LMFDB - Embedded newform 147.6.a.o.1.5

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:	$6$
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			1.5
Root			$3.75353$ 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)

$f(q)$	$=$	$q+8.20863 q^{2} +9.00000 q^{3} +35.3816 q^{4} +29.2259 q^{5} +73.8777 q^{6} +27.7583 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+8.20863 q^{2} +9.00000 q^{3} +35.3816 q^{4} +29.2259 q^{5} +73.8777 q^{6} +27.7583 q^{8} +81.0000 q^{9} +239.905 q^{10} +377.338 q^{11} +318.434 q^{12} +509.772 q^{13} +263.033 q^{15} -904.354 q^{16} +1605.98 q^{17} +664.899 q^{18} +2156.74 q^{19} +1034.06 q^{20} +3097.43 q^{22} -4434.38 q^{23} +249.825 q^{24} -2270.85 q^{25} +4184.53 q^{26} +729.000 q^{27} +4772.55 q^{29} +2159.14 q^{30} -7155.93 q^{31} -8311.77 q^{32} +3396.04 q^{33} +13182.9 q^{34} +2865.91 q^{36} +5574.32 q^{37} +17703.9 q^{38} +4587.95 q^{39} +811.262 q^{40} -9911.64 q^{41} -4886.16 q^{43} +13350.8 q^{44} +2367.30 q^{45} -36400.2 q^{46} +9266.09 q^{47} -8139.18 q^{48} -18640.5 q^{50} +14453.8 q^{51} +18036.6 q^{52} -9246.11 q^{53} +5984.09 q^{54} +11028.1 q^{55} +19410.7 q^{57} +39176.1 q^{58} -14120.7 q^{59} +9306.54 q^{60} -18030.9 q^{61} -58740.4 q^{62} -39288.9 q^{64} +14898.6 q^{65} +27876.9 q^{66} -46514.1 q^{67} +56822.2 q^{68} -39909.4 q^{69} +64269.9 q^{71} +2248.42 q^{72} -60921.0 q^{73} +45757.5 q^{74} -20437.6 q^{75} +76309.0 q^{76} +37660.8 q^{78} -71464.7 q^{79} -26430.6 q^{80} +6561.00 q^{81} -81361.0 q^{82} +11597.5 q^{83} +46936.3 q^{85} -40108.7 q^{86} +42953.0 q^{87} +10474.3 q^{88} +78238.9 q^{89} +19432.3 q^{90} -156896. q^{92} -64403.3 q^{93} +76061.9 q^{94} +63032.8 q^{95} -74805.9 q^{96} +151480. q^{97} +30564.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.20863	1.45109	0.725547	−	0.688172i	$-0.241587\pi$
$2$	8.20863	1.45109	0.725547	+	0.688172i	$0.241587\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	35.3816	1.10568
$5$	29.2259	0.522809	0.261405	−	0.965229i	$-0.415814\pi$
$5$	29.2259	0.522809	0.261405	+	0.965229i	$0.415814\pi$
$6$	73.8777	0.837790
$7$	0	0
$7$	0	0
$8$	27.7583	0.153344
$9$	81.0000	0.333333
$10$	239.905	0.758646
$11$	377.338	0.940262	0.470131	−	0.882597i	$-0.344207\pi$
$11$	377.338	0.940262	0.470131	+	0.882597i	$0.344207\pi$
$12$	318.434	0.638362
$13$	509.772	0.836600	0.418300	−	0.908309i	$-0.362626\pi$
$13$	509.772	0.836600	0.418300	+	0.908309i	$0.362626\pi$
$14$	0	0
$15$	263.033	0.301844
$16$	−904.354	−0.883158
$17$	1605.98	1.34778	0.673889	−	0.738833i	$-0.264623\pi$
$17$	1605.98	1.34778	0.673889	+	0.738833i	$0.264623\pi$
$18$	664.899	0.483698
$19$	2156.74	1.37061	0.685306	−	0.728256i	$-0.259669\pi$
$19$	2156.74	1.37061	0.685306	+	0.728256i	$0.259669\pi$
$20$	1034.06	0.578057
$21$	0	0
$22$	3097.43	1.36441
$23$	−4434.38	−1.74789	−0.873944	−	0.486027i	$-0.838446\pi$
$23$	−4434.38	−1.74789	−0.873944	+	0.486027i	$0.838446\pi$
$24$	249.825	0.0885335
$25$	−2270.85	−0.726671
$26$	4184.53	1.21399
$27$	729.000	0.192450
$28$	0	0
$29$	4772.55	1.05379	0.526897	−	0.849929i	$-0.323355\pi$
$29$	4772.55	1.05379	0.526897	+	0.849929i	$0.323355\pi$
$30$	2159.14	0.438004
$31$	−7155.93	−1.33740	−0.668701	−	0.743532i	$-0.733149\pi$
$31$	−7155.93	−1.33740	−0.668701	+	0.743532i	$0.733149\pi$
$32$	−8311.77	−1.43489
$33$	3396.04	0.542861
$34$	13182.9	1.95575
$35$	0	0
$36$	2865.91	0.368558
$37$	5574.32	0.669402	0.334701	−	0.942324i	$-0.391365\pi$
$37$	5574.32	0.669402	0.334701	+	0.942324i	$0.391365\pi$
$38$	17703.9	1.98889
$39$	4587.95	0.483011
$40$	811.262	0.0801699
$41$	−9911.64	−0.920844	−0.460422	−	0.887700i	$-0.652302\pi$
$41$	−9911.64	−0.920844	−0.460422	+	0.887700i	$0.652302\pi$
$42$	0	0
$43$	−4886.16	−0.402992	−0.201496	−	0.979489i	$-0.564580\pi$
$43$	−4886.16	−0.402992	−0.201496	+	0.979489i	$0.564580\pi$
$44$	13350.8	1.03962
$45$	2367.30	0.174270
$46$	−36400.2	−2.53635
$47$	9266.09	0.611859	0.305930	−	0.952054i	$-0.401033\pi$
$47$	9266.09	0.611859	0.305930	+	0.952054i	$0.401033\pi$
$48$	−8139.18	−0.509891
$49$	0	0
$50$	−18640.5	−1.05447
$51$	14453.8	0.778140
$52$	18036.6	0.925007
$53$	−9246.11	−0.452136	−0.226068	−	0.974111i	$-0.572587\pi$
$53$	−9246.11	−0.452136	−0.226068	+	0.974111i	$0.572587\pi$
$54$	5984.09	0.279263
$55$	11028.1	0.491578
$56$	0	0
$57$	19410.7	0.791323
$58$	39176.1	1.52915
$59$	−14120.7	−0.528114	−0.264057	−	0.964507i	$-0.585061\pi$
$59$	−14120.7	−0.528114	−0.264057	+	0.964507i	$0.585061\pi$
$60$	9306.54	0.333741
$61$	−18030.9	−0.620431	−0.310216	−	0.950666i	$-0.600401\pi$
$61$	−18030.9	−0.620431	−0.310216	+	0.950666i	$0.600401\pi$
$62$	−58740.4	−1.94070
$63$	0	0
$64$	−39288.9	−1.19900
$65$	14898.6	0.437382
$66$	27876.9	0.787742
$67$	−46514.1	−1.26589	−0.632947	−	0.774195i	$-0.718155\pi$
$67$	−46514.1	−1.26589	−0.632947	+	0.774195i	$0.718155\pi$
$68$	56822.2	1.49020
$69$	−39909.4	−1.00914
$70$	0	0
$71$	64269.9	1.51308	0.756540	−	0.653948i	$-0.226888\pi$
$71$	64269.9	1.51308	0.756540	+	0.653948i	$0.226888\pi$
$72$	2248.42	0.0511148
$73$	−60921.0	−1.33801	−0.669005	−	0.743258i	$-0.733280\pi$
$73$	−60921.0	−1.33801	−0.669005	+	0.743258i	$0.733280\pi$
$74$	45757.5	0.971366
$75$	−20437.6	−0.419543
$76$	76309.0	1.51545
$77$	0	0
$78$	37660.8	0.700895
$79$	−71464.7	−1.28832	−0.644160	−	0.764891i	$-0.722793\pi$
$79$	−71464.7	−1.28832	−0.644160	+	0.764891i	$0.722793\pi$
$80$	−26430.6	−0.461723
$81$	6561.00	0.111111
$82$	−81361.0	−1.33623
$83$	11597.5	0.184785	0.0923926	−	0.995723i	$-0.470549\pi$
$83$	11597.5	0.184785	0.0923926	+	0.995723i	$0.470549\pi$
$84$	0	0
$85$	46936.3	0.704630
$86$	−40108.7	−0.584780
$87$	42953.0	0.608408
$88$	10474.3	0.144184
$89$	78238.9	1.04700	0.523502	−	0.852025i	$-0.324625\pi$
$89$	78238.9	1.04700	0.523502	+	0.852025i	$0.324625\pi$
$90$	19432.3	0.252882
$91$	0	0
$92$	−156896.	−1.93260
$93$	−64403.3	−0.772149
$94$	76061.9	0.887866
$95$	63032.8	0.716568
$96$	−74805.9	−0.828434
$97$	151480.	1.63466	0.817330	−	0.576170i	$-0.195454\pi$
$97$	151480.	1.63466	0.817330	+	0.576170i	$0.195454\pi$
$98$	0	0
$99$	30564.4	0.313421
$100$	−80346.1	−0.803461
$101$	−91407.2	−0.891614	−0.445807	−	0.895129i	$-0.647083\pi$
$101$	−91407.2	−0.891614	−0.445807	+	0.895129i	$0.647083\pi$
$102$	118646.	1.12915
$103$	−56930.8	−0.528754	−0.264377	−	0.964419i	$-0.585166\pi$
$103$	−56930.8	−0.528754	−0.264377	+	0.964419i	$0.585166\pi$
$104$	14150.4	0.128288
$105$	0	0
$106$	−75897.9	−0.656093
$107$	−196209.	−1.65676	−0.828380	−	0.560166i	$-0.810737\pi$
$107$	−196209.	−1.65676	−0.828380	+	0.560166i	$0.810737\pi$
$108$	25793.2	0.212787
$109$	105853.	0.853368	0.426684	−	0.904401i	$-0.359682\pi$
$109$	105853.	0.853368	0.426684	+	0.904401i	$0.359682\pi$
$110$	90525.2	0.713326
$111$	50168.8	0.386480
$112$	0	0
$113$	−67589.3	−0.497945	−0.248973	−	0.968511i	$-0.580093\pi$
$113$	−67589.3	−0.497945	−0.248973	+	0.968511i	$0.580093\pi$
$114$	159335.	1.14828
$115$	−129599.	−0.913812
$116$	168861.	1.16515
$117$	41291.5	0.278867
$118$	−115912.	−0.766343
$119$	0	0
$120$	7301.36	0.0462861
$121$	−18667.0	−0.115907
$122$	−148009.	−0.900304
$123$	−89204.8	−0.531650
$124$	−253188.	−1.47873
$125$	−157699.	−0.902719
$126$	0	0
$127$	281805.	1.55039	0.775193	−	0.631724i	$-0.217653\pi$
$127$	281805.	1.55039	0.775193	+	0.631724i	$0.217653\pi$
$128$	−56531.6	−0.304977
$129$	−43975.5	−0.232668
$130$	122297.	0.634683
$131$	−88576.7	−0.450964	−0.225482	−	0.974247i	$-0.572396\pi$
$131$	−88576.7	−0.450964	−0.225482	+	0.974247i	$0.572396\pi$
$132$	120157.	0.600227
$133$	0	0
$134$	−381817.	−1.83693
$135$	21305.7	0.100615
$136$	44579.3	0.206674
$137$	−286830.	−1.30564	−0.652820	−	0.757513i	$-0.726414\pi$
$137$	−286830.	−1.30564	−0.652820	+	0.757513i	$0.726414\pi$
$138$	−327602.	−1.46436
$139$	−345909.	−1.51853	−0.759267	−	0.650779i	$-0.774442\pi$
$139$	−345909.	−1.51853	−0.759267	+	0.650779i	$0.774442\pi$
$140$	0	0
$141$	83394.8	0.353257
$142$	527568.	2.19562
$143$	192356.	0.786623
$144$	−73252.6	−0.294386
$145$	139482.	0.550933
$146$	−500078.	−1.94158
$147$	0	0
$148$	197228.	0.740142
$149$	−304757.	−1.12458	−0.562288	−	0.826942i	$-0.690079\pi$
$149$	−304757.	−1.12458	−0.562288	+	0.826942i	$0.690079\pi$
$150$	−167765.	−0.608797
$151$	348313.	1.24316	0.621581	−	0.783350i	$-0.286491\pi$
$151$	348313.	1.24316	0.621581	+	0.783350i	$0.286491\pi$
$152$	59867.5	0.210176
$153$	130084.	0.449259
$154$	0	0
$155$	−209139.	−0.699206
$156$	162329.	0.534053
$157$	188561.	0.610523	0.305262	−	0.952269i	$-0.401256\pi$
$157$	188561.	0.610523	0.305262	+	0.952269i	$0.401256\pi$
$158$	−586627.	−1.86947
$159$	−83215.0	−0.261041
$160$	−242919.	−0.750174
$161$	0	0
$162$	53856.8	0.161233
$163$	271248.	0.799645	0.399823	−	0.916593i	$-0.369072\pi$
$163$	271248.	0.799645	0.399823	+	0.916593i	$0.369072\pi$
$164$	−350690.	−1.01815
$165$	99252.5	0.283813
$166$	95199.2	0.268141
$167$	422260.	1.17163	0.585813	−	0.810446i	$-0.300775\pi$
$167$	422260.	1.17163	0.585813	+	0.810446i	$0.300775\pi$
$168$	0	0
$169$	−111425.	−0.300101
$170$	385283.	1.02249
$171$	174696.	0.456870
$172$	−172880.	−0.445578
$173$	301288.	0.765361	0.382681	−	0.923881i	$-0.375001\pi$
$173$	301288.	0.765361	0.382681	+	0.923881i	$0.375001\pi$
$174$	352585.	0.882858
$175$	0	0
$176$	−341247.	−0.830400
$177$	−127087.	−0.304907
$178$	642235.	1.51930
$179$	−285557.	−0.666131	−0.333065	−	0.942904i	$-0.608083\pi$
$179$	−285557.	−0.666131	−0.333065	+	0.942904i	$0.608083\pi$
$180$	83758.9	0.192686
$181$	536753.	1.21781	0.608903	−	0.793244i	$-0.291610\pi$
$181$	536753.	1.21781	0.608903	+	0.793244i	$0.291610\pi$
$182$	0	0
$183$	−162278.	−0.358206
$184$	−123091.	−0.268029
$185$	162915.	0.349970
$186$	−528663.	−1.12046
$187$	605998.	1.26726
$188$	327849.	0.676518
$189$	0	0
$190$	517413.	1.03981
$191$	−356684.	−0.707457	−0.353729	−	0.935348i	$-0.615086\pi$
$191$	−356684.	−0.707457	−0.353729	+	0.935348i	$0.615086\pi$
$192$	−353600.	−0.692245
$193$	750853.	1.45098	0.725490	−	0.688233i	$-0.241613\pi$
$193$	750853.	1.45098	0.725490	+	0.688233i	$0.241613\pi$
$194$	1.24345e6	2.37205
$195$	134087.	0.252523
$196$	0	0
$197$	296470.	0.544272	0.272136	−	0.962259i	$-0.412270\pi$
$197$	296470.	0.544272	0.272136	+	0.962259i	$0.412270\pi$
$198$	250892.	0.454803
$199$	484572.	0.867412	0.433706	−	0.901055i	$-0.357206\pi$
$199$	484572.	0.867412	0.433706	+	0.901055i	$0.357206\pi$
$200$	−63034.9	−0.111431
$201$	−418627.	−0.730864
$202$	−750328.	−1.29382
$203$	0	0
$204$	511400.	0.860369
$205$	−289677.	−0.481426
$206$	−467323.	−0.767272
$207$	−359185.	−0.582629
$208$	−461014.	−0.738849
$209$	813821.	1.28873
$210$	0	0
$211$	849306.	1.31328	0.656641	−	0.754203i	$-0.271977\pi$
$211$	849306.	1.31328	0.656641	+	0.754203i	$0.271977\pi$
$212$	−327142.	−0.499916
$213$	578429.	0.873577
$214$	−1.61061e6	−2.40412
$215$	−142803.	−0.210688
$216$	20235.8	0.0295112
$217$	0	0
$218$	868906.	1.23832
$219$	−548289.	−0.772501
$220$	390190.	0.543525
$221$	818684.	1.12755
$222$	411817.	0.560819
$223$	1.06822e6	1.43847	0.719233	−	0.694769i	$-0.244494\pi$
$223$	1.06822e6	1.43847	0.719233	+	0.694769i	$0.244494\pi$
$224$	0	0
$225$	−183938.	−0.242224
$226$	−554815.	−0.722566
$227$	32350.8	0.0416698	0.0208349	−	0.999783i	$-0.493368\pi$
$227$	32350.8	0.0416698	0.0208349	+	0.999783i	$0.493368\pi$
$228$	686781.	0.874946
$229$	1.18287e6	1.49056	0.745280	−	0.666752i	$-0.232316\pi$
$229$	1.18287e6	1.49056	0.745280	+	0.666752i	$0.232316\pi$
$230$	−1.06383e6	−1.32603
$231$	0	0
$232$	132478.	0.161593
$233$	329750.	0.397919	0.198960	−	0.980008i	$-0.436244\pi$
$233$	329750.	0.397919	0.198960	+	0.980008i	$0.436244\pi$
$234$	338947.	0.404662
$235$	270810.	0.319886
$236$	−499614.	−0.583922
$237$	−643182.	−0.743812
$238$	0	0
$239$	−459379.	−0.520207	−0.260104	−	0.965581i	$-0.583757\pi$
$239$	−459379.	−0.520207	−0.260104	+	0.965581i	$0.583757\pi$
$240$	−237875.	−0.266576
$241$	−1.45979e6	−1.61900	−0.809499	−	0.587121i	$-0.800261\pi$
$241$	−1.45979e6	−1.61900	−0.809499	+	0.587121i	$0.800261\pi$
$242$	−153230.	−0.168192
$243$	59049.0	0.0641500
$244$	−637963.	−0.685995
$245$	0	0
$246$	−732249.	−0.771474
$247$	1.09945e6	1.14665
$248$	−198636.	−0.205083
$249$	104377.	0.106686
$250$	−1.29449e6	−1.30993
$251$	523090.	0.524074	0.262037	−	0.965058i	$-0.415606\pi$
$251$	523090.	0.524074	0.262037	+	0.965058i	$0.415606\pi$
$252$	0	0
$253$	−1.67326e6	−1.64347
$254$	2.31324e6	2.24976
$255$	422426.	0.406818
$256$	793198.	0.756453
$257$	465448.	0.439580	0.219790	−	0.975547i	$-0.429463\pi$
$257$	465448.	0.439580	0.219790	+	0.975547i	$0.429463\pi$
$258$	−360978.	−0.337623
$259$	0	0
$260$	527135.	0.483602
$261$	386577.	0.351265
$262$	−727094.	−0.654391
$263$	129621.	0.115555	0.0577773	−	0.998329i	$-0.481599\pi$
$263$	129621.	0.115555	0.0577773	+	0.998329i	$0.481599\pi$
$264$	94268.4	0.0832447
$265$	−270226.	−0.236381
$266$	0	0
$267$	704150.	0.604488
$268$	−1.64574e6	−1.39967
$269$	1.40436e6	1.18331	0.591653	−	0.806193i	$-0.298476\pi$
$269$	1.40436e6	1.18331	0.591653	+	0.806193i	$0.298476\pi$
$270$	174891.	0.146001
$271$	−885085.	−0.732086	−0.366043	−	0.930598i	$-0.619288\pi$
$271$	−885085.	−0.732086	−0.366043	+	0.930598i	$0.619288\pi$
$272$	−1.45237e6	−1.19030
$273$	0	0
$274$	−2.35448e6	−1.89461
$275$	−856876.	−0.683261
$276$	−1.41206e6	−1.11578
$277$	−1.33714e6	−1.04707	−0.523535	−	0.852004i	$-0.675387\pi$
$277$	−1.33714e6	−1.04707	−0.523535	+	0.852004i	$0.675387\pi$
$278$	−2.83944e6	−2.20354
$279$	−579630.	−0.445800
$280$	0	0
$281$	−1.80115e6	−1.36077	−0.680383	−	0.732857i	$-0.738187\pi$
$281$	−1.80115e6	−1.36077	−0.680383	+	0.732857i	$0.738187\pi$
$282$	684557.	0.512610
$283$	−971887.	−0.721356	−0.360678	−	0.932690i	$-0.617455\pi$
$283$	−971887.	−0.721356	−0.360678	+	0.932690i	$0.617455\pi$
$284$	2.27397e6	1.67297
$285$	567295.	0.413711
$286$	1.57898e6	1.14146
$287$	0	0
$288$	−673253.	−0.478297
$289$	1.15932e6	0.816503
$290$	1.14496e6	0.799456
$291$	1.36332e6	0.943771
$292$	−2.15548e6	−1.47941
$293$	−675064.	−0.459384	−0.229692	−	0.973263i	$-0.573772\pi$
$293$	−675064.	−0.459384	−0.229692	+	0.973263i	$0.573772\pi$
$294$	0	0
$295$	−412692.	−0.276103
$296$	154734.	0.102649
$297$	275079.	0.180954
$298$	−2.50164e6	−1.63186
$299$	−2.26052e6	−1.46228
$300$	−723115.	−0.463879
$301$	0	0
$302$	2.85918e6	1.80395
$303$	−822665.	−0.514774
$304$	−1.95046e6	−1.21047
$305$	−526971.	−0.324367
$306$	1.06782e6	0.651917
$307$	894063.	0.541405	0.270702	−	0.962663i	$-0.412744\pi$
$307$	894063.	0.541405	0.270702	+	0.962663i	$0.412744\pi$
$308$	0	0
$309$	−512377.	−0.305276
$310$	−1.71674e6	−1.01461
$311$	−974011.	−0.571035	−0.285518	−	0.958373i	$-0.592166\pi$
$311$	−974011.	−0.571035	−0.285518	+	0.958373i	$0.592166\pi$
$312$	127354.	0.0740671
$313$	705256.	0.406899	0.203449	−	0.979085i	$-0.434785\pi$
$313$	705256.	0.406899	0.203449	+	0.979085i	$0.434785\pi$
$314$	1.54783e6	0.885927
$315$	0	0
$316$	−2.52854e6	−1.42446
$317$	−1.88491e6	−1.05352	−0.526761	−	0.850014i	$-0.676594\pi$
$317$	−1.88491e6	−1.05352	−0.526761	+	0.850014i	$0.676594\pi$
$318$	−683081.	−0.378795
$319$	1.80087e6	0.990842
$320$	−1.14826e6	−0.626850
$321$	−1.76588e6	−0.956531
$322$	0	0
$323$	3.46369e6	1.84728
$324$	232139.	0.122853
$325$	−1.15761e6	−0.607932
$326$	2.22657e6	1.16036
$327$	952675.	0.492692
$328$	−275131.	−0.141206
$329$	0	0
$330$	814727.	0.411839
$331$	605333.	0.303686	0.151843	−	0.988405i	$-0.451479\pi$
$331$	605333.	0.303686	0.151843	+	0.988405i	$0.451479\pi$
$332$	410336.	0.204312
$333$	451520.	0.223134
$334$	3.46618e6	1.70014
$335$	−1.35942e6	−0.661821
$336$	0	0
$337$	3.50499e6	1.68117	0.840586	−	0.541677i	$-0.182211\pi$
$337$	3.50499e6	1.68117	0.840586	+	0.541677i	$0.182211\pi$
$338$	−914650.	−0.435475
$339$	−608303.	−0.287489
$340$	1.66068e6	0.779092
$341$	−2.70020e6	−1.25751
$342$	1.43402e6	0.662962
$343$	0	0
$344$	−135632.	−0.0617966
$345$	−1.16639e6	−0.527589
$346$	2.47316e6	1.11061
$347$	−2.66338e6	−1.18743	−0.593717	−	0.804674i	$-0.702340\pi$
$347$	−2.66338e6	−1.18743	−0.593717	+	0.804674i	$0.702340\pi$
$348$	1.51974e6	0.672702
$349$	2.02690e6	0.890778	0.445389	−	0.895337i	$-0.353065\pi$
$349$	2.02690e6	0.890778	0.445389	+	0.895337i	$0.353065\pi$
$350$	0	0
$351$	371624.	0.161004
$352$	−3.13635e6	−1.34917
$353$	1.50563e6	0.643103	0.321551	−	0.946892i	$-0.395796\pi$
$353$	1.50563e6	0.643103	0.321551	+	0.946892i	$0.395796\pi$
$354$	−1.04321e6	−0.442448
$355$	1.87835e6	0.791052
$356$	2.76822e6	1.15765
$357$	0	0
$358$	−2.34403e6	−0.966619
$359$	2.08268e6	0.852877	0.426438	−	0.904517i	$-0.359768\pi$
$359$	2.08268e6	0.852877	0.426438	+	0.904517i	$0.359768\pi$
$360$	65712.3	0.0267233
$361$	2.17544e6	0.878575
$362$	4.40601e6	1.76715
$363$	−168003.	−0.0669191
$364$	0	0
$365$	−1.78047e6	−0.699524
$366$	−1.33208e6	−0.519791
$367$	−2.93430e6	−1.13721	−0.568603	−	0.822612i	$-0.692516\pi$
$367$	−2.93430e6	−1.13721	−0.568603	+	0.822612i	$0.692516\pi$
$368$	4.01025e6	1.54366
$369$	−802843.	−0.306948
$370$	1.33731e6	0.507839
$371$	0	0
$372$	−2.27869e6	−0.853746
$373$	−407769.	−0.151755	−0.0758774	−	0.997117i	$-0.524176\pi$
$373$	−407769.	−0.151755	−0.0758774	+	0.997117i	$0.524176\pi$
$374$	4.97441e6	1.83892
$375$	−1.41929e6	−0.521185
$376$	257211.	0.0938253
$377$	2.43291e6	0.881604
$378$	0	0
$379$	326165.	0.116638	0.0583188	−	0.998298i	$-0.481426\pi$
$379$	326165.	0.116638	0.0583188	+	0.998298i	$0.481426\pi$
$380$	2.23020e6	0.792292
$381$	2.53625e6	0.895116
$382$	−2.92789e6	−1.02659
$383$	1.76218e6	0.613838	0.306919	−	0.951736i	$-0.400702\pi$
$383$	1.76218e6	0.613838	0.306919	+	0.951736i	$0.400702\pi$
$384$	−508785.	−0.176078
$385$	0	0
$386$	6.16347e6	2.10551
$387$	−395779.	−0.134331
$388$	5.35962e6	1.80740
$389$	−3.55950e6	−1.19266	−0.596328	−	0.802741i	$-0.703374\pi$
$389$	−3.55950e6	−1.19266	−0.596328	+	0.802741i	$0.703374\pi$
$390$	1.10067e6	0.366434
$391$	−7.12153e6	−2.35576
$392$	0	0
$393$	−797191.	−0.260364
$394$	2.43362e6	0.789790
$395$	−2.08862e6	−0.673546
$396$	1.08142e6	0.346541
$397$	−635379.	−0.202328	−0.101164	−	0.994870i	$-0.532257\pi$
$397$	−635379.	−0.202328	−0.101164	+	0.994870i	$0.532257\pi$
$398$	3.97767e6	1.25870
$399$	0	0
$400$	2.05365e6	0.641765
$401$	1.97947e6	0.614734	0.307367	−	0.951591i	$-0.400552\pi$
$401$	1.97947e6	0.614734	0.307367	+	0.951591i	$0.400552\pi$
$402$	−3.43635e6	−1.06055
$403$	−3.64789e6	−1.11887
$404$	−3.23413e6	−0.985836
$405$	191751.	0.0580899
$406$	0	0
$407$	2.10340e6	0.629414
$408$	401214.	0.119323
$409$	5.28287e6	1.56157	0.780785	−	0.624799i	$-0.214819\pi$
$409$	5.28287e6	1.56157	0.780785	+	0.624799i	$0.214819\pi$
$410$	−2.37785e6	−0.698594
$411$	−2.58147e6	−0.753811
$412$	−2.01430e6	−0.584630
$413$	0	0
$414$	−2.94842e6	−0.845450
$415$	338946.	0.0966074
$416$	−4.23711e6	−1.20043
$417$	−3.11318e6	−0.876726
$418$	6.68036e6	1.87007
$419$	−318626.	−0.0886639	−0.0443319	−	0.999017i	$-0.514116\pi$
$419$	−318626.	−0.0886639	−0.0443319	+	0.999017i	$0.514116\pi$
$420$	0	0
$421$	−46024.4	−0.0126556	−0.00632780	−	0.999980i	$-0.502014\pi$
$421$	−46024.4	−0.0126556	−0.00632780	+	0.999980i	$0.502014\pi$
$422$	6.97164e6	1.90570
$423$	750553.	0.203953
$424$	−256656.	−0.0693326
$425$	−3.64693e6	−0.979390
$426$	4.74811e6	1.26764
$427$	0	0
$428$	−6.94219e6	−1.83184
$429$	1.73121e6	0.454157
$430$	−1.17221e6	−0.305728
$431$	−4.55645e6	−1.18150	−0.590749	−	0.806855i	$-0.701168\pi$
$431$	−4.55645e6	−1.18150	−0.590749	+	0.806855i	$0.701168\pi$
$432$	−659274.	−0.169964
$433$	−6.98232e6	−1.78970	−0.894850	−	0.446368i	$-0.852717\pi$
$433$	−6.98232e6	−1.78970	−0.894850	+	0.446368i	$0.852717\pi$
$434$	0	0
$435$	1.25534e6	0.318081
$436$	3.74524e6	0.943547
$437$	−9.56382e6	−2.39567
$438$	−4.50070e6	−1.12097
$439$	−1.66904e6	−0.413338	−0.206669	−	0.978411i	$-0.566262\pi$
$439$	−1.66904e6	−0.413338	−0.206669	+	0.978411i	$0.566262\pi$
$440$	306120.	0.0753807
$441$	0	0
$442$	6.72028e6	1.63618
$443$	−561410.	−0.135916	−0.0679580	−	0.997688i	$-0.521648\pi$
$443$	−561410.	−0.135916	−0.0679580	+	0.997688i	$0.521648\pi$
$444$	1.77505e6	0.427321
$445$	2.28661e6	0.547383
$446$	8.76864e6	2.08735
$447$	−2.74282e6	−0.649274
$448$	0	0
$449$	−3.64485e6	−0.853225	−0.426613	−	0.904434i	$-0.640293\pi$
$449$	−3.64485e6	−0.853225	−0.426613	+	0.904434i	$0.640293\pi$
$450$	−1.50988e6	−0.351489
$451$	−3.74004e6	−0.865835
$452$	−2.39142e6	−0.550566
$453$	3.13482e6	0.717740
$454$	265556.	0.0604667
$455$	0	0
$456$	538808.	0.121345
$457$	2.81947e6	0.631506	0.315753	−	0.948841i	$-0.397743\pi$
$457$	2.81947e6	0.631506	0.315753	+	0.948841i	$0.397743\pi$
$458$	9.70976e6	2.16294
$459$	1.17076e6	0.259380
$460$	−4.58542e6	−1.01038
$461$	803065.	0.175994	0.0879971	−	0.996121i	$-0.471953\pi$
$461$	803065.	0.175994	0.0879971	+	0.996121i	$0.471953\pi$
$462$	0	0
$463$	−114276.	−0.0247745	−0.0123872	−	0.999923i	$-0.503943\pi$
$463$	−114276.	−0.0247745	−0.0123872	+	0.999923i	$0.503943\pi$
$464$	−4.31607e6	−0.930666
$465$	−1.88225e6	−0.403687
$466$	2.70680e6	0.577418
$467$	−6.17863e6	−1.31099	−0.655496	−	0.755199i	$-0.727540\pi$
$467$	−6.17863e6	−1.31099	−0.655496	+	0.755199i	$0.727540\pi$
$468$	1.46096e6	0.308336
$469$	0	0
$470$	2.22298e6	0.464184
$471$	1.69705e6	0.352486
$472$	−391968.	−0.0809833
$473$	−1.84373e6	−0.378918
$474$	−5.27964e6	−1.07934
$475$	−4.89763e6	−0.995983
$476$	0	0
$477$	−748935.	−0.150712
$478$	−3.77087e6	−0.754869
$479$	1.38581e6	0.275972	0.137986	−	0.990434i	$-0.455937\pi$
$479$	1.38581e6	0.275972	0.137986	+	0.990434i	$0.455937\pi$
$480$	−2.18627e6	−0.433113
$481$	2.84163e6	0.560022
$482$	−1.19828e7	−2.34932
$483$	0	0
$484$	−660467.	−0.128156
$485$	4.42716e6	0.854615
$486$	484711.	0.0930878
$487$	218793.	0.0418033	0.0209017	−	0.999782i	$-0.493346\pi$
$487$	218793.	0.0418033	0.0209017	+	0.999782i	$0.493346\pi$
$488$	−500508.	−0.0951397
$489$	2.44123e6	0.461675
$490$	0	0
$491$	−8.85181e6	−1.65702	−0.828511	−	0.559973i	$-0.810812\pi$
$491$	−8.85181e6	−1.65702	−0.828511	+	0.559973i	$0.810812\pi$
$492$	−3.15621e6	−0.587832
$493$	7.66463e6	1.42028
$494$	9.02495e6	1.66390
$495$	893272.	0.163859
$496$	6.47149e6	1.18114
$497$	0	0
$498$	856793.	0.154811
$499$	3.66757e6	0.659367	0.329684	−	0.944091i	$-0.393058\pi$
$499$	3.66757e6	0.659367	0.329684	+	0.944091i	$0.393058\pi$
$500$	−5.57963e6	−0.998114
$501$	3.80034e6	0.676439
$502$	4.29385e6	0.760480
$503$	8.87701e6	1.56440	0.782198	−	0.623029i	$-0.214098\pi$
$503$	8.87701e6	1.56440	0.782198	+	0.623029i	$0.214098\pi$
$504$	0	0
$505$	−2.67146e6	−0.466144
$506$	−1.37352e7	−2.38483
$507$	−1.00283e6	−0.173263
$508$	9.97072e6	1.71422
$509$	5.29056e6	0.905121	0.452561	−	0.891734i	$-0.350511\pi$
$509$	5.29056e6	0.905121	0.452561	+	0.891734i	$0.350511\pi$
$510$	3.46754e6	0.590332
$511$	0	0
$512$	8.32008e6	1.40266
$513$	1.57227e6	0.263774
$514$	3.82069e6	0.637873
$515$	−1.66385e6	−0.276438
$516$	−1.55592e6	−0.257255
$517$	3.49645e6	0.575308
$518$	0	0
$519$	2.71159e6	0.441882
$520$	413559.	0.0670701
$521$	8.79675e6	1.41980	0.709901	−	0.704301i	$-0.248740\pi$
$521$	8.79675e6	1.41980	0.709901	+	0.704301i	$0.248740\pi$
$522$	3.17326e6	0.509718
$523$	−3.03365e6	−0.484966	−0.242483	−	0.970156i	$-0.577962\pi$
$523$	−3.03365e6	−0.484966	−0.242483	+	0.970156i	$0.577962\pi$
$524$	−3.13399e6	−0.498619
$525$	0	0
$526$	1.06401e6	0.167681
$527$	−1.14923e7	−1.80252
$528$	−3.07122e6	−0.479432
$529$	1.32274e7	2.05511
$530$	−2.21819e6	−0.343011
$531$	−1.14378e6	−0.176038
$532$	0	0
$533$	−5.05268e6	−0.770378
$534$	5.78011e6	0.877168
$535$	−5.73439e6	−0.866170
$536$	−1.29115e6	−0.194118
$537$	−2.57001e6	−0.384591
$538$	1.15279e7	1.71709
$539$	0	0
$540$	753830.	0.111247
$541$	−1.43726e6	−0.211126	−0.105563	−	0.994413i	$-0.533665\pi$
$541$	−1.43726e6	−0.211126	−0.105563	+	0.994413i	$0.533665\pi$
$542$	−7.26534e6	−1.06233
$543$	4.83078e6	0.703101
$544$	−1.33485e7	−1.93391
$545$	3.09365e6	0.446148
$546$	0	0
$547$	5.93548e6	0.848179	0.424089	−	0.905620i	$-0.360594\pi$
$547$	5.93548e6	0.848179	0.424089	+	0.905620i	$0.360594\pi$
$548$	−1.01485e7	−1.44361
$549$	−1.46051e6	−0.206810
$550$	−7.03378e6	−0.991476
$551$	1.02932e7	1.44434
$552$	−1.10782e6	−0.154747
$553$	0	0
$554$	−1.09761e7	−1.51940
$555$	1.46623e6	0.202055
$556$	−1.22388e7	−1.67901
$557$	4.39523e6	0.600266	0.300133	−	0.953897i	$-0.402969\pi$
$557$	4.39523e6	0.600266	0.300133	+	0.953897i	$0.402969\pi$
$558$	−4.75797e6	−0.646898
$559$	−2.49083e6	−0.337143
$560$	0	0
$561$	5.45398e6	0.731655
$562$	−1.47850e7	−1.97460
$563$	−6.46414e6	−0.859487	−0.429744	−	0.902951i	$-0.641396\pi$
$563$	−6.46414e6	−0.859487	−0.429744	+	0.902951i	$0.641396\pi$
$564$	2.95064e6	0.390588
$565$	−1.97536e6	−0.260330
$566$	−7.97786e6	−1.04676
$567$	0	0
$568$	1.78402e6	0.232022
$569$	7.30225e6	0.945531	0.472766	−	0.881188i	$-0.343256\pi$
$569$	7.30225e6	0.945531	0.472766	+	0.881188i	$0.343256\pi$
$570$	4.65672e6	0.600333
$571$	−9.15896e6	−1.17559	−0.587795	−	0.809010i	$-0.700004\pi$
$571$	−9.15896e6	−1.17559	−0.587795	+	0.809010i	$0.700004\pi$
$572$	6.80588e6	0.869749
$573$	−3.21015e6	−0.408451
$574$	0	0
$575$	1.00698e7	1.27014
$576$	−3.18240e6	−0.399668
$577$	6.14739e6	0.768690	0.384345	−	0.923190i	$-0.374427\pi$
$577$	6.14739e6	0.768690	0.384345	+	0.923190i	$0.374427\pi$
$578$	9.51641e6	1.18482
$579$	6.75767e6	0.837724
$580$	4.93510e6	0.609153
$581$	0	0
$582$	1.11910e7	1.36950
$583$	−3.48891e6	−0.425127
$584$	−1.69106e6	−0.205177
$585$	1.20678e6	0.145794
$586$	−5.54135e6	−0.666610
$587$	−8.30740e6	−0.995107	−0.497554	−	0.867433i	$-0.665768\pi$
$587$	−8.30740e6	−0.995107	−0.497554	+	0.867433i	$0.665768\pi$
$588$	0	0
$589$	−1.54335e7	−1.83306
$590$	−3.38763e6	−0.400651
$591$	2.66823e6	0.314236
$592$	−5.04115e6	−0.591188
$593$	−1.36669e7	−1.59600	−0.797999	−	0.602658i	$-0.794108\pi$
$593$	−1.36669e7	−1.59600	−0.797999	+	0.602658i	$0.794108\pi$
$594$	2.25803e6	0.262581
$595$	0	0
$596$	−1.07828e7	−1.24341
$597$	4.36114e6	0.500800
$598$	−1.85558e7	−2.12191
$599$	−3.01585e6	−0.343433	−0.171717	−	0.985146i	$-0.554931\pi$
$599$	−3.01585e6	−0.343433	−0.171717	+	0.985146i	$0.554931\pi$
$600$	−567314.	−0.0643347
$601$	1.31661e7	1.48686	0.743429	−	0.668815i	$-0.233198\pi$
$601$	1.31661e7	1.48686	0.743429	+	0.668815i	$0.233198\pi$
$602$	0	0
$603$	−3.76764e6	−0.421965
$604$	1.23239e7	1.37453
$605$	−545559.	−0.0605974
$606$	−6.75295e6	−0.746985
$607$	−1.26550e7	−1.39409	−0.697044	−	0.717028i	$-0.745502\pi$
$607$	−1.26550e7	−1.39409	−0.697044	+	0.717028i	$0.745502\pi$
$608$	−1.79263e7	−1.96668
$609$	0	0
$610$	−4.32571e6	−0.470687
$611$	4.72359e6	0.511881
$612$	4.60260e6	0.496735
$613$	−4.03470e6	−0.433671	−0.216835	−	0.976208i	$-0.569573\pi$
$613$	−4.03470e6	−0.433671	−0.216835	+	0.976208i	$0.569573\pi$
$614$	7.33903e6	0.785630
$615$	−2.60709e6	−0.277951
$616$	0	0
$617$	−1.52192e7	−1.60946	−0.804728	−	0.593644i	$-0.797689\pi$
$617$	−1.52192e7	−1.60946	−0.804728	+	0.593644i	$0.797689\pi$
$618$	−4.20591e6	−0.442985
$619$	1.04642e7	1.09769	0.548843	−	0.835925i	$-0.315068\pi$
$619$	1.04642e7	1.09769	0.548843	+	0.835925i	$0.315068\pi$
$620$	−7.39966e6	−0.773094
$621$	−3.23266e6	−0.336381
$622$	−7.99530e6	−0.828626
$623$	0	0
$624$	−4.14913e6	−0.426575
$625$	2.48751e6	0.254721
$626$	5.78919e6	0.590448
$627$	7.32439e6	0.744051
$628$	6.67158e6	0.675040
$629$	8.95225e6	0.902205
$630$	0	0
$631$	5.41229e6	0.541138	0.270569	−	0.962701i	$-0.412788\pi$
$631$	5.41229e6	0.541138	0.270569	+	0.962701i	$0.412788\pi$
$632$	−1.98374e6	−0.197557
$633$	7.64375e6	0.758224
$634$	−1.54726e7	−1.52876
$635$	8.23602e6	0.810556
$636$	−2.94428e6	−0.288627
$637$	0	0
$638$	1.47826e7	1.43781
$639$	5.20586e6	0.504360
$640$	−1.65219e6	−0.159445
$641$	9.82808e6	0.944765	0.472382	−	0.881394i	$-0.343394\pi$
$641$	9.82808e6	0.944765	0.472382	+	0.881394i	$0.343394\pi$
$642$	−1.44955e7	−1.38802
$643$	8.06067e6	0.768854	0.384427	−	0.923155i	$-0.374399\pi$
$643$	8.06067e6	0.768854	0.384427	+	0.923155i	$0.374399\pi$
$644$	0	0
$645$	−1.28522e6	−0.121641
$646$	2.84321e7	2.68058
$647$	−1.70359e7	−1.59994	−0.799971	−	0.600038i	$-0.795152\pi$
$647$	−1.70359e7	−1.59994	−0.799971	+	0.600038i	$0.795152\pi$
$648$	182122.	0.0170383
$649$	−5.32829e6	−0.496565
$650$	−9.50242e6	−0.882167
$651$	0	0
$652$	9.59718e6	0.884148
$653$	1.54447e7	1.41741	0.708707	−	0.705503i	$-0.249279\pi$
$653$	1.54447e7	1.41741	0.708707	+	0.705503i	$0.249279\pi$
$654$	7.82016e6	0.714943
$655$	−2.58874e6	−0.235768
$656$	8.96363e6	0.813251
$657$	−4.93460e6	−0.446004
$658$	0	0
$659$	−1.28485e7	−1.15250	−0.576248	−	0.817275i	$-0.695484\pi$
$659$	−1.28485e7	−1.15250	−0.576248	+	0.817275i	$0.695484\pi$
$660$	3.51171e6	0.313804
$661$	1.88793e7	1.68067	0.840337	−	0.542065i	$-0.182357\pi$
$661$	1.88793e7	1.68067	0.840337	+	0.542065i	$0.182357\pi$
$662$	4.96896e6	0.440677
$663$	7.36816e6	0.650991
$664$	321926.	0.0283358
$665$	0	0
$666$	3.70636e6	0.323789
$667$	−2.11633e7	−1.84191
$668$	1.49402e7	1.29544
$669$	9.61400e6	0.830498
$670$	−1.11589e7	−0.960365
$671$	−6.80376e6	−0.583368
$672$	0	0
$673$	1.42483e6	0.121262	0.0606311	−	0.998160i	$-0.480689\pi$
$673$	1.42483e6	0.121262	0.0606311	+	0.998160i	$0.480689\pi$
$674$	2.87712e7	2.43954
$675$	−1.65545e6	−0.139848
$676$	−3.94241e6	−0.331814
$677$	1.83981e7	1.54277	0.771386	−	0.636368i	$-0.219564\pi$
$677$	1.83981e7	1.54277	0.771386	+	0.636368i	$0.219564\pi$
$678$	−4.99334e6	−0.417173
$679$	0	0
$680$	1.30287e6	0.108051
$681$	291158.	0.0240580
$682$	−2.21650e7	−1.82476
$683$	−3.69137e6	−0.302786	−0.151393	−	0.988474i	$-0.548376\pi$
$683$	−3.69137e6	−0.302786	−0.151393	+	0.988474i	$0.548376\pi$
$684$	6.18103e6	0.505150
$685$	−8.38288e6	−0.682600
$686$	0	0
$687$	1.06459e7	0.860575
$688$	4.41882e6	0.355906
$689$	−4.71341e6	−0.378257
$690$	−9.57446e6	−0.765582
$691$	1.42711e7	1.13700	0.568502	−	0.822682i	$-0.307523\pi$
$691$	1.42711e7	1.13700	0.568502	+	0.822682i	$0.307523\pi$
$692$	1.06600e7	0.846241
$693$	0	0
$694$	−2.18627e7	−1.72308
$695$	−1.01095e7	−0.793904
$696$	1.19230e6	0.0932960
$697$	−1.59179e7	−1.24109
$698$	1.66381e7	1.29260
$699$	2.96775e6	0.229739
$700$	0	0
$701$	1.09094e7	0.838507	0.419254	−	0.907869i	$-0.362292\pi$
$701$	1.09094e7	0.838507	0.419254	+	0.907869i	$0.362292\pi$
$702$	3.05052e6	0.233632
$703$	1.20224e7	0.917490
$704$	−1.48252e7	−1.12738
$705$	2.43729e6	0.184686
$706$	1.23591e7	0.933203
$707$	0	0
$708$	−4.49653e6	−0.337128
$709$	−2.62686e6	−0.196255	−0.0981277	−	0.995174i	$-0.531285\pi$
$709$	−2.62686e6	−0.196255	−0.0981277	+	0.995174i	$0.531285\pi$
$710$	1.54187e7	1.14789
$711$	−5.78864e6	−0.429440
$712$	2.17178e6	0.160552
$713$	3.17321e7	2.33763
$714$	0	0
$715$	5.62179e6	0.411254
$716$	−1.01035e7	−0.736524
$717$	−4.13441e6	−0.300342
$718$	1.70959e7	1.23760
$719$	−2.38777e7	−1.72254	−0.861272	−	0.508144i	$-0.830332\pi$
$719$	−2.38777e7	−1.72254	−0.861272	+	0.508144i	$0.830332\pi$
$720$	−2.14088e6	−0.153908
$721$	0	0
$722$	1.78574e7	1.27490
$723$	−1.31381e7	−0.934729
$724$	1.89912e7	1.34650
$725$	−1.08377e7	−0.765761
$726$	−1.37907e6	−0.0971059
$727$	−2.62895e7	−1.84479	−0.922393	−	0.386253i	$-0.873769\pi$
$727$	−2.62895e7	−1.84479	−0.922393	+	0.386253i	$0.873769\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	−1.46152e7	−1.01508
$731$	−7.84708e6	−0.543144
$732$	−5.74167e6	−0.396060
$733$	1.13470e7	0.780051	0.390025	−	0.920804i	$-0.372466\pi$
$733$	1.13470e7	0.780051	0.390025	+	0.920804i	$0.372466\pi$
$734$	−2.40866e7	−1.65019
$735$	0	0
$736$	3.68576e7	2.50803
$737$	−1.75515e7	−1.19027
$738$	−6.59024e6	−0.445411
$739$	−4.89668e6	−0.329830	−0.164915	−	0.986308i	$-0.552735\pi$
$739$	−4.89668e6	−0.329830	−0.164915	+	0.986308i	$0.552735\pi$
$740$	5.76418e6	0.386953
$741$	9.89502e6	0.662020
$742$	0	0
$743$	1.56896e7	1.04265	0.521326	−	0.853357i	$-0.325437\pi$
$743$	1.56896e7	1.04265	0.521326	+	0.853357i	$0.325437\pi$
$744$	−1.78773e6	−0.118405
$745$	−8.90681e6	−0.587938
$746$	−3.34723e6	−0.220211
$747$	939393.	0.0615951
$748$	2.14412e7	1.40118
$749$	0	0
$750$	−1.16504e7	−0.756289
$751$	−1.36120e7	−0.880687	−0.440344	−	0.897829i	$-0.645143\pi$
$751$	−1.36120e7	−0.880687	−0.440344	+	0.897829i	$0.645143\pi$
$752$	−8.37982e6	−0.540368
$753$	4.70781e6	0.302574
$754$	1.99709e7	1.27929
$755$	1.01798e7	0.649937
$756$	0	0
$757$	5.65571e6	0.358713	0.179357	−	0.983784i	$-0.442598\pi$
$757$	5.65571e6	0.358713	0.179357	+	0.983784i	$0.442598\pi$
$758$	2.67737e6	0.169252
$759$	−1.50593e7	−0.948859
$760$	1.74968e6	0.109882
$761$	1.74718e7	1.09364	0.546822	−	0.837249i	$-0.315837\pi$
$761$	1.74718e7	1.09364	0.546822	+	0.837249i	$0.315837\pi$
$762$	2.08191e7	1.29890
$763$	0	0
$764$	−1.26200e7	−0.782218
$765$	3.80184e6	0.234877
$766$	1.44651e7	0.890737
$767$	−7.19836e6	−0.441820
$768$	7.13879e6	0.436738
$769$	1.34195e7	0.818316	0.409158	−	0.912464i	$-0.365823\pi$
$769$	1.34195e7	0.818316	0.409158	+	0.912464i	$0.365823\pi$
$770$	0	0
$771$	4.18903e6	0.253792
$772$	2.65664e7	1.60431
$773$	1.72891e7	1.04069	0.520347	−	0.853955i	$-0.325802\pi$
$773$	1.72891e7	1.04069	0.520347	+	0.853955i	$0.325802\pi$
$774$	−3.24880e6	−0.194927
$775$	1.62500e7	0.971850
$776$	4.20484e6	0.250666
$777$	0	0
$778$	−2.92186e7	−1.73066
$779$	−2.13769e7	−1.26212
$780$	4.74421e6	0.279208
$781$	2.42515e7	1.42269
$782$	−5.84580e7	−3.41843
$783$	3.47919e6	0.202803
$784$	0	0
$785$	5.51086e6	0.319187
$786$	−6.54384e6	−0.377813
$787$	−1.45247e7	−0.835932	−0.417966	−	0.908463i	$-0.637257\pi$
$787$	−1.45247e7	−0.835932	−0.417966	+	0.908463i	$0.637257\pi$
$788$	1.04896e7	0.601788
$789$	1.16659e6	0.0667155
$790$	−1.71447e7	−0.977378
$791$	0	0
$792$	848416.	0.0480613
$793$	−9.19167e6	−0.519053
$794$	−5.21559e6	−0.293597
$795$	−2.43204e6	−0.136475
$796$	1.71449e7	0.959075
$797$	1.33304e7	0.743354	0.371677	−	0.928362i	$-0.378783\pi$
$797$	1.33304e7	0.743354	0.371677	+	0.928362i	$0.378783\pi$
$798$	0	0
$799$	1.48812e7	0.824650
$800$	1.88747e7	1.04269
$801$	6.33735e6	0.349001
$802$	1.62487e7	0.892038
$803$	−2.29878e7	−1.25808
$804$	−1.48117e7	−0.808098
$805$	0	0
$806$	−2.99442e7	−1.62358
$807$	1.26392e7	0.683182
$808$	−2.53731e6	−0.136724
$809$	8.29655e6	0.445683	0.222842	−	0.974855i	$-0.428467\pi$
$809$	8.29655e6	0.445683	0.222842	+	0.974855i	$0.428467\pi$
$810$	1.57402e6	0.0842939
$811$	−4.73910e6	−0.253013	−0.126507	−	0.991966i	$-0.540377\pi$
$811$	−4.73910e6	−0.253013	−0.126507	+	0.991966i	$0.540377\pi$
$812$	0	0
$813$	−7.96577e6	−0.422670
$814$	1.72660e7	0.913339
$815$	7.92747e6	0.418062
$816$	−1.30714e7	−0.687220
$817$	−1.05382e7	−0.552346
$818$	4.33651e7	2.26599
$819$	0	0
$820$	−1.02492e7	−0.532300
$821$	−7.73294e6	−0.400393	−0.200197	−	0.979756i	$-0.564158\pi$
$821$	−7.73294e6	−0.400393	−0.200197	+	0.979756i	$0.564158\pi$
$822$	−2.11903e7	−1.09385
$823$	1.52365e7	0.784123	0.392062	−	0.919939i	$-0.371762\pi$
$823$	1.52365e7	0.784123	0.392062	+	0.919939i	$0.371762\pi$
$824$	−1.58030e6	−0.0810816
$825$	−7.71189e6	−0.394481
$826$	0	0
$827$	2.56525e7	1.30427	0.652133	−	0.758105i	$-0.273874\pi$
$827$	2.56525e7	1.30427	0.652133	+	0.758105i	$0.273874\pi$
$828$	−1.27085e7	−0.644198
$829$	2.26069e7	1.14250	0.571248	−	0.820778i	$-0.306459\pi$
$829$	2.26069e7	1.14250	0.571248	+	0.820778i	$0.306459\pi$
$830$	2.78228e6	0.140187
$831$	−1.20342e7	−0.604527
$832$	−2.00284e7	−1.00309
$833$	0	0
$834$	−2.55549e7	−1.27221
$835$	1.23409e7	0.612537
$836$	2.87943e7	1.42492
$837$	−5.21667e6	−0.257383
$838$	−2.61549e6	−0.128660
$839$	−1.59455e7	−0.782049	−0.391024	−	0.920380i	$-0.627879\pi$
$839$	−1.59455e7	−0.782049	−0.391024	+	0.920380i	$0.627879\pi$
$840$	0	0
$841$	2.26610e6	0.110481
$842$	−377797.	−0.0183645
$843$	−1.62103e7	−0.785639
$844$	3.00498e7	1.45206
$845$	−3.25651e6	−0.156896
$846$	6.16101e6	0.295955
$847$	0	0
$848$	8.36175e6	0.399308
$849$	−8.74699e6	−0.416475
$850$	−2.99363e7	−1.42119
$851$	−2.47186e7	−1.17004
$852$	2.04658e7	0.965892
$853$	−3.44060e7	−1.61906	−0.809528	−	0.587082i	$-0.800277\pi$
$853$	−3.44060e7	−1.61906	−0.809528	+	0.587082i	$0.800277\pi$
$854$	0	0
$855$	5.10566e6	0.238856
$856$	−5.44644e6	−0.254055
$857$	−5.53039e6	−0.257219	−0.128610	−	0.991695i	$-0.541051\pi$
$857$	−5.53039e6	−0.257219	−0.128610	+	0.991695i	$0.541051\pi$
$858$	1.42108e7	0.659025
$859$	−1.39566e7	−0.645351	−0.322676	−	0.946510i	$-0.604582\pi$
$859$	−1.39566e7	−0.645351	−0.322676	+	0.946510i	$0.604582\pi$
$860$	−5.05258e6	−0.232953
$861$	0	0
$862$	−3.74022e7	−1.71447
$863$	1.38532e7	0.633173	0.316586	−	0.948564i	$-0.397463\pi$
$863$	1.38532e7	0.633173	0.316586	+	0.948564i	$0.397463\pi$
$864$	−6.05928e6	−0.276145
$865$	8.80542e6	0.400138
$866$	−5.73153e7	−2.59702
$867$	1.04339e7	0.471408
$868$	0	0
$869$	−2.69663e7	−1.21136
$870$	1.03046e7	0.461566
$871$	−2.37116e7	−1.05905
$872$	2.93830e6	0.130859
$873$	1.22699e7	0.544886
$874$	−7.85058e7	−3.47635
$875$	0	0
$876$	−1.93993e7	−0.854135
$877$	−2.42739e7	−1.06571	−0.532856	−	0.846206i	$-0.678881\pi$
$877$	−2.42739e7	−1.06571	−0.532856	+	0.846206i	$0.678881\pi$
$878$	−1.37005e7	−0.599792
$879$	−6.07558e6	−0.265225
$880$	−9.97326e6	−0.434141
$881$	−1.86802e7	−0.810854	−0.405427	−	0.914127i	$-0.632877\pi$
$881$	−1.86802e7	−0.810854	−0.405427	+	0.914127i	$0.632877\pi$
$882$	0	0
$883$	2.91586e7	1.25854	0.629268	−	0.777188i	$-0.283355\pi$
$883$	2.91586e7	1.25854	0.629268	+	0.777188i	$0.283355\pi$
$884$	2.89664e7	1.24670
$885$	−3.71422e6	−0.159408
$886$	−4.60841e6	−0.197227
$887$	625102.	0.0266773	0.0133387	−	0.999911i	$-0.495754\pi$
$887$	625102.	0.0266773	0.0133387	+	0.999911i	$0.495754\pi$
$888$	1.39260e6	0.0592645
$889$	0	0
$890$	1.87699e7	0.794304
$891$	2.47572e6	0.104474
$892$	3.77954e7	1.59048
$893$	1.99846e7	0.838621
$894$	−2.25148e7	−0.942158
$895$	−8.34566e6	−0.348259
$896$	0	0
$897$	−2.03447e7	−0.844249
$898$	−2.99192e7	−1.23811
$899$	−3.41520e7	−1.40934
$900$	−6.50804e6	−0.267820
$901$	−1.48491e7	−0.609379
$902$	−3.07006e7	−1.25641
$903$	0	0
$904$	−1.87616e6	−0.0763572
$905$	1.56871e7	0.636681
$906$	2.57326e7	1.04151
$907$	−3.81672e6	−0.154054	−0.0770268	−	0.997029i	$-0.524543\pi$
$907$	−3.81672e6	−0.154054	−0.0770268	+	0.997029i	$0.524543\pi$
$908$	1.14462e6	0.0460732
$909$	−7.40399e6	−0.297205
$910$	0	0
$911$	9.41226e6	0.375749	0.187875	−	0.982193i	$-0.439840\pi$
$911$	9.41226e6	0.375749	0.187875	+	0.982193i	$0.439840\pi$
$912$	−1.75541e7	−0.698863
$913$	4.37616e6	0.173747
$914$	2.31440e7	0.916374
$915$	−4.74274e6	−0.187273
$916$	4.18519e7	1.64807
$917$	0	0
$918$	9.61034e6	0.376385
$919$	6.81092e6	0.266022	0.133011	−	0.991115i	$-0.457535\pi$
$919$	6.81092e6	0.266022	0.133011	+	0.991115i	$0.457535\pi$
$920$	−3.59745e6	−0.140128
$921$	8.04657e6	0.312580
$922$	6.59207e6	0.255384
$923$	3.27630e7	1.26584
$924$	0	0
$925$	−1.26584e7	−0.486435
$926$	−938053.	−0.0359501
$927$	−4.61139e6	−0.176251
$928$	−3.96683e7	−1.51208
$929$	−6.97913e6	−0.265315	−0.132658	−	0.991162i	$-0.542351\pi$
$929$	−6.97913e6	−0.265315	−0.132658	+	0.991162i	$0.542351\pi$
$930$	−1.54507e7	−0.585787
$931$	0	0
$932$	1.16671e7	0.439969
$933$	−8.76610e6	−0.329687
$934$	−5.07181e7	−1.90237
$935$	1.77108e7	0.662537
$936$	1.14618e6	0.0427626
$937$	2.31557e7	0.861606	0.430803	−	0.902446i	$-0.358230\pi$
$937$	2.31557e7	0.861606	0.430803	+	0.902446i	$0.358230\pi$
$938$	0	0
$939$	6.34731e6	0.234923
$940$	9.58169e6	0.353690
$941$	−1.82489e7	−0.671835	−0.335918	−	0.941891i	$-0.609046\pi$
$941$	−1.82489e7	−0.671835	−0.335918	+	0.941891i	$0.609046\pi$
$942$	1.39304e7	0.511490
$943$	4.39520e7	1.60953
$944$	1.27701e7	0.466408
$945$	0	0
$946$	−1.51345e7	−0.549846
$947$	1.46102e7	0.529395	0.264698	−	0.964331i	$-0.414728\pi$
$947$	1.46102e7	0.529395	0.264698	+	0.964331i	$0.414728\pi$
$948$	−2.27568e7	−0.822414
$949$	−3.10558e7	−1.11938
$950$	−4.02028e7	−1.44527
$951$	−1.69642e7	−0.608251
$952$	0	0
$953$	1.49338e7	0.532645	0.266322	−	0.963884i	$-0.414191\pi$
$953$	1.49338e7	0.532645	0.266322	+	0.963884i	$0.414191\pi$
$954$	−6.14773e6	−0.218698
$955$	−1.04244e7	−0.369865
$956$	−1.62536e7	−0.575180
$957$	1.62078e7	0.572063
$958$	1.13756e7	0.400462
$959$	0	0
$960$	−1.03343e7	−0.361912
$961$	2.25781e7	0.788641
$962$	2.33259e7	0.812645
$963$	−1.58929e7	−0.552254
$964$	−5.16495e7	−1.79009
$965$	2.19444e7	0.758586
$966$	0	0
$967$	−4.73806e6	−0.162942	−0.0814712	−	0.996676i	$-0.525962\pi$
$967$	−4.73806e6	−0.162942	−0.0814712	+	0.996676i	$0.525962\pi$
$968$	−518164.	−0.0177737
$969$	3.11732e7	1.06653
$970$	3.63409e7	1.24013
$971$	1.34756e7	0.458670	0.229335	−	0.973348i	$-0.426345\pi$
$971$	1.34756e7	0.458670	0.229335	+	0.973348i	$0.426345\pi$
$972$	2.08925e6	0.0709291
$973$	0	0
$974$	1.79599e6	0.0606606
$975$	−1.04185e7	−0.350990
$976$	1.63063e7	0.547939
$977$	2.33437e7	0.782410	0.391205	−	0.920304i	$-0.372058\pi$
$977$	2.33437e7	0.782410	0.391205	+	0.920304i	$0.372058\pi$
$978$	2.00392e7	0.669935
$979$	2.95225e7	0.984457
$980$	0	0
$981$	8.57408e6	0.284456
$982$	−7.26612e7	−2.40450
$983$	2.01946e7	0.666578	0.333289	−	0.942825i	$-0.391842\pi$
$983$	2.01946e7	0.666578	0.333289	+	0.942825i	$0.391842\pi$
$984$	−2.47618e6	−0.0815255
$985$	8.66462e6	0.284550
$986$	6.29161e7	2.06096
$987$	0	0
$988$	3.89002e7	1.26783
$989$	2.16671e7	0.704385
$990$	7.33254e6	0.237775
$991$	2.42175e7	0.783330	0.391665	−	0.920108i	$-0.371899\pi$
$991$	2.42175e7	0.783330	0.391665	+	0.920108i	$0.371899\pi$
$992$	5.94784e7	1.91902
$993$	5.44800e6	0.175333
$994$	0	0
$995$	1.41621e7	0.453491
$996$	3.69303e6	0.117960
$997$	5.84270e6	0.186155	0.0930776	−	0.995659i	$-0.470330\pi$
$997$	5.84270e6	0.186155	0.0930776	+	0.995659i	$0.470330\pi$
$998$	3.01057e7	0.956804
$999$	4.06368e6	0.128827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.o.1.5	yes	6
3.2	odd	2		441.6.a.ba.1.2		6
7.2	even	3		147.6.e.p.67.2		12
7.3	odd	6		147.6.e.q.79.2		12
7.4	even	3		147.6.e.p.79.2		12
7.5	odd	6		147.6.e.q.67.2		12
7.6	odd	2		147.6.a.n.1.5	✓	6
21.20	even	2		441.6.a.bb.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.5	✓	6	7.6	odd	2
147.6.a.o.1.5	yes	6	1.1	even	1	trivial
147.6.e.p.67.2		12	7.2	even	3
147.6.e.p.79.2		12	7.4	even	3
147.6.e.q.67.2		12	7.5	odd	6
147.6.e.q.79.2		12	7.3	odd	6
441.6.a.ba.1.2		6	3.2	odd	2
441.6.a.bb.1.2		6	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)

\(f(q)\)	\(=\)	\(q+8.20863 q^{2} +9.00000 q^{3} +35.3816 q^{4} +29.2259 q^{5} +73.8777 q^{6} +27.7583 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+8.20863 q^{2} +9.00000 q^{3} +35.3816 q^{4} +29.2259 q^{5} +73.8777 q^{6} +27.7583 q^{8} +81.0000 q^{9} +239.905 q^{10} +377.338 q^{11} +318.434 q^{12} +509.772 q^{13} +263.033 q^{15} -904.354 q^{16} +1605.98 q^{17} +664.899 q^{18} +2156.74 q^{19} +1034.06 q^{20} +3097.43 q^{22} -4434.38 q^{23} +249.825 q^{24} -2270.85 q^{25} +4184.53 q^{26} +729.000 q^{27} +4772.55 q^{29} +2159.14 q^{30} -7155.93 q^{31} -8311.77 q^{32} +3396.04 q^{33} +13182.9 q^{34} +2865.91 q^{36} +5574.32 q^{37} +17703.9 q^{38} +4587.95 q^{39} +811.262 q^{40} -9911.64 q^{41} -4886.16 q^{43} +13350.8 q^{44} +2367.30 q^{45} -36400.2 q^{46} +9266.09 q^{47} -8139.18 q^{48} -18640.5 q^{50} +14453.8 q^{51} +18036.6 q^{52} -9246.11 q^{53} +5984.09 q^{54} +11028.1 q^{55} +19410.7 q^{57} +39176.1 q^{58} -14120.7 q^{59} +9306.54 q^{60} -18030.9 q^{61} -58740.4 q^{62} -39288.9 q^{64} +14898.6 q^{65} +27876.9 q^{66} -46514.1 q^{67} +56822.2 q^{68} -39909.4 q^{69} +64269.9 q^{71} +2248.42 q^{72} -60921.0 q^{73} +45757.5 q^{74} -20437.6 q^{75} +76309.0 q^{76} +37660.8 q^{78} -71464.7 q^{79} -26430.6 q^{80} +6561.00 q^{81} -81361.0 q^{82} +11597.5 q^{83} +46936.3 q^{85} -40108.7 q^{86} +42953.0 q^{87} +10474.3 q^{88} +78238.9 q^{89} +19432.3 q^{90} -156896. q^{92} -64403.3 q^{93} +76061.9 q^{94} +63032.8 q^{95} -74805.9 q^{96} +151480. q^{97} +30564.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 54 q^{3} + 150 q^{4} + 100 q^{5} + 18 q^{6} - 114 q^{8} + 486 q^{9}+O(q^{10}) \) 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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