LMFDB - Embedded newform 1587.4.a.w.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1587,4,Mod(1,1587)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1587, 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("1587.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1587 = 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1587.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:	$93.6360311791$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	1587.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39239 q^{2} -3.00000 q^{3} -2.27649 q^{4} +14.9344 q^{5} +7.17716 q^{6} +25.5860 q^{7} +24.5853 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.39239 q^{2} -3.00000 q^{3} -2.27649 q^{4} +14.9344 q^{5} +7.17716 q^{6} +25.5860 q^{7} +24.5853 q^{8} +9.00000 q^{9} -35.7289 q^{10} +18.1855 q^{11} +6.82947 q^{12} -90.0393 q^{13} -61.2116 q^{14} -44.8032 q^{15} -40.6057 q^{16} -0.600139 q^{17} -21.5315 q^{18} +93.5751 q^{19} -33.9981 q^{20} -76.7581 q^{21} -43.5068 q^{22} -73.7560 q^{24} +98.0367 q^{25} +215.409 q^{26} -27.0000 q^{27} -58.2464 q^{28} +72.0946 q^{29} +107.187 q^{30} +260.686 q^{31} -99.5382 q^{32} -54.5565 q^{33} +1.43576 q^{34} +382.112 q^{35} -20.4884 q^{36} +129.151 q^{37} -223.868 q^{38} +270.118 q^{39} +367.168 q^{40} -225.266 q^{41} +183.635 q^{42} +471.059 q^{43} -41.3992 q^{44} +134.410 q^{45} +194.164 q^{47} +121.817 q^{48} +311.645 q^{49} -234.542 q^{50} +1.80042 q^{51} +204.974 q^{52} -487.987 q^{53} +64.5944 q^{54} +271.590 q^{55} +629.041 q^{56} -280.725 q^{57} -172.478 q^{58} +139.003 q^{59} +101.994 q^{60} -377.461 q^{61} -623.660 q^{62} +230.274 q^{63} +562.979 q^{64} -1344.68 q^{65} +130.520 q^{66} +309.963 q^{67} +1.36621 q^{68} -914.160 q^{70} +905.640 q^{71} +221.268 q^{72} +322.123 q^{73} -308.980 q^{74} -294.110 q^{75} -213.023 q^{76} +465.295 q^{77} -646.226 q^{78} -977.837 q^{79} -606.422 q^{80} +81.0000 q^{81} +538.923 q^{82} +1054.55 q^{83} +174.739 q^{84} -8.96273 q^{85} -1126.95 q^{86} -216.284 q^{87} +447.097 q^{88} -947.664 q^{89} -321.560 q^{90} -2303.75 q^{91} -782.057 q^{93} -464.514 q^{94} +1397.49 q^{95} +298.615 q^{96} -1229.55 q^{97} -745.574 q^{98} +163.670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} + 52 q^{5} - 6 q^{6} - 2 q^{7} + 18 q^{8} + 270 q^{9}+O(q^{10}) $ 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 + 52 * q^5 - 6 * q^6 - 2 * q^7 + 18 * q^8 + 270 * q^9	\( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} + 52 q^{5} - 6 q^{6} - 2 q^{7} + 18 q^{8} + 270 q^{9} - 39 q^{10} + 126 q^{11} - 354 q^{12} + 14 q^{13} + 42 q^{14} - 156 q^{15} + 438 q^{16} + 340 q^{17} + 18 q^{18} - 156 q^{19} + 617 q^{20} + 6 q^{21} + 311 q^{22} - 54 q^{24} + 624 q^{25} + 398 q^{26} - 810 q^{27} + 468 q^{28} - 196 q^{29} + 117 q^{30} - 380 q^{31} + 46 q^{32} - 378 q^{33} + 64 q^{34} - 636 q^{35} + 1062 q^{36} + 1082 q^{37} + 747 q^{38} - 42 q^{39} - 623 q^{40} + 768 q^{41} - 126 q^{42} + 68 q^{43} + 1657 q^{44} + 468 q^{45} - 720 q^{47} - 1314 q^{48} + 2926 q^{49} - 1008 q^{50} - 1020 q^{51} + 482 q^{52} + 2720 q^{53} - 54 q^{54} - 336 q^{55} + 576 q^{56} + 468 q^{57} - 690 q^{58} + 80 q^{59} - 1851 q^{60} + 906 q^{61} - 110 q^{62} - 18 q^{63} + 5740 q^{64} + 3490 q^{65} - 933 q^{66} + 1294 q^{67} + 2802 q^{68} + 1492 q^{70} - 1350 q^{71} + 162 q^{72} - 1824 q^{73} + 2629 q^{74} - 1872 q^{75} - 585 q^{76} - 864 q^{77} - 1194 q^{78} - 3540 q^{79} + 5233 q^{80} + 2430 q^{81} + 2166 q^{82} + 1410 q^{83} - 1404 q^{84} + 2468 q^{85} + 1597 q^{86} + 588 q^{87} + 5645 q^{88} + 2022 q^{89} - 351 q^{90} - 2718 q^{91} + 1140 q^{93} - 1548 q^{94} + 9230 q^{95} - 138 q^{96} + 2926 q^{97} - 11775 q^{98} + 1134 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 + 52 * q^5 - 6 * q^6 - 2 * q^7 + 18 * q^8 + 270 * q^9 - 39 * q^10 + 126 * q^11 - 354 * q^12 + 14 * q^13 + 42 * q^14 - 156 * q^15 + 438 * q^16 + 340 * q^17 + 18 * q^18 - 156 * q^19 + 617 * q^20 + 6 * q^21 + 311 * q^22 - 54 * q^24 + 624 * q^25 + 398 * q^26 - 810 * q^27 + 468 * q^28 - 196 * q^29 + 117 * q^30 - 380 * q^31 + 46 * q^32 - 378 * q^33 + 64 * q^34 - 636 * q^35 + 1062 * q^36 + 1082 * q^37 + 747 * q^38 - 42 * q^39 - 623 * q^40 + 768 * q^41 - 126 * q^42 + 68 * q^43 + 1657 * q^44 + 468 * q^45 - 720 * q^47 - 1314 * q^48 + 2926 * q^49 - 1008 * q^50 - 1020 * q^51 + 482 * q^52 + 2720 * q^53 - 54 * q^54 - 336 * q^55 + 576 * q^56 + 468 * q^57 - 690 * q^58 + 80 * q^59 - 1851 * q^60 + 906 * q^61 - 110 * q^62 - 18 * q^63 + 5740 * q^64 + 3490 * q^65 - 933 * q^66 + 1294 * q^67 + 2802 * q^68 + 1492 * q^70 - 1350 * q^71 + 162 * q^72 - 1824 * q^73 + 2629 * q^74 - 1872 * q^75 - 585 * q^76 - 864 * q^77 - 1194 * q^78 - 3540 * q^79 + 5233 * q^80 + 2430 * q^81 + 2166 * q^82 + 1410 * q^83 - 1404 * q^84 + 2468 * q^85 + 1597 * q^86 + 588 * q^87 + 5645 * q^88 + 2022 * q^89 - 351 * q^90 - 2718 * q^91 + 1140 * q^93 - 1548 * q^94 + 9230 * q^95 - 138 * q^96 + 2926 * q^97 - 11775 * q^98 + 1134 * 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 $

$2$	−2.39239	−0.845836	−0.422918	−	0.906168i	$-0.638994\pi$
$2$	−2.39239	−0.845836	−0.422918	+	0.906168i	$0.638994\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−2.27649	−0.284561
$5$	14.9344	1.33577	0.667887	−	0.744262i	$-0.267199\pi$
$5$	14.9344	1.33577	0.667887	+	0.744262i	$0.267199\pi$
$6$	7.17716	0.488344
$7$	25.5860	1.38152	0.690758	−	0.723086i	$-0.257277\pi$
$7$	25.5860	1.38152	0.690758	+	0.723086i	$0.257277\pi$
$8$	24.5853	1.08653
$9$	9.00000	0.333333
$10$	−35.7289	−1.12985
$11$	18.1855	0.498467	0.249234	−	0.968443i	$-0.419821\pi$
$11$	18.1855	0.498467	0.249234	+	0.968443i	$0.419821\pi$
$12$	6.82947	0.164292
$13$	−90.0393	−1.92096	−0.960478	−	0.278357i	$-0.910210\pi$
$13$	−90.0393	−1.92096	−0.960478	+	0.278357i	$0.910210\pi$
$14$	−61.2116	−1.16854
$15$	−44.8032	−0.771210
$16$	−40.6057	−0.634463
$17$	−0.600139	−0.00856207	−0.00428103	−	0.999991i	$-0.501363\pi$
$17$	−0.600139	−0.00856207	−0.00428103	+	0.999991i	$0.501363\pi$
$18$	−21.5315	−0.281945
$19$	93.5751	1.12987	0.564937	−	0.825134i	$-0.308900\pi$
$19$	93.5751	1.12987	0.564937	+	0.825134i	$0.308900\pi$
$20$	−33.9981	−0.380110
$21$	−76.7581	−0.797618
$22$	−43.5068	−0.421621
$23$	0	0
$23$	0	0
$24$	−73.7560	−0.627307
$25$	98.0367	0.784294
$26$	215.409	1.62481
$27$	−27.0000	−0.192450
$28$	−58.2464	−0.393126
$29$	72.0946	0.461643	0.230821	−	0.972996i	$-0.425859\pi$
$29$	72.0946	0.461643	0.230821	+	0.972996i	$0.425859\pi$
$30$	107.187	0.652317
$31$	260.686	1.51034	0.755170	−	0.655530i	$-0.227555\pi$
$31$	260.686	1.51034	0.755170	+	0.655530i	$0.227555\pi$
$32$	−99.5382	−0.549876
$33$	−54.5565	−0.287790
$34$	1.43576	0.00724211
$35$	382.112	1.84539
$36$	−20.4884	−0.0948538
$37$	129.151	0.573847	0.286924	−	0.957953i	$-0.407367\pi$
$37$	129.151	0.573847	0.286924	+	0.957953i	$0.407367\pi$
$38$	−223.868	−0.955688
$39$	270.118	1.10906
$40$	367.168	1.45136
$41$	−225.266	−0.858064	−0.429032	−	0.903289i	$-0.641145\pi$
$41$	−225.266	−0.858064	−0.429032	+	0.903289i	$0.641145\pi$
$42$	183.635	0.674654
$43$	471.059	1.67060	0.835300	−	0.549794i	$-0.185294\pi$
$43$	471.059	1.67060	0.835300	+	0.549794i	$0.185294\pi$
$44$	−41.3992	−0.141844
$45$	134.410	0.445258
$46$	0	0
$47$	194.164	0.602589	0.301294	−	0.953531i	$-0.402581\pi$
$47$	194.164	0.602589	0.301294	+	0.953531i	$0.402581\pi$
$48$	121.817	0.366308
$49$	311.645	0.908585
$50$	−234.542	−0.663384
$51$	1.80042	0.00494331
$52$	204.974	0.546630
$53$	−487.987	−1.26472	−0.632360	−	0.774675i	$-0.717914\pi$
$53$	−487.987	−1.26472	−0.632360	+	0.774675i	$0.717914\pi$
$54$	64.5944	0.162781
$55$	271.590	0.665840
$56$	629.041	1.50106
$57$	−280.725	−0.652333
$58$	−172.478	−0.390474
$59$	139.003	0.306723	0.153361	−	0.988170i	$-0.450990\pi$
$59$	139.003	0.306723	0.153361	+	0.988170i	$0.450990\pi$
$60$	101.994	0.219457
$61$	−377.461	−0.792278	−0.396139	−	0.918190i	$-0.629650\pi$
$61$	−377.461	−0.792278	−0.396139	+	0.918190i	$0.629650\pi$
$62$	−623.660	−1.27750
$63$	230.274	0.460505
$64$	562.979	1.09957
$65$	−1344.68	−2.56596
$66$	130.520	0.243423
$67$	309.963	0.565195	0.282597	−	0.959239i	$-0.408804\pi$
$67$	309.963	0.565195	0.282597	+	0.959239i	$0.408804\pi$
$68$	1.36621	0.00243643
$69$	0	0
$70$	−914.160	−1.56090
$71$	905.640	1.51380	0.756899	−	0.653532i	$-0.226713\pi$
$71$	905.640	1.51380	0.756899	+	0.653532i	$0.226713\pi$
$72$	221.268	0.362176
$73$	322.123	0.516461	0.258230	−	0.966083i	$-0.416861\pi$
$73$	322.123	0.516461	0.258230	+	0.966083i	$0.416861\pi$
$74$	−308.980	−0.485381
$75$	−294.110	−0.452812
$76$	−213.023	−0.321519
$77$	465.295	0.688640
$78$	−646.226	−0.938086
$79$	−977.837	−1.39260	−0.696299	−	0.717752i	$-0.745171\pi$
$79$	−977.837	−1.39260	−0.696299	+	0.717752i	$0.745171\pi$
$80$	−606.422	−0.847500
$81$	81.0000	0.111111
$82$	538.923	0.725782
$83$	1054.55	1.39460	0.697302	−	0.716777i	$-0.254384\pi$
$83$	1054.55	1.39460	0.697302	+	0.716777i	$0.254384\pi$
$84$	174.739	0.226971
$85$	−8.96273	−0.0114370
$86$	−1126.95	−1.41305
$87$	−216.284	−0.266529
$88$	447.097	0.541599
$89$	−947.664	−1.12868	−0.564338	−	0.825544i	$-0.690869\pi$
$89$	−947.664	−1.12868	−0.564338	+	0.825544i	$0.690869\pi$
$90$	−321.560	−0.376615
$91$	−2303.75	−2.65383
$92$	0	0
$93$	−782.057	−0.871995
$94$	−464.514	−0.509691
$95$	1397.49	1.50926
$96$	298.615	0.317471
$97$	−1229.55	−1.28703	−0.643515	−	0.765434i	$-0.722524\pi$
$97$	−1229.55	−1.28703	−0.643515	+	0.765434i	$0.722524\pi$
$98$	−745.574	−0.768514
$99$	163.670	0.166156
$100$	−223.180	−0.223180
$101$	−970.312	−0.955937	−0.477969	−	0.878377i	$-0.658627\pi$
$101$	−970.312	−0.955937	−0.477969	+	0.878377i	$0.658627\pi$
$102$	−4.30729	−0.00418123
$103$	387.282	0.370486	0.185243	−	0.982693i	$-0.440693\pi$
$103$	387.282	0.370486	0.185243	+	0.982693i	$0.440693\pi$
$104$	−2213.65	−2.08717
$105$	−1146.34	−1.06544
$106$	1167.45	1.06975
$107$	−462.873	−0.418202	−0.209101	−	0.977894i	$-0.567054\pi$
$107$	−462.873	−0.418202	−0.209101	+	0.977894i	$0.567054\pi$
$108$	61.4653	0.0547639
$109$	514.402	0.452026	0.226013	−	0.974124i	$-0.427431\pi$
$109$	514.402	0.452026	0.226013	+	0.974124i	$0.427431\pi$
$110$	−649.748	−0.563191
$111$	−387.454	−0.331311
$112$	−1038.94	−0.876521
$113$	1229.35	1.02343	0.511714	−	0.859156i	$-0.329011\pi$
$113$	1229.35	1.02343	0.511714	+	0.859156i	$0.329011\pi$
$114$	671.603	0.551767
$115$	0	0
$116$	−164.123	−0.131366
$117$	−810.354	−0.640318
$118$	−332.549	−0.259437
$119$	−15.3552	−0.0118286
$120$	−1101.50	−0.837941
$121$	−1000.29	−0.751531
$122$	903.033	0.670138
$123$	675.798	0.495404
$124$	−593.448	−0.429784
$125$	−402.681	−0.288135
$126$	−550.905	−0.389512
$127$	43.0070	0.0300492	0.0150246	−	0.999887i	$-0.495217\pi$
$127$	43.0070	0.0300492	0.0150246	+	0.999887i	$0.495217\pi$
$128$	−550.557	−0.380178
$129$	−1413.18	−0.964522
$130$	3217.00	2.17038
$131$	1335.93	0.890998	0.445499	−	0.895283i	$-0.353026\pi$
$131$	1335.93	0.890998	0.445499	+	0.895283i	$0.353026\pi$
$132$	124.197	0.0818940
$133$	2394.22	1.56094
$134$	−741.552	−0.478062
$135$	−403.229	−0.257070
$136$	−14.7546	−0.00930293
$137$	284.337	0.177318	0.0886590	−	0.996062i	$-0.471742\pi$
$137$	284.337	0.177318	0.0886590	+	0.996062i	$0.471742\pi$
$138$	0	0
$139$	1353.39	0.825847	0.412923	−	0.910766i	$-0.364508\pi$
$139$	1353.39	0.825847	0.412923	+	0.910766i	$0.364508\pi$
$140$	−869.875	−0.525128
$141$	−582.491	−0.347905
$142$	−2166.64	−1.28043
$143$	−1637.41	−0.957533
$144$	−365.451	−0.211488
$145$	1076.69	0.616650
$146$	−770.642	−0.436841
$147$	−934.934	−0.524572
$148$	−294.012	−0.163295
$149$	1085.81	0.597000	0.298500	−	0.954410i	$-0.403514\pi$
$149$	1085.81	0.597000	0.298500	+	0.954410i	$0.403514\pi$
$150$	703.625	0.383005
$151$	252.961	0.136329	0.0681644	−	0.997674i	$-0.478286\pi$
$151$	252.961	0.136329	0.0681644	+	0.997674i	$0.478286\pi$
$152$	2300.58	1.22764
$153$	−5.40125	−0.00285402
$154$	−1113.16	−0.582477
$155$	3893.19	2.01747
$156$	−614.921	−0.315597
$157$	−104.882	−0.0533151	−0.0266576	−	0.999645i	$-0.508486\pi$
$157$	−104.882	−0.0533151	−0.0266576	+	0.999645i	$0.508486\pi$
$158$	2339.36	1.17791
$159$	1463.96	0.730186
$160$	−1486.55	−0.734511
$161$	0	0
$162$	−193.783	−0.0939818
$163$	1440.97	0.692428	0.346214	−	0.938155i	$-0.387467\pi$
$163$	1440.97	0.692428	0.346214	+	0.938155i	$0.387467\pi$
$164$	512.816	0.244172
$165$	−814.770	−0.384423
$166$	−2522.90	−1.17961
$167$	−1213.39	−0.562245	−0.281123	−	0.959672i	$-0.590707\pi$
$167$	−1213.39	−0.562245	−0.281123	+	0.959672i	$0.590707\pi$
$168$	−1887.12	−0.866635
$169$	5910.08	2.69007
$170$	21.4423	0.00967382
$171$	842.176	0.376625
$172$	−1072.36	−0.475389
$173$	965.580	0.424345	0.212173	−	0.977232i	$-0.431946\pi$
$173$	965.580	0.424345	0.212173	+	0.977232i	$0.431946\pi$
$174$	517.434	0.225440
$175$	2508.37	1.08351
$176$	−738.435	−0.316259
$177$	−417.009	−0.177086
$178$	2267.18	0.954675
$179$	−4130.90	−1.72490	−0.862452	−	0.506138i	$-0.831073\pi$
$179$	−4130.90	−1.72490	−0.862452	+	0.506138i	$0.831073\pi$
$180$	−305.983	−0.126703
$181$	937.624	0.385044	0.192522	−	0.981293i	$-0.438333\pi$
$181$	937.624	0.385044	0.192522	+	0.981293i	$0.438333\pi$
$182$	5511.46	2.24470
$183$	1132.38	0.457422
$184$	0	0
$185$	1928.80	0.766530
$186$	1870.98	0.737565
$187$	−10.9138	−0.00426791
$188$	−442.012	−0.171474
$189$	−690.823	−0.265873
$190$	−3343.33	−1.27658
$191$	4994.15	1.89196	0.945979	−	0.324227i	$-0.105104\pi$
$191$	4994.15	1.89196	0.945979	+	0.324227i	$0.105104\pi$
$192$	−1688.94	−0.634836
$193$	2541.94	0.948047	0.474024	−	0.880512i	$-0.342801\pi$
$193$	2541.94	0.948047	0.474024	+	0.880512i	$0.342801\pi$
$194$	2941.56	1.08862
$195$	4034.05	1.48146
$196$	−709.456	−0.258548
$197$	−2375.92	−0.859276	−0.429638	−	0.903001i	$-0.641359\pi$
$197$	−2375.92	−0.859276	−0.429638	+	0.903001i	$0.641359\pi$
$198$	−391.561	−0.140540
$199$	−2129.44	−0.758554	−0.379277	−	0.925283i	$-0.623827\pi$
$199$	−2129.44	−0.758554	−0.379277	+	0.925283i	$0.623827\pi$
$200$	2410.27	0.852158
$201$	−929.890	−0.326315
$202$	2321.36	0.808566
$203$	1844.61	0.637766
$204$	−4.09864	−0.00140668
$205$	−3364.22	−1.14618
$206$	−926.528	−0.313370
$207$	0	0
$208$	3656.11	1.21878
$209$	1701.71	0.563205
$210$	2742.48	0.901186
$211$	−3256.58	−1.06252	−0.531261	−	0.847208i	$-0.678281\pi$
$211$	−3256.58	−1.06252	−0.531261	+	0.847208i	$0.678281\pi$
$212$	1110.90	0.359890
$213$	−2716.92	−0.873992
$214$	1107.37	0.353730
$215$	7034.99	2.23155
$216$	−663.804	−0.209102
$217$	6669.91	2.08656
$218$	−1230.65	−0.382340
$219$	−966.369	−0.298179
$220$	−618.272	−0.189472
$221$	54.0361	0.0164473
$222$	926.939	0.280235
$223$	−1906.50	−0.572506	−0.286253	−	0.958154i	$-0.592410\pi$
$223$	−1906.50	−0.572506	−0.286253	+	0.958154i	$0.592410\pi$
$224$	−2546.79	−0.759663
$225$	882.331	0.261431
$226$	−2941.08	−0.865653
$227$	961.240	0.281056	0.140528	−	0.990077i	$-0.455120\pi$
$227$	961.240	0.281056	0.140528	+	0.990077i	$0.455120\pi$
$228$	639.069	0.185629
$229$	−2604.64	−0.751614	−0.375807	−	0.926698i	$-0.622634\pi$
$229$	−2604.64	−0.751614	−0.375807	+	0.926698i	$0.622634\pi$
$230$	0	0
$231$	−1395.88	−0.397587
$232$	1772.47	0.501588
$233$	3555.12	0.999587	0.499794	−	0.866145i	$-0.333409\pi$
$233$	3555.12	0.999587	0.499794	+	0.866145i	$0.333409\pi$
$234$	1938.68	0.541604
$235$	2899.72	0.804923
$236$	−316.439	−0.0872814
$237$	2933.51	0.804017
$238$	36.7355	0.0100051
$239$	−2836.87	−0.767789	−0.383894	−	0.923377i	$-0.625417\pi$
$239$	−2836.87	−0.767789	−0.383894	+	0.923377i	$0.625417\pi$
$240$	1819.27	0.489304
$241$	2519.64	0.673463	0.336731	−	0.941601i	$-0.390679\pi$
$241$	2519.64	0.673463	0.336731	+	0.941601i	$0.390679\pi$
$242$	2393.07	0.635672
$243$	−243.000	−0.0641500
$244$	859.288	0.225452
$245$	4654.23	1.21367
$246$	−1616.77	−0.419030
$247$	−8425.44	−2.17044
$248$	6409.04	1.64103
$249$	−3163.66	−0.805175
$250$	963.367	0.243715
$251$	−2200.95	−0.553477	−0.276738	−	0.960945i	$-0.589254\pi$
$251$	−2200.95	−0.553477	−0.276738	+	0.960945i	$0.589254\pi$
$252$	−524.217	−0.131042
$253$	0	0
$254$	−102.889	−0.0254167
$255$	26.8882	0.00660315
$256$	−3186.69	−0.778000
$257$	6350.77	1.54144	0.770720	−	0.637174i	$-0.219897\pi$
$257$	6350.77	1.54144	0.770720	+	0.637174i	$0.219897\pi$
$258$	3380.86	0.815827
$259$	3304.47	0.792779
$260$	3061.16	0.730174
$261$	648.852	0.153881
$262$	−3196.06	−0.753638
$263$	−531.709	−0.124664	−0.0623319	−	0.998055i	$-0.519854\pi$
$263$	−531.709	−0.124664	−0.0623319	+	0.998055i	$0.519854\pi$
$264$	−1341.29	−0.312692
$265$	−7287.80	−1.68938
$266$	−5727.89	−1.32030
$267$	2842.99	0.651641
$268$	−705.629	−0.160833
$269$	−1463.86	−0.331796	−0.165898	−	0.986143i	$-0.553052\pi$
$269$	−1463.86	−0.331796	−0.165898	+	0.986143i	$0.553052\pi$
$270$	964.680	0.217439
$271$	−1798.53	−0.403148	−0.201574	−	0.979473i	$-0.564606\pi$
$271$	−1798.53	−0.403148	−0.201574	+	0.979473i	$0.564606\pi$
$272$	24.3691	0.00543232
$273$	6911.25	1.53219
$274$	−680.244	−0.149982
$275$	1782.85	0.390945
$276$	0	0
$277$	−7250.75	−1.57276	−0.786381	−	0.617741i	$-0.788048\pi$
$277$	−7250.75	−1.57276	−0.786381	+	0.617741i	$0.788048\pi$
$278$	−3237.82	−0.698531
$279$	2346.17	0.503446
$280$	9394.36	2.00507
$281$	174.091	0.0369588	0.0184794	−	0.999829i	$-0.494117\pi$
$281$	174.091	0.0369588	0.0184794	+	0.999829i	$0.494117\pi$
$282$	1393.54	0.294270
$283$	528.478	0.111006	0.0555031	−	0.998459i	$-0.482324\pi$
$283$	528.478	0.111006	0.0555031	+	0.998459i	$0.482324\pi$
$284$	−2061.68	−0.430769
$285$	−4192.47	−0.871370
$286$	3917.32	0.809916
$287$	−5763.66	−1.18543
$288$	−895.844	−0.183292
$289$	−4912.64	−0.999927
$290$	−2575.86	−0.521585
$291$	3688.65	0.743067
$292$	−733.310	−0.146965
$293$	6263.05	1.24878	0.624388	−	0.781114i	$-0.285348\pi$
$293$	6263.05	1.24878	0.624388	+	0.781114i	$0.285348\pi$
$294$	2236.72	0.443702
$295$	2075.93	0.409712
$296$	3175.23	0.623501
$297$	−491.009	−0.0959300
$298$	−2597.68	−0.504964
$299$	0	0
$300$	669.539	0.128853
$301$	12052.5	2.30796
$302$	−605.179	−0.115312
$303$	2910.94	0.551911
$304$	−3799.68	−0.716864
$305$	−5637.17	−1.05831
$306$	12.9219	0.00241404
$307$	4621.96	0.859248	0.429624	−	0.903008i	$-0.358646\pi$
$307$	4621.96	0.859248	0.429624	+	0.903008i	$0.358646\pi$
$308$	−1059.24	−0.195960
$309$	−1161.85	−0.213900
$310$	−9314.00	−1.70645
$311$	8991.10	1.63935	0.819676	−	0.572828i	$-0.194154\pi$
$311$	8991.10	1.63935	0.819676	+	0.572828i	$0.194154\pi$
$312$	6640.94	1.20503
$313$	1236.01	0.223206	0.111603	−	0.993753i	$-0.464402\pi$
$313$	1236.01	0.223206	0.111603	+	0.993753i	$0.464402\pi$
$314$	250.918	0.0450959
$315$	3439.01	0.615131
$316$	2226.04	0.396280
$317$	2438.23	0.432002	0.216001	−	0.976393i	$-0.430699\pi$
$317$	2438.23	0.432002	0.216001	+	0.976393i	$0.430699\pi$
$318$	−3502.36	−0.617618
$319$	1311.08	0.230114
$320$	8407.76	1.46878
$321$	1388.62	0.241449
$322$	0	0
$323$	−56.1581	−0.00967406
$324$	−184.396	−0.0316179
$325$	−8827.16	−1.50659
$326$	−3447.37	−0.585681
$327$	−1543.21	−0.260977
$328$	−5538.24	−0.932311
$329$	4967.88	0.832486
$330$	1949.24	0.325159
$331$	5288.69	0.878226	0.439113	−	0.898432i	$-0.355293\pi$
$331$	5288.69	0.878226	0.439113	+	0.898432i	$0.355293\pi$
$332$	−2400.68	−0.396851
$333$	1162.36	0.191282
$334$	2902.90	0.475567
$335$	4629.12	0.754973
$336$	3116.81	0.506060
$337$	590.245	0.0954087	0.0477043	−	0.998862i	$-0.484809\pi$
$337$	590.245	0.0954087	0.0477043	+	0.998862i	$0.484809\pi$
$338$	−14139.2	−2.27536
$339$	−3688.05	−0.590877
$340$	20.4036	0.00325453
$341$	4740.70	0.752854
$342$	−2014.81	−0.318563
$343$	−802.257	−0.126291
$344$	11581.1	1.81516
$345$	0	0
$346$	−2310.04	−0.358926
$347$	−5190.46	−0.802992	−0.401496	−	0.915861i	$-0.631510\pi$
$347$	−5190.46	−0.802992	−0.401496	+	0.915861i	$0.631510\pi$
$348$	492.368	0.0758440
$349$	10789.1	1.65481	0.827405	−	0.561606i	$-0.189816\pi$
$349$	10789.1	1.65481	0.827405	+	0.561606i	$0.189816\pi$
$350$	−6000.99	−0.916475
$351$	2431.06	0.369688
$352$	−1810.15	−0.274095
$353$	−5054.84	−0.762159	−0.381080	−	0.924542i	$-0.624448\pi$
$353$	−5054.84	−0.762159	−0.381080	+	0.924542i	$0.624448\pi$
$354$	997.646	0.149786
$355$	13525.2	2.02209
$356$	2157.35	0.321178
$357$	46.0655	0.00682926
$358$	9882.71	1.45899
$359$	4624.63	0.679885	0.339942	−	0.940446i	$-0.389592\pi$
$359$	4624.63	0.679885	0.339942	+	0.940446i	$0.389592\pi$
$360$	3304.51	0.483786
$361$	1897.30	0.276615
$362$	−2243.16	−0.325684
$363$	3000.86	0.433896
$364$	5244.46	0.755177
$365$	4810.72	0.689875
$366$	−2709.10	−0.386904
$367$	2474.30	0.351927	0.175964	−	0.984397i	$-0.443696\pi$
$367$	2474.30	0.351927	0.175964	+	0.984397i	$0.443696\pi$
$368$	0	0
$369$	−2027.39	−0.286021
$370$	−4614.43	−0.648359
$371$	−12485.6	−1.74723
$372$	1780.35	0.248136
$373$	6332.18	0.879002	0.439501	−	0.898242i	$-0.355155\pi$
$373$	6332.18	0.879002	0.439501	+	0.898242i	$0.355155\pi$
$374$	26.1101	0.00360995
$375$	1208.04	0.166355
$376$	4773.58	0.654730
$377$	−6491.35	−0.886795
$378$	1652.71	0.224885
$379$	−13070.0	−1.77140	−0.885699	−	0.464260i	$-0.846320\pi$
$379$	−13070.0	−1.77140	−0.885699	+	0.464260i	$0.846320\pi$
$380$	−3181.37	−0.429476
$381$	−129.021	−0.0173489
$382$	−11947.9	−1.60029
$383$	7997.48	1.06698	0.533488	−	0.845807i	$-0.320881\pi$
$383$	7997.48	1.06698	0.533488	+	0.845807i	$0.320881\pi$
$384$	1651.67	0.219496
$385$	6948.91	0.919868
$386$	−6081.31	−0.801893
$387$	4239.53	0.556867
$388$	2799.06	0.366239
$389$	2648.47	0.345200	0.172600	−	0.984992i	$-0.444783\pi$
$389$	2648.47	0.345200	0.172600	+	0.984992i	$0.444783\pi$
$390$	−9651.01	−1.25307
$391$	0	0
$392$	7661.89	0.987204
$393$	−4007.79	−0.514418
$394$	5684.12	0.726807
$395$	−14603.4	−1.86020
$396$	−372.592	−0.0472815
$397$	−13113.9	−1.65786	−0.828929	−	0.559354i	$-0.811049\pi$
$397$	−13113.9	−1.65786	−0.828929	+	0.559354i	$0.811049\pi$
$398$	5094.45	0.641612
$399$	−7182.65	−0.901208
$400$	−3980.85	−0.497606
$401$	−4259.58	−0.530456	−0.265228	−	0.964186i	$-0.585447\pi$
$401$	−4259.58	−0.530456	−0.265228	+	0.964186i	$0.585447\pi$
$402$	2224.65	0.276009
$403$	−23472.0	−2.90129
$404$	2208.91	0.272023
$405$	1209.69	0.148419
$406$	−4413.03	−0.539446
$407$	2348.68	0.286044
$408$	44.2639	0.00537105
$409$	−6187.28	−0.748023	−0.374012	−	0.927424i	$-0.622018\pi$
$409$	−6187.28	−0.748023	−0.374012	+	0.927424i	$0.622018\pi$
$410$	8048.50	0.969481
$411$	−853.011	−0.102375
$412$	−881.644	−0.105426
$413$	3556.53	0.423742
$414$	0	0
$415$	15749.1	1.86288
$416$	8962.36	1.05629
$417$	−4060.16	−0.476803
$418$	−4071.15	−0.476379
$419$	6931.63	0.808191	0.404096	−	0.914717i	$-0.367586\pi$
$419$	6931.63	0.808191	0.404096	+	0.914717i	$0.367586\pi$
$420$	2609.63	0.303183
$421$	7652.32	0.885869	0.442935	−	0.896554i	$-0.353937\pi$
$421$	7652.32	0.885869	0.442935	+	0.896554i	$0.353937\pi$
$422$	7790.99	0.898719
$423$	1747.47	0.200863
$424$	−11997.3	−1.37415
$425$	−58.8357	−0.00671518
$426$	6499.92	0.739254
$427$	−9657.74	−1.09455
$428$	1053.73	0.119004
$429$	4912.23	0.552832
$430$	−16830.4	−1.88752
$431$	910.576	0.101765	0.0508827	−	0.998705i	$-0.483797\pi$
$431$	910.576	0.101765	0.0508827	+	0.998705i	$0.483797\pi$
$432$	1096.35	0.122103
$433$	−10249.3	−1.13753	−0.568763	−	0.822501i	$-0.692578\pi$
$433$	−10249.3	−1.13753	−0.568763	+	0.822501i	$0.692578\pi$
$434$	−15957.0	−1.76489
$435$	−3230.07	−0.356023
$436$	−1171.03	−0.128629
$437$	0	0
$438$	2311.93	0.252210
$439$	12083.3	1.31368	0.656841	−	0.754029i	$-0.271892\pi$
$439$	12083.3	1.31368	0.656841	+	0.754029i	$0.271892\pi$
$440$	6677.13	0.723454
$441$	2804.80	0.302862
$442$	−129.275	−0.0139118
$443$	10876.1	1.16646	0.583228	−	0.812308i	$-0.301789\pi$
$443$	10876.1	1.16646	0.583228	+	0.812308i	$0.301789\pi$
$444$	882.035	0.0942783
$445$	−14152.8	−1.50766
$446$	4561.09	0.484246
$447$	−3257.43	−0.344678
$448$	14404.4	1.51907
$449$	10490.0	1.10257	0.551284	−	0.834318i	$-0.314138\pi$
$449$	10490.0	1.10257	0.551284	+	0.834318i	$0.314138\pi$
$450$	−2110.88	−0.221128
$451$	−4096.58	−0.427717
$452$	−2798.60	−0.291228
$453$	−758.882	−0.0787094
$454$	−2299.66	−0.237727
$455$	−34405.1	−3.54492
$456$	−6901.73	−0.708778
$457$	−19060.4	−1.95100	−0.975499	−	0.220002i	$-0.929393\pi$
$457$	−19060.4	−1.95100	−0.975499	+	0.220002i	$0.929393\pi$
$458$	6231.31	0.635742
$459$	16.2038	0.00164777
$460$	0	0
$461$	12528.0	1.26570	0.632852	−	0.774273i	$-0.281884\pi$
$461$	12528.0	1.26570	0.632852	+	0.774273i	$0.281884\pi$
$462$	3339.49	0.336293
$463$	14679.0	1.47342	0.736710	−	0.676209i	$-0.236379\pi$
$463$	14679.0	1.47342	0.736710	+	0.676209i	$0.236379\pi$
$464$	−2927.45	−0.292895
$465$	−11679.6	−1.16479
$466$	−8505.22	−0.845487
$467$	7724.66	0.765427	0.382714	−	0.923867i	$-0.374990\pi$
$467$	7724.66	0.765427	0.382714	+	0.923867i	$0.374990\pi$
$468$	1844.76	0.182210
$469$	7930.73	0.780825
$470$	−6937.25	−0.680833
$471$	314.645	0.0307815
$472$	3417.43	0.333263
$473$	8566.45	0.832740
$474$	−7018.09	−0.680066
$475$	9173.80	0.886153
$476$	34.9559	0.00336597
$477$	−4391.88	−0.421573
$478$	6786.88	0.649424
$479$	−2127.16	−0.202907	−0.101453	−	0.994840i	$-0.532349\pi$
$479$	−2127.16	−0.202907	−0.101453	+	0.994840i	$0.532349\pi$
$480$	4459.64	0.424070
$481$	−11628.7	−1.10233
$482$	−6027.96	−0.569639
$483$	0	0
$484$	2277.14	0.213857
$485$	−18362.6	−1.71918
$486$	581.350	0.0542604
$487$	3312.11	0.308185	0.154092	−	0.988056i	$-0.450755\pi$
$487$	3312.11	0.308185	0.154092	+	0.988056i	$0.450755\pi$
$488$	−9280.01	−0.860833
$489$	−4322.92	−0.399774
$490$	−11134.7	−1.02656
$491$	14203.7	1.30551	0.652755	−	0.757569i	$-0.273613\pi$
$491$	14203.7	1.30551	0.652755	+	0.757569i	$0.273613\pi$
$492$	−1538.45	−0.140973
$493$	−43.2668	−0.00395261
$494$	20156.9	1.83583
$495$	2444.31	0.221947
$496$	−10585.3	−0.958255
$497$	23171.7	2.09134
$498$	7568.69	0.681046
$499$	19048.0	1.70883	0.854416	−	0.519589i	$-0.173915\pi$
$499$	19048.0	1.70883	0.854416	+	0.519589i	$0.173915\pi$
$500$	916.699	0.0819920
$501$	3640.17	0.324612
$502$	5265.52	0.468151
$503$	4759.49	0.421899	0.210949	−	0.977497i	$-0.432344\pi$
$503$	4759.49	0.421899	0.210949	+	0.977497i	$0.432344\pi$
$504$	5661.37	0.500352
$505$	−14491.0	−1.27692
$506$	0	0
$507$	−17730.2	−1.55311
$508$	−97.9050	−0.00855085
$509$	−10139.4	−0.882953	−0.441476	−	0.897273i	$-0.645545\pi$
$509$	−10139.4	−0.882953	−0.441476	+	0.897273i	$0.645545\pi$
$510$	−64.3269	−0.00558518
$511$	8241.85	0.713499
$512$	12028.2	1.03824
$513$	−2526.53	−0.217444
$514$	−15193.5	−1.30381
$515$	5783.83	0.494885
$516$	3217.09	0.274466
$517$	3530.96	0.300371
$518$	−7905.56	−0.670561
$519$	−2896.74	−0.244996
$520$	−33059.5	−2.78799
$521$	−13250.8	−1.11426	−0.557128	−	0.830427i	$-0.688097\pi$
$521$	−13250.8	−1.11426	−0.557128	+	0.830427i	$0.688097\pi$
$522$	−1552.30	−0.130158
$523$	12599.4	1.05341	0.526703	−	0.850049i	$-0.323428\pi$
$523$	12599.4	1.05341	0.526703	+	0.850049i	$0.323428\pi$
$524$	−3041.23	−0.253544
$525$	−7525.11	−0.625567
$526$	1272.05	0.105445
$527$	−156.448	−0.0129316
$528$	2215.30	0.182592
$529$	0	0
$530$	17435.2	1.42894
$531$	1251.03	0.102241
$532$	−5450.41	−0.444183
$533$	20282.8	1.64830
$534$	−6801.53	−0.551182
$535$	−6912.73	−0.558623
$536$	7620.55	0.614100
$537$	12392.7	0.995874
$538$	3502.12	0.280645
$539$	5667.42	0.452900
$540$	917.948	0.0731522
$541$	10107.0	0.803201	0.401601	−	0.915815i	$-0.368454\pi$
$541$	10107.0	0.803201	0.401601	+	0.915815i	$0.368454\pi$
$542$	4302.78	0.340997
$543$	−2812.87	−0.222305
$544$	59.7368	0.00470808
$545$	7682.30	0.603805
$546$	−16534.4	−1.29598
$547$	7550.20	0.590171	0.295085	−	0.955471i	$-0.404652\pi$
$547$	7550.20	0.590171	0.295085	+	0.955471i	$0.404652\pi$
$548$	−647.291	−0.0504578
$549$	−3397.15	−0.264093
$550$	−4265.26	−0.330675
$551$	6746.26	0.521598
$552$	0	0
$553$	−25019.0	−1.92390
$554$	17346.6	1.33030
$555$	−5786.40	−0.442557
$556$	−3080.97	−0.235004
$557$	22986.2	1.74858	0.874288	−	0.485408i	$-0.161329\pi$
$557$	22986.2	1.74858	0.874288	+	0.485408i	$0.161329\pi$
$558$	−5612.94	−0.425833
$559$	−42413.8	−3.20915
$560$	−15515.9	−1.17083
$561$	32.7415	0.00246408
$562$	−416.493	−0.0312611
$563$	−12389.0	−0.927414	−0.463707	−	0.885988i	$-0.653481\pi$
$563$	−12389.0	−0.927414	−0.463707	+	0.885988i	$0.653481\pi$
$564$	1326.04	0.0990003
$565$	18359.6	1.36707
$566$	−1264.32	−0.0938930
$567$	2072.47	0.153502
$568$	22265.5	1.64478
$569$	20364.3	1.50038	0.750191	−	0.661221i	$-0.229961\pi$
$569$	20364.3	1.50038	0.750191	+	0.661221i	$0.229961\pi$
$570$	10030.0	0.737036
$571$	13850.8	1.01512	0.507562	−	0.861615i	$-0.330547\pi$
$571$	13850.8	1.01512	0.507562	+	0.861615i	$0.330547\pi$
$572$	3727.55	0.272477
$573$	−14982.5	−1.09232
$574$	13788.9	1.00268
$575$	0	0
$576$	5066.81	0.366523
$577$	−8219.09	−0.593007	−0.296504	−	0.955032i	$-0.595821\pi$
$577$	−8219.09	−0.593007	−0.296504	+	0.955032i	$0.595821\pi$
$578$	11752.9	0.845774
$579$	−7625.83	−0.547355
$580$	−2451.08	−0.175475
$581$	26981.8	1.92667
$582$	−8824.67	−0.628512
$583$	−8874.29	−0.630421
$584$	7919.50	0.561149
$585$	−12102.2	−0.855321
$586$	−14983.6	−1.05626
$587$	−3494.26	−0.245696	−0.122848	−	0.992425i	$-0.539203\pi$
$587$	−3494.26	−0.245696	−0.122848	+	0.992425i	$0.539203\pi$
$588$	2128.37	0.149273
$589$	24393.7	1.70649
$590$	−4966.42	−0.346550
$591$	7127.77	0.496104
$592$	−5244.27	−0.364085
$593$	9799.96	0.678644	0.339322	−	0.940670i	$-0.389802\pi$
$593$	9799.96	0.678644	0.339322	+	0.940670i	$0.389802\pi$
$594$	1174.68	0.0811411
$595$	−229.321	−0.0158004
$596$	−2471.84	−0.169883
$597$	6388.33	0.437951
$598$	0	0
$599$	−14512.6	−0.989932	−0.494966	−	0.868912i	$-0.664820\pi$
$599$	−14512.6	−0.989932	−0.494966	+	0.868912i	$0.664820\pi$
$600$	−7230.80	−0.491993
$601$	−7846.19	−0.532534	−0.266267	−	0.963899i	$-0.585790\pi$
$601$	−7846.19	−0.532534	−0.266267	+	0.963899i	$0.585790\pi$
$602$	−28834.3	−1.95216
$603$	2789.67	0.188398
$604$	−575.862	−0.0387939
$605$	−14938.7	−1.00388
$606$	−6964.08	−0.466826
$607$	−5572.13	−0.372596	−0.186298	−	0.982493i	$-0.559649\pi$
$607$	−5572.13	−0.372596	−0.186298	+	0.982493i	$0.559649\pi$
$608$	−9314.30	−0.621291
$609$	−5533.84	−0.368215
$610$	13486.3	0.895153
$611$	−17482.4	−1.15755
$612$	12.2959	0.000812145 0
$613$	−20619.6	−1.35859	−0.679295	−	0.733865i	$-0.737714\pi$
$613$	−20619.6	−1.35859	−0.679295	+	0.733865i	$0.737714\pi$
$614$	−11057.5	−0.726783
$615$	10092.6	0.661748
$616$	11439.4	0.748227
$617$	12738.1	0.831143	0.415572	−	0.909560i	$-0.363582\pi$
$617$	12738.1	0.831143	0.415572	+	0.909560i	$0.363582\pi$
$618$	2779.58	0.180924
$619$	−5880.95	−0.381866	−0.190933	−	0.981603i	$-0.561151\pi$
$619$	−5880.95	−0.381866	−0.190933	+	0.981603i	$0.561151\pi$
$620$	−8862.80	−0.574095
$621$	0	0
$622$	−21510.2	−1.38662
$623$	−24246.9	−1.55928
$624$	−10968.3	−0.703661
$625$	−18268.4	−1.16918
$626$	−2957.01	−0.188795
$627$	−5105.13	−0.325167
$628$	238.762	0.0151714
$629$	−77.5088	−0.00491332
$630$	−8227.44	−0.520300
$631$	−3751.31	−0.236667	−0.118334	−	0.992974i	$-0.537755\pi$
$631$	−3751.31	−0.236667	−0.118334	+	0.992974i	$0.537755\pi$
$632$	−24040.4	−1.51310
$633$	9769.73	0.613447
$634$	−5833.19	−0.365403
$635$	642.284	0.0401390
$636$	−3332.69	−0.207783
$637$	−28060.3	−1.74535
$638$	−3136.60	−0.194638
$639$	8150.76	0.504599
$640$	−8222.25	−0.507833
$641$	−18932.7	−1.16661	−0.583305	−	0.812253i	$-0.698241\pi$
$641$	−18932.7	−1.16661	−0.583305	+	0.812253i	$0.698241\pi$
$642$	−3322.11	−0.204226
$643$	−10695.9	−0.655994	−0.327997	−	0.944679i	$-0.606374\pi$
$643$	−10695.9	−0.655994	−0.327997	+	0.944679i	$0.606374\pi$
$644$	0	0
$645$	−21105.0	−1.28838
$646$	134.352	0.00818267
$647$	30022.8	1.82429	0.912146	−	0.409866i	$-0.134424\pi$
$647$	30022.8	1.82429	0.912146	+	0.409866i	$0.134424\pi$
$648$	1991.41	0.120725
$649$	2527.84	0.152891
$650$	21118.0	1.27433
$651$	−20009.7	−1.20467
$652$	−3280.37	−0.197038
$653$	20335.6	1.21867	0.609335	−	0.792913i	$-0.291436\pi$
$653$	20335.6	1.21867	0.609335	+	0.792913i	$0.291436\pi$
$654$	3691.95	0.220744
$655$	19951.3	1.19017
$656$	9147.07	0.544410
$657$	2899.11	0.172154
$658$	−11885.1	−0.704147
$659$	−12744.6	−0.753353	−0.376677	−	0.926345i	$-0.622933\pi$
$659$	−12744.6	−0.753353	−0.376677	+	0.926345i	$0.622933\pi$
$660$	1854.82	0.109392
$661$	−20256.5	−1.19196	−0.595980	−	0.802999i	$-0.703236\pi$
$661$	−20256.5	−1.19196	−0.595980	+	0.802999i	$0.703236\pi$
$662$	−12652.6	−0.742836
$663$	−162.108	−0.00949588
$664$	25926.5	1.51528
$665$	35756.2	2.08506
$666$	−2780.82	−0.161794
$667$	0	0
$668$	2762.27	0.159993
$669$	5719.51	0.330537
$670$	−11074.6	−0.638583
$671$	−6864.33	−0.394925
$672$	7640.36	0.438591
$673$	25011.7	1.43258	0.716292	−	0.697801i	$-0.245838\pi$
$673$	25011.7	1.43258	0.716292	+	0.697801i	$0.245838\pi$
$674$	−1412.09	−0.0807001
$675$	−2646.99	−0.150937
$676$	−13454.2	−0.765490
$677$	−5853.38	−0.332295	−0.166147	−	0.986101i	$-0.553133\pi$
$677$	−5853.38	−0.332295	−0.166147	+	0.986101i	$0.553133\pi$
$678$	8823.23	0.499785
$679$	−31459.3	−1.77805
$680$	−220.352	−0.0124266
$681$	−2883.72	−0.162268
$682$	−11341.6	−0.636791
$683$	13691.4	0.767037	0.383519	−	0.923533i	$-0.374712\pi$
$683$	13691.4	0.767037	0.383519	+	0.923533i	$0.374712\pi$
$684$	−1917.21	−0.107173
$685$	4246.41	0.236857
$686$	1919.31	0.106821
$687$	7813.93	0.433945
$688$	−19127.7	−1.05994
$689$	43938.0	2.42947
$690$	0	0
$691$	−26534.1	−1.46079	−0.730395	−	0.683025i	$-0.760664\pi$
$691$	−26534.1	−1.46079	−0.730395	+	0.683025i	$0.760664\pi$
$692$	−2198.14	−0.120752
$693$	4187.65	0.229547
$694$	12417.6	0.679200
$695$	20212.0	1.10314
$696$	−5317.41	−0.289592
$697$	135.191	0.00734680
$698$	−25811.7	−1.39970
$699$	−10665.4	−0.577112
$700$	−5710.28	−0.308326
$701$	31136.5	1.67761	0.838807	−	0.544429i	$-0.183253\pi$
$701$	31136.5	1.67761	0.838807	+	0.544429i	$0.183253\pi$
$702$	−5816.04	−0.312695
$703$	12085.3	0.648375
$704$	10238.1	0.548099
$705$	−8699.16	−0.464722
$706$	12093.1	0.644662
$707$	−24826.4	−1.32064
$708$	949.317	0.0503920
$709$	−11791.8	−0.624612	−0.312306	−	0.949982i	$-0.601101\pi$
$709$	−11791.8	−0.624612	−0.312306	+	0.949982i	$0.601101\pi$
$710$	−32357.5	−1.71036
$711$	−8800.53	−0.464199
$712$	−23298.6	−1.22634
$713$	0	0
$714$	−110.207	−0.00577644
$715$	−24453.8	−1.27905
$716$	9403.96	0.490841
$717$	8510.60	0.443283
$718$	−11063.9	−0.575071
$719$	30648.8	1.58972	0.794858	−	0.606796i	$-0.207545\pi$
$719$	30648.8	1.58972	0.794858	+	0.606796i	$0.207545\pi$
$720$	−5457.80	−0.282500
$721$	9909.00	0.511832
$722$	−4539.08	−0.233971
$723$	−7558.93	−0.388824
$724$	−2134.49	−0.109569
$725$	7067.92	0.362063
$726$	−7179.22	−0.367005
$727$	15116.4	0.771164	0.385582	−	0.922674i	$-0.374001\pi$
$727$	15116.4	0.771164	0.385582	+	0.922674i	$0.374001\pi$
$728$	−56638.4	−2.88346
$729$	729.000	0.0370370
$730$	−11509.1	−0.583521
$731$	−282.701	−0.0143038
$732$	−2577.86	−0.130165
$733$	17.5311	0.000883392 0	0.000441696	−	1.00000i	$-0.499859\pi$
$733$	17.5311	0.000883392 0	0.000441696		1.00000i	$0.499859\pi$
$734$	−5919.47	−0.297673
$735$	−13962.7	−0.700710
$736$	0	0
$737$	5636.84	0.281731
$738$	4850.31	0.241927
$739$	4705.50	0.234228	0.117114	−	0.993118i	$-0.462636\pi$
$739$	4705.50	0.234228	0.117114	+	0.993118i	$0.462636\pi$
$740$	−4390.89	−0.218125
$741$	25276.3	1.25310
$742$	29870.5	1.47787
$743$	24159.9	1.19292	0.596460	−	0.802643i	$-0.296573\pi$
$743$	24159.9	1.19292	0.596460	+	0.802643i	$0.296573\pi$
$744$	−19227.1	−0.947447
$745$	16215.9	0.797458
$746$	−15149.0	−0.743492
$747$	9490.97	0.464868
$748$	24.8453	0.00121448
$749$	−11843.1	−0.577752
$750$	−2890.10	−0.140709
$751$	14363.5	0.697910	0.348955	−	0.937139i	$-0.386537\pi$
$751$	14363.5	0.697910	0.348955	+	0.937139i	$0.386537\pi$
$752$	−7884.14	−0.382321
$753$	6602.85	0.319550
$754$	15529.8	0.750083
$755$	3777.82	0.182104
$756$	1572.65	0.0756571
$757$	23283.0	1.11788	0.558941	−	0.829207i	$-0.311208\pi$
$757$	23283.0	1.11788	0.558941	+	0.829207i	$0.311208\pi$
$758$	31268.4	1.49831
$759$	0	0
$760$	34357.7	1.63985
$761$	−10753.4	−0.512233	−0.256116	−	0.966646i	$-0.582443\pi$
$761$	−10753.4	−0.512233	−0.256116	+	0.966646i	$0.582443\pi$
$762$	308.668	0.0146743
$763$	13161.5	0.624481
$764$	−11369.1	−0.538378
$765$	−80.6646	−0.00381233
$766$	−19133.1	−0.902487
$767$	−12515.7	−0.589201
$768$	9560.06	0.449178
$769$	−24463.5	−1.14717	−0.573586	−	0.819145i	$-0.694448\pi$
$769$	−24463.5	−1.14717	−0.573586	+	0.819145i	$0.694448\pi$
$770$	−16624.5	−0.778057
$771$	−19052.3	−0.889951
$772$	−5786.71	−0.269778
$773$	−34557.5	−1.60795	−0.803976	−	0.594661i	$-0.797286\pi$
$773$	−34557.5	−1.60795	−0.803976	+	0.594661i	$0.797286\pi$
$774$	−10142.6	−0.471018
$775$	25556.8	1.18455
$776$	−30228.9	−1.39839
$777$	−9913.41	−0.457711
$778$	−6336.16	−0.291983
$779$	−21079.3	−0.969505
$780$	−9183.49	−0.421566
$781$	16469.5	0.754579
$782$	0	0
$783$	−1946.55	−0.0888432
$784$	−12654.5	−0.576464
$785$	−1566.35	−0.0712170
$786$	9588.17	0.435113
$787$	3536.44	0.160179	0.0800893	−	0.996788i	$-0.474479\pi$
$787$	3536.44	0.160179	0.0800893	+	0.996788i	$0.474479\pi$
$788$	5408.77	0.244517
$789$	1595.13	0.0719747
$790$	34937.0	1.57342
$791$	31454.2	1.41388
$792$	4023.87	0.180533
$793$	33986.4	1.52193
$794$	31373.6	1.40228
$795$	21863.4	0.975364
$796$	4847.66	0.215855
$797$	−26729.2	−1.18795	−0.593976	−	0.804483i	$-0.702443\pi$
$797$	−26729.2	−1.18795	−0.593976	+	0.804483i	$0.702443\pi$
$798$	17183.7	0.762274
$799$	−116.525	−0.00515941
$800$	−9758.40	−0.431265
$801$	−8528.97	−0.376225
$802$	10190.5	0.448679
$803$	5857.97	0.257439
$804$	2116.89	0.0928567
$805$	0	0
$806$	56154.0	2.45402
$807$	4391.58	0.191562
$808$	−23855.4	−1.03865
$809$	−35556.8	−1.54525	−0.772627	−	0.634860i	$-0.781058\pi$
$809$	−35556.8	−1.54525	−0.772627	+	0.634860i	$0.781058\pi$
$810$	−2894.04	−0.125538
$811$	37144.2	1.60827	0.804137	−	0.594444i	$-0.202628\pi$
$811$	37144.2	1.60827	0.804137	+	0.594444i	$0.202628\pi$
$812$	−4199.25	−0.181484
$813$	5395.60	0.232758
$814$	−5618.95	−0.241946
$815$	21520.1	0.924928
$816$	−73.1072	−0.00313635
$817$	44079.4	1.88757
$818$	14802.4	0.632705
$819$	−20733.7	−0.884610
$820$	7658.61	0.326159
$821$	−19116.2	−0.812618	−0.406309	−	0.913736i	$-0.633184\pi$
$821$	−19116.2	−0.812618	−0.406309	+	0.913736i	$0.633184\pi$
$822$	2040.73	0.0865921
$823$	−7021.28	−0.297383	−0.148692	−	0.988884i	$-0.547506\pi$
$823$	−7021.28	−0.297383	−0.148692	+	0.988884i	$0.547506\pi$
$824$	9521.45	0.402543
$825$	−5348.54	−0.225712
$826$	−8508.60	−0.358416
$827$	−31410.3	−1.32073	−0.660365	−	0.750944i	$-0.729599\pi$
$827$	−31410.3	−1.32073	−0.660365	+	0.750944i	$0.729599\pi$
$828$	0	0
$829$	14068.0	0.589389	0.294695	−	0.955592i	$-0.404782\pi$
$829$	14068.0	0.589389	0.294695	+	0.955592i	$0.404782\pi$
$830$	−37678.0	−1.57569
$831$	21752.2	0.908035
$832$	−50690.3	−2.11222
$833$	−187.030	−0.00777937
$834$	9713.46	0.403297
$835$	−18121.3	−0.751033
$836$	−3873.93	−0.160266
$837$	−7038.51	−0.290665
$838$	−16583.1	−0.683597
$839$	−15395.7	−0.633513	−0.316756	−	0.948507i	$-0.602594\pi$
$839$	−15395.7	−0.633513	−0.316756	+	0.948507i	$0.602594\pi$
$840$	−28183.1	−1.15763
$841$	−19191.4	−0.786886
$842$	−18307.3	−0.749300
$843$	−522.274	−0.0213382
$844$	7413.57	0.302352
$845$	88263.6	3.59333
$846$	−4180.63	−0.169897
$847$	−25593.4	−1.03825
$848$	19815.0	0.802418
$849$	−1585.43	−0.0640894
$850$	140.758	0.00567994
$851$	0	0
$852$	6185.04	0.248704
$853$	15457.9	0.620478	0.310239	−	0.950659i	$-0.399591\pi$
$853$	15457.9	0.620478	0.310239	+	0.950659i	$0.399591\pi$
$854$	23105.0	0.925806
$855$	12577.4	0.503086
$856$	−11379.9	−0.454388
$857$	−34305.5	−1.36739	−0.683695	−	0.729768i	$-0.739628\pi$
$857$	−34305.5	−1.36739	−0.683695	+	0.729768i	$0.739628\pi$
$858$	−11752.0	−0.467605
$859$	−30222.2	−1.20043	−0.600215	−	0.799839i	$-0.704918\pi$
$859$	−30222.2	−1.20043	−0.600215	+	0.799839i	$0.704918\pi$
$860$	−16015.1	−0.635012
$861$	17291.0	0.684408
$862$	−2178.45	−0.0860769
$863$	−18884.0	−0.744866	−0.372433	−	0.928059i	$-0.621476\pi$
$863$	−18884.0	−0.744866	−0.372433	+	0.928059i	$0.621476\pi$
$864$	2687.53	0.105824
$865$	14420.4	0.566830
$866$	24520.2	0.962161
$867$	14737.9	0.577308
$868$	−15184.0	−0.593754
$869$	−17782.5	−0.694164
$870$	7727.58	0.301137
$871$	−27908.9	−1.08571
$872$	12646.8	0.491139
$873$	−11065.9	−0.429010
$874$	0	0
$875$	−10303.0	−0.398063
$876$	2199.93	0.0848502
$877$	9851.36	0.379312	0.189656	−	0.981851i	$-0.439263\pi$
$877$	9851.36	0.379312	0.189656	+	0.981851i	$0.439263\pi$
$878$	−28908.0	−1.11116
$879$	−18789.2	−0.720981
$880$	−11028.1	−0.422451
$881$	−14657.2	−0.560513	−0.280257	−	0.959925i	$-0.590420\pi$
$881$	−14657.2	−0.560513	−0.280257	+	0.959925i	$0.590420\pi$
$882$	−6710.17	−0.256171
$883$	32355.2	1.23311	0.616557	−	0.787310i	$-0.288527\pi$
$883$	32355.2	1.23311	0.616557	+	0.787310i	$0.288527\pi$
$884$	−123.013	−0.00468028
$885$	−6227.78	−0.236548
$886$	−26019.9	−0.986631
$887$	−20331.3	−0.769627	−0.384814	−	0.922994i	$-0.625734\pi$
$887$	−20331.3	−0.769627	−0.384814	+	0.922994i	$0.625734\pi$
$888$	−9525.68	−0.359979
$889$	1100.38	0.0415135
$890$	33859.0	1.27523
$891$	1473.03	0.0553852
$892$	4340.14	0.162913
$893$	18168.9	0.680849
$894$	7793.03	0.291541
$895$	−61692.6	−2.30408
$896$	−14086.6	−0.525222
$897$	0	0
$898$	−25096.1	−0.932592
$899$	18794.0	0.697237
$900$	−2008.62	−0.0743933
$901$	292.860	0.0108286
$902$	9800.59	0.361778
$903$	−36157.6	−1.33250
$904$	30223.9	1.11198
$905$	14002.9	0.514332
$906$	1815.54	0.0665753
$907$	−10020.0	−0.366824	−0.183412	−	0.983036i	$-0.558714\pi$
$907$	−10020.0	−0.366824	−0.183412	+	0.983036i	$0.558714\pi$
$908$	−2188.26	−0.0799778
$909$	−8732.81	−0.318646
$910$	82310.4	2.99842
$911$	−10352.5	−0.376503	−0.188251	−	0.982121i	$-0.560282\pi$
$911$	−10352.5	−0.376503	−0.188251	+	0.982121i	$0.560282\pi$
$912$	11399.0	0.413881
$913$	19177.6	0.695164
$914$	45599.7	1.65022
$915$	16911.5	0.611013
$916$	5929.45	0.213880
$917$	34181.1	1.23093
$918$	−38.7656	−0.00139374
$919$	−6733.25	−0.241686	−0.120843	−	0.992672i	$-0.538560\pi$
$919$	−6733.25	−0.241686	−0.120843	+	0.992672i	$0.538560\pi$
$920$	0	0
$921$	−13865.9	−0.496087
$922$	−29971.9	−1.07058
$923$	−81543.2	−2.90794
$924$	3177.72	0.113138
$925$	12661.6	0.450065
$926$	−35117.9	−1.24627
$927$	3485.54	0.123495
$928$	−7176.17	−0.253846
$929$	44639.7	1.57651	0.788256	−	0.615347i	$-0.210984\pi$
$929$	44639.7	1.57651	0.788256	+	0.615347i	$0.210984\pi$
$930$	27942.0	0.985220
$931$	29162.2	1.02659
$932$	−8093.21	−0.284444
$933$	−26973.3	−0.946480
$934$	−18480.4	−0.647426
$935$	−162.992	−0.00570096
$936$	−19922.8	−0.695724
$937$	−33202.5	−1.15761	−0.578804	−	0.815467i	$-0.696480\pi$
$937$	−33202.5	−1.15761	−0.578804	+	0.815467i	$0.696480\pi$
$938$	−18973.4	−0.660450
$939$	−3708.03	−0.128868
$940$	−6601.19	−0.229050
$941$	8912.31	0.308749	0.154375	−	0.988012i	$-0.450664\pi$
$941$	8912.31	0.308749	0.154375	+	0.988012i	$0.450664\pi$
$942$	−752.753	−0.0260361
$943$	0	0
$944$	−5644.31	−0.194604
$945$	−10317.0	−0.355146
$946$	−20494.3	−0.704361
$947$	−3718.63	−0.127602	−0.0638011	−	0.997963i	$-0.520322\pi$
$947$	−3718.63	−0.127602	−0.0638011	+	0.997963i	$0.520322\pi$
$948$	−6678.11	−0.228792
$949$	−29003.7	−0.992098
$950$	−21947.3	−0.749540
$951$	−7314.69	−0.249416
$952$	−377.512	−0.0128521
$953$	−50563.3	−1.71868	−0.859342	−	0.511402i	$-0.829126\pi$
$953$	−50563.3	−1.71868	−0.859342	+	0.511402i	$0.829126\pi$
$954$	10507.1	0.356582
$955$	74584.7	2.52723
$956$	6458.10	0.218483
$957$	−3933.23	−0.132856
$958$	5088.98	0.171626
$959$	7275.06	0.244968
$960$	−25223.3	−0.847998
$961$	38166.0	1.28112
$962$	27820.3	0.932394
$963$	−4165.85	−0.139401
$964$	−5735.95	−0.191641
$965$	37962.4	1.26638
$966$	0	0
$967$	−23535.5	−0.782678	−0.391339	−	0.920247i	$-0.627988\pi$
$967$	−23535.5	−0.782678	−0.391339	+	0.920247i	$0.627988\pi$
$968$	−24592.4	−0.816559
$969$	168.474	0.00558532
$970$	43930.4	1.45415
$971$	−3018.54	−0.0997627	−0.0498814	−	0.998755i	$-0.515884\pi$
$971$	−3018.54	−0.0997627	−0.0498814	+	0.998755i	$0.515884\pi$
$972$	553.187	0.0182546
$973$	34627.8	1.14092
$974$	−7923.84	−0.260674
$975$	26481.5	0.869832
$976$	15327.1	0.502672
$977$	40242.3	1.31777	0.658887	−	0.752242i	$-0.271028\pi$
$977$	40242.3	1.31777	0.658887	+	0.752242i	$0.271028\pi$
$978$	10342.1	0.338143
$979$	−17233.8	−0.562608
$980$	−10595.3	−0.345362
$981$	4629.62	0.150675
$982$	−33980.8	−1.10425
$983$	−34926.0	−1.13323	−0.566615	−	0.823983i	$-0.691747\pi$
$983$	−34926.0	−1.13323	−0.566615	+	0.823983i	$0.691747\pi$
$984$	16614.7	0.538270
$985$	−35483.0	−1.14780
$986$	103.511	0.00334326
$987$	−14903.6	−0.480636
$988$	19180.4	0.617623
$989$	0	0
$990$	−5847.73	−0.187730
$991$	5761.12	0.184670	0.0923350	−	0.995728i	$-0.470567\pi$
$991$	5761.12	0.184670	0.0923350	+	0.995728i	$0.470567\pi$
$992$	−25948.2	−0.830500
$993$	−15866.1	−0.507044
$994$	−55435.7	−1.76893
$995$	−31802.0	−1.01326
$996$	7202.04	0.229122
$997$	10053.9	0.319370	0.159685	−	0.987168i	$-0.448952\pi$
$997$	10053.9	0.319370	0.159685	+	0.987168i	$0.448952\pi$
$998$	−45570.3	−1.44539
$999$	−3487.09	−0.110437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1587.4.a.w.1.9		30
23.4	even	11		69.4.e.b.16.5	yes	60
23.6	even	11		69.4.e.b.13.5	✓	60
23.22	odd	2		1587.4.a.v.1.9		30
69.29	odd	22		207.4.i.b.82.2		60
69.50	odd	22		207.4.i.b.154.2		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.4.e.b.13.5	✓	60	23.6	even	11
69.4.e.b.16.5	yes	60	23.4	even	11
207.4.i.b.82.2		60	69.29	odd	22
207.4.i.b.154.2		60	69.50	odd	22
1587.4.a.v.1.9		30	23.22	odd	2
1587.4.a.w.1.9		30	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:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1587.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39239 q^{2} -3.00000 q^{3} -2.27649 q^{4} +14.9344 q^{5} +7.17716 q^{6} +25.5860 q^{7} +24.5853 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.39239 q^{2} -3.00000 q^{3} -2.27649 q^{4} +14.9344 q^{5} +7.17716 q^{6} +25.5860 q^{7} +24.5853 q^{8} +9.00000 q^{9} -35.7289 q^{10} +18.1855 q^{11} +6.82947 q^{12} -90.0393 q^{13} -61.2116 q^{14} -44.8032 q^{15} -40.6057 q^{16} -0.600139 q^{17} -21.5315 q^{18} +93.5751 q^{19} -33.9981 q^{20} -76.7581 q^{21} -43.5068 q^{22} -73.7560 q^{24} +98.0367 q^{25} +215.409 q^{26} -27.0000 q^{27} -58.2464 q^{28} +72.0946 q^{29} +107.187 q^{30} +260.686 q^{31} -99.5382 q^{32} -54.5565 q^{33} +1.43576 q^{34} +382.112 q^{35} -20.4884 q^{36} +129.151 q^{37} -223.868 q^{38} +270.118 q^{39} +367.168 q^{40} -225.266 q^{41} +183.635 q^{42} +471.059 q^{43} -41.3992 q^{44} +134.410 q^{45} +194.164 q^{47} +121.817 q^{48} +311.645 q^{49} -234.542 q^{50} +1.80042 q^{51} +204.974 q^{52} -487.987 q^{53} +64.5944 q^{54} +271.590 q^{55} +629.041 q^{56} -280.725 q^{57} -172.478 q^{58} +139.003 q^{59} +101.994 q^{60} -377.461 q^{61} -623.660 q^{62} +230.274 q^{63} +562.979 q^{64} -1344.68 q^{65} +130.520 q^{66} +309.963 q^{67} +1.36621 q^{68} -914.160 q^{70} +905.640 q^{71} +221.268 q^{72} +322.123 q^{73} -308.980 q^{74} -294.110 q^{75} -213.023 q^{76} +465.295 q^{77} -646.226 q^{78} -977.837 q^{79} -606.422 q^{80} +81.0000 q^{81} +538.923 q^{82} +1054.55 q^{83} +174.739 q^{84} -8.96273 q^{85} -1126.95 q^{86} -216.284 q^{87} +447.097 q^{88} -947.664 q^{89} -321.560 q^{90} -2303.75 q^{91} -782.057 q^{93} -464.514 q^{94} +1397.49 q^{95} +298.615 q^{96} -1229.55 q^{97} -745.574 q^{98} +163.670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} + 52 q^{5} - 6 q^{6} - 2 q^{7} + 18 q^{8} + 270 q^{9}+O(q^{10}) \) 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 + 52 * q^5 - 6 * q^6 - 2 * q^7 + 18 * q^8 + 270 * q^9	\( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} + 52 q^{5} - 6 q^{6} - 2 q^{7} + 18 q^{8} + 270 q^{9} - 39 q^{10} + 126 q^{11} - 354 q^{12} + 14 q^{13} + 42 q^{14} - 156 q^{15} + 438 q^{16} + 340 q^{17} + 18 q^{18} - 156 q^{19} + 617 q^{20} + 6 q^{21} + 311 q^{22} - 54 q^{24} + 624 q^{25} + 398 q^{26} - 810 q^{27} + 468 q^{28} - 196 q^{29} + 117 q^{30} - 380 q^{31} + 46 q^{32} - 378 q^{33} + 64 q^{34} - 636 q^{35} + 1062 q^{36} + 1082 q^{37} + 747 q^{38} - 42 q^{39} - 623 q^{40} + 768 q^{41} - 126 q^{42} + 68 q^{43} + 1657 q^{44} + 468 q^{45} - 720 q^{47} - 1314 q^{48} + 2926 q^{49} - 1008 q^{50} - 1020 q^{51} + 482 q^{52} + 2720 q^{53} - 54 q^{54} - 336 q^{55} + 576 q^{56} + 468 q^{57} - 690 q^{58} + 80 q^{59} - 1851 q^{60} + 906 q^{61} - 110 q^{62} - 18 q^{63} + 5740 q^{64} + 3490 q^{65} - 933 q^{66} + 1294 q^{67} + 2802 q^{68} + 1492 q^{70} - 1350 q^{71} + 162 q^{72} - 1824 q^{73} + 2629 q^{74} - 1872 q^{75} - 585 q^{76} - 864 q^{77} - 1194 q^{78} - 3540 q^{79} + 5233 q^{80} + 2430 q^{81} + 2166 q^{82} + 1410 q^{83} - 1404 q^{84} + 2468 q^{85} + 1597 q^{86} + 588 q^{87} + 5645 q^{88} + 2022 q^{89} - 351 q^{90} - 2718 q^{91} + 1140 q^{93} - 1548 q^{94} + 9230 q^{95} - 138 q^{96} + 2926 q^{97} - 11775 q^{98} + 1134 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 + 52 * q^5 - 6 * q^6 - 2 * q^7 + 18 * q^8 + 270 * q^9 - 39 * q^10 + 126 * q^11 - 354 * q^12 + 14 * q^13 + 42 * q^14 - 156 * q^15 + 438 * q^16 + 340 * q^17 + 18 * q^18 - 156 * q^19 + 617 * q^20 + 6 * q^21 + 311 * q^22 - 54 * q^24 + 624 * q^25 + 398 * q^26 - 810 * q^27 + 468 * q^28 - 196 * q^29 + 117 * q^30 - 380 * q^31 + 46 * q^32 - 378 * q^33 + 64 * q^34 - 636 * q^35 + 1062 * q^36 + 1082 * q^37 + 747 * q^38 - 42 * q^39 - 623 * q^40 + 768 * q^41 - 126 * q^42 + 68 * q^43 + 1657 * q^44 + 468 * q^45 - 720 * q^47 - 1314 * q^48 + 2926 * q^49 - 1008 * q^50 - 1020 * q^51 + 482 * q^52 + 2720 * q^53 - 54 * q^54 - 336 * q^55 + 576 * q^56 + 468 * q^57 - 690 * q^58 + 80 * q^59 - 1851 * q^60 + 906 * q^61 - 110 * q^62 - 18 * q^63 + 5740 * q^64 + 3490 * q^65 - 933 * q^66 + 1294 * q^67 + 2802 * q^68 + 1492 * q^70 - 1350 * q^71 + 162 * q^72 - 1824 * q^73 + 2629 * q^74 - 1872 * q^75 - 585 * q^76 - 864 * q^77 - 1194 * q^78 - 3540 * q^79 + 5233 * q^80 + 2430 * q^81 + 2166 * q^82 + 1410 * q^83 - 1404 * q^84 + 2468 * q^85 + 1597 * q^86 + 588 * q^87 + 5645 * q^88 + 2022 * q^89 - 351 * q^90 - 2718 * q^91 + 1140 * q^93 - 1548 * q^94 + 9230 * q^95 - 138 * q^96 + 2926 * q^97 - 11775 * q^98 + 1134 * q^99

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