LMFDB - Embedded newform 294.6.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.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:	$47.1528430250$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -103.497 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -103.497 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +413.990 q^{10} +240.191 q^{11} -144.000 q^{12} -805.477 q^{13} +931.477 q^{15} +256.000 q^{16} +1293.27 q^{17} -324.000 q^{18} +275.377 q^{19} -1655.96 q^{20} -960.764 q^{22} +3796.57 q^{23} +576.000 q^{24} +7586.73 q^{25} +3221.91 q^{26} -729.000 q^{27} +1227.52 q^{29} -3725.91 q^{30} -5624.86 q^{31} -1024.00 q^{32} -2161.72 q^{33} -5173.06 q^{34} +1296.00 q^{36} -9078.49 q^{37} -1101.51 q^{38} +7249.30 q^{39} +6623.84 q^{40} +18207.4 q^{41} -11708.2 q^{43} +3843.05 q^{44} -8383.30 q^{45} -15186.3 q^{46} +23048.6 q^{47} -2304.00 q^{48} -30346.9 q^{50} -11639.4 q^{51} -12887.6 q^{52} +17662.8 q^{53} +2916.00 q^{54} -24859.2 q^{55} -2478.39 q^{57} -4910.07 q^{58} -18376.3 q^{59} +14903.6 q^{60} -11324.1 q^{61} +22499.5 q^{62} +4096.00 q^{64} +83364.9 q^{65} +8646.87 q^{66} +36079.3 q^{67} +20692.3 q^{68} -34169.2 q^{69} -63434.2 q^{71} -5184.00 q^{72} +52982.4 q^{73} +36314.0 q^{74} -68280.5 q^{75} +4406.03 q^{76} -28997.2 q^{78} -48564.0 q^{79} -26495.4 q^{80} +6561.00 q^{81} -72829.7 q^{82} -113161. q^{83} -133850. q^{85} +46832.9 q^{86} -11047.7 q^{87} -15372.2 q^{88} -108366. q^{89} +33533.2 q^{90} +60745.2 q^{92} +50623.8 q^{93} -92194.4 q^{94} -28500.8 q^{95} +9216.00 q^{96} -99641.2 q^{97} +19455.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 720 q^{13} + 972 q^{15} + 512 q^{16} + 1260 q^{17} - 648 q^{18} - 360 q^{19} - 1728 q^{20} - 496 q^{22} + 6524 q^{23} + 1152 q^{24} + 4482 q^{25} + 2880 q^{26} - 1458 q^{27} + 7088 q^{29} - 3888 q^{30} - 5904 q^{31} - 2048 q^{32} - 1116 q^{33} - 5040 q^{34} + 2592 q^{36} - 6040 q^{37} + 1440 q^{38} + 6480 q^{39} + 6912 q^{40} + 17388 q^{41} - 608 q^{43} + 1984 q^{44} - 8748 q^{45} - 26096 q^{46} + 30456 q^{47} - 4608 q^{48} - 17928 q^{50} - 11340 q^{51} - 11520 q^{52} + 3964 q^{53} + 5832 q^{54} - 24336 q^{55} + 3240 q^{57} - 28352 q^{58} - 40752 q^{59} + 15552 q^{60} + 1368 q^{61} + 23616 q^{62} + 8192 q^{64} + 82980 q^{65} + 4464 q^{66} - 16224 q^{67} + 20160 q^{68} - 58716 q^{69} - 3204 q^{71} - 10368 q^{72} - 23976 q^{73} + 24160 q^{74} - 40338 q^{75} - 5760 q^{76} - 25920 q^{78} - 82160 q^{79} - 27648 q^{80} + 13122 q^{81} - 69552 q^{82} - 173736 q^{83} - 133700 q^{85} + 2432 q^{86} - 63792 q^{87} - 7936 q^{88} - 200556 q^{89} + 34992 q^{90} + 104384 q^{92} + 53136 q^{93} - 121824 q^{94} - 25640 q^{95} + 18432 q^{96} - 251928 q^{97} + 10044 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 720 * q^13 + 972 * q^15 + 512 * q^16 + 1260 * q^17 - 648 * q^18 - 360 * q^19 - 1728 * q^20 - 496 * q^22 + 6524 * q^23 + 1152 * q^24 + 4482 * q^25 + 2880 * q^26 - 1458 * q^27 + 7088 * q^29 - 3888 * q^30 - 5904 * q^31 - 2048 * q^32 - 1116 * q^33 - 5040 * q^34 + 2592 * q^36 - 6040 * q^37 + 1440 * q^38 + 6480 * q^39 + 6912 * q^40 + 17388 * q^41 - 608 * q^43 + 1984 * q^44 - 8748 * q^45 - 26096 * q^46 + 30456 * q^47 - 4608 * q^48 - 17928 * q^50 - 11340 * q^51 - 11520 * q^52 + 3964 * q^53 + 5832 * q^54 - 24336 * q^55 + 3240 * q^57 - 28352 * q^58 - 40752 * q^59 + 15552 * q^60 + 1368 * q^61 + 23616 * q^62 + 8192 * q^64 + 82980 * q^65 + 4464 * q^66 - 16224 * q^67 + 20160 * q^68 - 58716 * q^69 - 3204 * q^71 - 10368 * q^72 - 23976 * q^73 + 24160 * q^74 - 40338 * q^75 - 5760 * q^76 - 25920 * q^78 - 82160 * q^79 - 27648 * q^80 + 13122 * q^81 - 69552 * q^82 - 173736 * q^83 - 133700 * q^85 + 2432 * q^86 - 63792 * q^87 - 7936 * q^88 - 200556 * q^89 + 34992 * q^90 + 104384 * q^92 + 53136 * q^93 - 121824 * q^94 - 25640 * q^95 + 18432 * q^96 - 251928 * q^97 + 10044 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	−103.497	−1.85142	−0.925710	−	0.378235i	$-0.876531\pi$
$5$	−103.497	−1.85142	−0.925710	+	0.378235i	$0.876531\pi$
$6$	36.0000	0.408248
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	413.990	1.30915
$11$	240.191	0.598515	0.299257	−	0.954172i	$-0.403261\pi$
$11$	240.191	0.598515	0.299257	+	0.954172i	$0.403261\pi$
$12$	−144.000	−0.288675
$13$	−805.477	−1.32189	−0.660944	−	0.750435i	$-0.729844\pi$
$13$	−805.477	−1.32189	−0.660944	+	0.750435i	$0.729844\pi$
$14$	0	0
$15$	931.477	1.06892
$16$	256.000	0.250000
$17$	1293.27	1.08534	0.542670	−	0.839946i	$-0.317414\pi$
$17$	1293.27	1.08534	0.542670	+	0.839946i	$0.317414\pi$
$18$	−324.000	−0.235702
$19$	275.377	0.175002	0.0875011	−	0.996164i	$-0.472112\pi$
$19$	275.377	0.175002	0.0875011	+	0.996164i	$0.472112\pi$
$20$	−1655.96	−0.925710
$21$	0	0
$22$	−960.764	−0.423214
$23$	3796.57	1.49648	0.748242	−	0.663426i	$-0.230898\pi$
$23$	3796.57	1.49648	0.748242	+	0.663426i	$0.230898\pi$
$24$	576.000	0.204124
$25$	7586.73	2.42775
$26$	3221.91	0.934717
$27$	−729.000	−0.192450
$28$	0	0
$29$	1227.52	0.271040	0.135520	−	0.990775i	$-0.456730\pi$
$29$	1227.52	0.271040	0.135520	+	0.990775i	$0.456730\pi$
$30$	−3725.91	−0.755839
$31$	−5624.86	−1.05125	−0.525627	−	0.850715i	$-0.676169\pi$
$31$	−5624.86	−1.05125	−0.525627	+	0.850715i	$0.676169\pi$
$32$	−1024.00	−0.176777
$33$	−2161.72	−0.345553
$34$	−5173.06	−0.767451
$35$	0	0
$36$	1296.00	0.166667
$37$	−9078.49	−1.09021	−0.545104	−	0.838368i	$-0.683510\pi$
$37$	−9078.49	−1.09021	−0.545104	+	0.838368i	$0.683510\pi$
$38$	−1101.51	−0.123745
$39$	7249.30	0.763193
$40$	6623.84	0.654576
$41$	18207.4	1.69156	0.845782	−	0.533528i	$-0.179134\pi$
$41$	18207.4	1.69156	0.845782	+	0.533528i	$0.179134\pi$
$42$	0	0
$43$	−11708.2	−0.965650	−0.482825	−	0.875717i	$-0.660389\pi$
$43$	−11708.2	−0.965650	−0.482825	+	0.875717i	$0.660389\pi$
$44$	3843.05	0.299257
$45$	−8383.30	−0.617140
$46$	−15186.3	−1.05817
$47$	23048.6	1.52195	0.760974	−	0.648782i	$-0.224721\pi$
$47$	23048.6	1.52195	0.760974	+	0.648782i	$0.224721\pi$
$48$	−2304.00	−0.144338
$49$	0	0
$50$	−30346.9	−1.71668
$51$	−11639.4	−0.626621
$52$	−12887.6	−0.660944
$53$	17662.8	0.863714	0.431857	−	0.901942i	$-0.357859\pi$
$53$	17662.8	0.863714	0.431857	+	0.901942i	$0.357859\pi$
$54$	2916.00	0.136083
$55$	−24859.2	−1.10810
$56$	0	0
$57$	−2478.39	−0.101038
$58$	−4910.07	−0.191654
$59$	−18376.3	−0.687271	−0.343636	−	0.939103i	$-0.611658\pi$
$59$	−18376.3	−0.687271	−0.343636	+	0.939103i	$0.611658\pi$
$60$	14903.6	0.534459
$61$	−11324.1	−0.389654	−0.194827	−	0.980838i	$-0.562414\pi$
$61$	−11324.1	−0.389654	−0.194827	+	0.980838i	$0.562414\pi$
$62$	22499.5	0.743349
$63$	0	0
$64$	4096.00	0.125000
$65$	83364.9	2.44737
$66$	8646.87	0.244343
$67$	36079.3	0.981910	0.490955	−	0.871185i	$-0.336648\pi$
$67$	36079.3	0.981910	0.490955	+	0.871185i	$0.336648\pi$
$68$	20692.3	0.542670
$69$	−34169.2	−0.863996
$70$	0	0
$71$	−63434.2	−1.49341	−0.746703	−	0.665158i	$-0.768364\pi$
$71$	−63434.2	−1.49341	−0.746703	+	0.665158i	$0.768364\pi$
$72$	−5184.00	−0.117851
$73$	52982.4	1.16366	0.581828	−	0.813312i	$-0.302338\pi$
$73$	52982.4	1.16366	0.581828	+	0.813312i	$0.302338\pi$
$74$	36314.0	0.770893
$75$	−68280.5	−1.40166
$76$	4406.03	0.0875011
$77$	0	0
$78$	−28997.2	−0.539659
$79$	−48564.0	−0.875481	−0.437741	−	0.899101i	$-0.644221\pi$
$79$	−48564.0	−0.875481	−0.437741	+	0.899101i	$0.644221\pi$
$80$	−26495.4	−0.462855
$81$	6561.00	0.111111
$82$	−72829.7	−1.19612
$83$	−113161.	−1.80303	−0.901513	−	0.432753i	$-0.857542\pi$
$83$	−113161.	−1.80303	−0.901513	+	0.432753i	$0.857542\pi$
$84$	0	0
$85$	−133850.	−2.00942
$86$	46832.9	0.682818
$87$	−11047.7	−0.156485
$88$	−15372.2	−0.211607
$89$	−108366.	−1.45017	−0.725083	−	0.688662i	$-0.758199\pi$
$89$	−108366.	−1.45017	−0.725083	+	0.688662i	$0.758199\pi$
$90$	33533.2	0.436384
$91$	0	0
$92$	60745.2	0.748242
$93$	50623.8	0.606942
$94$	−92194.4	−1.07618
$95$	−28500.8	−0.324002
$96$	9216.00	0.102062
$97$	−99641.2	−1.07525	−0.537625	−	0.843184i	$-0.680679\pi$
$97$	−99641.2	−1.07525	−0.537625	+	0.843184i	$0.680679\pi$
$98$	0	0
$99$	19455.5	0.199505
$100$	121388.	1.21388
$101$	−165200.	−1.61141	−0.805705	−	0.592317i	$-0.798213\pi$
$101$	−165200.	−1.61141	−0.805705	+	0.592317i	$0.798213\pi$
$102$	46557.6	0.443088
$103$	107247.	0.996077	0.498038	−	0.867155i	$-0.334054\pi$
$103$	107247.	0.996077	0.498038	+	0.867155i	$0.334054\pi$
$104$	51550.5	0.467358
$105$	0	0
$106$	−70651.2	−0.610738
$107$	−97422.3	−0.822620	−0.411310	−	0.911496i	$-0.634929\pi$
$107$	−97422.3	−0.822620	−0.411310	+	0.911496i	$0.634929\pi$
$108$	−11664.0	−0.0962250
$109$	59307.2	0.478125	0.239062	−	0.971004i	$-0.423160\pi$
$109$	59307.2	0.478125	0.239062	+	0.971004i	$0.423160\pi$
$110$	99436.6	0.783546
$111$	81706.4	0.629432
$112$	0	0
$113$	157268.	1.15863	0.579313	−	0.815105i	$-0.303321\pi$
$113$	157268.	1.15863	0.579313	+	0.815105i	$0.303321\pi$
$114$	9913.56	0.0714443
$115$	−392936.	−2.77062
$116$	19640.3	0.135520
$117$	−65243.7	−0.440630
$118$	73505.2	0.485974
$119$	0	0
$120$	−59614.5	−0.377919
$121$	−103359.	−0.641780
$122$	45296.3	0.275527
$123$	−163867.	−0.976625
$124$	−89997.8	−0.525627
$125$	−461778.	−2.64337
$126$	0	0
$127$	−92477.3	−0.508775	−0.254387	−	0.967102i	$-0.581874\pi$
$127$	−92477.3	−0.508775	−0.254387	+	0.967102i	$0.581874\pi$
$128$	−16384.0	−0.0883883
$129$	105374.	0.557518
$130$	−333459.	−1.73055
$131$	72328.4	0.368240	0.184120	−	0.982904i	$-0.441057\pi$
$131$	72328.4	0.368240	0.184120	+	0.982904i	$0.441057\pi$
$132$	−34587.5	−0.172776
$133$	0	0
$134$	−144317.	−0.694315
$135$	75449.7	0.356306
$136$	−82769.0	−0.383725
$137$	225662.	1.02720	0.513602	−	0.858028i	$-0.328311\pi$
$137$	225662.	1.02720	0.513602	+	0.858028i	$0.328311\pi$
$138$	136677.	0.610937
$139$	327971.	1.43979	0.719894	−	0.694084i	$-0.244190\pi$
$139$	327971.	1.43979	0.719894	+	0.694084i	$0.244190\pi$
$140$	0	0
$141$	−207437.	−0.878697
$142$	253737.	1.05600
$143$	−193468.	−0.791170
$144$	20736.0	0.0833333
$145$	−127045.	−0.501808
$146$	−211930.	−0.822829
$147$	0	0
$148$	−145256.	−0.545104
$149$	164011.	0.605211	0.302606	−	0.953116i	$-0.402144\pi$
$149$	164011.	0.605211	0.302606	+	0.953116i	$0.402144\pi$
$150$	273122.	0.991126
$151$	62308.8	0.222386	0.111193	−	0.993799i	$-0.464533\pi$
$151$	62308.8	0.222386	0.111193	+	0.993799i	$0.464533\pi$
$152$	−17624.1	−0.0618726
$153$	104755.	0.361780
$154$	0	0
$155$	582159.	1.94631
$156$	115989.	0.381596
$157$	239807.	0.776447	0.388224	−	0.921565i	$-0.373089\pi$
$157$	239807.	0.776447	0.388224	+	0.921565i	$0.373089\pi$
$158$	194256.	0.619059
$159$	−158965.	−0.498665
$160$	105981.	0.327288
$161$	0	0
$162$	−26244.0	−0.0785674
$163$	−436795.	−1.28768	−0.643841	−	0.765160i	$-0.722660\pi$
$163$	−436795.	−1.28768	−0.643841	+	0.765160i	$0.722660\pi$
$164$	291319.	0.845782
$165$	223732.	0.639763
$166$	452644.	1.27493
$167$	−38846.7	−0.107786	−0.0538931	−	0.998547i	$-0.517163\pi$
$167$	−38846.7	−0.107786	−0.0538931	+	0.998547i	$0.517163\pi$
$168$	0	0
$169$	277501.	0.747390
$170$	535399.	1.42087
$171$	22305.5	0.0583340
$172$	−187331.	−0.482825
$173$	−396277.	−1.00666	−0.503331	−	0.864093i	$-0.667892\pi$
$173$	−396277.	−1.00666	−0.503331	+	0.864093i	$0.667892\pi$
$174$	44190.7	0.110652
$175$	0	0
$176$	61488.9	0.149629
$177$	165387.	0.396796
$178$	433464.	1.02542
$179$	243883.	0.568918	0.284459	−	0.958688i	$-0.408186\pi$
$179$	243883.	0.568918	0.284459	+	0.958688i	$0.408186\pi$
$180$	−134133.	−0.308570
$181$	299273.	0.679002	0.339501	−	0.940606i	$-0.389742\pi$
$181$	299273.	0.679002	0.339501	+	0.940606i	$0.389742\pi$
$182$	0	0
$183$	101917.	0.224967
$184$	−242981.	−0.529087
$185$	939601.	2.01843
$186$	−202495.	−0.429173
$187$	310631.	0.649592
$188$	368778.	0.760974
$189$	0	0
$190$	114003.	0.229104
$191$	−776996.	−1.54112	−0.770558	−	0.637369i	$-0.780023\pi$
$191$	−776996.	−1.54112	−0.770558	+	0.637369i	$0.780023\pi$
$192$	−36864.0	−0.0721688
$193$	276421.	0.534168	0.267084	−	0.963673i	$-0.413940\pi$
$193$	276421.	0.534168	0.267084	+	0.963673i	$0.413940\pi$
$194$	398565.	0.760317
$195$	−750284.	−1.41299
$196$	0	0
$197$	−131615.	−0.241624	−0.120812	−	0.992675i	$-0.538550\pi$
$197$	−131615.	−0.241624	−0.120812	+	0.992675i	$0.538550\pi$
$198$	−77821.9	−0.141071
$199$	−564960.	−1.01131	−0.505656	−	0.862735i	$-0.668750\pi$
$199$	−564960.	−1.01131	−0.505656	+	0.862735i	$0.668750\pi$
$200$	−485551.	−0.858340
$201$	−324714.	−0.566906
$202$	660799.	1.13944
$203$	0	0
$204$	−186230.	−0.313311
$205$	−1.88442e6	−3.13180
$206$	−428989.	−0.704333
$207$	307522.	0.498828
$208$	−206202.	−0.330472
$209$	66143.0	0.104741
$210$	0	0
$211$	313637.	0.484977	0.242489	−	0.970154i	$-0.422036\pi$
$211$	313637.	0.484977	0.242489	+	0.970154i	$0.422036\pi$
$212$	282605.	0.431857
$213$	570908.	0.862218
$214$	389689.	0.581680
$215$	1.21177e6	1.78782
$216$	46656.0	0.0680414
$217$	0	0
$218$	−237229.	−0.338085
$219$	−476841.	−0.671837
$220$	−397746.	−0.554051
$221$	−1.04170e6	−1.43470
$222$	−326826.	−0.445076
$223$	279483.	0.376351	0.188176	−	0.982135i	$-0.439743\pi$
$223$	279483.	0.376351	0.188176	+	0.982135i	$0.439743\pi$
$224$	0	0
$225$	614525.	0.809251
$226$	−629071.	−0.819273
$227$	1.22351e6	1.57595	0.787974	−	0.615709i	$-0.211130\pi$
$227$	1.22351e6	1.57595	0.787974	+	0.615709i	$0.211130\pi$
$228$	−39654.3	−0.0505188
$229$	−254775.	−0.321046	−0.160523	−	0.987032i	$-0.551318\pi$
$229$	−254775.	−0.321046	−0.160523	+	0.987032i	$0.551318\pi$
$230$	1.57174e6	1.95912
$231$	0	0
$232$	−78561.2	−0.0958270
$233$	746173.	0.900429	0.450215	−	0.892920i	$-0.351347\pi$
$233$	746173.	0.900429	0.450215	+	0.892920i	$0.351347\pi$
$234$	260975.	0.311572
$235$	−2.38547e6	−2.81776
$236$	−294021.	−0.343636
$237$	437076.	0.505459
$238$	0	0
$239$	321036.	0.363546	0.181773	−	0.983341i	$-0.441816\pi$
$239$	321036.	0.363546	0.181773	+	0.983341i	$0.441816\pi$
$240$	238458.	0.267229
$241$	−1.24254e6	−1.37805	−0.689027	−	0.724735i	$-0.741962\pi$
$241$	−1.24254e6	−1.37805	−0.689027	+	0.724735i	$0.741962\pi$
$242$	413437.	0.453807
$243$	−59049.0	−0.0641500
$244$	−181185.	−0.194827
$245$	0	0
$246$	655467.	0.690578
$247$	−221810.	−0.231333
$248$	359991.	0.371675
$249$	1.01845e6	1.04098
$250$	1.84711e6	1.86914
$251$	−690235.	−0.691532	−0.345766	−	0.938321i	$-0.612381\pi$
$251$	−690235.	−0.691532	−0.345766	+	0.938321i	$0.612381\pi$
$252$	0	0
$253$	911902.	0.895668
$254$	369909.	0.359758
$255$	1.20465e6	1.16014
$256$	65536.0	0.0625000
$257$	−13786.7	−0.0130205	−0.00651024	−	0.999979i	$-0.502072\pi$
$257$	−13786.7	−0.0130205	−0.00651024	+	0.999979i	$0.502072\pi$
$258$	−421496.	−0.394225
$259$	0	0
$260$	1.33384e6	1.22369
$261$	99429.0	0.0903466
$262$	−289314.	−0.260385
$263$	574833.	0.512451	0.256226	−	0.966617i	$-0.417521\pi$
$263$	574833.	0.512451	0.256226	+	0.966617i	$0.417521\pi$
$264$	138350.	0.122171
$265$	−1.82806e6	−1.59910
$266$	0	0
$267$	975293.	0.837253
$268$	577270.	0.490955
$269$	1.11893e6	0.942804	0.471402	−	0.881918i	$-0.343748\pi$
$269$	1.11893e6	0.942804	0.471402	+	0.881918i	$0.343748\pi$
$270$	−301799.	−0.251946
$271$	−694869.	−0.574751	−0.287376	−	0.957818i	$-0.592783\pi$
$271$	−694869.	−0.574751	−0.287376	+	0.957818i	$0.592783\pi$
$272$	331076.	0.271335
$273$	0	0
$274$	−902648.	−0.726343
$275$	1.82226e6	1.45305
$276$	−546706.	−0.431998
$277$	−837654.	−0.655941	−0.327971	−	0.944688i	$-0.606365\pi$
$277$	−837654.	−0.655941	−0.327971	+	0.944688i	$0.606365\pi$
$278$	−1.31188e6	−1.01808
$279$	−455614.	−0.350418
$280$	0	0
$281$	−917687.	−0.693312	−0.346656	−	0.937992i	$-0.612683\pi$
$281$	−917687.	−0.693312	−0.346656	+	0.937992i	$0.612683\pi$
$282$	829750.	0.621333
$283$	415263.	0.308218	0.154109	−	0.988054i	$-0.450749\pi$
$283$	415263.	0.308218	0.154109	+	0.988054i	$0.450749\pi$
$284$	−1.01495e6	−0.746703
$285$	256507.	0.187063
$286$	773873.	0.559442
$287$	0	0
$288$	−82944.0	−0.0589256
$289$	252680.	0.177962
$290$	508180.	0.354832
$291$	896771.	0.620796
$292$	847718.	0.581828
$293$	1.21491e6	0.826752	0.413376	−	0.910561i	$-0.364350\pi$
$293$	1.21491e6	0.826752	0.413376	+	0.910561i	$0.364350\pi$
$294$	0	0
$295$	1.90190e6	1.27243
$296$	581023.	0.385447
$297$	−175099.	−0.115184
$298$	−656043.	−0.427949
$299$	−3.05805e6	−1.97819
$300$	−1.09249e6	−0.700832
$301$	0	0
$302$	−249235.	−0.157250
$303$	1.48680e6	0.930348
$304$	70496.5	0.0437505
$305$	1.17201e6	0.721412
$306$	−419018.	−0.255817
$307$	2.60119e6	1.57517	0.787584	−	0.616207i	$-0.211332\pi$
$307$	2.60119e6	1.57517	0.787584	+	0.616207i	$0.211332\pi$
$308$	0	0
$309$	−965225.	−0.575085
$310$	−2.32864e6	−1.37625
$311$	819164.	0.480253	0.240126	−	0.970742i	$-0.422811\pi$
$311$	819164.	0.480253	0.240126	+	0.970742i	$0.422811\pi$
$312$	−463955.	−0.269829
$313$	881939.	0.508836	0.254418	−	0.967094i	$-0.418116\pi$
$313$	881939.	0.508836	0.254418	+	0.967094i	$0.418116\pi$
$314$	−959226.	−0.549031
$315$	0	0
$316$	−777024.	−0.437741
$317$	−1.60438e6	−0.896726	−0.448363	−	0.893852i	$-0.647993\pi$
$317$	−1.60438e6	−0.896726	−0.448363	+	0.893852i	$0.647993\pi$
$318$	635861.	0.352610
$319$	294839.	0.162221
$320$	−423926.	−0.231427
$321$	876801.	0.474940
$322$	0	0
$323$	356135.	0.189937
$324$	104976.	0.0555556
$325$	−6.11094e6	−3.20922
$326$	1.74718e6	0.910528
$327$	−533765.	−0.276045
$328$	−1.16527e6	−0.598058
$329$	0	0
$330$	−894929.	−0.452381
$331$	1.00308e6	0.503229	0.251614	−	0.967828i	$-0.419039\pi$
$331$	1.00308e6	0.503229	0.251614	+	0.967828i	$0.419039\pi$
$332$	−1.81058e6	−0.901513
$333$	−735358.	−0.363403
$334$	155387.	0.0762164
$335$	−3.73412e6	−1.81793
$336$	0	0
$337$	−2.62317e6	−1.25821	−0.629103	−	0.777322i	$-0.716578\pi$
$337$	−2.62317e6	−1.25821	−0.629103	+	0.777322i	$0.716578\pi$
$338$	−1.11000e6	−0.528484
$339$	−1.41541e6	−0.668933
$340$	−2.14160e6	−1.00471
$341$	−1.35104e6	−0.629191
$342$	−89222.1	−0.0412484
$343$	0	0
$344$	749326.	0.341409
$345$	3.53642e6	1.59962
$346$	1.58511e6	0.711818
$347$	226234.	0.100863	0.0504317	−	0.998728i	$-0.483940\pi$
$347$	226234.	0.100863	0.0504317	+	0.998728i	$0.483940\pi$
$348$	−176763.	−0.0782424
$349$	1.46280e6	0.642866	0.321433	−	0.946932i	$-0.395835\pi$
$349$	1.46280e6	0.642866	0.321433	+	0.946932i	$0.395835\pi$
$350$	0	0
$351$	587193.	0.254398
$352$	−245955.	−0.105803
$353$	−2.80957e6	−1.20006	−0.600031	−	0.799977i	$-0.704845\pi$
$353$	−2.80957e6	−1.20006	−0.600031	+	0.799977i	$0.704845\pi$
$354$	−661547.	−0.280577
$355$	6.56528e6	2.76492
$356$	−1.73385e6	−0.725083
$357$	0	0
$358$	−975534.	−0.402286
$359$	−3.69900e6	−1.51478	−0.757388	−	0.652965i	$-0.773525\pi$
$359$	−3.69900e6	−1.51478	−0.757388	+	0.652965i	$0.773525\pi$
$360$	536531.	0.218192
$361$	−2.40027e6	−0.969374
$362$	−1.19709e6	−0.480127
$363$	930234.	0.370532
$364$	0	0
$365$	−5.48354e6	−2.15441
$366$	−407667.	−0.159075
$367$	−1.16925e6	−0.453148	−0.226574	−	0.973994i	$-0.572753\pi$
$367$	−1.16925e6	−0.453148	−0.226574	+	0.973994i	$0.572753\pi$
$368$	971923.	0.374121
$369$	1.47480e6	0.563855
$370$	−3.75840e6	−1.42725
$371$	0	0
$372$	809980.	0.303471
$373$	−4.57690e6	−1.70333	−0.851666	−	0.524084i	$-0.824408\pi$
$373$	−4.57690e6	−1.70333	−0.851666	+	0.524084i	$0.824408\pi$
$374$	−1.24252e6	−0.459331
$375$	4.15600e6	1.52615
$376$	−1.47511e6	−0.538090
$377$	−988738.	−0.358284
$378$	0	0
$379$	−2.35520e6	−0.842229	−0.421114	−	0.907007i	$-0.638361\pi$
$379$	−2.35520e6	−0.842229	−0.421114	+	0.907007i	$0.638361\pi$
$380$	−456013.	−0.162001
$381$	832295.	0.293741
$382$	3.10799e6	1.08973
$383$	−3.03946e6	−1.05876	−0.529382	−	0.848384i	$-0.677576\pi$
$383$	−3.03946e6	−1.05876	−0.529382	+	0.848384i	$0.677576\pi$
$384$	147456.	0.0510310
$385$	0	0
$386$	−1.10568e6	−0.377714
$387$	−948366.	−0.321883
$388$	−1.59426e6	−0.537625
$389$	−459273.	−0.153885	−0.0769426	−	0.997036i	$-0.524516\pi$
$389$	−459273.	−0.153885	−0.0769426	+	0.997036i	$0.524516\pi$
$390$	3.00114e6	0.999135
$391$	4.90998e6	1.62419
$392$	0	0
$393$	−650956.	−0.212603
$394$	526461.	0.170854
$395$	5.02625e6	1.62088
$396$	311287.	0.0997525
$397$	−5.42500e6	−1.72752	−0.863761	−	0.503901i	$-0.831898\pi$
$397$	−5.42500e6	−1.72752	−0.863761	+	0.503901i	$0.831898\pi$
$398$	2.25984e6	0.715106
$399$	0	0
$400$	1.94220e6	0.606938
$401$	2.11127e6	0.655667	0.327833	−	0.944736i	$-0.393682\pi$
$401$	2.11127e6	0.655667	0.327833	+	0.944736i	$0.393682\pi$
$402$	1.29886e6	0.400863
$403$	4.53070e6	1.38964
$404$	−2.64320e6	−0.805705
$405$	−679047.	−0.205713
$406$	0	0
$407$	−2.18057e6	−0.652506
$408$	744921.	0.221544
$409$	−2.55745e6	−0.755959	−0.377980	−	0.925814i	$-0.623381\pi$
$409$	−2.55745e6	−0.755959	−0.377980	+	0.925814i	$0.623381\pi$
$410$	7.53769e6	2.21451
$411$	−2.03096e6	−0.593057
$412$	1.71595e6	0.498038
$413$	0	0
$414$	−1.23009e6	−0.352725
$415$	1.17119e7	3.33816
$416$	824809.	0.233679
$417$	−2.95174e6	−0.831262
$418$	−264572.	−0.0740633
$419$	−2.17401e6	−0.604959	−0.302480	−	0.953156i	$-0.597814\pi$
$419$	−2.17401e6	−0.604959	−0.302480	+	0.953156i	$0.597814\pi$
$420$	0	0
$421$	−5.47930e6	−1.50668	−0.753338	−	0.657633i	$-0.771558\pi$
$421$	−5.47930e6	−1.50668	−0.753338	+	0.657633i	$0.771558\pi$
$422$	−1.25455e6	−0.342931
$423$	1.86694e6	0.507316
$424$	−1.13042e6	−0.305369
$425$	9.81166e6	2.63494
$426$	−2.28363e6	−0.609680
$427$	0	0
$428$	−1.55876e6	−0.411310
$429$	1.74121e6	0.456782
$430$	−4.84708e6	−1.26418
$431$	−6.16874e6	−1.59957	−0.799785	−	0.600286i	$-0.795053\pi$
$431$	−6.16874e6	−1.59957	−0.799785	+	0.600286i	$0.795053\pi$
$432$	−186624.	−0.0481125
$433$	−4.89596e6	−1.25493	−0.627463	−	0.778647i	$-0.715907\pi$
$433$	−4.89596e6	−1.25493	−0.627463	+	0.778647i	$0.715907\pi$
$434$	0	0
$435$	1.14341e6	0.289719
$436$	948915.	0.239062
$437$	1.04549e6	0.261888
$438$	1.90737e6	0.475060
$439$	3.54588e6	0.878137	0.439069	−	0.898454i	$-0.355309\pi$
$439$	3.54588e6	0.878137	0.439069	+	0.898454i	$0.355309\pi$
$440$	1.59099e6	0.391773
$441$	0	0
$442$	4.16679e6	1.01448
$443$	6.05652e6	1.46627	0.733134	−	0.680084i	$-0.238057\pi$
$443$	6.05652e6	1.46627	0.733134	+	0.680084i	$0.238057\pi$
$444$	1.30730e6	0.314716
$445$	1.12156e7	2.68486
$446$	−1.11793e6	−0.266121
$447$	−1.47610e6	−0.349419
$448$	0	0
$449$	−1.20801e6	−0.282783	−0.141392	−	0.989954i	$-0.545158\pi$
$449$	−1.20801e6	−0.282783	−0.141392	+	0.989954i	$0.545158\pi$
$450$	−2.45810e6	−0.572227
$451$	4.37326e6	1.01243
$452$	2.51628e6	0.579313
$453$	−560779.	−0.128394
$454$	−4.89403e6	−1.11436
$455$	0	0
$456$	158617.	0.0357222
$457$	−5.46550e6	−1.22416	−0.612082	−	0.790794i	$-0.709668\pi$
$457$	−5.46550e6	−1.22416	−0.612082	+	0.790794i	$0.709668\pi$
$458$	1.01910e6	0.227014
$459$	−942791.	−0.208874
$460$	−6.28697e6	−1.38531
$461$	−1.15956e6	−0.254121	−0.127061	−	0.991895i	$-0.540554\pi$
$461$	−1.15956e6	−0.254121	−0.127061	+	0.991895i	$0.540554\pi$
$462$	0	0
$463$	−4.31335e6	−0.935108	−0.467554	−	0.883964i	$-0.654865\pi$
$463$	−4.31335e6	−0.935108	−0.467554	+	0.883964i	$0.654865\pi$
$464$	314245.	0.0677599
$465$	−5.23943e6	−1.12370
$466$	−2.98469e6	−0.636700
$467$	5.98923e6	1.27081	0.635403	−	0.772181i	$-0.280834\pi$
$467$	5.98923e6	1.27081	0.635403	+	0.772181i	$0.280834\pi$
$468$	−1.04390e6	−0.220315
$469$	0	0
$470$	9.54189e6	1.99246
$471$	−2.15826e6	−0.448282
$472$	1.17608e6	0.242987
$473$	−2.81221e6	−0.577956
$474$	−1.74830e6	−0.357414
$475$	2.08921e6	0.424862
$476$	0	0
$477$	1.43069e6	0.287905
$478$	−1.28415e6	−0.257066
$479$	−3.54652e6	−0.706258	−0.353129	−	0.935575i	$-0.614882\pi$
$479$	−3.54652e6	−0.706258	−0.353129	+	0.935575i	$0.614882\pi$
$480$	−953833.	−0.188960
$481$	7.31252e6	1.44113
$482$	4.97015e6	0.974432
$483$	0	0
$484$	−1.65375e6	−0.320890
$485$	1.03126e7	1.99074
$486$	236196.	0.0453609
$487$	−8.78320e6	−1.67815	−0.839074	−	0.544017i	$-0.816903\pi$
$487$	−8.78320e6	−1.67815	−0.839074	+	0.544017i	$0.816903\pi$
$488$	724742.	0.137763
$489$	3.93115e6	0.743443
$490$	0	0
$491$	−586608.	−0.109811	−0.0549053	−	0.998492i	$-0.517486\pi$
$491$	−586608.	−0.109811	−0.0549053	+	0.998492i	$0.517486\pi$
$492$	−2.62187e6	−0.488313
$493$	1.58751e6	0.294170
$494$	887239.	0.163577
$495$	−2.01359e6	−0.369367
$496$	−1.43997e6	−0.262814
$497$	0	0
$498$	−4.07380e6	−0.736082
$499$	−9.59772e6	−1.72551	−0.862753	−	0.505626i	$-0.831262\pi$
$499$	−9.59772e6	−1.72551	−0.862753	+	0.505626i	$0.831262\pi$
$500$	−7.38844e6	−1.32168
$501$	349620.	0.0622304
$502$	2.76094e6	0.488987
$503$	7.21481e6	1.27147	0.635733	−	0.771909i	$-0.280698\pi$
$503$	7.21481e6	1.27147	0.635733	+	0.771909i	$0.280698\pi$
$504$	0	0
$505$	1.70978e7	2.98340
$506$	−3.64761e6	−0.633333
$507$	−2.49751e6	−0.431506
$508$	−1.47964e6	−0.254387
$509$	−4.38419e6	−0.750058	−0.375029	−	0.927013i	$-0.622367\pi$
$509$	−4.38419e6	−0.750058	−0.375029	+	0.927013i	$0.622367\pi$
$510$	−4.81859e6	−0.820342
$511$	0	0
$512$	−262144.	−0.0441942
$513$	−200750.	−0.0336792
$514$	55146.8	0.00920688
$515$	−1.10998e7	−1.84416
$516$	1.68598e6	0.278759
$517$	5.53606e6	0.910909
$518$	0	0
$519$	3.56650e6	0.581197
$520$	−5.33535e6	−0.865276
$521$	−2.06581e6	−0.333424	−0.166712	−	0.986006i	$-0.553315\pi$
$521$	−2.06581e6	−0.333424	−0.166712	+	0.986006i	$0.553315\pi$
$522$	−397716.	−0.0638847
$523$	−7.96570e6	−1.27341	−0.636707	−	0.771106i	$-0.719704\pi$
$523$	−7.96570e6	−1.27341	−0.636707	+	0.771106i	$0.719704\pi$
$524$	1.15725e6	0.184120
$525$	0	0
$526$	−2.29933e6	−0.362358
$527$	−7.27445e6	−1.14097
$528$	−553400.	−0.0863882
$529$	7.97762e6	1.23946
$530$	7.31222e6	1.13073
$531$	−1.48848e6	−0.229090
$532$	0	0
$533$	−1.46657e7	−2.23606
$534$	−3.90117e6	−0.592028
$535$	1.00830e7	1.52301
$536$	−2.30908e6	−0.347158
$537$	−2.19495e6	−0.328465
$538$	−4.47571e6	−0.666663
$539$	0	0
$540$	1.20719e6	0.178153
$541$	8.23423e6	1.20957	0.604784	−	0.796390i	$-0.293260\pi$
$541$	8.23423e6	1.20957	0.604784	+	0.796390i	$0.293260\pi$
$542$	2.77948e6	0.406411
$543$	−2.69346e6	−0.392022
$544$	−1.32430e6	−0.191863
$545$	−6.13815e6	−0.885209
$546$	0	0
$547$	5.20365e6	0.743601	0.371800	−	0.928313i	$-0.378741\pi$
$547$	5.20365e6	0.743601	0.371800	+	0.928313i	$0.378741\pi$
$548$	3.61059e6	0.513602
$549$	−917251.	−0.129885
$550$	−7.28905e6	−1.02746
$551$	338030.	0.0474325
$552$	2.18683e6	0.305469
$553$	0	0
$554$	3.35061e6	0.463821
$555$	−8.45641e6	−1.16534
$556$	5.24754e6	0.719894
$557$	−4.09165e6	−0.558806	−0.279403	−	0.960174i	$-0.590136\pi$
$557$	−4.09165e6	−0.558806	−0.279403	+	0.960174i	$0.590136\pi$
$558$	1.82246e6	0.247783
$559$	9.43070e6	1.27648
$560$	0	0
$561$	−2.79568e6	−0.375042
$562$	3.67075e6	0.490246
$563$	3.59052e6	0.477404	0.238702	−	0.971093i	$-0.423278\pi$
$563$	3.59052e6	0.477404	0.238702	+	0.971093i	$0.423278\pi$
$564$	−3.31900e6	−0.439349
$565$	−1.62768e7	−2.14510
$566$	−1.66105e6	−0.217943
$567$	0	0
$568$	4.05979e6	0.527999
$569$	9.79717e6	1.26859	0.634293	−	0.773093i	$-0.281291\pi$
$569$	9.79717e6	1.26859	0.634293	+	0.773093i	$0.281291\pi$
$570$	−1.02603e6	−0.132273
$571$	−2.21804e6	−0.284694	−0.142347	−	0.989817i	$-0.545465\pi$
$571$	−2.21804e6	−0.284694	−0.142347	+	0.989817i	$0.545465\pi$
$572$	−3.09549e6	−0.395585
$573$	6.99297e6	0.889764
$574$	0	0
$575$	2.88036e7	3.63309
$576$	331776.	0.0416667
$577$	2.65534e6	0.332032	0.166016	−	0.986123i	$-0.446910\pi$
$577$	2.65534e6	0.332032	0.166016	+	0.986123i	$0.446910\pi$
$578$	−1.01072e6	−0.125838
$579$	−2.48779e6	−0.308402
$580$	−2.03272e6	−0.250904
$581$	0	0
$582$	−3.58708e6	−0.438969
$583$	4.24244e6	0.516945
$584$	−3.39087e6	−0.411414
$585$	6.75255e6	0.815790
$586$	−4.85964e6	−0.584602
$587$	2.62690e6	0.314665	0.157332	−	0.987546i	$-0.449711\pi$
$587$	2.62690e6	0.314665	0.157332	+	0.987546i	$0.449711\pi$
$588$	0	0
$589$	−1.54896e6	−0.183972
$590$	−7.60760e6	−0.899742
$591$	1.18454e6	0.139502
$592$	−2.32409e6	−0.272552
$593$	1.15062e7	1.34368	0.671839	−	0.740697i	$-0.265505\pi$
$593$	1.15062e7	1.34368	0.671839	+	0.740697i	$0.265505\pi$
$594$	700397.	0.0814475
$595$	0	0
$596$	2.62417e6	0.302606
$597$	5.08464e6	0.583881
$598$	1.22322e7	1.39879
$599$	6.46264e6	0.735941	0.367970	−	0.929838i	$-0.380053\pi$
$599$	6.46264e6	0.735941	0.367970	+	0.929838i	$0.380053\pi$
$600$	4.36995e6	0.495563
$601$	−8.55332e6	−0.965937	−0.482968	−	0.875638i	$-0.660441\pi$
$601$	−8.55332e6	−0.965937	−0.482968	+	0.875638i	$0.660441\pi$
$602$	0	0
$603$	2.92243e6	0.327303
$604$	996941.	0.111193
$605$	1.06974e7	1.18820
$606$	−5.94719e6	−0.657856
$607$	−2.99042e6	−0.329428	−0.164714	−	0.986341i	$-0.552670\pi$
$607$	−2.99042e6	−0.329428	−0.164714	+	0.986341i	$0.552670\pi$
$608$	−281986.	−0.0309363
$609$	0	0
$610$	−4.68806e6	−0.510115
$611$	−1.85651e7	−2.01185
$612$	1.67607e6	0.180890
$613$	−1.77145e6	−0.190405	−0.0952023	−	0.995458i	$-0.530350\pi$
$613$	−1.77145e6	−0.190405	−0.0952023	+	0.995458i	$0.530350\pi$
$614$	−1.04048e7	−1.11381
$615$	1.69598e7	1.80814
$616$	0	0
$617$	1.40871e7	1.48974	0.744869	−	0.667210i	$-0.232512\pi$
$617$	1.40871e7	1.48974	0.744869	+	0.667210i	$0.232512\pi$
$618$	3.86090e6	0.406647
$619$	1.13430e7	1.18988	0.594940	−	0.803770i	$-0.297176\pi$
$619$	1.13430e7	1.18988	0.594940	+	0.803770i	$0.297176\pi$
$620$	9.31455e6	0.973156
$621$	−2.76770e6	−0.287999
$622$	−3.27666e6	−0.339590
$623$	0	0
$624$	1.85582e6	0.190798
$625$	2.40843e7	2.46623
$626$	−3.52776e6	−0.359801
$627$	−595287.	−0.0604724
$628$	3.83690e6	0.388224
$629$	−1.17409e7	−1.18325
$630$	0	0
$631$	−2.32628e6	−0.232588	−0.116294	−	0.993215i	$-0.537102\pi$
$631$	−2.32628e6	−0.232588	−0.116294	+	0.993215i	$0.537102\pi$
$632$	3.10810e6	0.309529
$633$	−2.82273e6	−0.280002
$634$	6.41753e6	0.634081
$635$	9.57116e6	0.941956
$636$	−2.54344e6	−0.249333
$637$	0	0
$638$	−1.17935e6	−0.114708
$639$	−5.13817e6	−0.497802
$640$	1.69570e6	0.163644
$641$	−2.56385e6	−0.246461	−0.123230	−	0.992378i	$-0.539325\pi$
$641$	−2.56385e6	−0.246461	−0.123230	+	0.992378i	$0.539325\pi$
$642$	−3.50720e6	−0.335833
$643$	5.95343e6	0.567858	0.283929	−	0.958845i	$-0.408362\pi$
$643$	5.95343e6	0.567858	0.283929	+	0.958845i	$0.408362\pi$
$644$	0	0
$645$	−1.09059e7	−1.03220
$646$	−1.42454e6	−0.134306
$647$	1.53522e6	0.144182	0.0720909	−	0.997398i	$-0.477033\pi$
$647$	1.53522e6	0.144182	0.0720909	+	0.997398i	$0.477033\pi$
$648$	−419904.	−0.0392837
$649$	−4.41382e6	−0.411342
$650$	2.44437e7	2.26926
$651$	0	0
$652$	−6.98871e6	−0.643841
$653$	−1.99582e7	−1.83163	−0.915815	−	0.401600i	$-0.868454\pi$
$653$	−1.99582e7	−1.83163	−0.915815	+	0.401600i	$0.868454\pi$
$654$	2.13506e6	0.195194
$655$	−7.48581e6	−0.681766
$656$	4.66110e6	0.422891
$657$	4.29157e6	0.387885
$658$	0	0
$659$	−1.05477e7	−0.946119	−0.473060	−	0.881030i	$-0.656850\pi$
$659$	−1.05477e7	−0.946119	−0.473060	+	0.881030i	$0.656850\pi$
$660$	3.57972e6	0.319881
$661$	1.22044e7	1.08646	0.543229	−	0.839585i	$-0.317202\pi$
$661$	1.22044e7	1.08646	0.543229	+	0.839585i	$0.317202\pi$
$662$	−4.01232e6	−0.355837
$663$	9.37527e6	0.828323
$664$	7.24231e6	0.637466
$665$	0	0
$666$	2.94143e6	0.256964
$667$	4.66036e6	0.405607
$668$	−621548.	−0.0538931
$669$	−2.51535e6	−0.217287
$670$	1.49365e7	1.28547
$671$	−2.71994e6	−0.233213
$672$	0	0
$673$	−7.97959e6	−0.679114	−0.339557	−	0.940585i	$-0.610277\pi$
$673$	−7.97959e6	−0.679114	−0.339557	+	0.940585i	$0.610277\pi$
$674$	1.04927e7	0.889686
$675$	−5.53072e6	−0.467221
$676$	4.44001e6	0.373695
$677$	−5.08381e6	−0.426302	−0.213151	−	0.977019i	$-0.568373\pi$
$677$	−5.08381e6	−0.426302	−0.213151	+	0.977019i	$0.568373\pi$
$678$	5.66164e6	0.473007
$679$	0	0
$680$	8.56639e6	0.710437
$681$	−1.10116e7	−0.909874
$682$	5.40416e6	0.444905
$683$	−1.60331e7	−1.31512	−0.657559	−	0.753403i	$-0.728411\pi$
$683$	−1.60331e7	−1.31512	−0.657559	+	0.753403i	$0.728411\pi$
$684$	356888.	0.0291670
$685$	−2.33554e7	−1.90179
$686$	0	0
$687$	2.29297e6	0.185356
$688$	−2.99730e6	−0.241412
$689$	−1.42270e7	−1.14173
$690$	−1.41457e7	−1.13110
$691$	1.10131e7	0.877438	0.438719	−	0.898624i	$-0.355432\pi$
$691$	1.10131e7	0.877438	0.438719	+	0.898624i	$0.355432\pi$
$692$	−6.34044e6	−0.503331
$693$	0	0
$694$	−904935.	−0.0713212
$695$	−3.39442e7	−2.66565
$696$	707050.	0.0553258
$697$	2.35470e7	1.83592
$698$	−5.85119e6	−0.454575
$699$	−6.71555e6	−0.519863
$700$	0	0
$701$	−3.10660e6	−0.238776	−0.119388	−	0.992848i	$-0.538093\pi$
$701$	−3.10660e6	−0.238776	−0.119388	+	0.992848i	$0.538093\pi$
$702$	−2.34877e6	−0.179886
$703$	−2.50001e6	−0.190789
$704$	983822.	0.0748143
$705$	2.14692e7	1.62684
$706$	1.12383e7	0.848571
$707$	0	0
$708$	2.64619e6	0.198398
$709$	−1.38036e7	−1.03128	−0.515640	−	0.856805i	$-0.672446\pi$
$709$	−1.38036e7	−1.03128	−0.515640	+	0.856805i	$0.672446\pi$
$710$	−2.62611e7	−1.95509
$711$	−3.93369e6	−0.291827
$712$	6.93542e6	0.512711
$713$	−2.13552e7	−1.57319
$714$	0	0
$715$	2.00235e7	1.46479
$716$	3.90214e6	0.284459
$717$	−2.88933e6	−0.209893
$718$	1.47960e7	1.07111
$719$	1.29855e7	0.936777	0.468389	−	0.883523i	$-0.344835\pi$
$719$	1.29855e7	0.936777	0.468389	+	0.883523i	$0.344835\pi$
$720$	−2.14612e6	−0.154285
$721$	0	0
$722$	9.60107e6	0.685451
$723$	1.11828e7	0.795620
$724$	4.78837e6	0.339501
$725$	9.31285e6	0.658017
$726$	−3.72094e6	−0.262006
$727$	8.61224e6	0.604338	0.302169	−	0.953254i	$-0.402289\pi$
$727$	8.61224e6	0.604338	0.302169	+	0.953254i	$0.402289\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	2.19342e7	1.52340
$731$	−1.51418e7	−1.04806
$732$	1.63067e6	0.112483
$733$	−6.02001e6	−0.413844	−0.206922	−	0.978357i	$-0.566345\pi$
$733$	−6.02001e6	−0.413844	−0.206922	+	0.978357i	$0.566345\pi$
$734$	4.67698e6	0.320424
$735$	0	0
$736$	−3.88769e6	−0.264544
$737$	8.66593e6	0.587688
$738$	−5.89920e6	−0.398706
$739$	−93692.5	−0.00631094	−0.00315547	−	0.999995i	$-0.501004\pi$
$739$	−93692.5	−0.00631094	−0.00315547	+	0.999995i	$0.501004\pi$
$740$	1.50336e7	1.00922
$741$	1.99629e6	0.133560
$742$	0	0
$743$	−1.29874e7	−0.863081	−0.431541	−	0.902094i	$-0.642030\pi$
$743$	−1.29874e7	−0.863081	−0.431541	+	0.902094i	$0.642030\pi$
$744$	−3.23992e6	−0.214586
$745$	−1.69747e7	−1.12050
$746$	1.83076e7	1.20444
$747$	−9.16605e6	−0.601008
$748$	4.97009e6	0.324796
$749$	0	0
$750$	−1.66240e7	−1.07915
$751$	−637441.	−0.0412420	−0.0206210	−	0.999787i	$-0.506564\pi$
$751$	−637441.	−0.0412420	−0.0206210	+	0.999787i	$0.506564\pi$
$752$	5.90044e6	0.380487
$753$	6.21211e6	0.399256
$754$	3.95495e6	0.253345
$755$	−6.44880e6	−0.411729
$756$	0	0
$757$	−4.86768e6	−0.308732	−0.154366	−	0.988014i	$-0.549334\pi$
$757$	−4.86768e6	−0.308732	−0.154366	+	0.988014i	$0.549334\pi$
$758$	9.42081e6	0.595546
$759$	−8.20712e6	−0.517114
$760$	1.82405e6	0.114552
$761$	−5.81787e6	−0.364169	−0.182084	−	0.983283i	$-0.558284\pi$
$761$	−5.81787e6	−0.364169	−0.182084	+	0.983283i	$0.558284\pi$
$762$	−3.32918e6	−0.207706
$763$	0	0
$764$	−1.24319e7	−0.770558
$765$	−1.08418e7	−0.669806
$766$	1.21578e7	0.748659
$767$	1.48017e7	0.908496
$768$	−589824.	−0.0360844
$769$	−1.94310e7	−1.18490	−0.592448	−	0.805609i	$-0.701839\pi$
$769$	−1.94310e7	−1.18490	−0.592448	+	0.805609i	$0.701839\pi$
$770$	0	0
$771$	124080.	0.00751738
$772$	4.42274e6	0.267084
$773$	−8.24179e6	−0.496104	−0.248052	−	0.968747i	$-0.579790\pi$
$773$	−8.24179e6	−0.496104	−0.248052	+	0.968747i	$0.579790\pi$
$774$	3.79346e6	0.227606
$775$	−4.26743e7	−2.55219
$776$	6.37704e6	0.380159
$777$	0	0
$778$	1.83709e6	0.108813
$779$	5.01390e6	0.296027
$780$	−1.20045e7	−0.706495
$781$	−1.52363e7	−0.893826
$782$	−1.96399e7	−1.14848
$783$	−894861.	−0.0521616
$784$	0	0
$785$	−2.48194e7	−1.43753
$786$	2.60382e6	0.150333
$787$	1.47863e7	0.850986	0.425493	−	0.904962i	$-0.360101\pi$
$787$	1.47863e7	0.850986	0.425493	+	0.904962i	$0.360101\pi$
$788$	−2.10585e6	−0.120812
$789$	−5.17350e6	−0.295864
$790$	−2.01050e7	−1.14614
$791$	0	0
$792$	−1.24515e6	−0.0705356
$793$	9.12129e6	0.515079
$794$	2.17000e7	1.22154
$795$	1.64525e7	0.923239
$796$	−9.03937e6	−0.505656
$797$	1.58158e7	0.881956	0.440978	−	0.897518i	$-0.354632\pi$
$797$	1.58158e7	0.881956	0.440978	+	0.897518i	$0.354632\pi$
$798$	0	0
$799$	2.98080e7	1.65183
$800$	−7.76881e6	−0.429170
$801$	−8.77764e6	−0.483389
$802$	−8.44508e6	−0.463626
$803$	1.27259e7	0.696465
$804$	−5.19543e6	−0.283453
$805$	0	0
$806$	−1.81228e7	−0.982625
$807$	−1.00704e7	−0.544328
$808$	1.05728e7	0.569720
$809$	1.19304e7	0.640888	0.320444	−	0.947267i	$-0.396168\pi$
$809$	1.19304e7	0.640888	0.320444	+	0.947267i	$0.396168\pi$
$810$	2.71619e6	0.145461
$811$	−1.89393e7	−1.01114	−0.505571	−	0.862785i	$-0.668718\pi$
$811$	−1.89393e7	−1.01114	−0.505571	+	0.862785i	$0.668718\pi$
$812$	0	0
$813$	6.25382e6	0.331833
$814$	8.72228e6	0.461391
$815$	4.52071e7	2.38404
$816$	−2.97969e6	−0.156655
$817$	−3.22417e6	−0.168991
$818$	1.02298e7	0.534544
$819$	0	0
$820$	−3.01507e7	−1.56590
$821$	3.20087e7	1.65733	0.828667	−	0.559741i	$-0.189100\pi$
$821$	3.20087e7	1.65733	0.828667	+	0.559741i	$0.189100\pi$
$822$	8.12383e6	0.419354
$823$	3.61430e7	1.86005	0.930025	−	0.367495i	$-0.119785\pi$
$823$	3.61430e7	1.86005	0.930025	+	0.367495i	$0.119785\pi$
$824$	−6.86382e6	−0.352166
$825$	−1.64004e7	−0.838916
$826$	0	0
$827$	−2.45831e7	−1.24989	−0.624946	−	0.780668i	$-0.714879\pi$
$827$	−2.45831e7	−1.24989	−0.624946	+	0.780668i	$0.714879\pi$
$828$	4.92036e6	0.249414
$829$	−2.10424e7	−1.06343	−0.531715	−	0.846923i	$-0.678452\pi$
$829$	−2.10424e7	−1.06343	−0.531715	+	0.846923i	$0.678452\pi$
$830$	−4.68475e7	−2.36043
$831$	7.53888e6	0.378708
$832$	−3.29923e6	−0.165236
$833$	0	0
$834$	1.18070e7	0.587791
$835$	4.02054e6	0.199557
$836$	1.05829e6	0.0523707
$837$	4.10053e6	0.202314
$838$	8.69604e6	0.427771
$839$	−1.12403e7	−0.551283	−0.275642	−	0.961260i	$-0.588890\pi$
$839$	−1.12403e7	−0.551283	−0.275642	+	0.961260i	$0.588890\pi$
$840$	0	0
$841$	−1.90043e7	−0.926537
$842$	2.19172e7	1.06538
$843$	8.25918e6	0.400284
$844$	5.01820e6	0.242489
$845$	−2.87206e7	−1.38373
$846$	−7.46775e6	−0.358727
$847$	0	0
$848$	4.52168e6	0.215928
$849$	−3.73737e6	−0.177950
$850$	−3.92466e7	−1.86318
$851$	−3.44672e7	−1.63148
$852$	9.13453e6	0.431109
$853$	2.63779e7	1.24127	0.620636	−	0.784099i	$-0.286874\pi$
$853$	2.63779e7	1.24127	0.620636	+	0.784099i	$0.286874\pi$
$854$	0	0
$855$	−2.30856e6	−0.108001
$856$	6.23503e6	0.290840
$857$	−4.26663e7	−1.98442	−0.992208	−	0.124595i	$-0.960237\pi$
$857$	−4.26663e7	−1.98442	−0.992208	+	0.124595i	$0.960237\pi$
$858$	−6.96486e6	−0.322994
$859$	−2.92617e7	−1.35306	−0.676530	−	0.736415i	$-0.736517\pi$
$859$	−2.92617e7	−1.35306	−0.676530	+	0.736415i	$0.736517\pi$
$860$	1.93883e7	0.893911
$861$	0	0
$862$	2.46750e7	1.13107
$863$	1.39448e7	0.637359	0.318680	−	0.947862i	$-0.396761\pi$
$863$	1.39448e7	0.637359	0.318680	+	0.947862i	$0.396761\pi$
$864$	746496.	0.0340207
$865$	4.10137e7	1.86375
$866$	1.95838e7	0.887366
$867$	−2.27412e6	−0.102746
$868$	0	0
$869$	−1.16646e7	−0.523988
$870$	−4.57362e6	−0.204862
$871$	−2.90611e7	−1.29798
$872$	−3.79566e6	−0.169043
$873$	−8.07094e6	−0.358417
$874$	−4.18195e6	−0.185183
$875$	0	0
$876$	−7.62946e6	−0.335918
$877$	3.40772e6	0.149611	0.0748057	−	0.997198i	$-0.476166\pi$
$877$	3.40772e6	0.149611	0.0748057	+	0.997198i	$0.476166\pi$
$878$	−1.41835e7	−0.620937
$879$	−1.09342e7	−0.477325
$880$	−6.36394e6	−0.277025
$881$	3.51391e6	0.152528	0.0762641	−	0.997088i	$-0.475701\pi$
$881$	3.51391e6	0.152528	0.0762641	+	0.997088i	$0.475701\pi$
$882$	0	0
$883$	2.14895e7	0.927524	0.463762	−	0.885960i	$-0.346499\pi$
$883$	2.14895e7	0.927524	0.463762	+	0.885960i	$0.346499\pi$
$884$	−1.66671e7	−0.717349
$885$	−1.71171e7	−0.734636
$886$	−2.42261e7	−1.03681
$887$	−2.45357e7	−1.04710	−0.523550	−	0.851995i	$-0.675393\pi$
$887$	−2.45357e7	−1.04710	−0.523550	+	0.851995i	$0.675393\pi$
$888$	−5.22921e6	−0.222538
$889$	0	0
$890$	−4.48624e7	−1.89849
$891$	1.57589e6	0.0665016
$892$	4.47173e6	0.188176
$893$	6.34705e6	0.266344
$894$	5.90439e6	0.247076
$895$	−2.52413e7	−1.05331
$896$	0	0
$897$	2.75225e7	1.14211
$898$	4.83203e6	0.199958
$899$	−6.90462e6	−0.284932
$900$	9.83240e6	0.404625
$901$	2.28427e7	0.937423
$902$	−1.74930e7	−0.715894
$903$	0	0
$904$	−1.00651e7	−0.409636
$905$	−3.09740e7	−1.25712
$906$	2.24312e6	0.0907886
$907$	−8.14146e6	−0.328613	−0.164306	−	0.986409i	$-0.552539\pi$
$907$	−8.14146e6	−0.328613	−0.164306	+	0.986409i	$0.552539\pi$
$908$	1.95761e7	0.787974
$909$	−1.33812e7	−0.537137
$910$	0	0
$911$	1.01384e7	0.404739	0.202370	−	0.979309i	$-0.435136\pi$
$911$	1.01384e7	0.404739	0.202370	+	0.979309i	$0.435136\pi$
$912$	−634468.	−0.0252594
$913$	−2.71803e7	−1.07914
$914$	2.18620e7	0.865615
$915$	−1.05481e7	−0.416507
$916$	−4.07639e6	−0.160523
$917$	0	0
$918$	3.77116e6	0.147696
$919$	−1.01176e7	−0.395175	−0.197587	−	0.980285i	$-0.563311\pi$
$919$	−1.01176e7	−0.395175	−0.197587	+	0.980285i	$0.563311\pi$
$920$	2.51479e7	0.979562
$921$	−2.34108e7	−0.909424
$922$	4.63824e6	0.179691
$923$	5.10948e7	1.97412
$924$	0	0
$925$	−6.88760e7	−2.64676
$926$	1.72534e7	0.661221
$927$	8.68702e6	0.332026
$928$	−1.25698e6	−0.0479135
$929$	−2.05111e7	−0.779739	−0.389870	−	0.920870i	$-0.627480\pi$
$929$	−2.05111e7	−0.779739	−0.389870	+	0.920870i	$0.627480\pi$
$930$	2.09577e7	0.794579
$931$	0	0
$932$	1.19388e7	0.450215
$933$	−7.37248e6	−0.277274
$934$	−2.39569e7	−0.898595
$935$	−3.21495e7	−1.20267
$936$	4.17559e6	0.155786
$937$	1.46527e7	0.545218	0.272609	−	0.962125i	$-0.412114\pi$
$937$	1.46527e7	0.545218	0.272609	+	0.962125i	$0.412114\pi$
$938$	0	0
$939$	−7.93745e6	−0.293777
$940$	−3.81676e7	−1.40888
$941$	−2.59341e7	−0.954765	−0.477382	−	0.878696i	$-0.658414\pi$
$941$	−2.59341e7	−0.954765	−0.477382	+	0.878696i	$0.658414\pi$
$942$	8.63303e6	0.316983
$943$	6.91258e7	2.53140
$944$	−4.70433e6	−0.171818
$945$	0	0
$946$	1.12488e7	0.408676
$947$	1.04490e7	0.378615	0.189307	−	0.981918i	$-0.439376\pi$
$947$	1.04490e7	0.378615	0.189307	+	0.981918i	$0.439376\pi$
$948$	6.99322e6	0.252730
$949$	−4.26761e7	−1.53822
$950$	−8.35683e6	−0.300423
$951$	1.44394e7	0.517725
$952$	0	0
$953$	1.15666e6	0.0412548	0.0206274	−	0.999787i	$-0.493434\pi$
$953$	1.15666e6	0.0412548	0.0206274	+	0.999787i	$0.493434\pi$
$954$	−5.72275e6	−0.203579
$955$	8.04172e7	2.85325
$956$	5.13658e6	0.181773
$957$	−2.65355e6	−0.0936585
$958$	1.41861e7	0.499400
$959$	0	0
$960$	3.81533e6	0.133615
$961$	3.00994e6	0.105135
$962$	−2.92501e7	−1.01904
$963$	−7.89121e6	−0.274207
$964$	−1.98806e7	−0.689027
$965$	−2.86089e7	−0.988969
$966$	0	0
$967$	2.00516e7	0.689577	0.344789	−	0.938680i	$-0.387951\pi$
$967$	2.00516e7	0.689577	0.344789	+	0.938680i	$0.387951\pi$
$968$	6.61500e6	0.226904
$969$	−3.20522e6	−0.109660
$970$	−4.12505e7	−1.40767
$971$	−6.10209e6	−0.207697	−0.103849	−	0.994593i	$-0.533116\pi$
$971$	−6.10209e6	−0.207697	−0.103849	+	0.994593i	$0.533116\pi$
$972$	−944784.	−0.0320750
$973$	0	0
$974$	3.51328e7	1.18663
$975$	5.49984e7	1.85284
$976$	−2.89897e6	−0.0974134
$977$	1.36743e7	0.458320	0.229160	−	0.973389i	$-0.426402\pi$
$977$	1.36743e7	0.458320	0.229160	+	0.973389i	$0.426402\pi$
$978$	−1.57246e7	−0.525694
$979$	−2.60285e7	−0.867945
$980$	0	0
$981$	4.80388e6	0.159375
$982$	2.34643e6	0.0776478
$983$	1.67033e7	0.551338	0.275669	−	0.961253i	$-0.411101\pi$
$983$	1.67033e7	0.551338	0.275669	+	0.961253i	$0.411101\pi$
$984$	1.04875e7	0.345289
$985$	1.36219e7	0.447348
$986$	−6.35003e6	−0.208010
$987$	0	0
$988$	−3.54896e6	−0.115667
$989$	−4.44511e7	−1.44508
$990$	8.05437e6	0.261182
$991$	5.74906e7	1.85957	0.929785	−	0.368102i	$-0.119992\pi$
$991$	5.74906e7	1.85957	0.929785	+	0.368102i	$0.119992\pi$
$992$	5.75986e6	0.185837
$993$	−9.02772e6	−0.290539
$994$	0	0
$995$	5.84720e7	1.87236
$996$	1.62952e7	0.520489
$997$	−3.94489e7	−1.25689	−0.628444	−	0.777855i	$-0.716308\pi$
$997$	−3.94489e7	−1.25689	−0.628444	+	0.777855i	$0.716308\pi$
$998$	3.83909e7	1.22012
$999$	6.61822e6	0.209811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.a.n.1.1	✓	2
3.2	odd	2		882.6.a.bu.1.2		2
7.2	even	3		294.6.e.z.67.2		4
7.3	odd	6		294.6.e.x.79.1		4
7.4	even	3		294.6.e.z.79.2		4
7.5	odd	6		294.6.e.x.67.1		4
7.6	odd	2		294.6.a.q.1.2	yes	2
21.20	even	2		882.6.a.bk.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.6.a.n.1.1	✓	2	1.1	even	1	trivial
294.6.a.q.1.2	yes	2	7.6	odd	2
294.6.e.x.67.1		4	7.5	odd	6
294.6.e.x.79.1		4	7.3	odd	6
294.6.e.z.67.2		4	7.2	even	3
294.6.e.z.79.2		4	7.4	even	3
882.6.a.bk.1.1		2	21.20	even	2
882.6.a.bu.1.2		2	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -103.497 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -103.497 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +413.990 q^{10} +240.191 q^{11} -144.000 q^{12} -805.477 q^{13} +931.477 q^{15} +256.000 q^{16} +1293.27 q^{17} -324.000 q^{18} +275.377 q^{19} -1655.96 q^{20} -960.764 q^{22} +3796.57 q^{23} +576.000 q^{24} +7586.73 q^{25} +3221.91 q^{26} -729.000 q^{27} +1227.52 q^{29} -3725.91 q^{30} -5624.86 q^{31} -1024.00 q^{32} -2161.72 q^{33} -5173.06 q^{34} +1296.00 q^{36} -9078.49 q^{37} -1101.51 q^{38} +7249.30 q^{39} +6623.84 q^{40} +18207.4 q^{41} -11708.2 q^{43} +3843.05 q^{44} -8383.30 q^{45} -15186.3 q^{46} +23048.6 q^{47} -2304.00 q^{48} -30346.9 q^{50} -11639.4 q^{51} -12887.6 q^{52} +17662.8 q^{53} +2916.00 q^{54} -24859.2 q^{55} -2478.39 q^{57} -4910.07 q^{58} -18376.3 q^{59} +14903.6 q^{60} -11324.1 q^{61} +22499.5 q^{62} +4096.00 q^{64} +83364.9 q^{65} +8646.87 q^{66} +36079.3 q^{67} +20692.3 q^{68} -34169.2 q^{69} -63434.2 q^{71} -5184.00 q^{72} +52982.4 q^{73} +36314.0 q^{74} -68280.5 q^{75} +4406.03 q^{76} -28997.2 q^{78} -48564.0 q^{79} -26495.4 q^{80} +6561.00 q^{81} -72829.7 q^{82} -113161. q^{83} -133850. q^{85} +46832.9 q^{86} -11047.7 q^{87} -15372.2 q^{88} -108366. q^{89} +33533.2 q^{90} +60745.2 q^{92} +50623.8 q^{93} -92194.4 q^{94} -28500.8 q^{95} +9216.00 q^{96} -99641.2 q^{97} +19455.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 720 q^{13} + 972 q^{15} + 512 q^{16} + 1260 q^{17} - 648 q^{18} - 360 q^{19} - 1728 q^{20} - 496 q^{22} + 6524 q^{23} + 1152 q^{24} + 4482 q^{25} + 2880 q^{26} - 1458 q^{27} + 7088 q^{29} - 3888 q^{30} - 5904 q^{31} - 2048 q^{32} - 1116 q^{33} - 5040 q^{34} + 2592 q^{36} - 6040 q^{37} + 1440 q^{38} + 6480 q^{39} + 6912 q^{40} + 17388 q^{41} - 608 q^{43} + 1984 q^{44} - 8748 q^{45} - 26096 q^{46} + 30456 q^{47} - 4608 q^{48} - 17928 q^{50} - 11340 q^{51} - 11520 q^{52} + 3964 q^{53} + 5832 q^{54} - 24336 q^{55} + 3240 q^{57} - 28352 q^{58} - 40752 q^{59} + 15552 q^{60} + 1368 q^{61} + 23616 q^{62} + 8192 q^{64} + 82980 q^{65} + 4464 q^{66} - 16224 q^{67} + 20160 q^{68} - 58716 q^{69} - 3204 q^{71} - 10368 q^{72} - 23976 q^{73} + 24160 q^{74} - 40338 q^{75} - 5760 q^{76} - 25920 q^{78} - 82160 q^{79} - 27648 q^{80} + 13122 q^{81} - 69552 q^{82} - 173736 q^{83} - 133700 q^{85} + 2432 q^{86} - 63792 q^{87} - 7936 q^{88} - 200556 q^{89} + 34992 q^{90} + 104384 q^{92} + 53136 q^{93} - 121824 q^{94} - 25640 q^{95} + 18432 q^{96} - 251928 q^{97} + 10044 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 720 * q^13 + 972 * q^15 + 512 * q^16 + 1260 * q^17 - 648 * q^18 - 360 * q^19 - 1728 * q^20 - 496 * q^22 + 6524 * q^23 + 1152 * q^24 + 4482 * q^25 + 2880 * q^26 - 1458 * q^27 + 7088 * q^29 - 3888 * q^30 - 5904 * q^31 - 2048 * q^32 - 1116 * q^33 - 5040 * q^34 + 2592 * q^36 - 6040 * q^37 + 1440 * q^38 + 6480 * q^39 + 6912 * q^40 + 17388 * q^41 - 608 * q^43 + 1984 * q^44 - 8748 * q^45 - 26096 * q^46 + 30456 * q^47 - 4608 * q^48 - 17928 * q^50 - 11340 * q^51 - 11520 * q^52 + 3964 * q^53 + 5832 * q^54 - 24336 * q^55 + 3240 * q^57 - 28352 * q^58 - 40752 * q^59 + 15552 * q^60 + 1368 * q^61 + 23616 * q^62 + 8192 * q^64 + 82980 * q^65 + 4464 * q^66 - 16224 * q^67 + 20160 * q^68 - 58716 * q^69 - 3204 * q^71 - 10368 * q^72 - 23976 * q^73 + 24160 * q^74 - 40338 * q^75 - 5760 * q^76 - 25920 * q^78 - 82160 * q^79 - 27648 * q^80 + 13122 * q^81 - 69552 * q^82 - 173736 * q^83 - 133700 * q^85 + 2432 * q^86 - 63792 * q^87 - 7936 * q^88 - 200556 * q^89 + 34992 * q^90 + 104384 * q^92 + 53136 * q^93 - 121824 * q^94 - 25640 * q^95 + 18432 * q^96 - 251928 * q^97 + 10044 * q^99

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