LMFDB - Embedded newform 147.6.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{193}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 48 $ x^2 - x - 48
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$7.44622$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.44622 q^{2} -9.00000 q^{3} +39.3387 q^{4} +36.0000 q^{5} +76.0160 q^{6} -61.9840 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-8.44622 q^{2} -9.00000 q^{3} +39.3387 q^{4} +36.0000 q^{5} +76.0160 q^{6} -61.9840 q^{8} +81.0000 q^{9} -304.064 q^{10} +295.570 q^{11} -354.048 q^{12} +1148.13 q^{13} -324.000 q^{15} -735.307 q^{16} -1032.38 q^{17} -684.144 q^{18} -2108.51 q^{19} +1416.19 q^{20} -2496.45 q^{22} -640.988 q^{23} +557.856 q^{24} -1829.00 q^{25} -9697.34 q^{26} -729.000 q^{27} +7631.58 q^{29} +2736.58 q^{30} +966.976 q^{31} +8194.05 q^{32} -2660.13 q^{33} +8719.74 q^{34} +3186.43 q^{36} -1773.21 q^{37} +17809.0 q^{38} -10333.2 q^{39} -2231.42 q^{40} +11976.4 q^{41} -19802.9 q^{43} +11627.3 q^{44} +2916.00 q^{45} +5413.93 q^{46} +27966.1 q^{47} +6617.76 q^{48} +15448.1 q^{50} +9291.46 q^{51} +45165.8 q^{52} -7114.33 q^{53} +6157.30 q^{54} +10640.5 q^{55} +18976.6 q^{57} -64458.0 q^{58} +20869.5 q^{59} -12745.7 q^{60} +23868.3 q^{61} -8167.30 q^{62} -45679.0 q^{64} +41332.6 q^{65} +22468.0 q^{66} +34671.5 q^{67} -40612.6 q^{68} +5768.90 q^{69} -28413.2 q^{71} -5020.70 q^{72} +15292.7 q^{73} +14976.9 q^{74} +16461.0 q^{75} -82946.0 q^{76} +87276.1 q^{78} -73059.5 q^{79} -26471.0 q^{80} +6561.00 q^{81} -101155. q^{82} +30340.9 q^{83} -37165.8 q^{85} +167260. q^{86} -68684.2 q^{87} -18320.6 q^{88} +36089.5 q^{89} -24629.2 q^{90} -25215.6 q^{92} -8702.79 q^{93} -236208. q^{94} -75906.4 q^{95} -73746.5 q^{96} +153963. q^{97} +23941.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 18 q^{3} + 37 q^{4} + 72 q^{5} + 27 q^{6} - 249 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 18 * q^3 + 37 * q^4 + 72 * q^5 + 27 * q^6 - 249 * q^8 + 162 * q^9	\( 2 q - 3 q^{2} - 18 q^{3} + 37 q^{4} + 72 q^{5} + 27 q^{6} - 249 q^{8} + 162 q^{9} - 108 q^{10} + 480 q^{11} - 333 q^{12} + 1296 q^{13} - 648 q^{15} - 1679 q^{16} + 936 q^{17} - 243 q^{18} - 216 q^{19} + 1332 q^{20} - 1492 q^{22} - 504 q^{23} + 2241 q^{24} - 3658 q^{25} - 8892 q^{26} - 1458 q^{27} + 6372 q^{29} + 972 q^{30} + 9936 q^{31} + 9039 q^{32} - 4320 q^{33} + 19440 q^{34} + 2997 q^{36} + 11124 q^{37} + 28116 q^{38} - 11664 q^{39} - 8964 q^{40} + 20952 q^{41} - 6264 q^{43} + 11196 q^{44} + 5832 q^{45} + 6160 q^{46} + 7920 q^{47} + 15111 q^{48} + 5487 q^{50} - 8424 q^{51} + 44820 q^{52} + 2220 q^{53} + 2187 q^{54} + 17280 q^{55} + 1944 q^{57} - 71318 q^{58} + 29736 q^{59} - 11988 q^{60} - 17280 q^{61} + 40680 q^{62} - 10879 q^{64} + 46656 q^{65} + 13428 q^{66} - 20680 q^{67} - 45216 q^{68} + 4536 q^{69} - 92280 q^{71} - 20169 q^{72} + 56592 q^{73} + 85218 q^{74} + 32922 q^{75} - 87372 q^{76} + 80028 q^{78} - 56096 q^{79} - 60444 q^{80} + 13122 q^{81} - 52272 q^{82} - 71352 q^{83} + 33696 q^{85} + 240996 q^{86} - 57348 q^{87} - 52812 q^{88} + 123192 q^{89} - 8748 q^{90} - 25536 q^{92} - 89424 q^{93} - 345384 q^{94} - 7776 q^{95} - 81351 q^{96} + 35856 q^{97} + 38880 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 18 * q^3 + 37 * q^4 + 72 * q^5 + 27 * q^6 - 249 * q^8 + 162 * q^9 - 108 * q^10 + 480 * q^11 - 333 * q^12 + 1296 * q^13 - 648 * q^15 - 1679 * q^16 + 936 * q^17 - 243 * q^18 - 216 * q^19 + 1332 * q^20 - 1492 * q^22 - 504 * q^23 + 2241 * q^24 - 3658 * q^25 - 8892 * q^26 - 1458 * q^27 + 6372 * q^29 + 972 * q^30 + 9936 * q^31 + 9039 * q^32 - 4320 * q^33 + 19440 * q^34 + 2997 * q^36 + 11124 * q^37 + 28116 * q^38 - 11664 * q^39 - 8964 * q^40 + 20952 * q^41 - 6264 * q^43 + 11196 * q^44 + 5832 * q^45 + 6160 * q^46 + 7920 * q^47 + 15111 * q^48 + 5487 * q^50 - 8424 * q^51 + 44820 * q^52 + 2220 * q^53 + 2187 * q^54 + 17280 * q^55 + 1944 * q^57 - 71318 * q^58 + 29736 * q^59 - 11988 * q^60 - 17280 * q^61 + 40680 * q^62 - 10879 * q^64 + 46656 * q^65 + 13428 * q^66 - 20680 * q^67 - 45216 * q^68 + 4536 * q^69 - 92280 * q^71 - 20169 * q^72 + 56592 * q^73 + 85218 * q^74 + 32922 * q^75 - 87372 * q^76 + 80028 * q^78 - 56096 * q^79 - 60444 * q^80 + 13122 * q^81 - 52272 * q^82 - 71352 * q^83 + 33696 * q^85 + 240996 * q^86 - 57348 * q^87 - 52812 * q^88 + 123192 * q^89 - 8748 * q^90 - 25536 * q^92 - 89424 * q^93 - 345384 * q^94 - 7776 * q^95 - 81351 * q^96 + 35856 * q^97 + 38880 * 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 $

$2$	−8.44622	−1.49310	−0.746548	−	0.665332i	$-0.768290\pi$
$2$	−8.44622	−1.49310	−0.746548	+	0.665332i	$0.768290\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	39.3387	1.22933
$5$	36.0000	0.643988	0.321994	−	0.946742i	$-0.395647\pi$
$5$	36.0000	0.643988	0.321994	+	0.946742i	$0.395647\pi$
$6$	76.0160	0.862039
$7$	0	0
$7$	0	0
$8$	−61.9840	−0.342416
$9$	81.0000	0.333333
$10$	−304.064	−0.961535
$11$	295.570	0.736509	0.368255	−	0.929725i	$-0.379955\pi$
$11$	295.570	0.736509	0.368255	+	0.929725i	$0.379955\pi$
$12$	−354.048	−0.709756
$13$	1148.13	1.88422	0.942111	−	0.335302i	$-0.108838\pi$
$13$	1148.13	1.88422	0.942111	+	0.335302i	$0.108838\pi$
$14$	0	0
$15$	−324.000	−0.371806
$16$	−735.307	−0.718073
$17$	−1032.38	−0.866401	−0.433200	−	0.901298i	$-0.642616\pi$
$17$	−1032.38	−0.866401	−0.433200	+	0.901298i	$0.642616\pi$
$18$	−684.144	−0.497698
$19$	−2108.51	−1.33996	−0.669980	−	0.742379i	$-0.733697\pi$
$19$	−2108.51	−1.33996	−0.669980	+	0.742379i	$0.733697\pi$
$20$	1416.19	0.791675
$21$	0	0
$22$	−2496.45	−1.09968
$23$	−640.988	−0.252657	−0.126328	−	0.991988i	$-0.540319\pi$
$23$	−640.988	−0.252657	−0.126328	+	0.991988i	$0.540319\pi$
$24$	557.856	0.197694
$25$	−1829.00	−0.585280
$26$	−9697.34	−2.81332
$27$	−729.000	−0.192450
$28$	0	0
$29$	7631.58	1.68508	0.842538	−	0.538637i	$-0.181060\pi$
$29$	7631.58	1.68508	0.842538	+	0.538637i	$0.181060\pi$
$30$	2736.58	0.555142
$31$	966.976	0.180722	0.0903611	−	0.995909i	$-0.471198\pi$
$31$	966.976	0.180722	0.0903611	+	0.995909i	$0.471198\pi$
$32$	8194.05	1.41457
$33$	−2660.13	−0.425224
$34$	8719.74	1.29362
$35$	0	0
$36$	3186.43	0.409778
$37$	−1773.21	−0.212939	−0.106470	−	0.994316i	$-0.533955\pi$
$37$	−1773.21	−0.212939	−0.106470	+	0.994316i	$0.533955\pi$
$38$	17809.0	2.00069
$39$	−10333.2	−1.08786
$40$	−2231.42	−0.220512
$41$	11976.4	1.11267	0.556335	−	0.830958i	$-0.312207\pi$
$41$	11976.4	1.11267	0.556335	+	0.830958i	$0.312207\pi$
$42$	0	0
$43$	−19802.9	−1.63327	−0.816636	−	0.577153i	$-0.804163\pi$
$43$	−19802.9	−1.63327	−0.816636	+	0.577153i	$0.804163\pi$
$44$	11627.3	0.905416
$45$	2916.00	0.214663
$46$	5413.93	0.377240
$47$	27966.1	1.84666	0.923332	−	0.384002i	$-0.125455\pi$
$47$	27966.1	1.84666	0.923332	+	0.384002i	$0.125455\pi$
$48$	6617.76	0.414580
$49$	0	0
$50$	15448.1	0.873879
$51$	9291.46	0.500217
$52$	45165.8	2.31634
$53$	−7114.33	−0.347892	−0.173946	−	0.984755i	$-0.555652\pi$
$53$	−7114.33	−0.347892	−0.173946	+	0.984755i	$0.555652\pi$
$54$	6157.30	0.287346
$55$	10640.5	0.474303
$56$	0	0
$57$	18976.6	0.773627
$58$	−64458.0	−2.51598
$59$	20869.5	0.780518	0.390259	−	0.920705i	$-0.372386\pi$
$59$	20869.5	0.780518	0.390259	+	0.920705i	$0.372386\pi$
$60$	−12745.7	−0.457074
$61$	23868.3	0.821291	0.410646	−	0.911795i	$-0.365303\pi$
$61$	23868.3	0.821291	0.410646	+	0.911795i	$0.365303\pi$
$62$	−8167.30	−0.269835
$63$	0	0
$64$	−45679.0	−1.39401
$65$	41332.6	1.21342
$66$	22468.0	0.634900
$67$	34671.5	0.943595	0.471798	−	0.881707i	$-0.343605\pi$
$67$	34671.5	0.943595	0.471798	+	0.881707i	$0.343605\pi$
$68$	−40612.6	−1.06510
$69$	5768.90	0.145871
$70$	0	0
$71$	−28413.2	−0.668921	−0.334461	−	0.942410i	$-0.608554\pi$
$71$	−28413.2	−0.668921	−0.334461	+	0.942410i	$0.608554\pi$
$72$	−5020.70	−0.114139
$73$	15292.7	0.335874	0.167937	−	0.985798i	$-0.446289\pi$
$73$	15292.7	0.335874	0.167937	+	0.985798i	$0.446289\pi$
$74$	14976.9	0.317939
$75$	16461.0	0.337912
$76$	−82946.0	−1.64726
$77$	0	0
$78$	87276.1	1.62427
$79$	−73059.5	−1.31707	−0.658535	−	0.752550i	$-0.728824\pi$
$79$	−73059.5	−1.31707	−0.658535	+	0.752550i	$0.728824\pi$
$80$	−26471.0	−0.462430
$81$	6561.00	0.111111
$82$	−101155.	−1.66132
$83$	30340.9	0.483429	0.241715	−	0.970347i	$-0.422290\pi$
$83$	30340.9	0.483429	0.241715	+	0.970347i	$0.422290\pi$
$84$	0	0
$85$	−37165.8	−0.557951
$86$	167260.	2.43863
$87$	−68684.2	−0.972879
$88$	−18320.6	−0.252193
$89$	36089.5	0.482954	0.241477	−	0.970407i	$-0.422368\pi$
$89$	36089.5	0.482954	0.241477	+	0.970407i	$0.422368\pi$
$90$	−24629.2	−0.320512
$91$	0	0
$92$	−25215.6	−0.310599
$93$	−8702.79	−0.104340
$94$	−236208.	−2.75725
$95$	−75906.4	−0.862918
$96$	−73746.5	−0.816701
$97$	153963.	1.66145	0.830724	−	0.556685i	$-0.187927\pi$
$97$	153963.	1.66145	0.830724	+	0.556685i	$0.187927\pi$
$98$	0	0
$99$	23941.2	0.245503
$100$	−71950.4	−0.719504
$101$	−139809.	−1.36374	−0.681869	−	0.731474i	$-0.738833\pi$
$101$	−139809.	−1.36374	−0.681869	+	0.731474i	$0.738833\pi$
$102$	−78477.7	−0.746871
$103$	115925.	1.07668	0.538339	−	0.842728i	$-0.319052\pi$
$103$	115925.	1.07668	0.538339	+	0.842728i	$0.319052\pi$
$104$	−71165.6	−0.645188
$105$	0	0
$106$	60089.2	0.519436
$107$	83061.8	0.701361	0.350681	−	0.936495i	$-0.385950\pi$
$107$	83061.8	0.701361	0.350681	+	0.936495i	$0.385950\pi$
$108$	−28677.9	−0.236585
$109$	45356.2	0.365654	0.182827	−	0.983145i	$-0.441475\pi$
$109$	45356.2	0.365654	0.182827	+	0.983145i	$0.441475\pi$
$110$	−89872.1	−0.708179
$111$	15958.9	0.122941
$112$	0	0
$113$	−355.533	−0.00261929	−0.00130965	−	0.999999i	$-0.500417\pi$
$113$	−355.533	−0.00261929	−0.00130965	+	0.999999i	$0.500417\pi$
$114$	−160281.	−1.15510
$115$	−23075.6	−0.162708
$116$	300216.	2.07152
$117$	92998.4	0.628074
$118$	−176269.	−1.16539
$119$	0	0
$120$	20082.8	0.127313
$121$	−73689.5	−0.457554
$122$	−201597.	−1.22627
$123$	−107787.	−0.642400
$124$	38039.6	0.222168
$125$	−178344.	−1.02090
$126$	0	0
$127$	168967.	0.929593	0.464797	−	0.885417i	$-0.346127\pi$
$127$	168967.	0.929593	0.464797	+	0.885417i	$0.346127\pi$
$128$	123605.	0.666824
$129$	178226.	0.942970
$130$	−349104.	−1.81174
$131$	173969.	0.885715	0.442858	−	0.896592i	$-0.353965\pi$
$131$	173969.	0.885715	0.442858	+	0.896592i	$0.353965\pi$
$132$	−104646.	−0.522742
$133$	0	0
$134$	−292843.	−1.40888
$135$	−26244.0	−0.123935
$136$	63991.3	0.296670
$137$	367723.	1.67386	0.836931	−	0.547308i	$-0.184347\pi$
$137$	367723.	1.67386	0.836931	+	0.547308i	$0.184347\pi$
$138$	−48725.4	−0.217800
$139$	−217967.	−0.956870	−0.478435	−	0.878123i	$-0.658796\pi$
$139$	−217967.	−0.956870	−0.478435	+	0.878123i	$0.658796\pi$
$140$	0	0
$141$	−251695.	−1.06617
$142$	239985.	0.998763
$143$	339352.	1.38775
$144$	−59559.8	−0.239358
$145$	274737.	1.08517
$146$	−129165.	−0.501492
$147$	0	0
$148$	−69755.7	−0.261773
$149$	−64906.1	−0.239508	−0.119754	−	0.992804i	$-0.538211\pi$
$149$	−64906.1	−0.239508	−0.119754	+	0.992804i	$0.538211\pi$
$150$	−139033.	−0.504534
$151$	−223777.	−0.798681	−0.399341	−	0.916803i	$-0.630761\pi$
$151$	−223777.	−0.798681	−0.399341	+	0.916803i	$0.630761\pi$
$152$	130694.	0.458825
$153$	−83623.1	−0.288800
$154$	0	0
$155$	34811.1	0.116383
$156$	−406492.	−1.33734
$157$	459973.	1.48930	0.744652	−	0.667453i	$-0.232616\pi$
$157$	459973.	1.48930	0.744652	+	0.667453i	$0.232616\pi$
$158$	617077.	1.96651
$159$	64028.9	0.200855
$160$	294986.	0.910964
$161$	0	0
$162$	−55415.7	−0.165899
$163$	91068.6	0.268472	0.134236	−	0.990949i	$-0.457142\pi$
$163$	91068.6	0.268472	0.134236	+	0.990949i	$0.457142\pi$
$164$	471135.	1.36784
$165$	−95764.6	−0.273839
$166$	−256266.	−0.721806
$167$	314772.	0.873384	0.436692	−	0.899611i	$-0.356150\pi$
$167$	314772.	0.873384	0.436692	+	0.899611i	$0.356150\pi$
$168$	0	0
$169$	946905.	2.55029
$170$	313911.	0.833075
$171$	−170789.	−0.446654
$172$	−779021.	−2.00784
$173$	362143.	0.919951	0.459975	−	0.887932i	$-0.347858\pi$
$173$	362143.	0.919951	0.459975	+	0.887932i	$0.347858\pi$
$174$	580122.	1.45260
$175$	0	0
$176$	−217334.	−0.528867
$177$	−187826.	−0.450632
$178$	−304820.	−0.721096
$179$	−173896.	−0.405656	−0.202828	−	0.979214i	$-0.565013\pi$
$179$	−173896.	−0.405656	−0.202828	+	0.979214i	$0.565013\pi$
$180$	114712.	0.263892
$181$	−134973.	−0.306233	−0.153116	−	0.988208i	$-0.548931\pi$
$181$	−134973.	−0.306233	−0.153116	+	0.988208i	$0.548931\pi$
$182$	0	0
$183$	−214815.	−0.474173
$184$	39731.0	0.0865138
$185$	−63835.6	−0.137130
$186$	73505.7	0.155790
$187$	−305141.	−0.638112
$188$	1.10015e6	2.27017
$189$	0	0
$190$	641123.	1.28842
$191$	181413.	0.359821	0.179910	−	0.983683i	$-0.442419\pi$
$191$	181413.	0.359821	0.179910	+	0.983683i	$0.442419\pi$
$192$	411111.	0.804833
$193$	965999.	1.86674	0.933369	−	0.358919i	$-0.116855\pi$
$193$	965999.	1.86674	0.933369	+	0.358919i	$0.116855\pi$
$194$	−1.30040e6	−2.48070
$195$	−371993.	−0.700566
$196$	0	0
$197$	−699058.	−1.28336	−0.641679	−	0.766974i	$-0.721762\pi$
$197$	−699058.	−1.28336	−0.641679	+	0.766974i	$0.721762\pi$
$198$	−202212.	−0.366560
$199$	416191.	0.745006	0.372503	−	0.928031i	$-0.378500\pi$
$199$	416191.	0.745006	0.372503	+	0.928031i	$0.378500\pi$
$200$	113369.	0.200410
$201$	−312044.	−0.544785
$202$	1.18086e6	2.03619
$203$	0	0
$204$	365513.	0.614933
$205$	431150.	0.716545
$206$	−979132.	−1.60758
$207$	−51920.1	−0.0842189
$208$	−844226.	−1.35301
$209$	−623212.	−0.986894
$210$	0	0
$211$	−407152.	−0.629580	−0.314790	−	0.949161i	$-0.601934\pi$
$211$	−407152.	−0.629580	−0.314790	+	0.949161i	$0.601934\pi$
$212$	−279868.	−0.427675
$213$	255719.	0.386202
$214$	−701558.	−1.04720
$215$	−712906.	−1.05181
$216$	45186.3	0.0658981
$217$	0	0
$218$	−383089.	−0.545957
$219$	−137634.	−0.193917
$220$	418584.	0.583076
$221$	−1.18531e6	−1.63249
$222$	−134792.	−0.183562
$223$	−882022.	−1.18773	−0.593865	−	0.804565i	$-0.702398\pi$
$223$	−882022.	−1.18773	−0.593865	+	0.804565i	$0.702398\pi$
$224$	0	0
$225$	−148149.	−0.195093
$226$	3002.91	0.00391085
$227$	1.12650e6	1.45100	0.725499	−	0.688223i	$-0.241609\pi$
$227$	1.12650e6	1.45100	0.725499	+	0.688223i	$0.241609\pi$
$228$	746514.	0.951045
$229$	−310084.	−0.390743	−0.195371	−	0.980729i	$-0.562591\pi$
$229$	−310084.	−0.390743	−0.195371	+	0.980729i	$0.562591\pi$
$230$	194902.	0.242938
$231$	0	0
$232$	−473036.	−0.576998
$233$	1.13654e6	1.37149	0.685746	−	0.727841i	$-0.259476\pi$
$233$	1.13654e6	1.37149	0.685746	+	0.727841i	$0.259476\pi$
$234$	−785485.	−0.937774
$235$	1.00678e6	1.18923
$236$	820980.	0.959516
$237$	657536.	0.760411
$238$	0	0
$239$	87506.8	0.0990940	0.0495470	−	0.998772i	$-0.484222\pi$
$239$	87506.8	0.0990940	0.0495470	+	0.998772i	$0.484222\pi$
$240$	238239.	0.266984
$241$	−537768.	−0.596421	−0.298210	−	0.954500i	$-0.596390\pi$
$241$	−537768.	−0.596421	−0.298210	+	0.954500i	$0.596390\pi$
$242$	622398.	0.683171
$243$	−59049.0	−0.0641500
$244$	938948.	1.00964
$245$	0	0
$246$	910397.	0.959164
$247$	−2.42084e6	−2.52478
$248$	−59937.1	−0.0618823
$249$	−273068.	−0.279108
$250$	1.50633e6	1.52430
$251$	−1.35353e6	−1.35607	−0.678036	−	0.735028i	$-0.737169\pi$
$251$	−1.35353e6	−1.35607	−0.678036	+	0.735028i	$0.737169\pi$
$252$	0	0
$253$	−189457.	−0.186084
$254$	−1.42713e6	−1.38797
$255$	334492.	0.322133
$256$	417731.	0.398380
$257$	976900.	0.922608	0.461304	−	0.887242i	$-0.347382\pi$
$257$	976900.	0.922608	0.461304	+	0.887242i	$0.347382\pi$
$258$	−1.50534e6	−1.40794
$259$	0	0
$260$	1.62597e6	1.49169
$261$	618158.	0.561692
$262$	−1.46938e6	−1.32246
$263$	−1.24375e6	−1.10877	−0.554387	−	0.832259i	$-0.687047\pi$
$263$	−1.24375e6	−1.10877	−0.554387	+	0.832259i	$0.687047\pi$
$264$	164885.	0.145604
$265$	−256116.	−0.224038
$266$	0	0
$267$	−324805.	−0.278833
$268$	1.36393e6	1.15999
$269$	1.08408e6	0.913445	0.456722	−	0.889609i	$-0.349023\pi$
$269$	1.08408e6	0.913445	0.456722	+	0.889609i	$0.349023\pi$
$270$	221663.	0.185047
$271$	2.16627e6	1.79180	0.895900	−	0.444256i	$-0.146532\pi$
$271$	2.16627e6	1.79180	0.895900	+	0.444256i	$0.146532\pi$
$272$	759119.	0.622139
$273$	0	0
$274$	−3.10587e6	−2.49924
$275$	−540597.	−0.431064
$276$	226941.	0.179324
$277$	253859.	0.198789	0.0993946	−	0.995048i	$-0.468309\pi$
$277$	253859.	0.198789	0.0993946	+	0.995048i	$0.468309\pi$
$278$	1.84099e6	1.42870
$279$	78325.1	0.0602407
$280$	0	0
$281$	1.14116e6	0.862143	0.431072	−	0.902318i	$-0.358136\pi$
$281$	1.14116e6	0.862143	0.431072	+	0.902318i	$0.358136\pi$
$282$	2.12587e6	1.59190
$283$	609918.	0.452694	0.226347	−	0.974047i	$-0.427322\pi$
$283$	609918.	0.452694	0.226347	+	0.974047i	$0.427322\pi$
$284$	−1.11774e6	−0.822327
$285$	683158.	0.498206
$286$	−2.86624e6	−2.07204
$287$	0	0
$288$	663718.	0.471523
$289$	−354040.	−0.249349
$290$	−2.32049e6	−1.62026
$291$	−1.38567e6	−0.959237
$292$	601593.	0.412901
$293$	−156438.	−0.106457	−0.0532283	−	0.998582i	$-0.516951\pi$
$293$	−156438.	−0.106457	−0.0532283	+	0.998582i	$0.516951\pi$
$294$	0	0
$295$	751303.	0.502644
$296$	109911.	0.0729139
$297$	−215470.	−0.141741
$298$	548211.	0.357608
$299$	−735937.	−0.476061
$300$	647554.	0.415406
$301$	0	0
$302$	1.89007e6	1.19251
$303$	1.25828e6	0.787354
$304$	1.55040e6	0.962189
$305$	859259.	0.528901
$306$	706299.	0.431206
$307$	−293229.	−0.177566	−0.0887831	−	0.996051i	$-0.528298\pi$
$307$	−293229.	−0.177566	−0.0887831	+	0.996051i	$0.528298\pi$
$308$	0	0
$309$	−1.04333e6	−0.621620
$310$	−294023.	−0.173771
$311$	−2.45216e6	−1.43763	−0.718816	−	0.695200i	$-0.755316\pi$
$311$	−2.45216e6	−1.43763	−0.718816	+	0.695200i	$0.755316\pi$
$312$	640490.	0.372500
$313$	−1.83541e6	−1.05894	−0.529471	−	0.848328i	$-0.677610\pi$
$313$	−1.83541e6	−1.05894	−0.529471	+	0.848328i	$0.677610\pi$
$314$	−3.88503e6	−2.22367
$315$	0	0
$316$	−2.87406e6	−1.61912
$317$	589960.	0.329742	0.164871	−	0.986315i	$-0.447279\pi$
$317$	589960.	0.329742	0.164871	+	0.986315i	$0.447279\pi$
$318$	−540803.	−0.299896
$319$	2.25567e6	1.24107
$320$	−1.64444e6	−0.897726
$321$	−747556.	−0.404931
$322$	0	0
$323$	2.17679e6	1.16094
$324$	258101.	0.136593
$325$	−2.09993e6	−1.10280
$326$	−769186.	−0.400855
$327$	−408206.	−0.211111
$328$	−742344.	−0.380996
$329$	0	0
$330$	808849.	0.408868
$331$	177318.	0.0889577	0.0444789	−	0.999010i	$-0.485837\pi$
$331$	177318.	0.0889577	0.0444789	+	0.999010i	$0.485837\pi$
$332$	1.19357e6	0.594296
$333$	−143630.	−0.0709798
$334$	−2.65864e6	−1.30405
$335$	1.24817e6	0.607664
$336$	0	0
$337$	−3.04781e6	−1.46189	−0.730943	−	0.682438i	$-0.760920\pi$
$337$	−3.04781e6	−1.46189	−0.730943	+	0.682438i	$0.760920\pi$
$338$	−7.99777e6	−3.80783
$339$	3199.80	0.00151225
$340$	−1.46205e6	−0.685908
$341$	285809.	0.133104
$342$	1.44253e6	0.666896
$343$	0	0
$344$	1.22747e6	0.559259
$345$	207680.	0.0939393
$346$	−3.05874e6	−1.37357
$347$	−2.42361e6	−1.08054	−0.540268	−	0.841493i	$-0.681677\pi$
$347$	−2.42361e6	−1.08054	−0.540268	+	0.841493i	$0.681677\pi$
$348$	−2.70195e6	−1.19599
$349$	2.67690e6	1.17644	0.588218	−	0.808702i	$-0.299830\pi$
$349$	2.67690e6	1.17644	0.588218	+	0.808702i	$0.299830\pi$
$350$	0	0
$351$	−836985.	−0.362619
$352$	2.42191e6	1.04184
$353$	−950412.	−0.405953	−0.202976	−	0.979184i	$-0.565061\pi$
$353$	−950412.	−0.405953	−0.202976	+	0.979184i	$0.565061\pi$
$354$	1.58642e6	0.672837
$355$	−1.02288e6	−0.430777
$356$	1.41971e6	0.593711
$357$	0	0
$358$	1.46877e6	0.605683
$359$	2.78881e6	1.14204	0.571022	−	0.820935i	$-0.306547\pi$
$359$	2.78881e6	1.14204	0.571022	+	0.820935i	$0.306547\pi$
$360$	−180745.	−0.0735040
$361$	1.96972e6	0.795495
$362$	1.14001e6	0.457235
$363$	663206.	0.264169
$364$	0	0
$365$	550536.	0.216299
$366$	1.81437e6	0.707985
$367$	−153881.	−0.0596377	−0.0298189	−	0.999555i	$-0.509493\pi$
$367$	−153881.	−0.0596377	−0.0298189	+	0.999555i	$0.509493\pi$
$368$	471323.	0.181426
$369$	970087.	0.370890
$370$	539169.	0.204749
$371$	0	0
$372$	−342356.	−0.128269
$373$	−2.38381e6	−0.887156	−0.443578	−	0.896236i	$-0.646291\pi$
$373$	−2.38381e6	−0.887156	−0.443578	+	0.896236i	$0.646291\pi$
$374$	2.57729e6	0.952763
$375$	1.60510e6	0.589417
$376$	−1.73345e6	−0.632328
$377$	8.76203e6	3.17506
$378$	0	0
$379$	3.65191e6	1.30594	0.652969	−	0.757385i	$-0.273523\pi$
$379$	3.65191e6	1.30594	0.652969	+	0.757385i	$0.273523\pi$
$380$	−2.98606e6	−1.06081
$381$	−1.52070e6	−0.536701
$382$	−1.53226e6	−0.537246
$383$	−2.15730e6	−0.751472	−0.375736	−	0.926727i	$-0.622610\pi$
$383$	−2.15730e6	−0.751472	−0.375736	+	0.926727i	$0.622610\pi$
$384$	−1.11245e6	−0.384991
$385$	0	0
$386$	−8.15904e6	−2.78722
$387$	−1.60404e6	−0.544424
$388$	6.05669e6	2.04247
$389$	−3.66471e6	−1.22791	−0.613954	−	0.789342i	$-0.710422\pi$
$389$	−3.66471e6	−1.22791	−0.613954	+	0.789342i	$0.710422\pi$
$390$	3.14194e6	1.04601
$391$	661746.	0.218902
$392$	0	0
$393$	−1.56572e6	−0.511368
$394$	5.90440e6	1.91617
$395$	−2.63014e6	−0.848177
$396$	941813.	0.301805
$397$	3.94648e6	1.25671	0.628353	−	0.777928i	$-0.283729\pi$
$397$	3.94648e6	1.25671	0.628353	+	0.777928i	$0.283729\pi$
$398$	−3.51524e6	−1.11236
$399$	0	0
$400$	1.34488e6	0.420274
$401$	25016.1	0.00776887	0.00388444	−	0.999992i	$-0.498764\pi$
$401$	25016.1	0.00776887	0.00388444	+	0.999992i	$0.498764\pi$
$402$	2.63559e6	0.813416
$403$	1.11021e6	0.340521
$404$	−5.49989e6	−1.67649
$405$	236196.	0.0715542
$406$	0	0
$407$	−524107.	−0.156832
$408$	−575922.	−0.171282
$409$	−832700.	−0.246139	−0.123069	−	0.992398i	$-0.539274\pi$
$409$	−832700.	−0.246139	−0.123069	+	0.992398i	$0.539274\pi$
$410$	−3.64159e6	−1.06987
$411$	−3.30951e6	−0.966405
$412$	4.56035e6	1.32360
$413$	0	0
$414$	438528.	0.125747
$415$	1.09227e6	0.311323
$416$	9.40782e6	2.66536
$417$	1.96170e6	0.552449
$418$	5.26379e6	1.47353
$419$	−3.95178e6	−1.09966	−0.549828	−	0.835278i	$-0.685307\pi$
$419$	−3.95178e6	−1.09966	−0.549828	+	0.835278i	$0.685307\pi$
$420$	0	0
$421$	4.72285e6	1.29867	0.649336	−	0.760502i	$-0.275047\pi$
$421$	4.72285e6	1.29867	0.649336	+	0.760502i	$0.275047\pi$
$422$	3.43890e6	0.940023
$423$	2.26526e6	0.615555
$424$	440974.	0.119124
$425$	1.88823e6	0.507087
$426$	−2.15986e6	−0.576636
$427$	0	0
$428$	3.26754e6	0.862207
$429$	−3.05417e6	−0.801216
$430$	6.02136e6	1.57045
$431$	4.07810e6	1.05746	0.528731	−	0.848790i	$-0.322668\pi$
$431$	4.07810e6	1.05746	0.528731	+	0.848790i	$0.322668\pi$
$432$	536039.	0.138193
$433$	1.79927e6	0.461186	0.230593	−	0.973050i	$-0.425933\pi$
$433$	1.79927e6	0.461186	0.230593	+	0.973050i	$0.425933\pi$
$434$	0	0
$435$	−2.47263e6	−0.626522
$436$	1.78425e6	0.449511
$437$	1.35153e6	0.338550
$438$	1.16249e6	0.289536
$439$	−4.51827e6	−1.11895	−0.559475	−	0.828847i	$-0.688997\pi$
$439$	−4.51827e6	−1.11895	−0.559475	+	0.828847i	$0.688997\pi$
$440$	−659542.	−0.162409
$441$	0	0
$442$	1.00114e7	2.43746
$443$	−2.85256e6	−0.690597	−0.345299	−	0.938493i	$-0.612222\pi$
$443$	−2.85256e6	−0.690597	−0.345299	+	0.938493i	$0.612222\pi$
$444$	627802.	0.151135
$445$	1.29922e6	0.311016
$446$	7.44976e6	1.77339
$447$	584155.	0.138280
$448$	0	0
$449$	−1.90246e6	−0.445348	−0.222674	−	0.974893i	$-0.571478\pi$
$449$	−1.90246e6	−0.445348	−0.222674	+	0.974893i	$0.571478\pi$
$450$	1.25130e6	0.291293
$451$	3.53986e6	0.819491
$452$	−13986.2	−0.00321998
$453$	2.01400e6	0.461119
$454$	−9.51468e6	−2.16648
$455$	0	0
$456$	−1.17625e6	−0.264903
$457$	2.64834e6	0.593176	0.296588	−	0.955006i	$-0.404151\pi$
$457$	2.64834e6	0.593176	0.296588	+	0.955006i	$0.404151\pi$
$458$	2.61904e6	0.583416
$459$	752608.	0.166739
$460$	−907763.	−0.200022
$461$	−1.09031e6	−0.238944	−0.119472	−	0.992838i	$-0.538120\pi$
$461$	−1.09031e6	−0.238944	−0.119472	+	0.992838i	$0.538120\pi$
$462$	0	0
$463$	−2.50851e6	−0.543831	−0.271916	−	0.962321i	$-0.587657\pi$
$463$	−2.50851e6	−0.543831	−0.271916	+	0.962321i	$0.587657\pi$
$464$	−5.61155e6	−1.21001
$465$	−313300.	−0.0671937
$466$	−9.59943e6	−2.04777
$467$	3.20935e6	0.680966	0.340483	−	0.940251i	$-0.389409\pi$
$467$	3.20935e6	0.680966	0.340483	+	0.940251i	$0.389409\pi$
$468$	3.65843e6	0.772112
$469$	0	0
$470$	−8.50350e6	−1.77563
$471$	−4.13976e6	−0.859850
$472$	−1.29358e6	−0.267262
$473$	−5.85315e6	−1.20292
$474$	−5.55369e6	−1.13537
$475$	3.85647e6	0.784252
$476$	0	0
$477$	−576260.	−0.115964
$478$	−739102.	−0.147957
$479$	−2.31462e6	−0.460936	−0.230468	−	0.973080i	$-0.574026\pi$
$479$	−2.31462e6	−0.460936	−0.230468	+	0.973080i	$0.574026\pi$
$480$	−2.65487e6	−0.525945
$481$	−2.03587e6	−0.401225
$482$	4.54211e6	0.890513
$483$	0	0
$484$	−2.89885e6	−0.562486
$485$	5.54266e6	1.06995
$486$	498741.	0.0957821
$487$	−4.63735e6	−0.886028	−0.443014	−	0.896515i	$-0.646091\pi$
$487$	−4.63735e6	−0.886028	−0.443014	+	0.896515i	$0.646091\pi$
$488$	−1.47945e6	−0.281224
$489$	−819618.	−0.155003
$490$	0	0
$491$	5.02151e6	0.940007	0.470003	−	0.882665i	$-0.344253\pi$
$491$	5.02151e6	0.940007	0.470003	+	0.882665i	$0.344253\pi$
$492$	−4.24021e6	−0.789724
$493$	−7.87872e6	−1.45995
$494$	2.04470e7	3.76974
$495$	861881.	0.158101
$496$	−711024.	−0.129772
$497$	0	0
$498$	2.30639e6	0.416735
$499$	3.37822e6	0.607347	0.303673	−	0.952776i	$-0.401787\pi$
$499$	3.37822e6	0.607347	0.303673	+	0.952776i	$0.401787\pi$
$500$	−7.01582e6	−1.25503
$501$	−2.83295e6	−0.504249
$502$	1.14322e7	2.02475
$503$	−5.03743e6	−0.887747	−0.443873	−	0.896090i	$-0.646396\pi$
$503$	−5.03743e6	−0.887747	−0.443873	+	0.896090i	$0.646396\pi$
$504$	0	0
$505$	−5.03311e6	−0.878230
$506$	1.60019e6	0.277841
$507$	−8.52214e6	−1.47241
$508$	6.64694e6	1.14278
$509$	−6.72466e6	−1.15047	−0.575236	−	0.817988i	$-0.695090\pi$
$509$	−6.72466e6	−1.15047	−0.575236	+	0.817988i	$0.695090\pi$
$510$	−2.82520e6	−0.480976
$511$	0	0
$512$	−7.48361e6	−1.26164
$513$	1.53711e6	0.257876
$514$	−8.25112e6	−1.37754
$515$	4.17332e6	0.693367
$516$	7.01119e6	1.15922
$517$	8.26595e6	1.36009
$518$	0	0
$519$	−3.25929e6	−0.531134
$520$	−2.56196e6	−0.415493
$521$	−4.42770e6	−0.714635	−0.357317	−	0.933983i	$-0.616309\pi$
$521$	−4.42770e6	−0.714635	−0.357317	+	0.933983i	$0.616309\pi$
$522$	−5.22110e6	−0.838660
$523$	−8.95911e6	−1.43222	−0.716111	−	0.697986i	$-0.754080\pi$
$523$	−8.95911e6	−1.43222	−0.716111	+	0.697986i	$0.754080\pi$
$524$	6.84372e6	1.08884
$525$	0	0
$526$	1.05050e7	1.65551
$527$	−998291.	−0.156578
$528$	1.95601e6	0.305342
$529$	−6.02548e6	−0.936165
$530$	2.16321e6	0.334510
$531$	1.69043e6	0.260173
$532$	0	0
$533$	1.37504e7	2.09652
$534$	2.74338e6	0.416325
$535$	2.99022e6	0.451668
$536$	−2.14908e6	−0.323103
$537$	1.56507e6	0.234205
$538$	−9.15641e6	−1.36386
$539$	0	0
$540$	−1.03240e6	−0.152358
$541$	−1.00467e7	−1.47581	−0.737907	−	0.674902i	$-0.764186\pi$
$541$	−1.00467e7	−1.47581	−0.737907	+	0.674902i	$0.764186\pi$
$542$	−1.82968e7	−2.67533
$543$	1.21476e6	0.176804
$544$	−8.45941e6	−1.22558
$545$	1.63282e6	0.235477
$546$	0	0
$547$	−1.31426e7	−1.87808	−0.939039	−	0.343811i	$-0.888282\pi$
$547$	−1.31426e7	−1.87808	−0.939039	+	0.343811i	$0.888282\pi$
$548$	1.44657e7	2.05774
$549$	1.93333e6	0.273764
$550$	4.56600e6	0.643620
$551$	−1.60913e7	−2.25794
$552$	−357579.	−0.0499487
$553$	0	0
$554$	−2.14415e6	−0.296811
$555$	574520.	0.0791722
$556$	−8.57452e6	−1.17631
$557$	9.06752e6	1.23837	0.619185	−	0.785245i	$-0.287463\pi$
$557$	9.06752e6	1.23837	0.619185	+	0.785245i	$0.287463\pi$
$558$	−661551.	−0.0899452
$559$	−2.27363e7	−3.07744
$560$	0	0
$561$	2.74627e6	0.368414
$562$	−9.63846e6	−1.28726
$563$	1.05180e7	1.39849	0.699247	−	0.714880i	$-0.253519\pi$
$563$	1.05180e7	1.39849	0.699247	+	0.714880i	$0.253519\pi$
$564$	−9.90136e6	−1.31068
$565$	−12799.2	−0.00168679
$566$	−5.15150e6	−0.675916
$567$	0	0
$568$	1.76117e6	0.229050
$569$	7.32307e6	0.948227	0.474114	−	0.880464i	$-0.342769\pi$
$569$	7.32307e6	0.948227	0.474114	+	0.880464i	$0.342769\pi$
$570$	−5.77010e6	−0.743869
$571$	−6.97981e6	−0.895887	−0.447943	−	0.894062i	$-0.647843\pi$
$571$	−6.97981e6	−0.895887	−0.447943	+	0.894062i	$0.647843\pi$
$572$	1.33497e7	1.70600
$573$	−1.63272e6	−0.207743
$574$	0	0
$575$	1.17237e6	0.147875
$576$	−3.70000e6	−0.464670
$577$	−5.81210e6	−0.726765	−0.363382	−	0.931640i	$-0.618378\pi$
$577$	−5.81210e6	−0.726765	−0.363382	+	0.931640i	$0.618378\pi$
$578$	2.99030e6	0.372302
$579$	−8.69399e6	−1.07776
$580$	1.08078e7	1.33403
$581$	0	0
$582$	1.17036e7	1.43223
$583$	−2.10278e6	−0.256226
$584$	−947901.	−0.115009
$585$	3.34794e6	0.404472
$586$	1.32131e6	0.158950
$587$	−7.37446e6	−0.883355	−0.441677	−	0.897174i	$-0.645616\pi$
$587$	−7.37446e6	−0.883355	−0.441677	+	0.897174i	$0.645616\pi$
$588$	0	0
$589$	−2.03888e6	−0.242161
$590$	−6.34567e6	−0.750495
$591$	6.29152e6	0.740947
$592$	1.30385e6	0.152906
$593$	9.46528e6	1.10534	0.552671	−	0.833399i	$-0.313609\pi$
$593$	9.46528e6	1.10534	0.552671	+	0.833399i	$0.313609\pi$
$594$	1.81991e6	0.211633
$595$	0	0
$596$	−2.55332e6	−0.294435
$597$	−3.74571e6	−0.430129
$598$	6.21589e6	0.710804
$599$	−8.52195e6	−0.970448	−0.485224	−	0.874390i	$-0.661262\pi$
$599$	−8.52195e6	−0.970448	−0.485224	+	0.874390i	$0.661262\pi$
$600$	−1.02032e6	−0.115706
$601$	−657065.	−0.0742031	−0.0371016	−	0.999311i	$-0.511813\pi$
$601$	−657065.	−0.0742031	−0.0371016	+	0.999311i	$0.511813\pi$
$602$	0	0
$603$	2.80839e6	0.314532
$604$	−8.80310e6	−0.981846
$605$	−2.65282e6	−0.294659
$606$	−1.06277e7	−1.17560
$607$	5.86885e6	0.646519	0.323260	−	0.946310i	$-0.395221\pi$
$607$	5.86885e6	0.646519	0.323260	+	0.946310i	$0.395221\pi$
$608$	−1.72773e7	−1.89547
$609$	0	0
$610$	−7.25750e6	−0.789700
$611$	3.21087e7	3.47952
$612$	−3.28962e6	−0.355032
$613$	3.84402e6	0.413175	0.206588	−	0.978428i	$-0.433764\pi$
$613$	3.84402e6	0.413175	0.206588	+	0.978428i	$0.433764\pi$
$614$	2.47667e6	0.265123
$615$	−3.88035e6	−0.413698
$616$	0	0
$617$	6.44660e6	0.681739	0.340869	−	0.940111i	$-0.389279\pi$
$617$	6.44660e6	0.681739	0.340869	+	0.940111i	$0.389279\pi$
$618$	8.81219e6	0.928138
$619$	6.73740e6	0.706749	0.353375	−	0.935482i	$-0.385034\pi$
$619$	6.73740e6	0.706749	0.353375	+	0.935482i	$0.385034\pi$
$620$	1.36942e6	0.143073
$621$	467281.	0.0486238
$622$	2.07115e7	2.14652
$623$	0	0
$624$	7.59804e6	0.781160
$625$	−704759.	−0.0721673
$626$	1.55023e7	1.58110
$627$	5.60891e6	0.569783
$628$	1.80947e7	1.83085
$629$	1.83063e6	0.184491
$630$	0	0
$631$	−9.14514e6	−0.914360	−0.457180	−	0.889374i	$-0.651140\pi$
$631$	−9.14514e6	−0.914360	−0.457180	+	0.889374i	$0.651140\pi$
$632$	4.52852e6	0.450987
$633$	3.66437e6	0.363488
$634$	−4.98293e6	−0.492336
$635$	6.08282e6	0.598647
$636$	2.51881e6	0.246918
$637$	0	0
$638$	−1.90518e7	−1.85304
$639$	−2.30147e6	−0.222974
$640$	4.44978e6	0.429426
$641$	−1.04088e6	−0.100059	−0.0500296	−	0.998748i	$-0.515932\pi$
$641$	−1.04088e6	−0.100059	−0.0500296	+	0.998748i	$0.515932\pi$
$642$	6.31403e6	0.604601
$643$	−9.08713e6	−0.866761	−0.433381	−	0.901211i	$-0.642679\pi$
$643$	−9.08713e6	−0.866761	−0.433381	+	0.901211i	$0.642679\pi$
$644$	0	0
$645$	6.41615e6	0.607261
$646$	−1.83857e7	−1.73340
$647$	2.20711e6	0.207283	0.103641	−	0.994615i	$-0.466951\pi$
$647$	2.20711e6	0.207283	0.103641	+	0.994615i	$0.466951\pi$
$648$	−406677.	−0.0380463
$649$	6.16840e6	0.574859
$650$	1.77364e7	1.64658
$651$	0	0
$652$	3.58252e6	0.330042
$653$	−1.83610e7	−1.68505	−0.842524	−	0.538658i	$-0.818931\pi$
$653$	−1.83610e7	−1.68505	−0.842524	+	0.538658i	$0.818931\pi$
$654$	3.44780e6	0.315208
$655$	6.26289e6	0.570390
$656$	−8.80632e6	−0.798978
$657$	1.23871e6	0.111958
$658$	0	0
$659$	6.21208e6	0.557216	0.278608	−	0.960405i	$-0.410127\pi$
$659$	6.21208e6	0.557216	0.278608	+	0.960405i	$0.410127\pi$
$660$	−3.76725e6	−0.336639
$661$	1.54230e7	1.37298	0.686491	−	0.727138i	$-0.259150\pi$
$661$	1.54230e7	1.37298	0.686491	+	0.727138i	$0.259150\pi$
$662$	−1.49767e6	−0.132822
$663$	1.06678e7	0.942519
$664$	−1.88065e6	−0.165534
$665$	0	0
$666$	1.21313e6	0.105980
$667$	−4.89176e6	−0.425746
$668$	1.23827e7	1.07368
$669$	7.93820e6	0.685736
$670$	−1.05424e7	−0.907300
$671$	7.05475e6	0.604889
$672$	0	0
$673$	−2.27201e7	−1.93362	−0.966811	−	0.255491i	$-0.917763\pi$
$673$	−2.27201e7	−1.93362	−0.966811	+	0.255491i	$0.917763\pi$
$674$	2.57425e7	2.18274
$675$	1.33334e6	0.112637
$676$	3.72500e7	3.13516
$677$	1.36173e7	1.14188	0.570940	−	0.820992i	$-0.306579\pi$
$677$	1.36173e7	1.14188	0.570940	+	0.820992i	$0.306579\pi$
$678$	−27026.2	−0.00225793
$679$	0	0
$680$	2.30369e6	0.191052
$681$	−1.01385e7	−0.837734
$682$	−2.41401e6	−0.198736
$683$	2.39985e6	0.196849	0.0984245	−	0.995145i	$-0.468620\pi$
$683$	2.39985e6	0.196849	0.0984245	+	0.995145i	$0.468620\pi$
$684$	−6.71863e6	−0.549086
$685$	1.32380e7	1.07795
$686$	0	0
$687$	2.79076e6	0.225595
$688$	1.45612e7	1.17281
$689$	−8.16816e6	−0.655505
$690$	−1.75411e6	−0.140260
$691$	−1.40365e6	−0.111831	−0.0559156	−	0.998435i	$-0.517808\pi$
$691$	−1.40365e6	−0.111831	−0.0559156	+	0.998435i	$0.517808\pi$
$692$	1.42462e7	1.13093
$693$	0	0
$694$	2.04703e7	1.61334
$695$	−7.84680e6	−0.616212
$696$	4.25732e6	0.333130
$697$	−1.23642e7	−0.964018
$698$	−2.26097e7	−1.75653
$699$	−1.02288e7	−0.791831
$700$	0	0
$701$	−5.78991e6	−0.445017	−0.222509	−	0.974931i	$-0.571425\pi$
$701$	−5.78991e6	−0.445017	−0.222509	+	0.974931i	$0.571425\pi$
$702$	7.06936e6	0.541424
$703$	3.73884e6	0.285330
$704$	−1.35013e7	−1.02670
$705$	−9.06103e6	−0.686602
$706$	8.02739e6	0.606126
$707$	0	0
$708$	−7.38882e6	−0.553977
$709$	−1.13143e7	−0.845304	−0.422652	−	0.906292i	$-0.638901\pi$
$709$	−1.13143e7	−0.845304	−0.422652	+	0.906292i	$0.638901\pi$
$710$	8.63944e6	0.643191
$711$	−5.91782e6	−0.439024
$712$	−2.23697e6	−0.165371
$713$	−619821.	−0.0456607
$714$	0	0
$715$	1.22167e7	0.893692
$716$	−6.84085e6	−0.498686
$717$	−787562.	−0.0572119
$718$	−2.35549e7	−1.70518
$719$	−2.73780e7	−1.97506	−0.987529	−	0.157437i	$-0.949677\pi$
$719$	−2.73780e7	−1.97506	−0.987529	+	0.157437i	$0.949677\pi$
$720$	−2.14415e6	−0.154143
$721$	0	0
$722$	−1.66367e7	−1.18775
$723$	4.83992e6	0.344344
$724$	−5.30967e6	−0.376462
$725$	−1.39582e7	−0.986241
$726$	−5.60158e6	−0.394429
$727$	−9.86471e6	−0.692226	−0.346113	−	0.938193i	$-0.612499\pi$
$727$	−9.86471e6	−0.692226	−0.346113	+	0.938193i	$0.612499\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	−4.64995e6	−0.322954
$731$	2.04442e7	1.41507
$732$	−8.45053e6	−0.582916
$733$	3.87876e6	0.266645	0.133322	−	0.991073i	$-0.457435\pi$
$733$	3.87876e6	0.266645	0.133322	+	0.991073i	$0.457435\pi$
$734$	1.29972e6	0.0890448
$735$	0	0
$736$	−5.25229e6	−0.357400
$737$	1.02479e7	0.694967
$738$	−8.19357e6	−0.553774
$739$	−7.95498e6	−0.535831	−0.267916	−	0.963442i	$-0.586335\pi$
$739$	−7.95498e6	−0.535831	−0.267916	+	0.963442i	$0.586335\pi$
$740$	−2.51121e6	−0.168579
$741$	2.17876e7	1.45768
$742$	0	0
$743$	1.65977e7	1.10300	0.551500	−	0.834175i	$-0.314056\pi$
$743$	1.65977e7	1.10300	0.551500	+	0.834175i	$0.314056\pi$
$744$	539433.	0.0357277
$745$	−2.33662e6	−0.154240
$746$	2.01342e7	1.32461
$747$	2.45761e6	0.161143
$748$	−1.20039e7	−0.784453
$749$	0	0
$750$	−1.35570e7	−0.880056
$751$	1.51072e7	0.977426	0.488713	−	0.872445i	$-0.337467\pi$
$751$	1.51072e7	0.977426	0.488713	+	0.872445i	$0.337467\pi$
$752$	−2.05637e7	−1.32604
$753$	1.21818e7	0.782929
$754$	−7.40061e7	−4.74066
$755$	−8.05598e6	−0.514341
$756$	0	0
$757$	5.80923e6	0.368450	0.184225	−	0.982884i	$-0.441022\pi$
$757$	5.80923e6	0.368450	0.184225	+	0.982884i	$0.441022\pi$
$758$	−3.08449e7	−1.94989
$759$	1.70511e6	0.107436
$760$	4.70498e6	0.295477
$761$	2.54270e7	1.59160	0.795799	−	0.605561i	$-0.207051\pi$
$761$	2.54270e7	1.59160	0.795799	+	0.605561i	$0.207051\pi$
$762$	1.28442e7	0.801346
$763$	0	0
$764$	7.13656e6	0.442340
$765$	−3.01043e6	−0.185984
$766$	1.82210e7	1.12202
$767$	2.39609e7	1.47067
$768$	−3.75958e6	−0.230005
$769$	1.53909e7	0.938532	0.469266	−	0.883057i	$-0.344519\pi$
$769$	1.53909e7	0.938532	0.469266	+	0.883057i	$0.344519\pi$
$770$	0	0
$771$	−8.79210e6	−0.532668
$772$	3.80011e7	2.29484
$773$	905393.	0.0544990	0.0272495	−	0.999629i	$-0.491325\pi$
$773$	905393.	0.0544990	0.0272495	+	0.999629i	$0.491325\pi$
$774$	1.35481e7	0.812877
$775$	−1.76860e6	−0.105773
$776$	−9.54323e6	−0.568907
$777$	0	0
$778$	3.09530e7	1.83338
$779$	−2.52523e7	−1.49093
$780$	−1.46337e7	−0.861229
$781$	−8.39810e6	−0.492667
$782$	−5.58926e6	−0.326841
$783$	−5.56342e6	−0.324293
$784$	0	0
$785$	1.65590e7	0.959093
$786$	1.32244e7	0.763521
$787$	−2.79334e7	−1.60763	−0.803817	−	0.594877i	$-0.797201\pi$
$787$	−2.79334e7	−1.60763	−0.803817	+	0.594877i	$0.797201\pi$
$788$	−2.75000e7	−1.57767
$789$	1.11937e7	0.640151
$790$	2.22148e7	1.26641
$791$	0	0
$792$	−1.48397e6	−0.0840643
$793$	2.74039e7	1.54749
$794$	−3.33328e7	−1.87638
$795$	2.30504e6	0.129348
$796$	1.63724e7	0.915860
$797$	2.18824e7	1.22025	0.610126	−	0.792304i	$-0.291119\pi$
$797$	2.18824e7	1.22025	0.610126	+	0.792304i	$0.291119\pi$
$798$	0	0
$799$	−2.88718e7	−1.59995
$800$	−1.49869e7	−0.827918
$801$	2.92325e6	0.160985
$802$	−211291.	−0.0115997
$803$	4.52005e6	0.247374
$804$	−1.22754e7	−0.669722
$805$	0	0
$806$	−9.37710e6	−0.508430
$807$	−9.75676e6	−0.527377
$808$	8.66590e6	0.466966
$809$	2.44194e7	1.31179	0.655893	−	0.754854i	$-0.272292\pi$
$809$	2.44194e7	1.31179	0.655893	+	0.754854i	$0.272292\pi$
$810$	−1.99496e6	−0.106837
$811$	4.46711e6	0.238492	0.119246	−	0.992865i	$-0.461952\pi$
$811$	4.46711e6	0.238492	0.119246	+	0.992865i	$0.461952\pi$
$812$	0	0
$813$	−1.94964e7	−1.03450
$814$	4.42673e6	0.234165
$815$	3.27847e6	0.172893
$816$	−6.83207e6	−0.359192
$817$	4.17547e7	2.18852
$818$	7.03317e6	0.367509
$819$	0	0
$820$	1.69609e7	0.880873
$821$	1.34708e7	0.697485	0.348743	−	0.937219i	$-0.386609\pi$
$821$	1.34708e7	0.697485	0.348743	+	0.937219i	$0.386609\pi$
$822$	2.79529e7	1.44293
$823$	−4.03958e6	−0.207891	−0.103946	−	0.994583i	$-0.533147\pi$
$823$	−4.03958e6	−0.207891	−0.103946	+	0.994583i	$0.533147\pi$
$824$	−7.18552e6	−0.368672
$825$	4.86537e6	0.248875
$826$	0	0
$827$	1.24927e7	0.635175	0.317588	−	0.948229i	$-0.397127\pi$
$827$	1.24927e7	0.635175	0.317588	+	0.948229i	$0.397127\pi$
$828$	−2.04247e6	−0.103533
$829$	−1.45980e7	−0.737749	−0.368874	−	0.929479i	$-0.620257\pi$
$829$	−1.45980e7	−0.737749	−0.368874	+	0.929479i	$0.620257\pi$
$830$	−9.22557e6	−0.464834
$831$	−2.28473e6	−0.114771
$832$	−5.24453e7	−2.62663
$833$	0	0
$834$	−1.65690e7	−0.824859
$835$	1.13318e7	0.562449
$836$	−2.45163e7	−1.21322
$837$	−704926.	−0.0347800
$838$	3.33776e7	1.64189
$839$	−9.15983e6	−0.449244	−0.224622	−	0.974446i	$-0.572115\pi$
$839$	−9.15983e6	−0.449244	−0.224622	+	0.974446i	$0.572115\pi$
$840$	0	0
$841$	3.77299e7	1.83948
$842$	−3.98903e7	−1.93904
$843$	−1.02704e7	−0.497759
$844$	−1.60168e7	−0.773964
$845$	3.40886e7	1.64236
$846$	−1.91329e7	−0.919082
$847$	0	0
$848$	5.23121e6	0.249812
$849$	−5.48926e6	−0.261363
$850$	−1.59484e7	−0.757129
$851$	1.13661e6	0.0538005
$852$	1.00597e7	0.474771
$853$	−8.68253e6	−0.408577	−0.204289	−	0.978911i	$-0.565488\pi$
$853$	−8.68253e6	−0.408577	−0.204289	+	0.978911i	$0.565488\pi$
$854$	0	0
$855$	−6.14842e6	−0.287639
$856$	−5.14850e6	−0.240158
$857$	1.04988e7	0.488302	0.244151	−	0.969737i	$-0.421491\pi$
$857$	1.04988e7	0.488302	0.244151	+	0.969737i	$0.421491\pi$
$858$	2.57962e7	1.19629
$859$	9.03780e6	0.417907	0.208954	−	0.977926i	$-0.432994\pi$
$859$	9.03780e6	0.417907	0.208954	+	0.977926i	$0.432994\pi$
$860$	−2.80448e7	−1.29302
$861$	0	0
$862$	−3.44445e7	−1.57889
$863$	−1.59858e7	−0.730645	−0.365322	−	0.930881i	$-0.619041\pi$
$863$	−1.59858e7	−0.730645	−0.365322	+	0.930881i	$0.619041\pi$
$864$	−5.97346e6	−0.272234
$865$	1.30371e7	0.592437
$866$	−1.51970e7	−0.688594
$867$	3.18636e6	0.143962
$868$	0	0
$869$	−2.15942e7	−0.970035
$870$	2.08844e7	0.935457
$871$	3.98073e7	1.77794
$872$	−2.81136e6	−0.125206
$873$	1.24710e7	0.553816
$874$	−1.14153e7	−0.505487
$875$	0	0
$876$	−5.41434e6	−0.238388
$877$	2.67453e7	1.17422	0.587109	−	0.809508i	$-0.300266\pi$
$877$	2.67453e7	1.17422	0.587109	+	0.809508i	$0.300266\pi$
$878$	3.81623e7	1.67070
$879$	1.40794e6	0.0614628
$880$	−7.82404e6	−0.340584
$881$	−6.40715e6	−0.278115	−0.139058	−	0.990284i	$-0.544407\pi$
$881$	−6.40715e6	−0.278115	−0.139058	+	0.990284i	$0.544407\pi$
$882$	0	0
$883$	4.96462e6	0.214281	0.107141	−	0.994244i	$-0.465831\pi$
$883$	4.96462e6	0.214281	0.107141	+	0.994244i	$0.465831\pi$
$884$	−4.66285e7	−2.00688
$885$	−6.76173e6	−0.290201
$886$	2.40933e7	1.03113
$887$	8.71625e6	0.371981	0.185990	−	0.982552i	$-0.440451\pi$
$887$	8.71625e6	0.371981	0.185990	+	0.982552i	$0.440451\pi$
$888$	−989196.	−0.0420969
$889$	0	0
$890$	−1.09735e7	−0.464377
$891$	1.93923e6	0.0818344
$892$	−3.46976e7	−1.46011
$893$	−5.89669e7	−2.47446
$894$	−4.93390e6	−0.206465
$895$	−6.26026e6	−0.261237
$896$	0	0
$897$	6.62343e6	0.274854
$898$	1.60686e7	0.664946
$899$	7.37956e6	0.304531
$900$	−5.82798e6	−0.239835
$901$	7.34472e6	0.301414
$902$	−2.98984e7	−1.22358
$903$	0	0
$904$	22037.4	0.000896888 0
$905$	−4.85904e6	−0.197210
$906$	−1.70107e7	−0.688494
$907$	−2.36255e7	−0.953594	−0.476797	−	0.879014i	$-0.658202\pi$
$907$	−2.36255e7	−0.953594	−0.476797	+	0.879014i	$0.658202\pi$
$908$	4.43151e7	1.78376
$909$	−1.13245e7	−0.454579
$910$	0	0
$911$	−1.69360e7	−0.676105	−0.338053	−	0.941127i	$-0.609768\pi$
$911$	−1.69360e7	−0.676105	−0.338053	+	0.941127i	$0.609768\pi$
$912$	−1.39536e7	−0.555520
$913$	8.96785e6	0.356050
$914$	−2.23685e7	−0.885668
$915$	−7.73334e6	−0.305361
$916$	−1.21983e7	−0.480353
$917$	0	0
$918$	−6.35669e6	−0.248957
$919$	−3.13804e7	−1.22566	−0.612829	−	0.790216i	$-0.709968\pi$
$919$	−3.13804e7	−1.22566	−0.612829	+	0.790216i	$0.709968\pi$
$920$	1.43032e6	0.0557138
$921$	2.63906e6	0.102518
$922$	9.20896e6	0.356766
$923$	−3.26220e7	−1.26040
$924$	0	0
$925$	3.24320e6	0.124629
$926$	2.11875e7	0.811992
$927$	9.38996e6	0.358893
$928$	6.25336e7	2.38365
$929$	−1.43089e7	−0.543959	−0.271980	−	0.962303i	$-0.587678\pi$
$929$	−1.43089e7	−0.543959	−0.271980	+	0.962303i	$0.587678\pi$
$930$	2.64620e6	0.100327
$931$	0	0
$932$	4.47098e7	1.68602
$933$	2.20694e7	0.830017
$934$	−2.71069e7	−1.01675
$935$	−1.09851e7	−0.410937
$936$	−5.76441e6	−0.215063
$937$	2.81206e7	1.04635	0.523173	−	0.852227i	$-0.324748\pi$
$937$	2.81206e7	1.04635	0.523173	+	0.852227i	$0.324748\pi$
$938$	0	0
$939$	1.65187e7	0.611381
$940$	3.96054e7	1.46196
$941$	−3.29569e7	−1.21331	−0.606656	−	0.794964i	$-0.707490\pi$
$941$	−3.29569e7	−1.21331	−0.606656	+	0.794964i	$0.707490\pi$
$942$	3.49653e7	1.28384
$943$	−7.67672e6	−0.281123
$944$	−1.53455e7	−0.560469
$945$	0	0
$946$	4.94370e7	1.79607
$947$	1.62975e7	0.590535	0.295268	−	0.955415i	$-0.404591\pi$
$947$	1.62975e7	0.590535	0.295268	+	0.955415i	$0.404591\pi$
$948$	2.58666e7	0.934799
$949$	1.75579e7	0.632861
$950$	−3.25726e7	−1.17096
$951$	−5.30964e6	−0.190377
$952$	0	0
$953$	−3.03230e7	−1.08153	−0.540767	−	0.841172i	$-0.681866\pi$
$953$	−3.03230e7	−1.08153	−0.540767	+	0.841172i	$0.681866\pi$
$954$	4.86722e6	0.173145
$955$	6.53088e6	0.231720
$956$	3.44240e6	0.121820
$957$	−2.03010e7	−0.716535
$958$	1.95498e7	0.688221
$959$	0	0
$960$	1.48000e7	0.518302
$961$	−2.76941e7	−0.967339
$962$	1.71954e7	0.599067
$963$	6.72801e6	0.233787
$964$	−2.11551e7	−0.733200
$965$	3.47759e7	1.20216
$966$	0	0
$967$	−1.49059e7	−0.512616	−0.256308	−	0.966595i	$-0.582506\pi$
$967$	−1.49059e7	−0.512616	−0.256308	+	0.966595i	$0.582506\pi$
$968$	4.56757e6	0.156674
$969$	−1.95911e7	−0.670271
$970$	−4.68145e7	−1.59754
$971$	1.65608e7	0.563679	0.281840	−	0.959462i	$-0.409055\pi$
$971$	1.65608e7	0.563679	0.281840	+	0.959462i	$0.409055\pi$
$972$	−2.32291e6	−0.0788618
$973$	0	0
$974$	3.91681e7	1.32292
$975$	1.88993e7	0.636700
$976$	−1.75505e7	−0.589747
$977$	7.56862e6	0.253676	0.126838	−	0.991923i	$-0.459517\pi$
$977$	7.56862e6	0.253676	0.126838	+	0.991923i	$0.459517\pi$
$978$	6.92267e6	0.231434
$979$	1.06670e7	0.355700
$980$	0	0
$981$	3.67386e6	0.121885
$982$	−4.24128e7	−1.40352
$983$	−3.32042e7	−1.09600	−0.547998	−	0.836480i	$-0.684610\pi$
$983$	−3.32042e7	−1.09600	−0.547998	+	0.836480i	$0.684610\pi$
$984$	6.68110e6	0.219968
$985$	−2.51661e7	−0.826466
$986$	6.65454e7	2.17985
$987$	0	0
$988$	−9.52327e7	−3.10380
$989$	1.26935e7	0.412657
$990$	−7.27964e6	−0.236060
$991$	3.48003e7	1.12564	0.562819	−	0.826580i	$-0.309717\pi$
$991$	3.48003e7	1.12564	0.562819	+	0.826580i	$0.309717\pi$
$992$	7.92345e6	0.255644
$993$	−1.59586e6	−0.0513598
$994$	0	0
$995$	1.49829e7	0.479774
$996$	−1.07421e7	−0.343117
$997$	9.40852e6	0.299767	0.149883	−	0.988704i	$-0.452110\pi$
$997$	9.40852e6	0.299767	0.149883	+	0.988704i	$0.452110\pi$
$998$	−2.85332e7	−0.906826
$999$	1.29267e6	0.0409802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.h.1.1	✓	2
3.2	odd	2		441.6.a.q.1.2		2
7.2	even	3		147.6.e.n.67.2		4
7.3	odd	6		147.6.e.m.79.2		4
7.4	even	3		147.6.e.n.79.2		4
7.5	odd	6		147.6.e.m.67.2		4
7.6	odd	2		147.6.a.j.1.1	yes	2
21.20	even	2		441.6.a.r.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.h.1.1	✓	2	1.1	even	1	trivial
147.6.a.j.1.1	yes	2	7.6	odd	2
147.6.e.m.67.2		4	7.5	odd	6
147.6.e.m.79.2		4	7.3	odd	6
147.6.e.n.67.2		4	7.2	even	3
147.6.e.n.79.2		4	7.4	even	3
441.6.a.q.1.2		2	3.2	odd	2
441.6.a.r.1.2		2	21.20	even	2

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q-8.44622 q^{2} -9.00000 q^{3} +39.3387 q^{4} +36.0000 q^{5} +76.0160 q^{6} -61.9840 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-8.44622 q^{2} -9.00000 q^{3} +39.3387 q^{4} +36.0000 q^{5} +76.0160 q^{6} -61.9840 q^{8} +81.0000 q^{9} -304.064 q^{10} +295.570 q^{11} -354.048 q^{12} +1148.13 q^{13} -324.000 q^{15} -735.307 q^{16} -1032.38 q^{17} -684.144 q^{18} -2108.51 q^{19} +1416.19 q^{20} -2496.45 q^{22} -640.988 q^{23} +557.856 q^{24} -1829.00 q^{25} -9697.34 q^{26} -729.000 q^{27} +7631.58 q^{29} +2736.58 q^{30} +966.976 q^{31} +8194.05 q^{32} -2660.13 q^{33} +8719.74 q^{34} +3186.43 q^{36} -1773.21 q^{37} +17809.0 q^{38} -10333.2 q^{39} -2231.42 q^{40} +11976.4 q^{41} -19802.9 q^{43} +11627.3 q^{44} +2916.00 q^{45} +5413.93 q^{46} +27966.1 q^{47} +6617.76 q^{48} +15448.1 q^{50} +9291.46 q^{51} +45165.8 q^{52} -7114.33 q^{53} +6157.30 q^{54} +10640.5 q^{55} +18976.6 q^{57} -64458.0 q^{58} +20869.5 q^{59} -12745.7 q^{60} +23868.3 q^{61} -8167.30 q^{62} -45679.0 q^{64} +41332.6 q^{65} +22468.0 q^{66} +34671.5 q^{67} -40612.6 q^{68} +5768.90 q^{69} -28413.2 q^{71} -5020.70 q^{72} +15292.7 q^{73} +14976.9 q^{74} +16461.0 q^{75} -82946.0 q^{76} +87276.1 q^{78} -73059.5 q^{79} -26471.0 q^{80} +6561.00 q^{81} -101155. q^{82} +30340.9 q^{83} -37165.8 q^{85} +167260. q^{86} -68684.2 q^{87} -18320.6 q^{88} +36089.5 q^{89} -24629.2 q^{90} -25215.6 q^{92} -8702.79 q^{93} -236208. q^{94} -75906.4 q^{95} -73746.5 q^{96} +153963. q^{97} +23941.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 18 q^{3} + 37 q^{4} + 72 q^{5} + 27 q^{6} - 249 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 18 * q^3 + 37 * q^4 + 72 * q^5 + 27 * q^6 - 249 * q^8 + 162 * q^9	\( 2 q - 3 q^{2} - 18 q^{3} + 37 q^{4} + 72 q^{5} + 27 q^{6} - 249 q^{8} + 162 q^{9} - 108 q^{10} + 480 q^{11} - 333 q^{12} + 1296 q^{13} - 648 q^{15} - 1679 q^{16} + 936 q^{17} - 243 q^{18} - 216 q^{19} + 1332 q^{20} - 1492 q^{22} - 504 q^{23} + 2241 q^{24} - 3658 q^{25} - 8892 q^{26} - 1458 q^{27} + 6372 q^{29} + 972 q^{30} + 9936 q^{31} + 9039 q^{32} - 4320 q^{33} + 19440 q^{34} + 2997 q^{36} + 11124 q^{37} + 28116 q^{38} - 11664 q^{39} - 8964 q^{40} + 20952 q^{41} - 6264 q^{43} + 11196 q^{44} + 5832 q^{45} + 6160 q^{46} + 7920 q^{47} + 15111 q^{48} + 5487 q^{50} - 8424 q^{51} + 44820 q^{52} + 2220 q^{53} + 2187 q^{54} + 17280 q^{55} + 1944 q^{57} - 71318 q^{58} + 29736 q^{59} - 11988 q^{60} - 17280 q^{61} + 40680 q^{62} - 10879 q^{64} + 46656 q^{65} + 13428 q^{66} - 20680 q^{67} - 45216 q^{68} + 4536 q^{69} - 92280 q^{71} - 20169 q^{72} + 56592 q^{73} + 85218 q^{74} + 32922 q^{75} - 87372 q^{76} + 80028 q^{78} - 56096 q^{79} - 60444 q^{80} + 13122 q^{81} - 52272 q^{82} - 71352 q^{83} + 33696 q^{85} + 240996 q^{86} - 57348 q^{87} - 52812 q^{88} + 123192 q^{89} - 8748 q^{90} - 25536 q^{92} - 89424 q^{93} - 345384 q^{94} - 7776 q^{95} - 81351 q^{96} + 35856 q^{97} + 38880 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 18 * q^3 + 37 * q^4 + 72 * q^5 + 27 * q^6 - 249 * q^8 + 162 * q^9 - 108 * q^10 + 480 * q^11 - 333 * q^12 + 1296 * q^13 - 648 * q^15 - 1679 * q^16 + 936 * q^17 - 243 * q^18 - 216 * q^19 + 1332 * q^20 - 1492 * q^22 - 504 * q^23 + 2241 * q^24 - 3658 * q^25 - 8892 * q^26 - 1458 * q^27 + 6372 * q^29 + 972 * q^30 + 9936 * q^31 + 9039 * q^32 - 4320 * q^33 + 19440 * q^34 + 2997 * q^36 + 11124 * q^37 + 28116 * q^38 - 11664 * q^39 - 8964 * q^40 + 20952 * q^41 - 6264 * q^43 + 11196 * q^44 + 5832 * q^45 + 6160 * q^46 + 7920 * q^47 + 15111 * q^48 + 5487 * q^50 - 8424 * q^51 + 44820 * q^52 + 2220 * q^53 + 2187 * q^54 + 17280 * q^55 + 1944 * q^57 - 71318 * q^58 + 29736 * q^59 - 11988 * q^60 - 17280 * q^61 + 40680 * q^62 - 10879 * q^64 + 46656 * q^65 + 13428 * q^66 - 20680 * q^67 - 45216 * q^68 + 4536 * q^69 - 92280 * q^71 - 20169 * q^72 + 56592 * q^73 + 85218 * q^74 + 32922 * q^75 - 87372 * q^76 + 80028 * q^78 - 56096 * q^79 - 60444 * q^80 + 13122 * q^81 - 52272 * q^82 - 71352 * q^83 + 33696 * q^85 + 240996 * q^86 - 57348 * q^87 - 52812 * q^88 + 123192 * q^89 - 8748 * q^90 - 25536 * q^92 - 89424 * q^93 - 345384 * q^94 - 7776 * q^95 - 81351 * q^96 + 35856 * q^97 + 38880 * q^99

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