$609$	1.58397e7	1.73063
$610$	−2.29673e6	−0.249911
$611$	−88758.6	−0.00961850
$612$	0	0
$613$	1.54281e7	1.65829	0.829146	−	0.559032i	$-0.188827\pi$
$613$	1.54281e7	1.65829	0.829146	+	0.559032i	$0.188827\pi$
$614$	−5.72735e6	−0.613102
$615$	−1.42910e6	−0.152362
$616$	1.16968e6	0.124198
$617$	−6.43675e6	−0.680697	−0.340349	−	0.940299i	$-0.610545\pi$
$617$	−6.43675e6	−0.680697	−0.340349	+	0.940299i	$0.610545\pi$
$618$	−4.58086e6	−0.482476
$619$	39643.3	0.00415857	0.00207928	−	0.999998i	$-0.499338\pi$
$619$	39643.3	0.00415857	0.00207928	+	0.999998i	$0.499338\pi$
$620$	1.50981e7	1.57740
$621$	−4.80863e6	−0.500371
$622$	1.79079e7	1.85597
$623$	−1.00734e7	−1.03982
$624$	−57226.5	−0.00588350
$625$	−1.20276e7	−1.23162
$626$	8.12361e6	0.828539
$627$	−2.17584e6	−0.221034
$628$	−1.46656e7	−1.48389
$629$	0	0
$630$	−4.00214e7	−4.01736
$631$	1.87530e6	0.187498	0.0937492	−	0.995596i	$-0.470115\pi$
$631$	1.87530e6	0.187498	0.0937492	+	0.995596i	$0.470115\pi$
$632$	1.07567e7	1.07124
$633$	1.16168e6	0.115233
$634$	1.67696e7	1.65691
$635$	−1.84225e7	−1.81307
$636$	−4.36079e7	−4.27486
$637$	−31215.5	−0.00304805
$638$	3.06363e6	0.297979
$639$	−2.51510e7	−2.43670
$640$	1.68615e7	1.62722
$641$	−418005.	−0.0401825	−0.0200912	−	0.999798i	$-0.506396\pi$
$641$	−418005.	−0.0401825	−0.0200912	+	0.999798i	$0.506396\pi$
$642$	−5.35376e7	−5.12650
$643$	1.52112e6	0.145089	0.0725447	−	0.997365i	$-0.476888\pi$
$643$	1.52112e6	0.145089	0.0725447	+	0.997365i	$0.476888\pi$
$644$	−2.50752e6	−0.238248
$645$	−3.77676e7	−3.57454
$646$	0	0
$647$	6.73245e6	0.632284	0.316142	−	0.948712i	$-0.397612\pi$
$647$	6.73245e6	0.632284	0.316142	+	0.948712i	$0.397612\pi$
$648$	−2.28544e7	−2.13812
$649$	−2.08514e6	−0.194323
$650$	−81115.8	−0.00753047
$651$	1.58599e7	1.46672
$652$	1.50145e7	1.38322
$653$	−7.87453e6	−0.722673	−0.361336	−	0.932435i	$-0.617679\pi$
$653$	−7.87453e6	−0.722673	−0.361336	+	0.932435i	$0.617679\pi$
$654$	−4.01839e7	−3.67373
$655$	1.96010e7	1.78515
$656$	186027.	0.0168779
$657$	1.48083e7	1.33842
$658$	1.13353e7	1.02063
$659$	−1.65775e6	−0.148698	−0.0743490	−	0.997232i	$-0.523688\pi$
$659$	−1.65775e6	−0.148698	−0.0743490	+	0.997232i	$0.523688\pi$
$660$	−6.52287e6	−0.582880
$661$	7.27874e6	0.647967	0.323983	−	0.946063i	$-0.394978\pi$
$661$	7.27874e6	0.647967	0.323983	+	0.946063i	$0.394978\pi$
$662$	2.41737e7	2.14387
$663$	0	0
$664$	−6.03189e6	−0.530925
$665$	7.77116e6	0.681447
$666$	−1.60959e7	−1.40614
$667$	−2.20163e6	−0.191616
$668$	6.66114e6	0.577574
$669$	−2.57701e7	−2.22613
$670$	1.39596e7	1.20139
$671$	−280299.	−0.0240334
$672$	2.25707e7	1.92807
$673$	−1.48558e7	−1.26433	−0.632164	−	0.774835i	$-0.717833\pi$
$673$	−1.48558e7	−1.26433	−0.632164	+	0.774835i	$0.717833\pi$
$674$	−2.75242e7	−2.33380
$675$	1.19329e7	1.00806
$676$	−1.78696e7	−1.50400
$677$	248580.	0.0208446	0.0104223	−	0.999946i	$-0.496682\pi$
$677$	248580.	0.0208446	0.0104223	+	0.999946i	$0.496682\pi$
$678$	3.86015e7	3.22500
$679$	9.62582e6	0.801241
$680$	0	0
$681$	−1.05001e7	−0.867612
$682$	3.06754e6	0.252540
$683$	−1.90776e7	−1.56485	−0.782424	−	0.622746i	$-0.786017\pi$
$683$	−1.90776e7	−1.56485	−0.782424	+	0.622746i	$0.786017\pi$
$684$	3.04434e7	2.48801
$685$	−4.61752e6	−0.375995
$686$	2.10640e7	1.70895
$687$	−9.09194e6	−0.734962
$688$	4.91624e6	0.395969
$689$	−247783.	−0.0198849
$690$	7.80376e6	0.623995
$691$	6.77989e6	0.540166	0.270083	−	0.962837i	$-0.412949\pi$
$691$	6.77989e6	0.540166	0.270083	+	0.962837i	$0.412949\pi$
$692$	−1.39118e6	−0.110438
$693$	−4.88432e6	−0.386341
$694$	43612.2	0.00343723
$695$	−2.93834e6	−0.230749
$696$	−2.01579e7	−1.57733
$697$	0	0
$698$	−1.08134e6	−0.0840090
$699$	3.93587e7	3.04683
$700$	6.22258e6	0.479982
$701$	−7.12995e6	−0.548014	−0.274007	−	0.961728i	$-0.588349\pi$
$701$	−7.12995e6	−0.548014	−0.274007	+	0.961728i	$0.588349\pi$
$702$	−746271.	−0.0571549
$703$	3.12542e6	0.238518
$704$	3.80106e6	0.289050
$705$	−2.11902e7	−1.60569
$706$	−3.92953e7	−2.96708
$707$	6.92309e6	0.520897
$708$	4.09274e7	3.06853
$709$	4.22233e6	0.315455	0.157727	−	0.987483i	$-0.449583\pi$
$709$	4.22233e6	0.315455	0.157727	+	0.987483i	$0.449583\pi$
$710$	2.43734e7	1.81456
$711$	−4.49175e7	−3.33228
$712$	1.28197e7	0.947714
$713$	−2.20445e6	−0.162396
$714$	0	0
$715$	−37063.3	−0.00271131
$716$	1.47151e7	1.07271
$717$	1.91639e7	1.39215
$718$	2.21071e7	1.60037
$719$	−1.72944e7	−1.24762	−0.623811	−	0.781575i	$-0.714417\pi$
$719$	−1.72944e7	−1.24762	−0.623811	+	0.781575i	$0.714417\pi$
$720$	−9.73886e6	−0.700127
$721$	1.99672e6	0.143047
$722$	1.23247e7	0.879899
$723$	−3.78741e7	−2.69461
$724$	3.58002e7	2.53828
$725$	5.46350e6	0.386034
$726$	4.06132e7	2.85973
$727$	4.38911e6	0.307992	0.153996	−	0.988071i	$-0.450786\pi$
$727$	4.38911e6	0.307992	0.153996	+	0.988071i	$0.450786\pi$
$728$	−130452.	−0.00912269
$729$	2.13703e7	1.48934
$730$	−1.43505e7	−0.996686
$731$	0	0
$732$	5.50174e6	0.379509
$733$	−3.64598e6	−0.250643	−0.125321	−	0.992116i	$-0.539996\pi$
$733$	−3.64598e6	−0.250643	−0.125321	+	0.992116i	$0.539996\pi$
$734$	9.40583e6	0.644402
$735$	−7.45236e6	−0.508834
$736$	−3.13721e6	−0.213476
$737$	1.70367e6	0.115536
$738$	4.06254e6	0.274572
$739$	−2.25185e7	−1.51680	−0.758399	−	0.651791i	$-0.774018\pi$
$739$	−2.25185e7	−1.51680	−0.758399	+	0.651791i	$0.774018\pi$
$740$	9.36958e6	0.628986
$741$	242667.	0.0162355
$742$	3.16440e7	2.11000
$743$	−1.47859e7	−0.982598	−0.491299	−	0.870991i	$-0.663478\pi$
$743$	−1.47859e7	−0.982598	−0.491299	+	0.870991i	$0.663478\pi$
$744$	−2.01837e7	−1.33681
$745$	3.30165e6	0.217942
$746$	−3.85996e7	−2.53943
$747$	2.51878e7	1.65154
$748$	0	0
$749$	2.33361e7	1.51993
$750$	3.37720e7	2.19232
$751$	1.51642e7	0.981116	0.490558	−	0.871408i	$-0.336793\pi$
$751$	1.51642e7	0.981116	0.490558	+	0.871408i	$0.336793\pi$
$752$	2.75834e6	0.177870
$753$	−5.55201e6	−0.356831
$754$	−341681.	−0.0218873
$755$	−1.62959e7	−1.04042
$756$	5.72481e7	3.64298
$757$	1.05063e7	0.666361	0.333181	−	0.942863i	$-0.391878\pi$
$757$	1.05063e7	0.666361	0.333181	+	0.942863i	$0.391878\pi$
$758$	2.51734e7	1.59136
$759$	952393.	0.0600083
$760$	−9.88975e6	−0.621085
$761$	1.05491e7	0.660321	0.330160	−	0.943925i	$-0.392897\pi$
$761$	1.05491e7	0.660321	0.330160	+	0.943925i	$0.392897\pi$
$762$	7.34676e7	4.58362
$763$	1.75155e7	1.08921
$764$	3.38958e7	2.10093
$765$	0	0
$766$	−4.54920e7	−2.80132
$767$	232552.	0.0142735
$768$	−1.76448e7	−1.07948
$769$	−1.78390e7	−1.08781	−0.543907	−	0.839146i	$-0.683055\pi$
$769$	−1.78390e7	−1.08781	−0.543907	+	0.839146i	$0.683055\pi$
$770$	4.73332e6	0.287699
$771$	−6.46759e6	−0.391838
$772$	−1.45231e7	−0.877032
$773$	−2.66656e7	−1.60510	−0.802551	−	0.596584i	$-0.796524\pi$
$773$	−2.66656e7	−1.60510	−0.802551	+	0.596584i	$0.796524\pi$
$774$	1.07363e8	6.44171
$775$	5.47048e6	0.327168
$776$	−1.22500e7	−0.730269
$777$	9.84235e6	0.584852
$778$	8.76495e6	0.519159
$779$	−788843.	−0.0465744
$780$	727483.	0.0428140
$781$	2.97460e6	0.174502
$782$	0	0
$783$	5.02645e7	2.92993
$784$	970079.	0.0563659
$785$	−1.98944e7	−1.15228
$786$	−7.81673e7	−4.51303
$787$	−2.73815e7	−1.57587	−0.787936	−	0.615757i	$-0.788850\pi$
$787$	−2.73815e7	−1.57587	−0.787936	+	0.615757i	$0.788850\pi$
$788$	3.59438e7	2.06210
$789$	3.04723e7	1.74266
$790$	4.35288e7	2.48147
$791$	−1.68257e7	−0.956165
$792$	6.21590e6	0.352120
$793$	31261.2	0.00176532
$794$	−1.07971e7	−0.607793
$795$	−5.91555e7	−3.31953
$796$	−1.35618e7	−0.758641
$797$	−1.55110e7	−0.864955	−0.432477	−	0.901645i	$-0.642360\pi$
$797$	−1.55110e7	−0.864955	−0.432477	+	0.901645i	$0.642360\pi$
$798$	−3.09908e7	−1.72276
$799$	0	0
$800$	7.78520e6	0.430076
$801$	−5.35321e7	−2.94804
$802$	−6.97584e6	−0.382967
$803$	−1.75137e6	−0.0958493
$804$	−3.34397e7	−1.82441
$805$	−3.40153e6	−0.185006
$806$	−342117.	−0.0185497
$807$	2.58298e7	1.39617
$808$	−8.81048e6	−0.474757
$809$	−1.15647e7	−0.621245	−0.310622	−	0.950533i	$-0.600537\pi$
$809$	−1.15647e7	−0.621245	−0.310622	+	0.950533i	$0.600537\pi$
$810$	−9.24843e7	−4.95285
$811$	2.46908e7	1.31821	0.659104	−	0.752052i	$-0.270936\pi$
$811$	2.46908e7	1.31821	0.659104	+	0.752052i	$0.270936\pi$
$812$	2.62111e7	1.39507
$813$	−1.35472e7	−0.718823
$814$	1.90366e6	0.100700
$815$	2.03676e7	1.07410
$816$	0	0
$817$	−2.08472e7	−1.09268
$818$	−3.11475e7	−1.62757
$819$	544739.	0.0283778
$820$	−2.36484e6	−0.122820
$821$	2.81857e7	1.45939	0.729694	−	0.683774i	$-0.239662\pi$
$821$	2.81857e7	1.45939	0.729694	+	0.683774i	$0.239662\pi$
$822$	1.84143e7	0.950552
$823$	4.82720e6	0.248425	0.124213	−	0.992256i	$-0.460360\pi$
$823$	4.82720e6	0.248425	0.124213	+	0.992256i	$0.460360\pi$
$824$	−2.54107e6	−0.130376
$825$	−2.36342e6	−0.120895
$826$	−2.96989e7	−1.51458
$827$	3.02726e6	0.153917	0.0769583	−	0.997034i	$-0.475479\pi$
$827$	3.02726e6	0.153917	0.0769583	+	0.997034i	$0.475479\pi$
$828$	−1.33254e7	−0.675468
$829$	3.35129e7	1.69366	0.846829	−	0.531866i	$-0.178509\pi$
$829$	3.35129e7	1.69366	0.846829	+	0.531866i	$0.178509\pi$
$830$	−2.44091e7	−1.22986
$831$	−8.20480e6	−0.412160
$832$	−423925.	−0.0212315
$833$	0	0
$834$	1.17179e7	0.583356
$835$	9.03604e6	0.448500
$836$	−3.60053e6	−0.178176
$837$	5.03287e7	2.48315
$838$	−2.68808e7	−1.32231
$839$	1.09079e7	0.534978	0.267489	−	0.963561i	$-0.413806\pi$
$839$	1.09079e7	0.534978	0.267489	+	0.963561i	$0.413806\pi$
$840$	−3.11441e7	−1.52292
$841$	2.50252e6	0.122008
$842$	−1.98663e6	−0.0965687
$843$	−5.71077e7	−2.76774
$844$	1.92232e6	0.0928901
$845$	−2.42407e7	−1.16789
$846$	6.02376e7	2.89362
$847$	−1.77026e7	−0.847869
$848$	7.70030e6	0.367721
$849$	1.36766e6	0.0651191
$850$	0	0
$851$	−1.36804e6	−0.0647550
$852$	−5.83857e7	−2.75554
$853$	−1.48850e7	−0.700450	−0.350225	−	0.936666i	$-0.613895\pi$
$853$	−1.48850e7	−0.700450	−0.350225	+	0.936666i	$0.613895\pi$
$854$	−3.99233e6	−0.187319
$855$	4.12974e7	1.93200
$856$	−2.96981e7	−1.38530
$857$	5.53226e6	0.257307	0.128653	−	0.991690i	$-0.458935\pi$
$857$	5.53226e6	0.257307	0.128653	+	0.991690i	$0.458935\pi$
$858$	147806.	0.00685446
$859$	1.92478e7	0.890015	0.445008	−	0.895527i	$-0.353201\pi$
$859$	1.92478e7	0.890015	0.445008	+	0.895527i	$0.353201\pi$
$860$	−6.24969e7	−2.88146
$861$	−2.48417e6	−0.114202
$862$	3.29400e7	1.50992
$863$	2.69550e7	1.23201	0.616003	−	0.787744i	$-0.288751\pi$
$863$	2.69550e7	1.23201	0.616003	+	0.787744i	$0.288751\pi$
$864$	7.16243e7	3.26420
$865$	−1.88718e6	−0.0857579
$866$	4.48913e7	2.03408
$867$	0	0
$868$	2.62446e7	1.18233
$869$	5.31238e6	0.238638
$870$	−8.15726e7	−3.65381
$871$	−190006.	−0.00848639
$872$	−2.22906e7	−0.992728
$873$	5.11534e7	2.27164
$874$	4.30756e6	0.190745
$875$	−1.47207e7	−0.649991
$876$	3.43760e7	1.51355
$877$	2.53398e7	1.11251	0.556256	−	0.831011i	$-0.312237\pi$
$877$	2.53398e7	1.11251	0.556256	+	0.831011i	$0.312237\pi$
$878$	1.40073e7	0.613223
$879$	−1.11702e7	−0.487629
$880$	1.15181e6	0.0501389
$881$	−2.81220e6	−0.122069	−0.0610346	−	0.998136i	$-0.519440\pi$
$881$	−2.81220e6	−0.122069	−0.0610346	+	0.998136i	$0.519440\pi$
$882$	2.11850e7	0.916972
$883$	−2.57166e7	−1.10997	−0.554987	−	0.831859i	$-0.687277\pi$
$883$	−2.57166e7	−1.10997	−0.554987	+	0.831859i	$0.687277\pi$
$884$	0	0
$885$	5.55193e7	2.38279
$886$	5.04613e7	2.15960
$887$	1.95804e6	0.0835628	0.0417814	−	0.999127i	$-0.486697\pi$
$887$	1.95804e6	0.0835628	0.0417814	+	0.999127i	$0.486697\pi$
$888$	−1.25256e7	−0.533047
$889$	−3.20233e7	−1.35898
$890$	5.18771e7	2.19533
$891$	−1.12870e7	−0.476306
$892$	−4.26436e7	−1.79449
$893$	−1.16966e7	−0.490832
$894$	−1.31667e7	−0.550978
$895$	1.99615e7	0.832983
$896$	2.93098e7	1.21967
$897$	−106218.	−0.00440777
$898$	−6.75390e7	−2.79489
$899$	2.30431e7	0.950913
$900$	3.30679e7	1.36082
$901$	0	0
$902$	−480475.	−0.0196632
$903$	−6.56503e7	−2.67928
$904$	2.14128e7	0.871470
$905$	4.85640e7	1.97103
$906$	6.49866e7	2.63029
$907$	−1.59053e7	−0.641981	−0.320991	−	0.947082i	$-0.604016\pi$
$907$	−1.59053e7	−0.641981	−0.320991	+	0.947082i	$0.604016\pi$
$908$	−1.73753e7	−0.699386
$909$	3.67906e7	1.47682
$910$	−527897.	−0.0211323
$911$	−7.78112e6	−0.310632	−0.155316	−	0.987865i	$-0.549640\pi$
$911$	−7.78112e6	−0.310632	−0.155316	+	0.987865i	$0.549640\pi$
$912$	−7.54134e6	−0.300235
$913$	−2.97895e6	−0.118273
$914$	1.78085e6	0.0705116
$915$	7.46327e6	0.294698
$916$	−1.50451e7	−0.592456
$917$	3.40718e7	1.33805
$918$	0	0
$919$	−8.44485e6	−0.329840	−0.164920	−	0.986307i	$-0.552737\pi$
$919$	−8.44485e6	−0.329840	−0.164920	+	0.986307i	$0.552737\pi$
$920$	4.32886e6	0.168618
$921$	1.86112e7	0.722977
$922$	−2.20636e7	−0.854771
$923$	−331751.	−0.0128176
$924$	−1.13385e7	−0.436894
$925$	3.39487e6	0.130457
$926$	3.26294e7	1.25050
$927$	1.06109e7	0.405559
$928$	3.27933e7	1.25001
$929$	−4.26009e7	−1.61950	−0.809748	−	0.586778i	$-0.800396\pi$
$929$	−4.26009e7	−1.61950	−0.809748	+	0.586778i	$0.800396\pi$
$930$	−8.16768e7	−3.09664
$931$	−4.11359e6	−0.155542
$932$	6.51297e7	2.45606
$933$	−5.81923e7	−2.18858
$934$	−6.33694e7	−2.37691
$935$	0	0
$936$	−693246.	−0.0258641
$937$	−1.37155e7	−0.510345	−0.255173	−	0.966896i	$-0.582132\pi$
$937$	−1.37155e7	−0.510345	−0.255173	+	0.966896i	$0.582132\pi$
$938$	2.42655e7	0.900497
$939$	−2.63979e7	−0.977023
$940$	−3.50649e7	−1.29435
$941$	−9.21347e6	−0.339195	−0.169597	−	0.985513i	$-0.554247\pi$
$941$	−9.21347e6	−0.339195	−0.169597	+	0.985513i	$0.554247\pi$
$942$	7.93373e7	2.91306
$943$	345286.	0.0126445
$944$	−7.22698e6	−0.263953
$945$	7.76588e7	2.82886
$946$	−1.26977e7	−0.461316
$947$	542881.	0.0196712	0.00983558	−	0.999952i	$-0.496869\pi$
$947$	542881.	0.0196712	0.00983558	+	0.999952i	$0.496869\pi$
$948$	−1.04272e8	−3.76831
$949$	195327.	0.00704038
$950$	−1.06895e7	−0.384280
$951$	−5.44931e7	−1.95384
$952$	0	0
$953$	−3.85657e7	−1.37553	−0.687763	−	0.725935i	$-0.741407\pi$
$953$	−3.85657e7	−1.37553	−0.687763	+	0.725935i	$0.741407\pi$
$954$	1.68162e8	5.98215
$955$	4.59807e7	1.63142
$956$	3.17118e7	1.12222
$957$	−9.95535e6	−0.351380
$958$	−4.40229e7	−1.54976
$959$	−8.02649e6	−0.281825
$960$	−1.01207e8	−3.54433
$961$	−5.55668e6	−0.194092
$962$	−212311.	−0.00739665
$963$	1.24012e8	4.30923
$964$	−6.26730e7	−2.17214
$965$	−1.97010e7	−0.681036
$966$	1.35650e7	0.467712
$967$	7.29986e6	0.251043	0.125522	−	0.992091i	$-0.459940\pi$
$967$	7.29986e6	0.251043	0.125522	+	0.992091i	$0.459940\pi$
$968$	2.25287e7	0.772767
$969$	0	0
$970$	−4.95719e7	−1.69163
$971$	1.86581e7	0.635066	0.317533	−	0.948247i	$-0.397145\pi$
$971$	1.86581e7	0.635066	0.317533	+	0.948247i	$0.397145\pi$
$972$	9.89833e7	3.36044
$973$	−5.10762e6	−0.172956
$974$	7.63012e7	2.57712
$975$	263588.	0.00888002
$976$	−971499.	−0.0326451
$977$	−1.64674e7	−0.551935	−0.275968	−	0.961167i	$-0.588998\pi$
$977$	−1.64674e7	−0.551935	−0.275968	+	0.961167i	$0.588998\pi$
$978$	−8.12245e7	−2.71544
$979$	6.33122e6	0.211121
$980$	−1.23320e7	−0.410173
$981$	9.30804e7	3.08806
$982$	5.18030e6	0.171426
$983$	−43139.2	−0.00142393	−0.000711964	−	1.00000i	$-0.500227\pi$
$983$	−43139.2	−0.00142393	−0.000711964		1.00000i	$0.500227\pi$
$984$	3.16141e6	0.104086
$985$	4.87589e7	1.60127
$986$	0	0
$987$	−3.68342e7	−1.20353
$988$	401559.	0.0130875
$989$	9.12505e6	0.296650
$990$	2.51537e7	0.815669
$991$	−5.50136e7	−1.77945	−0.889725	−	0.456496i	$-0.849104\pi$
$991$	−5.50136e7	−1.77945	−0.889725	+	0.456496i	$0.849104\pi$
$992$	3.28351e7	1.05940
$993$	−7.85530e7	−2.52807
$994$	4.23675e7	1.36009
$995$	−1.83971e7	−0.589103
$996$	5.84712e7	1.86764
$997$	−2.89324e7	−0.921821	−0.460911	−	0.887447i	$-0.652477\pi$
$997$	−2.89324e7	−0.921821	−0.460911	+	0.887447i	$0.652477\pi$
$998$	−3.34522e7	−1.06316
$999$	3.12330e7	0.990148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.6.a.j.1.4		28
17.3	odd	16		17.6.d.a.9.1	yes	28
17.6	odd	16		17.6.d.a.2.1	✓	28
17.16	even	2	inner	289.6.a.j.1.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.d.a.2.1	✓	28	17.6	odd	16
17.6.d.a.9.1	yes	28	17.3	odd	16
289.6.a.j.1.3		28	17.16	even	2	inner
289.6.a.j.1.4		28	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-8.95189 q^{2} +29.0894 q^{3} +48.1363 q^{4} +65.2984 q^{5} -260.405 q^{6} +113.506 q^{7} -144.450 q^{8} +603.192 q^{9} +O(q^{10})\)	\(q-8.95189 q^{2} +29.0894 q^{3} +48.1363 q^{4} +65.2984 q^{5} -260.405 q^{6} +113.506 q^{7} -144.450 q^{8} +603.192 q^{9} -584.544 q^{10} -71.3393 q^{11} +1400.26 q^{12} +7.95633 q^{13} -1016.09 q^{14} +1899.49 q^{15} -247.258 q^{16} -5399.71 q^{18} +1048.49 q^{19} +3143.22 q^{20} +3301.82 q^{21} +638.622 q^{22} -458.936 q^{23} -4201.97 q^{24} +1138.88 q^{25} -71.2242 q^{26} +10477.8 q^{27} +5463.77 q^{28} +4797.26 q^{29} -17004.0 q^{30} +4803.38 q^{31} +6835.84 q^{32} -2075.22 q^{33} +7411.77 q^{35} +29035.4 q^{36} +2980.88 q^{37} -9385.96 q^{38} +231.445 q^{39} -9432.38 q^{40} -752.362 q^{41} -29557.6 q^{42} -19883.0 q^{43} -3434.01 q^{44} +39387.5 q^{45} +4108.35 q^{46} -11155.7 q^{47} -7192.57 q^{48} -3923.35 q^{49} -10195.1 q^{50} +382.989 q^{52} -31142.8 q^{53} -93795.8 q^{54} -4658.34 q^{55} -16396.0 q^{56} +30499.9 q^{57} -42944.5 q^{58} +29228.5 q^{59} +91434.4 q^{60} +3929.09 q^{61} -42999.3 q^{62} +68466.0 q^{63} -53281.4 q^{64} +519.536 q^{65} +18577.1 q^{66} -23881.2 q^{67} -13350.2 q^{69} -66349.3 q^{70} -41696.4 q^{71} -87131.4 q^{72} +24549.8 q^{73} -26684.5 q^{74} +33129.3 q^{75} +50470.4 q^{76} -8097.46 q^{77} -2071.87 q^{78} -74466.3 q^{79} -16145.5 q^{80} +158216. q^{81} +6735.06 q^{82} +41757.5 q^{83} +158938. q^{84} +177991. q^{86} +139549. q^{87} +10305.0 q^{88} -88747.9 q^{89} -352592. q^{90} +903.093 q^{91} -22091.5 q^{92} +139727. q^{93} +99864.7 q^{94} +68464.7 q^{95} +198850. q^{96} +84804.4 q^{97} +35121.4 q^{98} -43031.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9}+O(q^{10}) \) 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9	\( 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9} + 304 q^{13} + 4392 q^{15} + 7176 q^{16} + 1896 q^{18} + 9288 q^{19} + 12032 q^{21} + 17692 q^{25} + 29600 q^{26} - 17784 q^{30} + 19032 q^{32} + 38800 q^{33} + 26056 q^{35} + 77816 q^{36} + 36384 q^{38} + 123904 q^{42} + 46520 q^{43} + 71808 q^{47} + 38748 q^{49} + 241632 q^{50} + 6008 q^{52} + 61360 q^{53} + 46680 q^{55} + 256920 q^{59} + 330504 q^{60} - 72496 q^{64} + 10736 q^{66} + 250608 q^{67} - 107696 q^{69} + 273320 q^{70} + 463640 q^{72} + 974048 q^{76} + 482672 q^{77} + 242060 q^{81} + 458584 q^{83} + 1605472 q^{84} + 718272 q^{86} + 1009400 q^{87} + 501088 q^{89} + 903248 q^{93} + 1315264 q^{94} - 156256 q^{98}+O(q^{100}) \) 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9 + 304 * q^13 + 4392 * q^15 + 7176 * q^16 + 1896 * q^18 + 9288 * q^19 + 12032 * q^21 + 17692 * q^25 + 29600 * q^26 - 17784 * q^30 + 19032 * q^32 + 38800 * q^33 + 26056 * q^35 + 77816 * q^36 + 36384 * q^38 + 123904 * q^42 + 46520 * q^43 + 71808 * q^47 + 38748 * q^49 + 241632 * q^50 + 6008 * q^52 + 61360 * q^53 + 46680 * q^55 + 256920 * q^59 + 330504 * q^60 - 72496 * q^64 + 10736 * q^66 + 250608 * q^67 - 107696 * q^69 + 273320 * q^70 + 463640 * q^72 + 974048 * q^76 + 482672 * q^77 + 242060 * q^81 + 458584 * q^83 + 1605472 * q^84 + 718272 * q^86 + 1009400 * q^87 + 501088 * q^89 + 903248 * q^93 + 1315264 * q^94 - 156256 * q^98

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