LMFDB - Embedded newform 147.6.a.n.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:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 59x^{4} + 122x^{3} + 941x^{2} - 1856x - 2338 $ x^6 - 2x^5 - 59x^4 + 122x^3 + 941x^2 - 1856*x - 2338
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.61145$ 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)

$f(q)$	$=$	$q-11.1881 q^{2} -9.00000 q^{3} +93.1729 q^{4} +62.3150 q^{5} +100.693 q^{6} -684.407 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-11.1881 q^{2} -9.00000 q^{3} +93.1729 q^{4} +62.3150 q^{5} +100.693 q^{6} -684.407 q^{8} +81.0000 q^{9} -697.185 q^{10} -173.495 q^{11} -838.557 q^{12} -348.244 q^{13} -560.835 q^{15} +4675.66 q^{16} -999.206 q^{17} -906.234 q^{18} +2042.17 q^{19} +5806.07 q^{20} +1941.07 q^{22} -1949.67 q^{23} +6159.67 q^{24} +758.159 q^{25} +3896.18 q^{26} -729.000 q^{27} +738.129 q^{29} +6274.66 q^{30} +2459.99 q^{31} -30410.6 q^{32} +1561.45 q^{33} +11179.2 q^{34} +7547.01 q^{36} +8786.52 q^{37} -22848.0 q^{38} +3134.20 q^{39} -42648.8 q^{40} -17617.4 q^{41} -10317.1 q^{43} -16165.0 q^{44} +5047.51 q^{45} +21813.1 q^{46} +75.0582 q^{47} -42081.0 q^{48} -8482.34 q^{50} +8992.86 q^{51} -32446.9 q^{52} +27705.5 q^{53} +8156.10 q^{54} -10811.3 q^{55} -18379.5 q^{57} -8258.24 q^{58} +3457.57 q^{59} -52254.6 q^{60} -15956.4 q^{61} -27522.5 q^{62} +190615. q^{64} -21700.8 q^{65} -17469.7 q^{66} +14413.2 q^{67} -93099.0 q^{68} +17547.0 q^{69} -30337.6 q^{71} -55437.0 q^{72} -85880.9 q^{73} -98304.2 q^{74} -6823.43 q^{75} +190275. q^{76} -35065.6 q^{78} +7613.25 q^{79} +291364. q^{80} +6561.00 q^{81} +197104. q^{82} -63725.4 q^{83} -62265.5 q^{85} +115428. q^{86} -6643.16 q^{87} +118741. q^{88} -46391.3 q^{89} -56472.0 q^{90} -181657. q^{92} -22139.9 q^{93} -839.757 q^{94} +127258. q^{95} +273696. q^{96} -21461.2 q^{97} -14053.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 54 q^{3} + 150 q^{4} - 100 q^{5} - 18 q^{6} - 114 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 54 * q^3 + 150 * q^4 - 100 * q^5 - 18 * q^6 - 114 * q^8 + 486 * q^9	\( 6 q + 2 q^{2} - 54 q^{3} + 150 q^{4} - 100 q^{5} - 18 q^{6} - 114 q^{8} + 486 q^{9} - 864 q^{10} + 604 q^{11} - 1350 q^{12} - 1352 q^{13} + 900 q^{15} + 4578 q^{16} - 3028 q^{17} + 162 q^{18} - 1728 q^{19} - 452 q^{20} - 4116 q^{22} - 4484 q^{23} + 1026 q^{24} + 4806 q^{25} - 14172 q^{26} - 4374 q^{27} - 5320 q^{29} + 7776 q^{30} - 3976 q^{31} - 37326 q^{32} - 5436 q^{33} + 16336 q^{34} + 12150 q^{36} + 22680 q^{37} - 52744 q^{38} + 12168 q^{39} - 100600 q^{40} - 28756 q^{41} - 6768 q^{43} - 64940 q^{44} - 8100 q^{45} + 540 q^{46} - 51552 q^{47} - 41202 q^{48} - 40622 q^{50} + 27252 q^{51} - 119296 q^{52} + 80884 q^{53} - 1458 q^{54} - 11656 q^{55} + 15552 q^{57} - 70464 q^{58} - 8872 q^{59} + 4068 q^{60} - 50896 q^{61} - 11824 q^{62} + 199590 q^{64} + 3492 q^{65} + 37044 q^{66} + 6480 q^{67} - 37348 q^{68} + 40356 q^{69} - 110852 q^{71} - 9234 q^{72} - 64232 q^{73} - 27464 q^{74} - 43254 q^{75} + 194864 q^{76} + 127548 q^{78} + 111696 q^{79} + 308940 q^{80} + 39366 q^{81} + 189640 q^{82} - 101128 q^{83} - 23292 q^{85} + 3824 q^{86} + 47880 q^{87} - 97788 q^{88} + 35012 q^{89} - 69984 q^{90} - 449260 q^{92} + 35784 q^{93} + 121016 q^{94} - 119080 q^{95} + 335934 q^{96} - 70952 q^{97} + 48924 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 54 * q^3 + 150 * q^4 - 100 * q^5 - 18 * q^6 - 114 * q^8 + 486 * q^9 - 864 * q^10 + 604 * q^11 - 1350 * q^12 - 1352 * q^13 + 900 * q^15 + 4578 * q^16 - 3028 * q^17 + 162 * q^18 - 1728 * q^19 - 452 * q^20 - 4116 * q^22 - 4484 * q^23 + 1026 * q^24 + 4806 * q^25 - 14172 * q^26 - 4374 * q^27 - 5320 * q^29 + 7776 * q^30 - 3976 * q^31 - 37326 * q^32 - 5436 * q^33 + 16336 * q^34 + 12150 * q^36 + 22680 * q^37 - 52744 * q^38 + 12168 * q^39 - 100600 * q^40 - 28756 * q^41 - 6768 * q^43 - 64940 * q^44 - 8100 * q^45 + 540 * q^46 - 51552 * q^47 - 41202 * q^48 - 40622 * q^50 + 27252 * q^51 - 119296 * q^52 + 80884 * q^53 - 1458 * q^54 - 11656 * q^55 + 15552 * q^57 - 70464 * q^58 - 8872 * q^59 + 4068 * q^60 - 50896 * q^61 - 11824 * q^62 + 199590 * q^64 + 3492 * q^65 + 37044 * q^66 + 6480 * q^67 - 37348 * q^68 + 40356 * q^69 - 110852 * q^71 - 9234 * q^72 - 64232 * q^73 - 27464 * q^74 - 43254 * q^75 + 194864 * q^76 + 127548 * q^78 + 111696 * q^79 + 308940 * q^80 + 39366 * q^81 + 189640 * q^82 - 101128 * q^83 - 23292 * q^85 + 3824 * q^86 + 47880 * q^87 - 97788 * q^88 + 35012 * q^89 - 69984 * q^90 - 449260 * q^92 + 35784 * q^93 + 121016 * q^94 - 119080 * q^95 + 335934 * q^96 - 70952 * q^97 + 48924 * 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 $

$2$	−11.1881	−1.97779	−0.988895	−	0.148615i	$-0.952519\pi$
$2$	−11.1881	−1.97779	−0.988895	+	0.148615i	$0.952519\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	93.1729	2.91165
$5$	62.3150	1.11472	0.557362	−	0.830269i	$-0.311813\pi$
$5$	62.3150	1.11472	0.557362	+	0.830269i	$0.311813\pi$
$6$	100.693	1.14188
$7$	0	0
$7$	0	0
$8$	−684.407	−3.78085
$9$	81.0000	0.333333
$10$	−697.185	−2.20469
$11$	−173.495	−0.432320	−0.216160	−	0.976358i	$-0.569353\pi$
$11$	−173.495	−0.432320	−0.216160	+	0.976358i	$0.569353\pi$
$12$	−838.557	−1.68104
$13$	−348.244	−0.571512	−0.285756	−	0.958302i	$-0.592245\pi$
$13$	−348.244	−0.571512	−0.285756	+	0.958302i	$0.592245\pi$
$14$	0	0
$15$	−560.835	−0.643587
$16$	4675.66	4.56608
$17$	−999.206	−0.838557	−0.419279	−	0.907858i	$-0.637717\pi$
$17$	−999.206	−0.838557	−0.419279	+	0.907858i	$0.637717\pi$
$18$	−906.234	−0.659263
$19$	2042.17	1.29780	0.648901	−	0.760873i	$-0.275229\pi$
$19$	2042.17	1.29780	0.648901	+	0.760873i	$0.275229\pi$
$20$	5806.07	3.24569
$21$	0	0
$22$	1941.07	0.855038
$23$	−1949.67	−0.768496	−0.384248	−	0.923230i	$-0.625539\pi$
$23$	−1949.67	−0.768496	−0.384248	+	0.923230i	$0.625539\pi$
$24$	6159.67	2.18288
$25$	758.159	0.242611
$26$	3896.18	1.13033
$27$	−729.000	−0.192450
$28$	0	0
$29$	738.129	0.162981	0.0814906	−	0.996674i	$-0.474032\pi$
$29$	738.129	0.162981	0.0814906	+	0.996674i	$0.474032\pi$
$30$	6274.66	1.27288
$31$	2459.99	0.459758	0.229879	−	0.973219i	$-0.426167\pi$
$31$	2459.99	0.459758	0.229879	+	0.973219i	$0.426167\pi$
$32$	−30410.6	−5.24989
$33$	1561.45	0.249600
$34$	11179.2	1.65849
$35$	0	0
$36$	7547.01	0.970552
$37$	8786.52	1.05515	0.527573	−	0.849510i	$-0.323102\pi$
$37$	8786.52	1.05515	0.527573	+	0.849510i	$0.323102\pi$
$38$	−22848.0	−2.56678
$39$	3134.20	0.329963
$40$	−42648.8	−4.21461
$41$	−17617.4	−1.63675	−0.818374	−	0.574686i	$-0.805124\pi$
$41$	−17617.4	−1.63675	−0.818374	+	0.574686i	$0.805124\pi$
$42$	0	0
$43$	−10317.1	−0.850914	−0.425457	−	0.904979i	$-0.639887\pi$
$43$	−10317.1	−0.850914	−0.425457	+	0.904979i	$0.639887\pi$
$44$	−16165.0	−1.25877
$45$	5047.51	0.371575
$46$	21813.1	1.51992
$47$	75.0582	0.00495626	0.00247813	−	0.999997i	$-0.499211\pi$
$47$	75.0582	0.00495626	0.00247813	+	0.999997i	$0.499211\pi$
$48$	−42081.0	−2.63623
$49$	0	0
$50$	−8482.34	−0.479833
$51$	8992.86	0.484141
$52$	−32446.9	−1.66405
$53$	27705.5	1.35481	0.677403	−	0.735612i	$-0.263105\pi$
$53$	27705.5	1.35481	0.677403	+	0.735612i	$0.263105\pi$
$54$	8156.10	0.380626
$55$	−10811.3	−0.481917
$56$	0	0
$57$	−18379.5	−0.749286
$58$	−8258.24	−0.322342
$59$	3457.57	0.129313	0.0646564	−	0.997908i	$-0.479405\pi$
$59$	3457.57	0.129313	0.0646564	+	0.997908i	$0.479405\pi$
$60$	−52254.6	−1.87390
$61$	−15956.4	−0.549048	−0.274524	−	0.961580i	$-0.588520\pi$
$61$	−15956.4	−0.549048	−0.274524	+	0.961580i	$0.588520\pi$
$62$	−27522.5	−0.909304
$63$	0	0
$64$	190615.	5.81711
$65$	−21700.8	−0.637079
$66$	−17469.7	−0.493656
$67$	14413.2	0.392259	0.196129	−	0.980578i	$-0.437163\pi$
$67$	14413.2	0.392259	0.196129	+	0.980578i	$0.437163\pi$
$68$	−93099.0	−2.44159
$69$	17547.0	0.443691
$70$	0	0
$71$	−30337.6	−0.714225	−0.357112	−	0.934061i	$-0.616239\pi$
$71$	−30337.6	−0.714225	−0.357112	+	0.934061i	$0.616239\pi$
$72$	−55437.0	−1.26028
$73$	−85880.9	−1.88621	−0.943104	−	0.332498i	$-0.892108\pi$
$73$	−85880.9	−1.88621	−0.943104	+	0.332498i	$0.892108\pi$
$74$	−98304.2	−2.08686
$75$	−6823.43	−0.140071
$76$	190275.	3.77875
$77$	0	0
$78$	−35065.6	−0.652597
$79$	7613.25	0.137247	0.0686234	−	0.997643i	$-0.478139\pi$
$79$	7613.25	0.137247	0.0686234	+	0.997643i	$0.478139\pi$
$80$	291364.	5.08992
$81$	6561.00	0.111111
$82$	197104.	3.23714
$83$	−63725.4	−1.01535	−0.507677	−	0.861548i	$-0.669496\pi$
$83$	−63725.4	−1.01535	−0.507677	+	0.861548i	$0.669496\pi$
$84$	0	0
$85$	−62265.5	−0.934761
$86$	115428.	1.68293
$87$	−6643.16	−0.0940972
$88$	118741.	1.63454
$89$	−46391.3	−0.620815	−0.310407	−	0.950604i	$-0.600465\pi$
$89$	−46391.3	−0.620815	−0.310407	+	0.950604i	$0.600465\pi$
$90$	−56472.0	−0.734897
$91$	0	0
$92$	−181657.	−2.23759
$93$	−22139.9	−0.265441
$94$	−839.757	−0.00980244
$95$	127258.	1.44669
$96$	273696.	3.03103
$97$	−21461.2	−0.231592	−0.115796	−	0.993273i	$-0.536942\pi$
$97$	−21461.2	−0.231592	−0.115796	+	0.993273i	$0.536942\pi$
$98$	0	0
$99$	−14053.1	−0.144107
$100$	70639.9	0.706399
$101$	−145933.	−1.42347	−0.711737	−	0.702446i	$-0.752091\pi$
$101$	−145933.	−1.42347	−0.711737	+	0.702446i	$0.752091\pi$
$102$	−100613.	−0.957530
$103$	−165629.	−1.53830	−0.769152	−	0.639066i	$-0.779321\pi$
$103$	−165629.	−1.53830	−0.769152	+	0.639066i	$0.779321\pi$
$104$	238341.	2.16080
$105$	0	0
$106$	−309972.	−2.67952
$107$	215048.	1.81584	0.907918	−	0.419147i	$-0.137671\pi$
$107$	215048.	1.81584	0.907918	+	0.419147i	$0.137671\pi$
$108$	−67923.1	−0.560348
$109$	−40463.9	−0.326213	−0.163107	−	0.986608i	$-0.552151\pi$
$109$	−40463.9	−0.326213	−0.163107	+	0.986608i	$0.552151\pi$
$110$	120958.	0.953131
$111$	−79078.7	−0.609189
$112$	0	0
$113$	−15002.6	−0.110528	−0.0552638	−	0.998472i	$-0.517600\pi$
$113$	−15002.6	−0.110528	−0.0552638	+	0.998472i	$0.517600\pi$
$114$	205632.	1.48193
$115$	−121494.	−0.856661
$116$	68773.7	0.474545
$117$	−28207.8	−0.190504
$118$	−38683.6	−0.255753
$119$	0	0
$120$	383840.	2.43331
$121$	−130951.	−0.813100
$122$	178521.	1.08590
$123$	158556.	0.944977
$124$	229204.	1.33866
$125$	−147490.	−0.844280
$126$	0	0
$127$	118326.	0.650986	0.325493	−	0.945544i	$-0.394470\pi$
$127$	118326.	0.650986	0.325493	+	0.945544i	$0.394470\pi$
$128$	−1.15947e6	−6.25513
$129$	92853.7	0.491275
$130$	242791.	1.26001
$131$	219465.	1.11735	0.558673	−	0.829388i	$-0.311311\pi$
$131$	219465.	1.11735	0.558673	+	0.829388i	$0.311311\pi$
$132$	145485.	0.726749
$133$	0	0
$134$	−161256.	−0.775805
$135$	−45427.6	−0.214529
$136$	683864.	3.17046
$137$	−143983.	−0.655405	−0.327702	−	0.944781i	$-0.606274\pi$
$137$	−143983.	−0.655405	−0.327702	+	0.944781i	$0.606274\pi$
$138$	−196317.	−0.877528
$139$	−244306.	−1.07250	−0.536249	−	0.844060i	$-0.680159\pi$
$139$	−244306.	−1.07250	−0.536249	+	0.844060i	$0.680159\pi$
$140$	0	0
$141$	−675.524	−0.00286150
$142$	339419.	1.41259
$143$	60418.6	0.247076
$144$	378729.	1.52203
$145$	45996.5	0.181679
$146$	960842.	3.73052
$147$	0	0
$148$	818666.	3.07222
$149$	−279769.	−1.03237	−0.516184	−	0.856478i	$-0.672648\pi$
$149$	−279769.	−1.03237	−0.516184	+	0.856478i	$0.672648\pi$
$150$	76341.0	0.277032
$151$	−200417.	−0.715307	−0.357653	−	0.933854i	$-0.616423\pi$
$151$	−200417.	−0.715307	−0.357653	+	0.933854i	$0.616423\pi$
$152$	−1.39768e6	−4.90679
$153$	−80935.7	−0.279519
$154$	0	0
$155$	153294.	0.512503
$156$	292023.	0.960738
$157$	−470002.	−1.52178	−0.760888	−	0.648883i	$-0.775236\pi$
$157$	−470002.	−1.52178	−0.760888	+	0.648883i	$0.775236\pi$
$158$	−85177.6	−0.271446
$159$	−249350.	−0.782197
$160$	−1.89504e6	−5.85218
$161$	0	0
$162$	−73404.9	−0.219754
$163$	−587005.	−1.73051	−0.865253	−	0.501335i	$-0.832842\pi$
$163$	−587005.	−1.73051	−0.865253	+	0.501335i	$0.832842\pi$
$164$	−1.64146e6	−4.76564
$165$	97302.0	0.278235
$166$	712964.	2.00816
$167$	−172819.	−0.479513	−0.239757	−	0.970833i	$-0.577068\pi$
$167$	−172819.	−0.479513	−0.239757	+	0.970833i	$0.577068\pi$
$168$	0	0
$169$	−250019.	−0.673374
$170$	696631.	1.84876
$171$	165416.	0.432600
$172$	−961273.	−2.47757
$173$	5090.06	0.0129303	0.00646514	−	0.999979i	$-0.497942\pi$
$173$	5090.06	0.0129303	0.00646514	+	0.999979i	$0.497942\pi$
$174$	74324.2	0.186105
$175$	0	0
$176$	−811204.	−1.97400
$177$	−31118.2	−0.0746587
$178$	519030.	1.22784
$179$	242278.	0.565174	0.282587	−	0.959242i	$-0.408807\pi$
$179$	242278.	0.565174	0.282587	+	0.959242i	$0.408807\pi$
$180$	470292.	1.08190
$181$	492254.	1.11684	0.558422	−	0.829557i	$-0.311407\pi$
$181$	492254.	1.11684	0.558422	+	0.829557i	$0.311407\pi$
$182$	0	0
$183$	143608.	0.316993
$184$	1.33437e6	2.90557
$185$	547532.	1.17620
$186$	247703.	0.524987
$187$	173357.	0.362525
$188$	6993.40	0.0144309
$189$	0	0
$190$	−1.42377e6	−2.86125
$191$	−203729.	−0.404083	−0.202041	−	0.979377i	$-0.564758\pi$
$191$	−203729.	−0.404083	−0.202041	+	0.979377i	$0.564758\pi$
$192$	−1.71554e6	−3.35851
$193$	−61060.4	−0.117996	−0.0589979	−	0.998258i	$-0.518791\pi$
$193$	−61060.4	−0.117996	−0.0589979	+	0.998258i	$0.518791\pi$
$194$	240109.	0.458041
$195$	195308.	0.367818
$196$	0	0
$197$	457733.	0.840325	0.420162	−	0.907449i	$-0.361973\pi$
$197$	457733.	0.840325	0.420162	+	0.907449i	$0.361973\pi$
$198$	157227.	0.285013
$199$	270547.	0.484295	0.242148	−	0.970239i	$-0.422148\pi$
$199$	270547.	0.484295	0.242148	+	0.970239i	$0.422148\pi$
$200$	−518889.	−0.917276
$201$	−129719.	−0.226471
$202$	1.63271e6	2.81533
$203$	0	0
$204$	837891.	1.40965
$205$	−1.09783e6	−1.82452
$206$	1.85306e6	3.04244
$207$	−157923.	−0.256165
$208$	−1.62827e6	−2.60957
$209$	−354306.	−0.561065
$210$	0	0
$211$	933127.	1.44289	0.721447	−	0.692469i	$-0.243477\pi$
$211$	933127.	1.44289	0.721447	+	0.692469i	$0.243477\pi$
$212$	2.58141e6	3.94473
$213$	273038.	0.412358
$214$	−2.40598e6	−3.59134
$215$	−642909.	−0.948535
$216$	498933.	0.727625
$217$	0	0
$218$	452713.	0.645182
$219$	772928.	1.08900
$220$	−1.00732e6	−1.40318
$221$	347968.	0.479246
$222$	884738.	1.20485
$223$	197037.	0.265329	0.132664	−	0.991161i	$-0.457647\pi$
$223$	197037.	0.265329	0.132664	+	0.991161i	$0.457647\pi$
$224$	0	0
$225$	61410.9	0.0808703
$226$	167850.	0.218600
$227$	1.19839e6	1.54359	0.771795	−	0.635872i	$-0.219359\pi$
$227$	1.19839e6	1.54359	0.771795	+	0.635872i	$0.219359\pi$
$228$	−1.71248e6	−2.18166
$229$	244069.	0.307555	0.153778	−	0.988105i	$-0.450856\pi$
$229$	244069.	0.307555	0.153778	+	0.988105i	$0.450856\pi$
$230$	1.35928e6	1.69430
$231$	0	0
$232$	−505181.	−0.616207
$233$	−152260.	−0.183737	−0.0918686	−	0.995771i	$-0.529284\pi$
$233$	−152260.	−0.183737	−0.0918686	+	0.995771i	$0.529284\pi$
$234$	315591.	0.376777
$235$	4677.25	0.00552486
$236$	322152.	0.376514
$237$	−68519.3	−0.0792395
$238$	0	0
$239$	1.51074e6	1.71078	0.855390	−	0.517984i	$-0.173317\pi$
$239$	1.51074e6	1.71078	0.855390	+	0.517984i	$0.173317\pi$
$240$	−2.62228e6	−2.93867
$241$	−232939.	−0.258345	−0.129172	−	0.991622i	$-0.541232\pi$
$241$	−232939.	−0.258345	−0.129172	+	0.991622i	$0.541232\pi$
$242$	1.46508e6	1.60814
$243$	−59049.0	−0.0641500
$244$	−1.48670e6	−1.59864
$245$	0	0
$246$	−1.77394e6	−1.86897
$247$	−711175.	−0.741709
$248$	−1.68363e6	−1.73828
$249$	573528.	0.586215
$250$	1.65013e6	1.66981
$251$	−762727.	−0.764161	−0.382081	−	0.924129i	$-0.624792\pi$
$251$	−762727.	−0.764161	−0.382081	+	0.924129i	$0.624792\pi$
$252$	0	0
$253$	338258.	0.332236
$254$	−1.32384e6	−1.28751
$255$	560390.	0.539684
$256$	6.87260e6	6.55422
$257$	−1.38112e6	−1.30436	−0.652181	−	0.758064i	$-0.726146\pi$
$257$	−1.38112e6	−1.30436	−0.652181	+	0.758064i	$0.726146\pi$
$258$	−1.03885e6	−0.971640
$259$	0	0
$260$	−2.02193e6	−1.85495
$261$	59788.5	0.0543270
$262$	−2.45539e6	−2.20988
$263$	−633610.	−0.564850	−0.282425	−	0.959289i	$-0.591139\pi$
$263$	−633610.	−0.564850	−0.282425	+	0.959289i	$0.591139\pi$
$264$	−1.06867e6	−0.943700
$265$	1.72647e6	1.51023
$266$	0	0
$267$	417522.	0.358427
$268$	1.34292e6	1.14212
$269$	20533.7	0.0173016	0.00865081	−	0.999963i	$-0.497246\pi$
$269$	20533.7	0.0173016	0.00865081	+	0.999963i	$0.497246\pi$
$270$	508248.	0.424293
$271$	2.20939e6	1.82746	0.913732	−	0.406318i	$-0.133187\pi$
$271$	2.20939e6	1.82746	0.913732	+	0.406318i	$0.133187\pi$
$272$	−4.67195e6	−3.82892
$273$	0	0
$274$	1.61089e6	1.29625
$275$	−131537.	−0.104885
$276$	1.63491e6	1.29188
$277$	−679840.	−0.532362	−0.266181	−	0.963923i	$-0.585762\pi$
$277$	−679840.	−0.532362	−0.266181	+	0.963923i	$0.585762\pi$
$278$	2.73331e6	2.12118
$279$	199259.	0.153253
$280$	0	0
$281$	−831855.	−0.628466	−0.314233	−	0.949346i	$-0.601747\pi$
$281$	−831855.	−0.628466	−0.314233	+	0.949346i	$0.601747\pi$
$282$	7557.81	0.00565944
$283$	−2.31071e6	−1.71506	−0.857531	−	0.514433i	$-0.828003\pi$
$283$	−2.31071e6	−1.71506	−0.857531	+	0.514433i	$0.828003\pi$
$284$	−2.82664e6	−2.07958
$285$	−1.14532e6	−0.835247
$286$	−675968.	−0.488665
$287$	0	0
$288$	−2.46326e6	−1.74996
$289$	−421444.	−0.296821
$290$	−514612.	−0.359323
$291$	193151.	0.133710
$292$	−8.00178e6	−5.49198
$293$	−1.54768e6	−1.05321	−0.526603	−	0.850111i	$-0.676535\pi$
$293$	−1.54768e6	−1.05321	−0.526603	+	0.850111i	$0.676535\pi$
$294$	0	0
$295$	215459.	0.144148
$296$	−6.01356e6	−3.98935
$297$	126478.	0.0831999
$298$	3.13008e6	2.04181
$299$	678962.	0.439205
$300$	−635759.	−0.407840
$301$	0	0
$302$	2.24228e6	1.41473
$303$	1.31340e6	0.821843
$304$	9.54851e6	5.92586
$305$	−994323.	−0.612037
$306$	905514.	0.552830
$307$	−149665.	−0.0906303	−0.0453151	−	0.998973i	$-0.514429\pi$
$307$	−149665.	−0.0906303	−0.0453151	+	0.998973i	$0.514429\pi$
$308$	0	0
$309$	1.49066e6	0.888140
$310$	−1.71507e6	−1.01362
$311$	146487.	0.0858812	0.0429406	−	0.999078i	$-0.486327\pi$
$311$	146487.	0.0858812	0.0429406	+	0.999078i	$0.486327\pi$
$312$	−2.14507e6	−1.24754
$313$	−318335.	−0.183664	−0.0918319	−	0.995775i	$-0.529272\pi$
$313$	−318335.	−0.183664	−0.0918319	+	0.995775i	$0.529272\pi$
$314$	5.25842e6	3.00975
$315$	0	0
$316$	709349.	0.399615
$317$	2.16592e6	1.21058	0.605291	−	0.796004i	$-0.293057\pi$
$317$	2.16592e6	1.21058	0.605291	+	0.796004i	$0.293057\pi$
$318$	2.78974e6	1.54702
$319$	−128062.	−0.0704599
$320$	1.18782e7	6.48447
$321$	−1.93544e6	−1.04837
$322$	0	0
$323$	−2.04055e6	−1.08828
$324$	611308.	0.323517
$325$	−264024.	−0.138655
$326$	6.56746e6	3.42258
$327$	364175.	0.188339
$328$	1.20575e7	6.18830
$329$	0	0
$330$	−1.08862e6	−0.550291
$331$	−2.54345e6	−1.27601	−0.638005	−	0.770033i	$-0.720240\pi$
$331$	−2.54345e6	−1.27601	−0.638005	+	0.770033i	$0.720240\pi$
$332$	−5.93748e6	−2.95636
$333$	711708.	0.351715
$334$	1.93351e6	0.948377
$335$	898156.	0.437260
$336$	0	0
$337$	−2.57641e6	−1.23578	−0.617888	−	0.786266i	$-0.712012\pi$
$337$	−2.57641e6	−1.23578	−0.617888	+	0.786266i	$0.712012\pi$
$338$	2.79723e6	1.33179
$339$	135024.	0.0638132
$340$	−5.80146e6	−2.72170
$341$	−426796.	−0.198762
$342$	−1.85068e6	−0.855593
$343$	0	0
$344$	7.06108e6	3.21718
$345$	1.09344e6	0.494594
$346$	−56948.0	−0.0255734
$347$	−1.99035e6	−0.887374	−0.443687	−	0.896182i	$-0.646330\pi$
$347$	−1.99035e6	−0.887374	−0.443687	+	0.896182i	$0.646330\pi$
$348$	−618963.	−0.273979
$349$	−1.37419e6	−0.603926	−0.301963	−	0.953320i	$-0.597642\pi$
$349$	−1.37419e6	−0.603926	−0.301963	+	0.953320i	$0.597642\pi$
$350$	0	0
$351$	253870.	0.109988
$352$	5.27609e6	2.26963
$353$	2.93667e6	1.25435	0.627174	−	0.778879i	$-0.284211\pi$
$353$	2.93667e6	1.25435	0.627174	+	0.778879i	$0.284211\pi$
$354$	348152.	0.147659
$355$	−1.89049e6	−0.796164
$356$	−4.32242e6	−1.80760
$357$	0	0
$358$	−2.71063e6	−1.11779
$359$	1.38575e6	0.567476	0.283738	−	0.958902i	$-0.408425\pi$
$359$	1.38575e6	0.567476	0.283738	+	0.958902i	$0.408425\pi$
$360$	−3.45456e6	−1.40487
$361$	1.69436e6	0.684288
$362$	−5.50737e6	−2.20888
$363$	1.17855e6	0.469443
$364$	0	0
$365$	−5.35167e6	−2.10260
$366$	−1.60669e6	−0.626946
$367$	−3.64088e6	−1.41105	−0.705523	−	0.708687i	$-0.749288\pi$
$367$	−3.64088e6	−1.41105	−0.705523	+	0.708687i	$0.749288\pi$
$368$	−9.11600e6	−3.50901
$369$	−1.42701e6	−0.545582
$370$	−6.12583e6	−2.32627
$371$	0	0
$372$	−2.06284e6	−0.772873
$373$	4.14938e6	1.54423	0.772114	−	0.635484i	$-0.219200\pi$
$373$	4.14938e6	1.54423	0.772114	+	0.635484i	$0.219200\pi$
$374$	−1.93953e6	−0.716998
$375$	1.32741e6	0.487445
$376$	−51370.4	−0.0187389
$377$	−257049.	−0.0931457
$378$	0	0
$379$	−1.26316e6	−0.451711	−0.225856	−	0.974161i	$-0.572518\pi$
$379$	−1.26316e6	−0.451711	−0.225856	+	0.974161i	$0.572518\pi$
$380$	1.18570e7	4.21226
$381$	−1.06494e6	−0.375847
$382$	2.27934e6	0.799191
$383$	2.28188e6	0.794869	0.397435	−	0.917631i	$-0.369901\pi$
$383$	2.28188e6	0.794869	0.397435	+	0.917631i	$0.369901\pi$
$384$	1.04353e7	3.61140
$385$	0	0
$386$	683148.	0.233371
$387$	−835683.	−0.283638
$388$	−1.99960e6	−0.674317
$389$	3.25869e6	1.09186	0.545932	−	0.837829i	$-0.316176\pi$
$389$	3.25869e6	1.09186	0.545932	+	0.837829i	$0.316176\pi$
$390$	−2.18512e6	−0.727466
$391$	1.94812e6	0.644428
$392$	0	0
$393$	−1.97519e6	−0.645100
$394$	−5.12115e6	−1.66199
$395$	474420.	0.152992
$396$	−1.30937e6	−0.419588
$397$	4.49485e6	1.43133	0.715663	−	0.698445i	$-0.246124\pi$
$397$	4.49485e6	1.43133	0.715663	+	0.698445i	$0.246124\pi$
$398$	−3.02690e6	−0.957835
$399$	0	0
$400$	3.54490e6	1.10778
$401$	552039.	0.171439	0.0857194	−	0.996319i	$-0.472681\pi$
$401$	552039.	0.171439	0.0857194	+	0.996319i	$0.472681\pi$
$402$	1.45130e6	0.447911
$403$	−856677.	−0.262757
$404$	−1.35970e7	−4.14467
$405$	408849.	0.123858
$406$	0	0
$407$	−1.52442e6	−0.456160
$408$	−6.15478e6	−1.83047
$409$	−6.05239e6	−1.78903	−0.894517	−	0.447035i	$-0.852480\pi$
$409$	−6.05239e6	−1.78903	−0.894517	+	0.447035i	$0.852480\pi$
$410$	1.22826e7	3.60852
$411$	1.29585e6	0.378398
$412$	−1.54321e7	−4.47901
$413$	0	0
$414$	1.76686e6	0.506641
$415$	−3.97105e6	−1.13184
$416$	1.05903e7	3.00038
$417$	2.19875e6	0.619207
$418$	3.96400e6	1.10967
$419$	1.48630e6	0.413592	0.206796	−	0.978384i	$-0.433696\pi$
$419$	1.48630e6	0.413592	0.206796	+	0.978384i	$0.433696\pi$
$420$	0	0
$421$	−1.40434e6	−0.386159	−0.193079	−	0.981183i	$-0.561847\pi$
$421$	−1.40434e6	−0.386159	−0.193079	+	0.981183i	$0.561847\pi$
$422$	−1.04399e7	−2.85374
$423$	6079.72	0.00165209
$424$	−1.89619e7	−5.12232
$425$	−757557.	−0.203443
$426$	−3.05477e6	−0.815557
$427$	0	0
$428$	2.00367e7	5.28709
$429$	−543767.	−0.142649
$430$	7.19291e6	1.87600
$431$	−2.70173e6	−0.700567	−0.350283	−	0.936644i	$-0.613915\pi$
$431$	−2.70173e6	−0.700567	−0.350283	+	0.936644i	$0.613915\pi$
$432$	−3.40856e6	−0.878742
$433$	4.76987e6	1.22261	0.611304	−	0.791396i	$-0.290645\pi$
$433$	4.76987e6	1.22261	0.611304	+	0.791396i	$0.290645\pi$
$434$	0	0
$435$	−413969.	−0.104892
$436$	−3.77014e6	−0.949821
$437$	−3.98156e6	−0.997355
$438$	−8.64758e6	−2.15382
$439$	−6327.49	−0.00156700	−0.000783502	−	1.00000i	$-0.500249\pi$
$439$	−6327.49	−0.00156700	−0.000783502		1.00000i	$0.500249\pi$
$440$	7.39935e6	1.82206
$441$	0	0
$442$	−3.89309e6	−0.947848
$443$	1.41589e6	0.342783	0.171392	−	0.985203i	$-0.445174\pi$
$443$	1.41589e6	0.342783	0.171392	+	0.985203i	$0.445174\pi$
$444$	−7.36799e6	−1.77375
$445$	−2.89088e6	−0.692037
$446$	−2.20446e6	−0.524765
$447$	2.51792e6	0.596038
$448$	0	0
$449$	−1.88150e6	−0.440442	−0.220221	−	0.975450i	$-0.570678\pi$
$449$	−1.88150e6	−0.440442	−0.220221	+	0.975450i	$0.570678\pi$
$450$	−687069.	−0.159944
$451$	3.05652e6	0.707598
$452$	−1.39784e6	−0.321818
$453$	1.80375e6	0.412983
$454$	−1.34076e7	−3.05290
$455$	0	0
$456$	1.25791e7	2.83294
$457$	7.44422e6	1.66736	0.833678	−	0.552250i	$-0.186231\pi$
$457$	7.44422e6	1.66736	0.833678	+	0.552250i	$0.186231\pi$
$458$	−2.73066e6	−0.608280
$459$	728421.	0.161380
$460$	−1.13199e7	−2.49430
$461$	−7.95698e6	−1.74380	−0.871899	−	0.489686i	$-0.837112\pi$
$461$	−7.95698e6	−1.74380	−0.871899	+	0.489686i	$0.837112\pi$
$462$	0	0
$463$	6.64462e6	1.44051	0.720257	−	0.693707i	$-0.244024\pi$
$463$	6.64462e6	1.44051	0.720257	+	0.693707i	$0.244024\pi$
$464$	3.45124e6	0.744184
$465$	−1.37965e6	−0.295894
$466$	1.70350e6	0.363394
$467$	2.97533e6	0.631311	0.315655	−	0.948874i	$-0.397776\pi$
$467$	2.97533e6	0.631311	0.315655	+	0.948874i	$0.397776\pi$
$468$	−2.62820e6	−0.554682
$469$	0	0
$470$	−52329.5	−0.0109270
$471$	4.23002e6	0.878598
$472$	−2.36639e6	−0.488912
$473$	1.78996e6	0.367867
$474$	766598.	0.156719
$475$	1.54829e6	0.314861
$476$	0	0
$477$	2.24415e6	0.451602
$478$	−1.69022e7	−3.38356
$479$	3.40858e6	0.678789	0.339395	−	0.940644i	$-0.389778\pi$
$479$	3.40858e6	0.678789	0.339395	+	0.940644i	$0.389778\pi$
$480$	1.70553e7	3.37876
$481$	−3.05985e6	−0.603029
$482$	2.60614e6	0.510951
$483$	0	0
$484$	−1.22010e7	−2.36747
$485$	−1.33735e6	−0.258162
$486$	660644.	0.126875
$487$	5.91307e6	1.12977	0.564886	−	0.825169i	$-0.308920\pi$
$487$	5.91307e6	1.12977	0.564886	+	0.825169i	$0.308920\pi$
$488$	1.09207e7	2.07587
$489$	5.28305e6	0.999108
$490$	0	0
$491$	549890.	0.102937	0.0514686	−	0.998675i	$-0.483610\pi$
$491$	549890.	0.102937	0.0514686	+	0.998675i	$0.483610\pi$
$492$	1.47732e7	2.75145
$493$	−737543.	−0.136669
$494$	7.95667e6	1.46695
$495$	−875718.	−0.160639
$496$	1.15021e7	2.09929
$497$	0	0
$498$	−6.41668e6	−1.15941
$499$	5.60945e6	1.00848	0.504241	−	0.863563i	$-0.331772\pi$
$499$	5.60945e6	1.00848	0.504241	+	0.863563i	$0.331772\pi$
$500$	−1.37420e7	−2.45825
$501$	1.55537e6	0.276847
$502$	8.53345e6	1.51135
$503$	−1.43167e6	−0.252304	−0.126152	−	0.992011i	$-0.540263\pi$
$503$	−1.43167e6	−0.252304	−0.126152	+	0.992011i	$0.540263\pi$
$504$	0	0
$505$	−9.09381e6	−1.58678
$506$	−3.78445e6	−0.657093
$507$	2.25017e6	0.388772
$508$	1.10248e7	1.89545
$509$	5.39838e6	0.923568	0.461784	−	0.886992i	$-0.347210\pi$
$509$	5.39838e6	0.923568	0.461784	+	0.886992i	$0.347210\pi$
$510$	−6.26968e6	−1.06738
$511$	0	0
$512$	−3.97880e7	−6.70775
$513$	−1.48874e6	−0.249762
$514$	1.54520e7	2.57975
$515$	−1.03211e7	−1.71478
$516$	8.65145e6	1.43042
$517$	−13022.2	−0.00214269
$518$	0	0
$519$	−45810.6	−0.00746530
$520$	1.48522e7	2.40870
$521$	1.56889e6	0.253220	0.126610	−	0.991953i	$-0.459590\pi$
$521$	1.56889e6	0.253220	0.126610	+	0.991953i	$0.459590\pi$
$522$	−668918.	−0.107447
$523$	−4.63319e6	−0.740671	−0.370336	−	0.928898i	$-0.620757\pi$
$523$	−4.63319e6	−0.740671	−0.370336	+	0.928898i	$0.620757\pi$
$524$	2.04482e7	3.25333
$525$	0	0
$526$	7.08888e6	1.11715
$527$	−2.45804e6	−0.385533
$528$	7.30083e6	1.13969
$529$	−2.63513e6	−0.409414
$530$	−1.93159e7	−2.98693
$531$	280063.	0.0431042
$532$	0	0
$533$	6.13515e6	0.935421
$534$	−4.67127e6	−0.708894
$535$	1.34007e7	2.02416
$536$	−9.86448e6	−1.48307
$537$	−2.18050e6	−0.326303
$538$	−229733.	−0.0342190
$539$	0	0
$540$	−4.23263e6	−0.624634
$541$	1.03758e7	1.52415	0.762074	−	0.647490i	$-0.224181\pi$
$541$	1.03758e7	1.52415	0.762074	+	0.647490i	$0.224181\pi$
$542$	−2.47188e7	−3.61434
$543$	−4.43028e6	−0.644810
$544$	3.03865e7	4.40234
$545$	−2.52151e6	−0.363638
$546$	0	0
$547$	1.07555e7	1.53695	0.768476	−	0.639879i	$-0.221015\pi$
$547$	1.07555e7	1.53695	0.768476	+	0.639879i	$0.221015\pi$
$548$	−1.34153e7	−1.90831
$549$	−1.29247e6	−0.183016
$550$	1.47164e6	0.207441
$551$	1.50739e6	0.211517
$552$	−1.20093e7	−1.67753
$553$	0	0
$554$	7.60610e6	1.05290
$555$	−4.92779e6	−0.679078
$556$	−2.27627e7	−3.12274
$557$	−3.37312e6	−0.460674	−0.230337	−	0.973111i	$-0.573983\pi$
$557$	−3.37312e6	−0.460674	−0.230337	+	0.973111i	$0.573983\pi$
$558$	−2.22933e6	−0.303101
$559$	3.59286e6	0.486308
$560$	0	0
$561$	−1.56021e6	−0.209304
$562$	9.30685e6	1.24297
$563$	9.76402e6	1.29825	0.649124	−	0.760683i	$-0.275136\pi$
$563$	9.76402e6	1.29825	0.649124	+	0.760683i	$0.275136\pi$
$564$	−62940.6	−0.00833169
$565$	−934888.	−0.123208
$566$	2.58524e7	3.39203
$567$	0	0
$568$	2.07633e7	2.70038
$569$	−9.03945e6	−1.17047	−0.585236	−	0.810863i	$-0.698998\pi$
$569$	−9.03945e6	−1.17047	−0.585236	+	0.810863i	$0.698998\pi$
$570$	1.28139e7	1.65194
$571$	−1.06993e7	−1.37329	−0.686646	−	0.726991i	$-0.740918\pi$
$571$	−1.06993e7	−1.37329	−0.686646	+	0.726991i	$0.740918\pi$
$572$	5.62938e6	0.719400
$573$	1.83356e6	0.233297
$574$	0	0
$575$	−1.47816e6	−0.186445
$576$	1.54398e7	1.93904
$577$	5.00063e6	0.625295	0.312648	−	0.949869i	$-0.398784\pi$
$577$	5.00063e6	0.625295	0.312648	+	0.949869i	$0.398784\pi$
$578$	4.71515e6	0.587051
$579$	549543.	0.0681248
$580$	4.28563e6	0.528987
$581$	0	0
$582$	−2.16098e6	−0.264450
$583$	−4.80677e6	−0.585709
$584$	5.87775e7	7.13147
$585$	−1.75777e6	−0.212360
$586$	1.73156e7	2.08302
$587$	7.54203e6	0.903427	0.451713	−	0.892163i	$-0.350813\pi$
$587$	7.54203e6	0.903427	0.451713	+	0.892163i	$0.350813\pi$
$588$	0	0
$589$	5.02372e6	0.596674
$590$	−2.41057e6	−0.285095
$591$	−4.11960e6	−0.485162
$592$	4.10828e7	4.81788
$593$	5.99664e6	0.700279	0.350139	−	0.936698i	$-0.386134\pi$
$593$	5.99664e6	0.700279	0.350139	+	0.936698i	$0.386134\pi$
$594$	−1.41504e6	−0.164552
$595$	0	0
$596$	−2.60669e7	−3.00590
$597$	−2.43493e6	−0.279608
$598$	−7.59627e6	−0.868655
$599$	−7.54150e6	−0.858797	−0.429399	−	0.903115i	$-0.641274\pi$
$599$	−7.54150e6	−0.858797	−0.429399	+	0.903115i	$0.641274\pi$
$600$	4.67001e6	0.529589
$601$	2.34440e6	0.264756	0.132378	−	0.991199i	$-0.457739\pi$
$601$	2.34440e6	0.264756	0.132378	+	0.991199i	$0.457739\pi$
$602$	0	0
$603$	1.16747e6	0.130753
$604$	−1.86734e7	−2.08273
$605$	−8.16018e6	−0.906382
$606$	−1.46944e7	−1.62543
$607$	−1.41940e7	−1.56363	−0.781816	−	0.623509i	$-0.785706\pi$
$607$	−1.41940e7	−1.56363	−0.781816	+	0.623509i	$0.785706\pi$
$608$	−6.21037e7	−6.81332
$609$	0	0
$610$	1.11246e7	1.21048
$611$	−26138.6	−0.00283256
$612$	−7.54102e6	−0.813863
$613$	1.53799e7	1.65311	0.826555	−	0.562856i	$-0.190297\pi$
$613$	1.53799e7	1.65311	0.826555	+	0.562856i	$0.190297\pi$
$614$	1.67446e6	0.179248
$615$	9.88044e6	1.05339
$616$	0	0
$617$	−3.26335e6	−0.345105	−0.172552	−	0.985000i	$-0.555201\pi$
$617$	−3.26335e6	−0.345105	−0.172552	+	0.985000i	$0.555201\pi$
$618$	−1.66776e7	−1.75655
$619$	1.14762e7	1.20385	0.601924	−	0.798553i	$-0.294401\pi$
$619$	1.14762e7	1.20385	0.601924	+	0.798553i	$0.294401\pi$
$620$	1.42829e7	1.49223
$621$	1.42131e6	0.147897
$622$	−1.63891e6	−0.169855
$623$	0	0
$624$	1.46545e7	1.50664
$625$	−1.15601e7	−1.18375
$626$	3.56155e6	0.363248
$627$	3.18876e6	0.323931
$628$	−4.37915e7	−4.43089
$629$	−8.77954e6	−0.884800
$630$	0	0
$631$	9.11249e6	0.911095	0.455548	−	0.890211i	$-0.349444\pi$
$631$	9.11249e6	0.911095	0.455548	+	0.890211i	$0.349444\pi$
$632$	−5.21056e6	−0.518910
$633$	−8.39814e6	−0.833056
$634$	−2.42325e7	−2.39428
$635$	7.37350e6	0.725670
$636$	−2.32327e7	−2.27749
$637$	0	0
$638$	1.43276e6	0.139355
$639$	−2.45734e6	−0.238075
$640$	−7.22526e7	−6.97275
$641$	−1.34121e7	−1.28930	−0.644649	−	0.764479i	$-0.722996\pi$
$641$	−1.34121e7	−1.28930	−0.644649	+	0.764479i	$0.722996\pi$
$642$	2.16538e7	2.07346
$643$	−5.00517e6	−0.477410	−0.238705	−	0.971092i	$-0.576723\pi$
$643$	−5.00517e6	−0.477410	−0.238705	+	0.971092i	$0.576723\pi$
$644$	0	0
$645$	5.78618e6	0.547637
$646$	2.28298e7	2.15239
$647$	5.83524e6	0.548022	0.274011	−	0.961727i	$-0.411650\pi$
$647$	5.83524e6	0.548022	0.274011	+	0.961727i	$0.411650\pi$
$648$	−4.49040e6	−0.420095
$649$	−599871.	−0.0559044
$650$	2.95392e6	0.274231
$651$	0	0
$652$	−5.46930e7	−5.03864
$653$	1.51369e7	1.38916	0.694581	−	0.719415i	$-0.255590\pi$
$653$	1.51369e7	1.38916	0.694581	+	0.719415i	$0.255590\pi$
$654$	−4.07442e6	−0.372496
$655$	1.36760e7	1.24553
$656$	−8.23729e7	−7.47352
$657$	−6.95635e6	−0.628736
$658$	0	0
$659$	1.26786e7	1.13725	0.568625	−	0.822597i	$-0.307475\pi$
$659$	1.26786e7	1.13725	0.568625	+	0.822597i	$0.307475\pi$
$660$	9.06591e6	0.810124
$661$	−1.40024e6	−0.124652	−0.0623261	−	0.998056i	$-0.519852\pi$
$661$	−1.40024e6	−0.124652	−0.0623261	+	0.998056i	$0.519852\pi$
$662$	2.84563e7	2.52368
$663$	−3.13171e6	−0.276693
$664$	4.36141e7	3.83890
$665$	0	0
$666$	−7.96264e6	−0.695619
$667$	−1.43911e6	−0.125250
$668$	−1.61021e7	−1.39618
$669$	−1.77333e6	−0.153188
$670$	−1.00486e7	−0.864809
$671$	2.76835e6	0.237364
$672$	0	0
$673$	−6.01514e6	−0.511927	−0.255963	−	0.966686i	$-0.582393\pi$
$673$	−6.01514e6	−0.511927	−0.255963	+	0.966686i	$0.582393\pi$
$674$	2.88250e7	2.44411
$675$	−552698.	−0.0466905
$676$	−2.32950e7	−1.96063
$677$	6.60009e6	0.553450	0.276725	−	0.960949i	$-0.410751\pi$
$677$	6.60009e6	0.553450	0.276725	+	0.960949i	$0.410751\pi$
$678$	−1.51065e6	−0.126209
$679$	0	0
$680$	4.26150e7	3.53419
$681$	−1.07855e7	−0.891192
$682$	4.77502e6	0.393110
$683$	213734.	0.0175316	0.00876581	−	0.999962i	$-0.497210\pi$
$683$	213734.	0.0175316	0.00876581	+	0.999962i	$0.497210\pi$
$684$	1.54123e7	1.25958
$685$	−8.97230e6	−0.730596
$686$	0	0
$687$	−2.19662e6	−0.177567
$688$	−4.82392e7	−3.88534
$689$	−9.64830e6	−0.774288
$690$	−1.22335e7	−0.978203
$691$	1.43510e6	0.114337	0.0571684	−	0.998365i	$-0.481793\pi$
$691$	1.43510e6	0.114337	0.0571684	+	0.998365i	$0.481793\pi$
$692$	474256.	0.0376485
$693$	0	0
$694$	2.22682e7	1.75504
$695$	−1.52239e7	−1.19554
$696$	4.54663e6	0.355768
$697$	1.76034e7	1.37251
$698$	1.53745e7	1.19444
$699$	1.37034e6	0.106081
$700$	0	0
$701$	−1.27397e7	−0.979186	−0.489593	−	0.871951i	$-0.662855\pi$
$701$	−1.27397e7	−0.979186	−0.489593	+	0.871951i	$0.662855\pi$
$702$	−2.84032e6	−0.217532
$703$	1.79436e7	1.36937
$704$	−3.30707e7	−2.51485
$705$	−42095.3	−0.00318978
$706$	−3.28557e7	−2.48084
$707$	0	0
$708$	−2.89937e6	−0.217380
$709$	7.79504e6	0.582375	0.291187	−	0.956666i	$-0.405950\pi$
$709$	7.79504e6	0.582375	0.291187	+	0.956666i	$0.405950\pi$
$710$	2.11509e7	1.57465
$711$	616673.	0.0457490
$712$	3.17506e7	2.34721
$713$	−4.79617e6	−0.353322
$714$	0	0
$715$	3.76498e6	0.275422
$716$	2.25738e7	1.64559
$717$	−1.35966e7	−0.987719
$718$	−1.55038e7	−1.12235
$719$	−4.86960e6	−0.351294	−0.175647	−	0.984453i	$-0.556202\pi$
$719$	−4.86960e6	−0.351294	−0.175647	+	0.984453i	$0.556202\pi$
$720$	2.36005e7	1.69664
$721$	0	0
$722$	−1.89567e7	−1.35338
$723$	2.09645e6	0.149155
$724$	4.58647e7	3.25186
$725$	559619.	0.0395410
$726$	−1.31858e7	−0.928461
$727$	1.29961e7	0.911966	0.455983	−	0.889989i	$-0.349288\pi$
$727$	1.29961e7	0.911966	0.455983	+	0.889989i	$0.349288\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	5.98749e7	4.15851
$731$	1.03089e7	0.713540
$732$	1.33803e7	0.922974
$733$	4.80604e6	0.330391	0.165195	−	0.986261i	$-0.447175\pi$
$733$	4.80604e6	0.330391	0.165195	+	0.986261i	$0.447175\pi$
$734$	4.07344e7	2.79075
$735$	0	0
$736$	5.92907e7	4.03452
$737$	−2.50061e6	−0.169581
$738$	1.59655e7	1.07905
$739$	1.85725e7	1.25101	0.625503	−	0.780222i	$-0.284894\pi$
$739$	1.85725e7	1.25101	0.625503	+	0.780222i	$0.284894\pi$
$740$	5.10152e7	3.42468
$741$	6.40057e6	0.428226
$742$	0	0
$743$	1.17402e7	0.780192	0.390096	−	0.920774i	$-0.372442\pi$
$743$	1.17402e7	0.780192	0.390096	+	0.920774i	$0.372442\pi$
$744$	1.51527e7	1.00359
$745$	−1.74338e7	−1.15081
$746$	−4.64236e7	−3.05416
$747$	−5.16176e6	−0.338451
$748$	1.61522e7	1.05555
$749$	0	0
$750$	−1.48511e7	−0.964065
$751$	1.50501e7	0.973734	0.486867	−	0.873476i	$-0.338140\pi$
$751$	1.50501e7	0.973734	0.486867	+	0.873476i	$0.338140\pi$
$752$	350947.	0.0226307
$753$	6.86454e6	0.441189
$754$	2.87589e6	0.184223
$755$	−1.24890e7	−0.797370
$756$	0	0
$757$	2.04785e6	0.129885	0.0649423	−	0.997889i	$-0.479314\pi$
$757$	2.04785e6	0.129885	0.0649423	+	0.997889i	$0.479314\pi$
$758$	1.41323e7	0.893390
$759$	−3.04432e6	−0.191816
$760$	−8.70962e7	−5.46972
$761$	−1.65151e7	−1.03376	−0.516881	−	0.856057i	$-0.672907\pi$
$761$	−1.65151e7	−1.03376	−0.516881	+	0.856057i	$0.672907\pi$
$762$	1.19146e7	0.743347
$763$	0	0
$764$	−1.89821e7	−1.17655
$765$	−5.04351e6	−0.311587
$766$	−2.55298e7	−1.57208
$767$	−1.20408e6	−0.0739038
$768$	−6.18534e7	−3.78408
$769$	−2.10148e7	−1.28147	−0.640736	−	0.767761i	$-0.721371\pi$
$769$	−2.10148e7	−1.28147	−0.640736	+	0.767761i	$0.721371\pi$
$770$	0	0
$771$	1.24301e7	0.753073
$772$	−5.68917e6	−0.343563
$773$	−2.79653e7	−1.68333	−0.841667	−	0.539996i	$-0.818426\pi$
$773$	−2.79653e7	−1.68333	−0.841667	+	0.539996i	$0.818426\pi$
$774$	9.34969e6	0.560976
$775$	1.86506e6	0.111542
$776$	1.46882e7	0.875616
$777$	0	0
$778$	−3.64584e7	−2.15948
$779$	−3.59777e7	−2.12417
$780$	1.81974e7	1.07096
$781$	5.26341e6	0.308773
$782$	−2.17957e7	−1.27454
$783$	−538096.	−0.0313657
$784$	0	0
$785$	−2.92882e7	−1.69636
$786$	2.20985e7	1.27587
$787$	2.67284e6	0.153828	0.0769141	−	0.997038i	$-0.475493\pi$
$787$	2.67284e6	0.153828	0.0769141	+	0.997038i	$0.475493\pi$
$788$	4.26484e7	2.44673
$789$	5.70249e6	0.326116
$790$	−5.30784e6	−0.302587
$791$	0	0
$792$	9.61803e6	0.544845
$793$	5.55673e6	0.313788
$794$	−5.02887e7	−2.83086
$795$	−1.55382e7	−0.871934
$796$	2.52077e7	1.41010
$797$	−8.17692e6	−0.455978	−0.227989	−	0.973664i	$-0.573215\pi$
$797$	−8.17692e6	−0.455978	−0.227989	+	0.973664i	$0.573215\pi$
$798$	0	0
$799$	−74998.7	−0.00415611
$800$	−2.30561e7	−1.27368
$801$	−3.75770e6	−0.206938
$802$	−6.17625e6	−0.339070
$803$	1.48999e7	0.815445
$804$	−1.20863e7	−0.659404
$805$	0	0
$806$	9.58457e6	0.519679
$807$	−184803.	−0.00998910
$808$	9.98775e7	5.38195
$809$	2.37801e7	1.27745	0.638723	−	0.769436i	$-0.279463\pi$
$809$	2.37801e7	1.27745	0.638723	+	0.769436i	$0.279463\pi$
$810$	−4.57423e6	−0.244966
$811$	−2.42489e7	−1.29461	−0.647306	−	0.762231i	$-0.724104\pi$
$811$	−2.42489e7	−1.29461	−0.647306	+	0.762231i	$0.724104\pi$
$812$	0	0
$813$	−1.98845e7	−1.05509
$814$	1.70553e7	0.902189
$815$	−3.65792e7	−1.92904
$816$	4.20476e7	2.21063
$817$	−2.10692e7	−1.10432
$818$	6.77145e7	3.53833
$819$	0	0
$820$	−1.02288e8	−5.31238
$821$	−3.60109e6	−0.186456	−0.0932280	−	0.995645i	$-0.529719\pi$
$821$	−3.60109e6	−0.186456	−0.0932280	+	0.995645i	$0.529719\pi$
$822$	−1.44980e7	−0.748392
$823$	−1.68438e7	−0.866844	−0.433422	−	0.901191i	$-0.642694\pi$
$823$	−1.68438e7	−0.866844	−0.433422	+	0.901191i	$0.642694\pi$
$824$	1.13357e8	5.81610
$825$	1.18383e6	0.0605556
$826$	0	0
$827$	−1.81504e7	−0.922829	−0.461415	−	0.887185i	$-0.652658\pi$
$827$	−1.81504e7	−0.922829	−0.461415	+	0.887185i	$0.652658\pi$
$828$	−1.47142e7	−0.745865
$829$	−1.07241e7	−0.541969	−0.270985	−	0.962584i	$-0.587349\pi$
$829$	−1.07241e7	−0.541969	−0.270985	+	0.962584i	$0.587349\pi$
$830$	4.44284e7	2.23854
$831$	6.11856e6	0.307360
$832$	−6.63806e7	−3.32455
$833$	0	0
$834$	−2.45998e7	−1.22466
$835$	−1.07692e7	−0.534525
$836$	−3.30118e7	−1.63363
$837$	−1.79333e6	−0.0884804
$838$	−1.66288e7	−0.817997
$839$	−1.18159e7	−0.579510	−0.289755	−	0.957101i	$-0.593574\pi$
$839$	−1.18159e7	−0.579510	−0.289755	+	0.957101i	$0.593574\pi$
$840$	0	0
$841$	−1.99663e7	−0.973437
$842$	1.57118e7	0.763741
$843$	7.48669e6	0.362845
$844$	8.69422e7	4.20121
$845$	−1.55799e7	−0.750626
$846$	−68020.3	−0.00326748
$847$	0	0
$848$	1.29542e8	6.18615
$849$	2.07964e7	0.990191
$850$	8.47560e6	0.402368
$851$	−1.71308e7	−0.810875
$852$	2.54398e7	1.20064
$853$	−6.26477e6	−0.294803	−0.147402	−	0.989077i	$-0.547091\pi$
$853$	−6.26477e6	−0.294803	−0.147402	+	0.989077i	$0.547091\pi$
$854$	0	0
$855$	1.03079e7	0.482230
$856$	−1.47181e8	−6.86541
$857$	2.51137e7	1.16804	0.584020	−	0.811739i	$-0.301479\pi$
$857$	2.51137e7	1.16804	0.584020	+	0.811739i	$0.301479\pi$
$858$	6.08371e6	0.282131
$859$	−4.14654e6	−0.191736	−0.0958679	−	0.995394i	$-0.530563\pi$
$859$	−4.14654e6	−0.191736	−0.0958679	+	0.995394i	$0.530563\pi$
$860$	−5.99017e7	−2.76180
$861$	0	0
$862$	3.02272e7	1.38557
$863$	−1.38124e7	−0.631308	−0.315654	−	0.948874i	$-0.602224\pi$
$863$	−1.38124e7	−0.631308	−0.315654	+	0.948874i	$0.602224\pi$
$864$	2.21693e7	1.01034
$865$	317187.	0.0144137
$866$	−5.33657e7	−2.41806
$867$	3.79300e6	0.171370
$868$	0	0
$869$	−1.32086e6	−0.0593345
$870$	4.63151e6	0.207455
$871$	−5.01930e6	−0.224181
$872$	2.76938e7	1.23336
$873$	−1.73836e6	−0.0771975
$874$	4.45460e7	1.97256
$875$	0	0
$876$	7.20160e7	3.17080
$877$	9.15841e6	0.402088	0.201044	−	0.979582i	$-0.435567\pi$
$877$	9.15841e6	0.402088	0.201044	+	0.979582i	$0.435567\pi$
$878$	70792.4	0.00309920
$879$	1.39292e7	0.608069
$880$	−5.05502e7	−2.20047
$881$	−2.45789e7	−1.06690	−0.533449	−	0.845833i	$-0.679104\pi$
$881$	−2.45789e7	−1.06690	−0.533449	+	0.845833i	$0.679104\pi$
$882$	0	0
$883$	−1.10185e7	−0.475575	−0.237787	−	0.971317i	$-0.576422\pi$
$883$	−1.10185e7	−0.475575	−0.237787	+	0.971317i	$0.576422\pi$
$884$	3.24212e7	1.39540
$885$	−1.93913e6	−0.0832239
$886$	−1.58411e7	−0.677954
$887$	−2.86983e7	−1.22475	−0.612374	−	0.790569i	$-0.709785\pi$
$887$	−2.86983e7	−1.22475	−0.612374	+	0.790569i	$0.709785\pi$
$888$	5.41220e7	2.30325
$889$	0	0
$890$	3.23433e7	1.36870
$891$	−1.13830e6	−0.0480355
$892$	1.83585e7	0.772546
$893$	153282.	0.00643224
$894$	−2.81707e7	−1.17884
$895$	1.50976e7	0.630013
$896$	0	0
$897$	−6.11065e6	−0.253575
$898$	2.10504e7	0.871103
$899$	1.81579e6	0.0749318
$900$	5.72183e6	0.235466
$901$	−2.76835e7	−1.13608
$902$	−3.41966e7	−1.39948
$903$	0	0
$904$	1.02679e7	0.417889
$905$	3.06748e7	1.24497
$906$	−2.01805e7	−0.816793
$907$	−1.55637e7	−0.628195	−0.314098	−	0.949391i	$-0.601702\pi$
$907$	−1.55637e7	−0.628195	−0.314098	+	0.949391i	$0.601702\pi$
$908$	1.11657e8	4.49440
$909$	−1.18206e7	−0.474491
$910$	0	0
$911$	2.36784e7	0.945273	0.472637	−	0.881257i	$-0.343302\pi$
$911$	2.36784e7	0.945273	0.472637	+	0.881257i	$0.343302\pi$
$912$	−8.59366e7	−3.42130
$913$	1.10560e7	0.438957
$914$	−8.32864e7	−3.29768
$915$	8.94891e6	0.353360
$916$	2.27406e7	0.895495
$917$	0	0
$918$	−8.14963e6	−0.319177
$919$	1.31869e7	0.515054	0.257527	−	0.966271i	$-0.417092\pi$
$919$	1.31869e7	0.515054	0.257527	+	0.966271i	$0.417092\pi$
$920$	8.31512e7	3.23891
$921$	1.34698e6	0.0523254
$922$	8.90233e7	3.44887
$923$	1.05649e7	0.408188
$924$	0	0
$925$	6.66158e6	0.255990
$926$	−7.43405e7	−2.84903
$927$	−1.34159e7	−0.512768
$928$	−2.24470e7	−0.855633
$929$	−2.36801e7	−0.900211	−0.450105	−	0.892975i	$-0.648614\pi$
$929$	−2.36801e7	−0.900211	−0.450105	+	0.892975i	$0.648614\pi$
$930$	1.54356e7	0.585216
$931$	0	0
$932$	−1.41865e7	−0.534979
$933$	−1.31838e6	−0.0495836
$934$	−3.32882e7	−1.24860
$935$	1.08028e7	0.404115
$936$	1.93056e7	0.720268
$937$	−9.81602e6	−0.365247	−0.182623	−	0.983183i	$-0.558459\pi$
$937$	−9.81602e6	−0.365247	−0.182623	+	0.983183i	$0.558459\pi$
$938$	0	0
$939$	2.86501e6	0.106038
$940$	435794.	0.0160865
$941$	3.32172e7	1.22289	0.611446	−	0.791286i	$-0.290588\pi$
$941$	3.32172e7	1.22289	0.611446	+	0.791286i	$0.290588\pi$
$942$	−4.73258e7	−1.73768
$943$	3.43481e7	1.25783
$944$	1.61664e7	0.590452
$945$	0	0
$946$	−2.00262e7	−0.727563
$947$	7.39103e6	0.267812	0.133906	−	0.990994i	$-0.457248\pi$
$947$	7.39103e6	0.267812	0.133906	+	0.990994i	$0.457248\pi$
$948$	−6.38414e6	−0.230718
$949$	2.99075e7	1.07799
$950$	−1.73224e7	−0.622728
$951$	−1.94933e7	−0.698930
$952$	0	0
$953$	−1.81495e7	−0.647341	−0.323671	−	0.946170i	$-0.604917\pi$
$953$	−1.81495e7	−0.647341	−0.323671	+	0.946170i	$0.604917\pi$
$954$	−2.51077e7	−0.893174
$955$	−1.26954e7	−0.450441
$956$	1.40760e8	4.98120
$957$	1.15255e6	0.0406801
$958$	−3.81354e7	−1.34250
$959$	0	0
$960$	−1.06904e8	−3.74381
$961$	−2.25776e7	−0.788623
$962$	3.42339e7	1.19266
$963$	1.74189e7	0.605279
$964$	−2.17036e7	−0.752210
$965$	−3.80498e6	−0.131533
$966$	0	0
$967$	3.12321e7	1.07408	0.537038	−	0.843558i	$-0.319543\pi$
$967$	3.12321e7	1.07408	0.537038	+	0.843558i	$0.319543\pi$
$968$	8.96235e7	3.07421
$969$	1.83650e7	0.628319
$970$	1.49624e7	0.510590
$971$	1.36711e7	0.465323	0.232662	−	0.972558i	$-0.425257\pi$
$971$	1.36711e7	0.465323	0.232662	+	0.972558i	$0.425257\pi$
$972$	−5.50177e6	−0.186783
$973$	0	0
$974$	−6.61558e7	−2.23445
$975$	2.37622e6	0.0800526
$976$	−7.46068e7	−2.50700
$977$	4.99027e7	1.67258	0.836291	−	0.548285i	$-0.184719\pi$
$977$	4.99027e7	1.67258	0.836291	+	0.548285i	$0.184719\pi$
$978$	−5.91071e7	−1.97603
$979$	8.04866e6	0.268390
$980$	0	0
$981$	−3.27758e6	−0.108738
$982$	−6.15221e6	−0.203588
$983$	2.21662e7	0.731656	0.365828	−	0.930682i	$-0.380786\pi$
$983$	2.21662e7	0.731656	0.365828	+	0.930682i	$0.380786\pi$
$984$	−1.08517e8	−3.57282
$985$	2.85237e7	0.936730
$986$	8.25169e6	0.270303
$987$	0	0
$988$	−6.62622e7	−2.15960
$989$	2.01149e7	0.653924
$990$	9.79759e6	0.317710
$991$	−4.18915e7	−1.35501	−0.677504	−	0.735519i	$-0.736938\pi$
$991$	−4.18915e7	−1.35501	−0.677504	+	0.735519i	$0.736938\pi$
$992$	−7.48098e7	−2.41368
$993$	2.28911e7	0.736704
$994$	0	0
$995$	1.68592e7	0.539856
$996$	5.34373e7	1.70685
$997$	−4.23041e7	−1.34786	−0.673930	−	0.738795i	$-0.735395\pi$
$997$	−4.23041e7	−1.34786	−0.673930	+	0.738795i	$0.735395\pi$
$998$	−6.27589e7	−1.99457
$999$	−6.40537e6	−0.203063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.n.1.1	✓	6
3.2	odd	2		441.6.a.bb.1.6		6
7.2	even	3		147.6.e.q.67.6		12
7.3	odd	6		147.6.e.p.79.6		12
7.4	even	3		147.6.e.q.79.6		12
7.5	odd	6		147.6.e.p.67.6		12
7.6	odd	2		147.6.a.o.1.1	yes	6
21.20	even	2		441.6.a.ba.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.1	✓	6	1.1	even	1	trivial
147.6.a.o.1.1	yes	6	7.6	odd	2
147.6.e.p.67.6		12	7.5	odd	6
147.6.e.p.79.6		12	7.3	odd	6
147.6.e.q.67.6		12	7.2	even	3
147.6.e.q.79.6		12	7.4	even	3
441.6.a.ba.1.6		6	21.20	even	2
441.6.a.bb.1.6		6	3.2	odd	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)

\(f(q)\)	\(=\)	\(q-11.1881 q^{2} -9.00000 q^{3} +93.1729 q^{4} +62.3150 q^{5} +100.693 q^{6} -684.407 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-11.1881 q^{2} -9.00000 q^{3} +93.1729 q^{4} +62.3150 q^{5} +100.693 q^{6} -684.407 q^{8} +81.0000 q^{9} -697.185 q^{10} -173.495 q^{11} -838.557 q^{12} -348.244 q^{13} -560.835 q^{15} +4675.66 q^{16} -999.206 q^{17} -906.234 q^{18} +2042.17 q^{19} +5806.07 q^{20} +1941.07 q^{22} -1949.67 q^{23} +6159.67 q^{24} +758.159 q^{25} +3896.18 q^{26} -729.000 q^{27} +738.129 q^{29} +6274.66 q^{30} +2459.99 q^{31} -30410.6 q^{32} +1561.45 q^{33} +11179.2 q^{34} +7547.01 q^{36} +8786.52 q^{37} -22848.0 q^{38} +3134.20 q^{39} -42648.8 q^{40} -17617.4 q^{41} -10317.1 q^{43} -16165.0 q^{44} +5047.51 q^{45} +21813.1 q^{46} +75.0582 q^{47} -42081.0 q^{48} -8482.34 q^{50} +8992.86 q^{51} -32446.9 q^{52} +27705.5 q^{53} +8156.10 q^{54} -10811.3 q^{55} -18379.5 q^{57} -8258.24 q^{58} +3457.57 q^{59} -52254.6 q^{60} -15956.4 q^{61} -27522.5 q^{62} +190615. q^{64} -21700.8 q^{65} -17469.7 q^{66} +14413.2 q^{67} -93099.0 q^{68} +17547.0 q^{69} -30337.6 q^{71} -55437.0 q^{72} -85880.9 q^{73} -98304.2 q^{74} -6823.43 q^{75} +190275. q^{76} -35065.6 q^{78} +7613.25 q^{79} +291364. q^{80} +6561.00 q^{81} +197104. q^{82} -63725.4 q^{83} -62265.5 q^{85} +115428. q^{86} -6643.16 q^{87} +118741. q^{88} -46391.3 q^{89} -56472.0 q^{90} -181657. q^{92} -22139.9 q^{93} -839.757 q^{94} +127258. q^{95} +273696. q^{96} -21461.2 q^{97} -14053.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 54 q^{3} + 150 q^{4} - 100 q^{5} - 18 q^{6} - 114 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 54 * q^3 + 150 * q^4 - 100 * q^5 - 18 * q^6 - 114 * q^8 + 486 * q^9	\( 6 q + 2 q^{2} - 54 q^{3} + 150 q^{4} - 100 q^{5} - 18 q^{6} - 114 q^{8} + 486 q^{9} - 864 q^{10} + 604 q^{11} - 1350 q^{12} - 1352 q^{13} + 900 q^{15} + 4578 q^{16} - 3028 q^{17} + 162 q^{18} - 1728 q^{19} - 452 q^{20} - 4116 q^{22} - 4484 q^{23} + 1026 q^{24} + 4806 q^{25} - 14172 q^{26} - 4374 q^{27} - 5320 q^{29} + 7776 q^{30} - 3976 q^{31} - 37326 q^{32} - 5436 q^{33} + 16336 q^{34} + 12150 q^{36} + 22680 q^{37} - 52744 q^{38} + 12168 q^{39} - 100600 q^{40} - 28756 q^{41} - 6768 q^{43} - 64940 q^{44} - 8100 q^{45} + 540 q^{46} - 51552 q^{47} - 41202 q^{48} - 40622 q^{50} + 27252 q^{51} - 119296 q^{52} + 80884 q^{53} - 1458 q^{54} - 11656 q^{55} + 15552 q^{57} - 70464 q^{58} - 8872 q^{59} + 4068 q^{60} - 50896 q^{61} - 11824 q^{62} + 199590 q^{64} + 3492 q^{65} + 37044 q^{66} + 6480 q^{67} - 37348 q^{68} + 40356 q^{69} - 110852 q^{71} - 9234 q^{72} - 64232 q^{73} - 27464 q^{74} - 43254 q^{75} + 194864 q^{76} + 127548 q^{78} + 111696 q^{79} + 308940 q^{80} + 39366 q^{81} + 189640 q^{82} - 101128 q^{83} - 23292 q^{85} + 3824 q^{86} + 47880 q^{87} - 97788 q^{88} + 35012 q^{89} - 69984 q^{90} - 449260 q^{92} + 35784 q^{93} + 121016 q^{94} - 119080 q^{95} + 335934 q^{96} - 70952 q^{97} + 48924 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 54 * q^3 + 150 * q^4 - 100 * q^5 - 18 * q^6 - 114 * q^8 + 486 * q^9 - 864 * q^10 + 604 * q^11 - 1350 * q^12 - 1352 * q^13 + 900 * q^15 + 4578 * q^16 - 3028 * q^17 + 162 * q^18 - 1728 * q^19 - 452 * q^20 - 4116 * q^22 - 4484 * q^23 + 1026 * q^24 + 4806 * q^25 - 14172 * q^26 - 4374 * q^27 - 5320 * q^29 + 7776 * q^30 - 3976 * q^31 - 37326 * q^32 - 5436 * q^33 + 16336 * q^34 + 12150 * q^36 + 22680 * q^37 - 52744 * q^38 + 12168 * q^39 - 100600 * q^40 - 28756 * q^41 - 6768 * q^43 - 64940 * q^44 - 8100 * q^45 + 540 * q^46 - 51552 * q^47 - 41202 * q^48 - 40622 * q^50 + 27252 * q^51 - 119296 * q^52 + 80884 * q^53 - 1458 * q^54 - 11656 * q^55 + 15552 * q^57 - 70464 * q^58 - 8872 * q^59 + 4068 * q^60 - 50896 * q^61 - 11824 * q^62 + 199590 * q^64 + 3492 * q^65 + 37044 * q^66 + 6480 * q^67 - 37348 * q^68 + 40356 * q^69 - 110852 * q^71 - 9234 * q^72 - 64232 * q^73 - 27464 * q^74 - 43254 * q^75 + 194864 * q^76 + 127548 * q^78 + 111696 * q^79 + 308940 * q^80 + 39366 * q^81 + 189640 * q^82 - 101128 * q^83 - 23292 * q^85 + 3824 * q^86 + 47880 * q^87 - 97788 * q^88 + 35012 * q^89 - 69984 * q^90 - 449260 * q^92 + 35784 * q^93 + 121016 * q^94 - 119080 * q^95 + 335934 * q^96 - 70952 * q^97 + 48924 * q^99

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