LMFDB - Embedded newform 294.6.a.u.1.2

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:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -46.9289 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -46.9289 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} -187.716 q^{10} -87.4558 q^{11} +144.000 q^{12} -754.566 q^{13} -422.360 q^{15} +256.000 q^{16} +1449.04 q^{17} +324.000 q^{18} -2540.24 q^{19} -750.863 q^{20} -349.823 q^{22} -912.248 q^{23} +576.000 q^{24} -922.675 q^{25} -3018.26 q^{26} +729.000 q^{27} +173.217 q^{29} -1689.44 q^{30} -4531.13 q^{31} +1024.00 q^{32} -787.103 q^{33} +5796.16 q^{34} +1296.00 q^{36} +6829.96 q^{37} -10161.0 q^{38} -6791.09 q^{39} -3003.45 q^{40} -13069.3 q^{41} -12277.7 q^{43} -1399.29 q^{44} -3801.24 q^{45} -3648.99 q^{46} -13492.8 q^{47} +2304.00 q^{48} -3690.70 q^{50} +13041.4 q^{51} -12073.0 q^{52} -9677.70 q^{53} +2916.00 q^{54} +4104.21 q^{55} -22862.1 q^{57} +692.868 q^{58} -30369.2 q^{59} -6757.77 q^{60} -732.473 q^{61} -18124.5 q^{62} +4096.00 q^{64} +35411.0 q^{65} -3148.41 q^{66} +46399.9 q^{67} +23184.6 q^{68} -8210.23 q^{69} -3295.39 q^{71} +5184.00 q^{72} -10238.2 q^{73} +27319.8 q^{74} -8304.08 q^{75} -40643.8 q^{76} -27164.4 q^{78} +98584.0 q^{79} -12013.8 q^{80} +6561.00 q^{81} -52277.1 q^{82} -87792.7 q^{83} -68001.9 q^{85} -49110.8 q^{86} +1558.95 q^{87} -5597.17 q^{88} +69099.8 q^{89} -15205.0 q^{90} -14596.0 q^{92} -40780.2 q^{93} -53971.2 q^{94} +119211. q^{95} +9216.00 q^{96} +42181.4 q^{97} -7083.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 2 q + 8 q^{2} + 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} + 128 q^{8} + 162 q^{9} - 432 q^{10} - 124 q^{11} + 288 q^{12} - 720 q^{13} - 972 q^{15} + 512 q^{16} - 612 q^{17} + 648 q^{18} - 2088 q^{19} - 1728 q^{20} - 496 q^{22} + 772 q^{23} + 1152 q^{24} - 318 q^{25} - 2880 q^{26} + 1458 q^{27} - 4592 q^{29} - 3888 q^{30} - 9792 q^{31} + 2048 q^{32} - 1116 q^{33} - 2448 q^{34} + 2592 q^{36} - 5992 q^{37} - 8352 q^{38} - 6480 q^{39} - 6912 q^{40} - 20196 q^{41} - 1136 q^{43} - 1984 q^{44} - 8748 q^{45} + 3088 q^{46} - 36936 q^{47} + 4608 q^{48} - 1272 q^{50} - 5508 q^{51} - 11520 q^{52} - 16708 q^{53} + 5832 q^{54} + 6336 q^{55} - 18792 q^{57} - 18368 q^{58} - 74592 q^{59} - 15552 q^{60} + 18648 q^{61} - 39168 q^{62} + 8192 q^{64} + 33300 q^{65} - 4464 q^{66} + 67344 q^{67} - 9792 q^{68} + 6948 q^{69} + 76548 q^{71} + 10368 q^{72} - 47304 q^{73} - 23968 q^{74} - 2862 q^{75} - 33408 q^{76} - 25920 q^{78} + 140656 q^{79} - 27648 q^{80} + 13122 q^{81} - 80784 q^{82} - 94104 q^{83} + 57868 q^{85} - 4544 q^{86} - 41328 q^{87} - 7936 q^{88} + 17604 q^{89} - 34992 q^{90} + 12352 q^{92} - 88128 q^{93} - 147744 q^{94} + 91592 q^{95} + 18432 q^{96} - 85176 q^{97} - 10044 q^{99}+O(q^{100}) \) 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 - 612 * q^17 + 648 * q^18 - 2088 * q^19 - 1728 * q^20 - 496 * q^22 + 772 * q^23 + 1152 * q^24 - 318 * q^25 - 2880 * q^26 + 1458 * q^27 - 4592 * q^29 - 3888 * q^30 - 9792 * q^31 + 2048 * q^32 - 1116 * q^33 - 2448 * q^34 + 2592 * q^36 - 5992 * q^37 - 8352 * q^38 - 6480 * q^39 - 6912 * q^40 - 20196 * q^41 - 1136 * q^43 - 1984 * q^44 - 8748 * q^45 + 3088 * q^46 - 36936 * q^47 + 4608 * q^48 - 1272 * q^50 - 5508 * q^51 - 11520 * q^52 - 16708 * q^53 + 5832 * q^54 + 6336 * q^55 - 18792 * q^57 - 18368 * q^58 - 74592 * q^59 - 15552 * q^60 + 18648 * q^61 - 39168 * q^62 + 8192 * q^64 + 33300 * q^65 - 4464 * q^66 + 67344 * q^67 - 9792 * q^68 + 6948 * q^69 + 76548 * q^71 + 10368 * q^72 - 47304 * q^73 - 23968 * q^74 - 2862 * q^75 - 33408 * q^76 - 25920 * q^78 + 140656 * q^79 - 27648 * q^80 + 13122 * q^81 - 80784 * q^82 - 94104 * q^83 + 57868 * q^85 - 4544 * q^86 - 41328 * q^87 - 7936 * q^88 + 17604 * q^89 - 34992 * q^90 + 12352 * q^92 - 88128 * q^93 - 147744 * q^94 + 91592 * q^95 + 18432 * q^96 - 85176 * 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
$5$	−46.9289	−0.839490	−0.419745	−	0.907642i	$-0.637881\pi$
$5$	−46.9289	−0.839490	−0.419745	+	0.907642i	$0.637881\pi$
$6$	36.0000	0.408248
$7$	0	0
$7$	0	0
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−187.716	−0.593609
$11$	−87.4558	−0.217925	−0.108963	−	0.994046i	$-0.534753\pi$
$11$	−87.4558	−0.217925	−0.108963	+	0.994046i	$0.534753\pi$
$12$	144.000	0.288675
$13$	−754.566	−1.23834	−0.619168	−	0.785258i	$-0.712530\pi$
$13$	−754.566	−1.23834	−0.619168	+	0.785258i	$0.712530\pi$
$14$	0	0
$15$	−422.360	−0.484680
$16$	256.000	0.250000
$17$	1449.04	1.21607	0.608034	−	0.793911i	$-0.291958\pi$
$17$	1449.04	1.21607	0.608034	+	0.793911i	$0.291958\pi$
$18$	324.000	0.235702
$19$	−2540.24	−1.61432	−0.807161	−	0.590331i	$-0.798997\pi$
$19$	−2540.24	−1.61432	−0.807161	+	0.590331i	$0.798997\pi$
$20$	−750.863	−0.419745
$21$	0	0
$22$	−349.823	−0.154096
$23$	−912.248	−0.359578	−0.179789	−	0.983705i	$-0.557542\pi$
$23$	−912.248	−0.359578	−0.179789	+	0.983705i	$0.557542\pi$
$24$	576.000	0.204124
$25$	−922.675	−0.295256
$26$	−3018.26	−0.875636
$27$	729.000	0.192450
$28$	0	0
$29$	173.217	0.0382468	0.0191234	−	0.999817i	$-0.493912\pi$
$29$	173.217	0.0382468	0.0191234	+	0.999817i	$0.493912\pi$
$30$	−1689.44	−0.342720
$31$	−4531.13	−0.846842	−0.423421	−	0.905933i	$-0.639171\pi$
$31$	−4531.13	−0.846842	−0.423421	+	0.905933i	$0.639171\pi$
$32$	1024.00	0.176777
$33$	−787.103	−0.125819
$34$	5796.16	0.859890
$35$	0	0
$36$	1296.00	0.166667
$37$	6829.96	0.820188	0.410094	−	0.912043i	$-0.365496\pi$
$37$	6829.96	0.820188	0.410094	+	0.912043i	$0.365496\pi$
$38$	−10161.0	−1.14150
$39$	−6791.09	−0.714954
$40$	−3003.45	−0.296805
$41$	−13069.3	−1.21420	−0.607102	−	0.794624i	$-0.707668\pi$
$41$	−13069.3	−1.21420	−0.607102	+	0.794624i	$0.707668\pi$
$42$	0	0
$43$	−12277.7	−1.01262	−0.506309	−	0.862352i	$-0.668990\pi$
$43$	−12277.7	−1.01262	−0.506309	+	0.862352i	$0.668990\pi$
$44$	−1399.29	−0.108963
$45$	−3801.24	−0.279830
$46$	−3648.99	−0.254260
$47$	−13492.8	−0.890958	−0.445479	−	0.895292i	$-0.646967\pi$
$47$	−13492.8	−0.890958	−0.445479	+	0.895292i	$0.646967\pi$
$48$	2304.00	0.144338
$49$	0	0
$50$	−3690.70	−0.208778
$51$	13041.4	0.702097
$52$	−12073.0	−0.619168
$53$	−9677.70	−0.473241	−0.236621	−	0.971602i	$-0.576040\pi$
$53$	−9677.70	−0.473241	−0.236621	+	0.971602i	$0.576040\pi$
$54$	2916.00	0.136083
$55$	4104.21	0.182946
$56$	0	0
$57$	−22862.1	−0.932030
$58$	692.868	0.0270446
$59$	−30369.2	−1.13580	−0.567902	−	0.823096i	$-0.692245\pi$
$59$	−30369.2	−1.13580	−0.567902	+	0.823096i	$0.692245\pi$
$60$	−6757.77	−0.242340
$61$	−732.473	−0.0252038	−0.0126019	−	0.999921i	$-0.504011\pi$
$61$	−732.473	−0.0252038	−0.0126019	+	0.999921i	$0.504011\pi$
$62$	−18124.5	−0.598808
$63$	0	0
$64$	4096.00	0.125000
$65$	35411.0	1.03957
$66$	−3148.41	−0.0889675
$67$	46399.9	1.26279	0.631394	−	0.775462i	$-0.282483\pi$
$67$	46399.9	1.26279	0.631394	+	0.775462i	$0.282483\pi$
$68$	23184.6	0.608034
$69$	−8210.23	−0.207603
$70$	0	0
$71$	−3295.39	−0.0775821	−0.0387910	−	0.999247i	$-0.512351\pi$
$71$	−3295.39	−0.0775821	−0.0387910	+	0.999247i	$0.512351\pi$
$72$	5184.00	0.117851
$73$	−10238.2	−0.224862	−0.112431	−	0.993660i	$-0.535864\pi$
$73$	−10238.2	−0.224862	−0.112431	+	0.993660i	$0.535864\pi$
$74$	27319.8	0.579961
$75$	−8304.08	−0.170466
$76$	−40643.8	−0.807161
$77$	0	0
$78$	−27164.4	−0.505549
$79$	98584.0	1.77721	0.888605	−	0.458674i	$-0.151675\pi$
$79$	98584.0	1.77721	0.888605	+	0.458674i	$0.151675\pi$
$80$	−12013.8	−0.209873
$81$	6561.00	0.111111
$82$	−52277.1	−0.858571
$83$	−87792.7	−1.39882	−0.699412	−	0.714719i	$-0.746555\pi$
$83$	−87792.7	−1.39882	−0.699412	+	0.714719i	$0.746555\pi$
$84$	0	0
$85$	−68001.9	−1.02088
$86$	−49110.8	−0.716029
$87$	1558.95	0.0220818
$88$	−5597.17	−0.0770481
$89$	69099.8	0.924702	0.462351	−	0.886697i	$-0.347006\pi$
$89$	69099.8	0.924702	0.462351	+	0.886697i	$0.347006\pi$
$90$	−15205.0	−0.197870
$91$	0	0
$92$	−14596.0	−0.179789
$93$	−40780.2	−0.488925
$94$	−53971.2	−0.630003
$95$	119211.	1.35521
$96$	9216.00	0.102062
$97$	42181.4	0.455189	0.227594	−	0.973756i	$-0.426914\pi$
$97$	42181.4	0.455189	0.227594	+	0.973756i	$0.426914\pi$
$98$	0	0
$99$	−7083.92	−0.0726417
$100$	−14762.8	−0.147628
$101$	−178474.	−1.74089	−0.870445	−	0.492266i	$-0.836169\pi$
$101$	−178474.	−1.74089	−0.870445	+	0.492266i	$0.836169\pi$
$102$	52165.4	0.496458
$103$	−35226.2	−0.327169	−0.163585	−	0.986529i	$-0.552306\pi$
$103$	−35226.2	−0.327169	−0.163585	+	0.986529i	$0.552306\pi$
$104$	−48292.2	−0.437818
$105$	0	0
$106$	−38710.8	−0.334632
$107$	89960.9	0.759616	0.379808	−	0.925065i	$-0.375990\pi$
$107$	89960.9	0.759616	0.379808	+	0.925065i	$0.375990\pi$
$108$	11664.0	0.0962250
$109$	185002.	1.49146	0.745729	−	0.666249i	$-0.232101\pi$
$109$	185002.	1.49146	0.745729	+	0.666249i	$0.232101\pi$
$110$	16416.8	0.129362
$111$	61469.6	0.473536
$112$	0	0
$113$	−228275.	−1.68175	−0.840877	−	0.541227i	$-0.817960\pi$
$113$	−228275.	−1.68175	−0.840877	+	0.541227i	$0.817960\pi$
$114$	−91448.6	−0.659045
$115$	42810.8	0.301862
$116$	2771.47	0.0191234
$117$	−61119.8	−0.412779
$118$	−121477.	−0.803134
$119$	0	0
$120$	−27031.1	−0.171360
$121$	−153402.	−0.952509
$122$	−2929.89	−0.0178218
$123$	−117623.	−0.701021
$124$	−72498.1	−0.423421
$125$	189953.	1.08735
$126$	0	0
$127$	−343515.	−1.88989	−0.944944	−	0.327232i	$-0.893884\pi$
$127$	−343515.	−1.88989	−0.944944	+	0.327232i	$0.893884\pi$
$128$	16384.0	0.0883883
$129$	−110499.	−0.584635
$130$	141644.	0.735088
$131$	361272.	1.83931	0.919657	−	0.392722i	$-0.128467\pi$
$131$	361272.	1.83931	0.919657	+	0.392722i	$0.128467\pi$
$132$	−12593.6	−0.0629095
$133$	0	0
$134$	185600.	0.892926
$135$	−34211.2	−0.161560
$136$	92738.5	0.429945
$137$	−304627.	−1.38665	−0.693325	−	0.720625i	$-0.743855\pi$
$137$	−304627.	−1.38665	−0.693325	+	0.720625i	$0.743855\pi$
$138$	−32840.9	−0.146797
$139$	−129737.	−0.569543	−0.284772	−	0.958595i	$-0.591918\pi$
$139$	−129737.	−0.569543	−0.284772	+	0.958595i	$0.591918\pi$
$140$	0	0
$141$	−121435.	−0.514395
$142$	−13181.6	−0.0548588
$143$	65991.2	0.269864
$144$	20736.0	0.0833333
$145$	−8128.88	−0.0321078
$146$	−40952.7	−0.159001
$147$	0	0
$148$	109279.	0.410094
$149$	373908.	1.37975	0.689873	−	0.723931i	$-0.257667\pi$
$149$	373908.	1.37975	0.689873	+	0.723931i	$0.257667\pi$
$150$	−33216.3	−0.120538
$151$	−86639.8	−0.309225	−0.154613	−	0.987975i	$-0.549413\pi$
$151$	−86639.8	−0.309225	−0.154613	+	0.987975i	$0.549413\pi$
$152$	−162575.	−0.570749
$153$	117372.	0.405356
$154$	0	0
$155$	212641.	0.710916
$156$	−108657.	−0.357477
$157$	462173.	1.49643	0.748214	−	0.663458i	$-0.230912\pi$
$157$	462173.	1.49643	0.748214	+	0.663458i	$0.230912\pi$
$158$	394336.	1.25668
$159$	−87099.3	−0.273226
$160$	−48055.2	−0.148402
$161$	0	0
$162$	26244.0	0.0785674
$163$	609032.	1.79544	0.897721	−	0.440565i	$-0.145222\pi$
$163$	609032.	1.79544	0.897721	+	0.440565i	$0.145222\pi$
$164$	−209108.	−0.607102
$165$	36937.9	0.105624
$166$	−351171.	−0.989118
$167$	127786.	0.354562	0.177281	−	0.984160i	$-0.443270\pi$
$167$	127786.	0.354562	0.177281	+	0.984160i	$0.443270\pi$
$168$	0	0
$169$	198076.	0.533477
$170$	−272007.	−0.721869
$171$	−205759.	−0.538108
$172$	−196443.	−0.506309
$173$	142539.	0.362092	0.181046	−	0.983475i	$-0.442052\pi$
$173$	142539.	0.362092	0.181046	+	0.983475i	$0.442052\pi$
$174$	6235.81	0.0156142
$175$	0	0
$176$	−22388.7	−0.0544813
$177$	−273323.	−0.655756
$178$	276399.	0.653863
$179$	−296634.	−0.691973	−0.345986	−	0.938240i	$-0.612456\pi$
$179$	−296634.	−0.691973	−0.345986	+	0.938240i	$0.612456\pi$
$180$	−60819.9	−0.139915
$181$	277654.	0.629952	0.314976	−	0.949100i	$-0.398004\pi$
$181$	277654.	0.629952	0.314976	+	0.949100i	$0.398004\pi$
$182$	0	0
$183$	−6592.25	−0.0145514
$184$	−58383.9	−0.127130
$185$	−320523.	−0.688540
$186$	−163121.	−0.345722
$187$	−126727.	−0.265012
$188$	−215885.	−0.445479
$189$	0	0
$190$	476843.	0.958277
$191$	−242584.	−0.481149	−0.240574	−	0.970631i	$-0.577336\pi$
$191$	−242584.	−0.481149	−0.240574	+	0.970631i	$0.577336\pi$
$192$	36864.0	0.0721688
$193$	−581525.	−1.12376	−0.561882	−	0.827218i	$-0.689922\pi$
$193$	−581525.	−1.12376	−0.561882	+	0.827218i	$0.689922\pi$
$194$	168726.	0.321867
$195$	318699.	0.600197
$196$	0	0
$197$	748916.	1.37489	0.687444	−	0.726237i	$-0.258733\pi$
$197$	748916.	1.37489	0.687444	+	0.726237i	$0.258733\pi$
$198$	−28335.7	−0.0513654
$199$	725693.	1.29903	0.649516	−	0.760348i	$-0.274971\pi$
$199$	725693.	1.29903	0.649516	+	0.760348i	$0.274971\pi$
$200$	−59051.2	−0.104389
$201$	417599.	0.729071
$202$	−713896.	−1.23100
$203$	0	0
$204$	208662.	0.351049
$205$	613327.	1.01931
$206$	−140905.	−0.231343
$207$	−73892.1	−0.119859
$208$	−193169.	−0.309584
$209$	222159.	0.351801
$210$	0	0
$211$	814718.	1.25980	0.629899	−	0.776677i	$-0.283096\pi$
$211$	814718.	1.25980	0.629899	+	0.776677i	$0.283096\pi$
$212$	−154843.	−0.236621
$213$	−29658.5	−0.0447920
$214$	359843.	0.537130
$215$	576179.	0.850083
$216$	46656.0	0.0680414
$217$	0	0
$218$	740010.	1.05462
$219$	−92143.7	−0.129824
$220$	65667.4	0.0914730
$221$	−1.09339e6	−1.50590
$222$	245878.	0.334840
$223$	335874.	0.452288	0.226144	−	0.974094i	$-0.427388\pi$
$223$	335874.	0.452288	0.226144	+	0.974094i	$0.427388\pi$
$224$	0	0
$225$	−74736.7	−0.0984187
$226$	−913100.	−1.18918
$227$	64721.2	0.0833647	0.0416823	−	0.999131i	$-0.486728\pi$
$227$	64721.2	0.0833647	0.0416823	+	0.999131i	$0.486728\pi$
$228$	−365794.	−0.466015
$229$	−750789.	−0.946083	−0.473041	−	0.881040i	$-0.656844\pi$
$229$	−750789.	−0.946083	−0.473041	+	0.881040i	$0.656844\pi$
$230$	171243.	0.213449
$231$	0	0
$232$	11085.9	0.0135223
$233$	−1.38718e6	−1.67395	−0.836974	−	0.547242i	$-0.815678\pi$
$233$	−1.38718e6	−1.67395	−0.836974	+	0.547242i	$0.815678\pi$
$234$	−244479.	−0.291879
$235$	633203.	0.747951
$236$	−485907.	−0.567902
$237$	887256.	1.02607
$238$	0	0
$239$	−160907.	−0.182213	−0.0911064	−	0.995841i	$-0.529040\pi$
$239$	−160907.	−0.182213	−0.0911064	+	0.995841i	$0.529040\pi$
$240$	−108124.	−0.121170
$241$	1.28482e6	1.42495	0.712473	−	0.701699i	$-0.247575\pi$
$241$	1.28482e6	1.42495	0.712473	+	0.701699i	$0.247575\pi$
$242$	−613610.	−0.673525
$243$	59049.0	0.0641500
$244$	−11719.6	−0.0126019
$245$	0	0
$246$	−470493.	−0.495696
$247$	1.91678e6	1.99907
$248$	−289993.	−0.299404
$249$	−790134.	−0.807611
$250$	759812.	0.768876
$251$	481311.	0.482216	0.241108	−	0.970498i	$-0.422489\pi$
$251$	481311.	0.482216	0.241108	+	0.970498i	$0.422489\pi$
$252$	0	0
$253$	79781.4	0.0783611
$254$	−1.37406e6	−1.33635
$255$	−612017.	−0.589404
$256$	65536.0	0.0625000
$257$	−33088.7	−0.0312497	−0.0156249	−	0.999878i	$-0.504974\pi$
$257$	−33088.7	−0.0312497	−0.0156249	+	0.999878i	$0.504974\pi$
$258$	−441997.	−0.413399
$259$	0	0
$260$	566575.	0.519786
$261$	14030.6	0.0127489
$262$	1.44509e6	1.30059
$263$	446200.	0.397778	0.198889	−	0.980022i	$-0.436267\pi$
$263$	446200.	0.397778	0.198889	+	0.980022i	$0.436267\pi$
$264$	−50374.6	−0.0444838
$265$	454164.	0.397281
$266$	0	0
$267$	621898.	0.533877
$268$	742399.	0.631394
$269$	1.94854e6	1.64183	0.820915	−	0.571051i	$-0.193464\pi$
$269$	1.94854e6	1.64183	0.820915	+	0.571051i	$0.193464\pi$
$270$	−136845.	−0.114240
$271$	96873.0	0.0801271	0.0400636	−	0.999197i	$-0.487244\pi$
$271$	96873.0	0.0801271	0.0400636	+	0.999197i	$0.487244\pi$
$272$	370954.	0.304017
$273$	0	0
$274$	−1.21851e6	−0.980510
$275$	80693.3	0.0643437
$276$	−131364.	−0.103801
$277$	1.63679e6	1.28172	0.640859	−	0.767658i	$-0.278578\pi$
$277$	1.63679e6	1.28172	0.640859	+	0.767658i	$0.278578\pi$
$278$	−518948.	−0.402728
$279$	−367022.	−0.282281
$280$	0	0
$281$	−1.79558e6	−1.35656	−0.678281	−	0.734803i	$-0.737275\pi$
$281$	−1.79558e6	−1.35656	−0.678281	+	0.734803i	$0.737275\pi$
$282$	−485741.	−0.363732
$283$	1.28048e6	0.950397	0.475199	−	0.879879i	$-0.342376\pi$
$283$	1.28048e6	0.950397	0.475199	+	0.879879i	$0.342376\pi$
$284$	−52726.3	−0.0387910
$285$	1.07290e6	0.782430
$286$	263965.	0.190823
$287$	0	0
$288$	82944.0	0.0589256
$289$	679857.	0.478821
$290$	−32515.5	−0.0227037
$291$	379632.	0.262803
$292$	−163811.	−0.112431
$293$	330814.	0.225120	0.112560	−	0.993645i	$-0.464095\pi$
$293$	330814.	0.225120	0.112560	+	0.993645i	$0.464095\pi$
$294$	0	0
$295$	1.42519e6	0.953496
$296$	437117.	0.289980
$297$	−63755.3	−0.0419397
$298$	1.49563e6	0.975627
$299$	688351.	0.445279
$300$	−132865.	−0.0852331
$301$	0	0
$302$	−346559.	−0.218655
$303$	−1.60627e6	−1.00510
$304$	−650301.	−0.403581
$305$	34374.2	0.0211584
$306$	469489.	0.286630
$307$	−554088.	−0.335531	−0.167766	−	0.985827i	$-0.553655\pi$
$307$	−554088.	−0.335531	−0.167766	+	0.985827i	$0.553655\pi$
$308$	0	0
$309$	−317035.	−0.188891
$310$	850565.	0.502693
$311$	−1.75926e6	−1.03140	−0.515701	−	0.856769i	$-0.672469\pi$
$311$	−1.75926e6	−1.03140	−0.515701	+	0.856769i	$0.672469\pi$
$312$	−434630.	−0.252774
$313$	−2.33819e6	−1.34902	−0.674512	−	0.738264i	$-0.735646\pi$
$313$	−2.33819e6	−1.34902	−0.674512	+	0.738264i	$0.735646\pi$
$314$	1.84869e6	1.05813
$315$	0	0
$316$	1.57734e6	0.888605
$317$	−967392.	−0.540697	−0.270349	−	0.962762i	$-0.587139\pi$
$317$	−967392.	−0.540697	−0.270349	+	0.962762i	$0.587139\pi$
$318$	−348397.	−0.193200
$319$	−15148.8	−0.00833494
$320$	−192221.	−0.104936
$321$	809648.	0.438565
$322$	0	0
$323$	−3.68090e6	−1.96313
$324$	104976.	0.0555556
$325$	696219.	0.365626
$326$	2.43613e6	1.26957
$327$	1.66502e6	0.861094
$328$	−836433.	−0.429286
$329$	0	0
$330$	147752.	0.0746874
$331$	−327808.	−0.164456	−0.0822281	−	0.996614i	$-0.526204\pi$
$331$	−327808.	−0.164456	−0.0822281	+	0.996614i	$0.526204\pi$
$332$	−1.40468e6	−0.699412
$333$	553226.	0.273396
$334$	511144.	0.250713
$335$	−2.17750e6	−1.06010
$336$	0	0
$337$	1.34052e6	0.642983	0.321491	−	0.946913i	$-0.395816\pi$
$337$	1.34052e6	0.642983	0.321491	+	0.946913i	$0.395816\pi$
$338$	792305.	0.377225
$339$	−2.05447e6	−0.970961
$340$	−1.08803e6	−0.510439
$341$	396274.	0.184548
$342$	−823037.	−0.380500
$343$	0	0
$344$	−785772.	−0.358014
$345$	385297.	0.174280
$346$	570157.	0.256038
$347$	−3.53374e6	−1.57547	−0.787736	−	0.616013i	$-0.788747\pi$
$347$	−3.53374e6	−1.57547	−0.787736	+	0.616013i	$0.788747\pi$
$348$	24943.2	0.0110409
$349$	−3.98108e6	−1.74959	−0.874796	−	0.484491i	$-0.839005\pi$
$349$	−3.98108e6	−1.74959	−0.874796	+	0.484491i	$0.839005\pi$
$350$	0	0
$351$	−550078.	−0.238318
$352$	−89554.8	−0.0385241
$353$	44279.1	0.0189131	0.00945654	−	0.999955i	$-0.496990\pi$
$353$	44279.1	0.0189131	0.00945654	+	0.999955i	$0.496990\pi$
$354$	−1.09329e6	−0.463690
$355$	154649.	0.0651294
$356$	1.10560e6	0.462351
$357$	0	0
$358$	−1.18654e6	−0.489299
$359$	−1.75114e6	−0.717108	−0.358554	−	0.933509i	$-0.616730\pi$
$359$	−1.75114e6	−0.717108	−0.358554	+	0.933509i	$0.616730\pi$
$360$	−243280.	−0.0989349
$361$	3.97671e6	1.60604
$362$	1.11062e6	0.445443
$363$	−1.38062e6	−0.549931
$364$	0	0
$365$	480467.	0.188769
$366$	−26369.0	−0.0102894
$367$	−3.97114e6	−1.53904	−0.769521	−	0.638621i	$-0.779505\pi$
$367$	−3.97114e6	−1.53904	−0.769521	+	0.638621i	$0.779505\pi$
$368$	−233536.	−0.0898945
$369$	−1.05861e6	−0.404734
$370$	−1.28209e6	−0.486871
$371$	0	0
$372$	−652483.	−0.244462
$373$	2.23960e6	0.833486	0.416743	−	0.909024i	$-0.363172\pi$
$373$	2.23960e6	0.833486	0.416743	+	0.909024i	$0.363172\pi$
$374$	−506908.	−0.187392
$375$	1.70958e6	0.627785
$376$	−863539.	−0.315001
$377$	−130703.	−0.0473624
$378$	0	0
$379$	−4.25421e6	−1.52132	−0.760661	−	0.649149i	$-0.775125\pi$
$379$	−4.25421e6	−1.52132	−0.760661	+	0.649149i	$0.775125\pi$
$380$	1.90737e6	0.677604
$381$	−3.09163e6	−1.09113
$382$	−970338.	−0.340224
$383$	−1.61883e6	−0.563904	−0.281952	−	0.959429i	$-0.590982\pi$
$383$	−1.61883e6	−0.563904	−0.281952	+	0.959429i	$0.590982\pi$
$384$	147456.	0.0510310
$385$	0	0
$386$	−2.32610e6	−0.794621
$387$	−994493.	−0.337539
$388$	674902.	0.227594
$389$	−1.35315e6	−0.453391	−0.226696	−	0.973966i	$-0.572792\pi$
$389$	−1.35315e6	−0.453391	−0.226696	+	0.973966i	$0.572792\pi$
$390$	1.27479e6	0.424403
$391$	−1.32188e6	−0.437271
$392$	0	0
$393$	3.25145e6	1.06193
$394$	2.99566e6	0.972193
$395$	−4.62644e6	−1.49195
$396$	−113343.	−0.0363208
$397$	428056.	0.136309	0.0681545	−	0.997675i	$-0.478289\pi$
$397$	428056.	0.136309	0.0681545	+	0.997675i	$0.478289\pi$
$398$	2.90277e6	0.918555
$399$	0	0
$400$	−236205.	−0.0738140
$401$	−118228.	−0.0367164	−0.0183582	−	0.999831i	$-0.505844\pi$
$401$	−118228.	−0.0367164	−0.0183582	+	0.999831i	$0.505844\pi$
$402$	1.67040e6	0.515531
$403$	3.41904e6	1.04868
$404$	−2.85558e6	−0.870445
$405$	−307901.	−0.0932767
$406$	0	0
$407$	−597320.	−0.178740
$408$	834646.	0.248229
$409$	−1.20974e6	−0.357589	−0.178795	−	0.983886i	$-0.557220\pi$
$409$	−1.20974e6	−0.357589	−0.178795	+	0.983886i	$0.557220\pi$
$410$	2.45331e6	0.720762
$411$	−2.74164e6	−0.800583
$412$	−563619.	−0.163585
$413$	0	0
$414$	−295568.	−0.0847534
$415$	4.12002e6	1.17430
$416$	−772675.	−0.218909
$417$	−1.16763e6	−0.328826
$418$	888635.	0.248761
$419$	−4.12593e6	−1.14812	−0.574059	−	0.818814i	$-0.694632\pi$
$419$	−4.12593e6	−1.14812	−0.574059	+	0.818814i	$0.694632\pi$
$420$	0	0
$421$	3.12374e6	0.858953	0.429477	−	0.903078i	$-0.358698\pi$
$421$	3.12374e6	0.858953	0.429477	+	0.903078i	$0.358698\pi$
$422$	3.25887e6	0.890812
$423$	−1.09292e6	−0.296986
$424$	−619373.	−0.167316
$425$	−1.33699e6	−0.359051
$426$	−118634.	−0.0316728
$427$	0	0
$428$	1.43937e6	0.379808
$429$	593921.	0.155806
$430$	2.30472e6	0.601099
$431$	1.11459e6	0.289015	0.144507	−	0.989504i	$-0.453840\pi$
$431$	1.11459e6	0.289015	0.144507	+	0.989504i	$0.453840\pi$
$432$	186624.	0.0481125
$433$	−266138.	−0.0682161	−0.0341080	−	0.999418i	$-0.510859\pi$
$433$	−266138.	−0.0682161	−0.0341080	+	0.999418i	$0.510859\pi$
$434$	0	0
$435$	−73159.9	−0.0185375
$436$	2.96004e6	0.745729
$437$	2.31733e6	0.580475
$438$	−368575.	−0.0917995
$439$	−2.46047e6	−0.609336	−0.304668	−	0.952459i	$-0.598545\pi$
$439$	−2.46047e6	−0.609336	−0.304668	+	0.952459i	$0.598545\pi$
$440$	262669.	0.0646812
$441$	0	0
$442$	−4.37358e6	−1.06483
$443$	−1.21081e6	−0.293134	−0.146567	−	0.989201i	$-0.546822\pi$
$443$	−1.21081e6	−0.293134	−0.146567	+	0.989201i	$0.546822\pi$
$444$	983514.	0.236768
$445$	−3.24278e6	−0.776279
$446$	1.34350e6	0.319816
$447$	3.36517e6	0.796596
$448$	0	0
$449$	−3.66337e6	−0.857561	−0.428781	−	0.903409i	$-0.641057\pi$
$449$	−3.66337e6	−0.857561	−0.428781	+	0.903409i	$0.641057\pi$
$450$	−298947.	−0.0695925
$451$	1.14298e6	0.264605
$452$	−3.65240e6	−0.840877
$453$	−779758.	−0.178531
$454$	258885.	0.0589477
$455$	0	0
$456$	−1.46318e6	−0.329522
$457$	−8.73868e6	−1.95729	−0.978645	−	0.205556i	$-0.934100\pi$
$457$	−8.73868e6	−1.95729	−0.978645	+	0.205556i	$0.934100\pi$
$458$	−3.00316e6	−0.668982
$459$	1.05635e6	0.234032
$460$	684973.	0.150931
$461$	−1.23476e6	−0.270602	−0.135301	−	0.990805i	$-0.543200\pi$
$461$	−1.23476e6	−0.270602	−0.135301	+	0.990805i	$0.543200\pi$
$462$	0	0
$463$	−4.07764e6	−0.884008	−0.442004	−	0.897013i	$-0.645732\pi$
$463$	−4.07764e6	−0.884008	−0.442004	+	0.897013i	$0.645732\pi$
$464$	44343.5	0.00956170
$465$	1.91377e6	0.410447
$466$	−5.54871e6	−1.18366
$467$	−5.25021e6	−1.11400	−0.556999	−	0.830513i	$-0.688047\pi$
$467$	−5.25021e6	−1.11400	−0.556999	+	0.830513i	$0.688047\pi$
$468$	−977917.	−0.206389
$469$	0	0
$470$	2.53281e6	0.528881
$471$	4.15956e6	0.863963
$472$	−1.94363e6	−0.401567
$473$	1.07376e6	0.220675
$474$	3.54902e6	0.725543
$475$	2.34381e6	0.476639
$476$	0	0
$477$	−783894.	−0.157747
$478$	−643626.	−0.128844
$479$	−1.68707e6	−0.335965	−0.167982	−	0.985790i	$-0.553725\pi$
$479$	−1.68707e6	−0.335965	−0.167982	+	0.985790i	$0.553725\pi$
$480$	−432497.	−0.0856801
$481$	−5.15365e6	−1.01567
$482$	5.13927e6	1.00759
$483$	0	0
$484$	−2.45444e6	−0.476254
$485$	−1.97953e6	−0.382126
$486$	236196.	0.0453609
$487$	4.39520e6	0.839762	0.419881	−	0.907579i	$-0.362072\pi$
$487$	4.39520e6	0.839762	0.419881	+	0.907579i	$0.362072\pi$
$488$	−46878.2	−0.00891091
$489$	5.48129e6	1.03660
$490$	0	0
$491$	2.13582e6	0.399817	0.199909	−	0.979815i	$-0.435935\pi$
$491$	2.13582e6	0.399817	0.199909	+	0.979815i	$0.435935\pi$
$492$	−1.88197e6	−0.350510
$493$	250998.	0.0465107
$494$	7.66710e6	1.41356
$495$	332441.	0.0609820
$496$	−1.15997e6	−0.211711
$497$	0	0
$498$	−3.16054e6	−0.571067
$499$	−1.93439e6	−0.347771	−0.173885	−	0.984766i	$-0.555632\pi$
$499$	−1.93439e6	−0.347771	−0.173885	+	0.984766i	$0.555632\pi$
$500$	3.03925e6	0.543677
$501$	1.15007e6	0.204706
$502$	1.92524e6	0.340978
$503$	−9.47334e6	−1.66949	−0.834744	−	0.550639i	$-0.814384\pi$
$503$	−9.47334e6	−1.66949	−0.834744	+	0.550639i	$0.814384\pi$
$504$	0	0
$505$	8.37559e6	1.46146
$506$	319126.	0.0554097
$507$	1.78269e6	0.308003
$508$	−5.49624e6	−0.944944
$509$	1.05589e7	1.80645	0.903225	−	0.429167i	$-0.141193\pi$
$509$	1.05589e7	1.80645	0.903225	+	0.429167i	$0.141193\pi$
$510$	−2.44807e6	−0.416771
$511$	0	0
$512$	262144.	0.0441942
$513$	−1.85183e6	−0.310677
$514$	−132355.	−0.0220969
$515$	1.65313e6	0.274655
$516$	−1.76799e6	−0.292318
$517$	1.18002e6	0.194162
$518$	0	0
$519$	1.28285e6	0.209054
$520$	2.26630e6	0.367544
$521$	7.53190e6	1.21565	0.607827	−	0.794069i	$-0.292041\pi$
$521$	7.53190e6	1.21565	0.607827	+	0.794069i	$0.292041\pi$
$522$	56122.3	0.00901486
$523$	7.33316e6	1.17230	0.586148	−	0.810204i	$-0.300644\pi$
$523$	7.33316e6	1.17230	0.586148	+	0.810204i	$0.300644\pi$
$524$	5.78035e6	0.919657
$525$	0	0
$526$	1.78480e6	0.281271
$527$	−6.56579e6	−1.02982
$528$	−201498.	−0.0314548
$529$	−5.60415e6	−0.870704
$530$	1.81666e6	0.280920
$531$	−2.45990e6	−0.378601
$532$	0	0
$533$	9.86162e6	1.50359
$534$	2.48759e6	0.377508
$535$	−4.22177e6	−0.637690
$536$	2.96960e6	0.446463
$537$	−2.66971e6	−0.399511
$538$	7.79415e6	1.16095
$539$	0	0
$540$	−547379.	−0.0807800
$541$	−1.25979e7	−1.85056	−0.925281	−	0.379282i	$-0.876171\pi$
$541$	−1.25979e7	−1.85056	−0.925281	+	0.379282i	$0.876171\pi$
$542$	387492.	0.0566584
$543$	2.49888e6	0.363703
$544$	1.48382e6	0.214972
$545$	−8.68197e6	−1.25206
$546$	0	0
$547$	−4.21767e6	−0.602704	−0.301352	−	0.953513i	$-0.597438\pi$
$547$	−4.21767e6	−0.602704	−0.301352	+	0.953513i	$0.597438\pi$
$548$	−4.87403e6	−0.693325
$549$	−59330.3	−0.00840128
$550$	322773.	0.0454979
$551$	−440012.	−0.0617427
$552$	−525455.	−0.0733986
$553$	0	0
$554$	6.54715e6	0.906312
$555$	−2.88470e6	−0.397529
$556$	−2.07579e6	−0.284772
$557$	−9.56529e6	−1.30635	−0.653176	−	0.757206i	$-0.726564\pi$
$557$	−9.56529e6	−1.30635	−0.653176	+	0.757206i	$0.726564\pi$
$558$	−1.46809e6	−0.199603
$559$	9.26432e6	1.25396
$560$	0	0
$561$	−1.14054e6	−0.153005
$562$	−7.18233e6	−0.959234
$563$	9.39186e6	1.24876	0.624382	−	0.781119i	$-0.285351\pi$
$563$	9.39186e6	1.24876	0.624382	+	0.781119i	$0.285351\pi$
$564$	−1.94296e6	−0.257197
$565$	1.07127e7	1.41182
$566$	5.12190e6	0.672032
$567$	0	0
$568$	−210905.	−0.0274294
$569$	1.03867e7	1.34493	0.672463	−	0.740131i	$-0.265237\pi$
$569$	1.03867e7	1.34493	0.672463	+	0.740131i	$0.265237\pi$
$570$	4.29158e6	0.553261
$571$	4.42960e6	0.568557	0.284279	−	0.958742i	$-0.408246\pi$
$571$	4.42960e6	0.568557	0.284279	+	0.958742i	$0.408246\pi$
$572$	1.05586e6	0.134932
$573$	−2.18326e6	−0.277791
$574$	0	0
$575$	841709.	0.106168
$576$	331776.	0.0416667
$577$	1.20182e7	1.50280	0.751398	−	0.659849i	$-0.229380\pi$
$577$	1.20182e7	1.50280	0.751398	+	0.659849i	$0.229380\pi$
$578$	2.71943e6	0.338577
$579$	−5.23372e6	−0.648805
$580$	−130062.	−0.0160539
$581$	0	0
$582$	1.51853e6	0.185830
$583$	846372.	0.103131
$584$	−655244.	−0.0795007
$585$	2.86829e6	0.346524
$586$	1.32326e6	0.159184
$587$	−6.97624e6	−0.835653	−0.417826	−	0.908527i	$-0.637208\pi$
$587$	−6.97624e6	−0.835653	−0.417826	+	0.908527i	$0.637208\pi$
$588$	0	0
$589$	1.15102e7	1.36708
$590$	5.70077e6	0.674223
$591$	6.74024e6	0.793792
$592$	1.74847e6	0.205047
$593$	1.78148e6	0.208038	0.104019	−	0.994575i	$-0.466830\pi$
$593$	1.78148e6	0.208038	0.104019	+	0.994575i	$0.466830\pi$
$594$	−255021.	−0.0296558
$595$	0	0
$596$	5.98253e6	0.689873
$597$	6.53124e6	0.749997
$598$	2.75340e6	0.314860
$599$	1.60365e6	0.182617	0.0913085	−	0.995823i	$-0.470895\pi$
$599$	1.60365e6	0.182617	0.0913085	+	0.995823i	$0.470895\pi$
$600$	−531461.	−0.0602689
$601$	1.51165e7	1.70712	0.853562	−	0.520991i	$-0.174438\pi$
$601$	1.51165e7	1.70712	0.853562	+	0.520991i	$0.174438\pi$
$602$	0	0
$603$	3.75839e6	0.420929
$604$	−1.38624e6	−0.154613
$605$	7.19901e6	0.799622
$606$	−6.42506e6	−0.710715
$607$	−1.05167e7	−1.15853	−0.579263	−	0.815141i	$-0.696660\pi$
$607$	−1.05167e7	−1.15853	−0.579263	+	0.815141i	$0.696660\pi$
$608$	−2.60120e6	−0.285375
$609$	0	0
$610$	137497.	0.0149612
$611$	1.01812e7	1.10331
$612$	1.87795e6	0.202678
$613$	2.71298e6	0.291605	0.145802	−	0.989314i	$-0.453424\pi$
$613$	2.71298e6	0.291605	0.145802	+	0.989314i	$0.453424\pi$
$614$	−2.21635e6	−0.237256
$615$	5.51994e6	0.588500
$616$	0	0
$617$	1.14961e7	1.21573	0.607864	−	0.794041i	$-0.292026\pi$
$617$	1.14961e7	1.21573	0.607864	+	0.794041i	$0.292026\pi$
$618$	−1.26814e6	−0.133566
$619$	−1.09950e7	−1.15337	−0.576684	−	0.816967i	$-0.695654\pi$
$619$	−1.09950e7	−1.15337	−0.576684	+	0.816967i	$0.695654\pi$
$620$	3.40226e6	0.355458
$621$	−665029.	−0.0692009
$622$	−7.03702e6	−0.729312
$623$	0	0
$624$	−1.73852e6	−0.178738
$625$	−6.03093e6	−0.617568
$626$	−9.35277e6	−0.953904
$627$	1.99943e6	0.203113
$628$	7.39477e6	0.748214
$629$	9.89687e6	0.997405
$630$	0	0
$631$	−4.19503e6	−0.419432	−0.209716	−	0.977762i	$-0.567254\pi$
$631$	−4.19503e6	−0.419432	−0.209716	+	0.977762i	$0.567254\pi$
$632$	6.30938e6	0.628338
$633$	7.33246e6	0.727345
$634$	−3.86957e6	−0.382331
$635$	1.61208e7	1.58654
$636$	−1.39359e6	−0.136613
$637$	0	0
$638$	−60595.3	−0.00589369
$639$	−266927.	−0.0258607
$640$	−768884.	−0.0742012
$641$	−1.06270e7	−1.02157	−0.510784	−	0.859709i	$-0.670645\pi$
$641$	−1.06270e7	−1.02157	−0.510784	+	0.859709i	$0.670645\pi$
$642$	3.23859e6	0.310112
$643$	−1.54228e6	−0.147108	−0.0735538	−	0.997291i	$-0.523434\pi$
$643$	−1.54228e6	−0.147108	−0.0735538	+	0.997291i	$0.523434\pi$
$644$	0	0
$645$	5.18561e6	0.490795
$646$	−1.47236e7	−1.38814
$647$	1.28170e7	1.20372	0.601861	−	0.798601i	$-0.294426\pi$
$647$	1.28170e7	1.20372	0.601861	+	0.798601i	$0.294426\pi$
$648$	419904.	0.0392837
$649$	2.65596e6	0.247520
$650$	2.78488e6	0.258537
$651$	0	0
$652$	9.74452e6	0.897721
$653$	−2.84549e6	−0.261141	−0.130570	−	0.991439i	$-0.541681\pi$
$653$	−2.84549e6	−0.261141	−0.130570	+	0.991439i	$0.541681\pi$
$654$	6.66009e6	0.608885
$655$	−1.69541e7	−1.54409
$656$	−3.34573e6	−0.303551
$657$	−829293.	−0.0749540
$658$	0	0
$659$	−2.04185e7	−1.83151	−0.915755	−	0.401736i	$-0.868407\pi$
$659$	−2.04185e7	−1.83151	−0.915755	+	0.401736i	$0.868407\pi$
$660$	591006.	0.0528119
$661$	−2.18928e7	−1.94893	−0.974467	−	0.224529i	$-0.927916\pi$
$661$	−2.18928e7	−1.94893	−0.974467	+	0.224529i	$0.927916\pi$
$662$	−1.31123e6	−0.116288
$663$	−9.84055e6	−0.869432
$664$	−5.61873e6	−0.494559
$665$	0	0
$666$	2.21291e6	0.193320
$667$	−158017.	−0.0137527
$668$	2.04458e6	0.177281
$669$	3.02287e6	0.261128
$670$	−8.71000e6	−0.749602
$671$	64059.0	0.00549255
$672$	0	0
$673$	−992084.	−0.0844327	−0.0422164	−	0.999108i	$-0.513442\pi$
$673$	−992084.	−0.0844327	−0.0422164	+	0.999108i	$0.513442\pi$
$674$	5.36209e6	0.454657
$675$	−672630.	−0.0568221
$676$	3.16922e6	0.266738
$677$	7.83497e6	0.657000	0.328500	−	0.944504i	$-0.393457\pi$
$677$	7.83497e6	0.657000	0.328500	+	0.944504i	$0.393457\pi$
$678$	−8.21790e6	−0.686573
$679$	0	0
$680$	−4.35212e6	−0.360935
$681$	582491.	0.0481306
$682$	1.58510e6	0.130495
$683$	−7.41182e6	−0.607957	−0.303979	−	0.952679i	$-0.598315\pi$
$683$	−7.41182e6	−0.607957	−0.303979	+	0.952679i	$0.598315\pi$
$684$	−3.29215e6	−0.269054
$685$	1.42958e7	1.16408
$686$	0	0
$687$	−6.75710e6	−0.546221
$688$	−3.14309e6	−0.253154
$689$	7.30246e6	0.586032
$690$	1.54119e6	0.123235
$691$	−1.00517e7	−0.800836	−0.400418	−	0.916333i	$-0.631135\pi$
$691$	−1.00517e7	−0.800836	−0.400418	+	0.916333i	$0.631135\pi$
$692$	2.28063e6	0.181046
$693$	0	0
$694$	−1.41350e7	−1.11403
$695$	6.08841e6	0.478126
$696$	99772.9	0.00780710
$697$	−1.89379e7	−1.47655
$698$	−1.59243e7	−1.23715
$699$	−1.24846e7	−0.966455
$700$	0	0
$701$	1.59518e7	1.22607	0.613034	−	0.790057i	$-0.289949\pi$
$701$	1.59518e7	1.22607	0.613034	+	0.790057i	$0.289949\pi$
$702$	−2.20031e6	−0.168516
$703$	−1.73497e7	−1.32405
$704$	−358219.	−0.0272406
$705$	5.69882e6	0.431830
$706$	177116.	0.0133736
$707$	0	0
$708$	−4.37316e6	−0.327878
$709$	−3.82623e6	−0.285862	−0.142931	−	0.989733i	$-0.545653\pi$
$709$	−3.82623e6	−0.285862	−0.142931	+	0.989733i	$0.545653\pi$
$710$	618597.	0.0460534
$711$	7.98530e6	0.592403
$712$	4.42239e6	0.326932
$713$	4.13352e6	0.304506
$714$	0	0
$715$	−3.09690e6	−0.226549
$716$	−4.74615e6	−0.345986
$717$	−1.44816e6	−0.105201
$718$	−7.00456e6	−0.507072
$719$	−7.92731e6	−0.571878	−0.285939	−	0.958248i	$-0.592306\pi$
$719$	−7.92731e6	−0.571878	−0.285939	+	0.958248i	$0.592306\pi$
$720$	−973118.	−0.0699575
$721$	0	0
$722$	1.59068e7	1.13564
$723$	1.15633e7	0.822693
$724$	4.44246e6	0.314976
$725$	−159823.	−0.0112926
$726$	−5.52249e6	−0.388860
$727$	3.24519e6	0.227722	0.113861	−	0.993497i	$-0.463678\pi$
$727$	3.24519e6	0.227722	0.113861	+	0.993497i	$0.463678\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	1.92187e6	0.133480
$731$	−1.77908e7	−1.23141
$732$	−105476.	−0.00727572
$733$	5.97679e6	0.410874	0.205437	−	0.978670i	$-0.434138\pi$
$733$	5.97679e6	0.410874	0.205437	+	0.978670i	$0.434138\pi$
$734$	−1.58846e7	−1.08827
$735$	0	0
$736$	−934142.	−0.0635650
$737$	−4.05794e6	−0.275193
$738$	−4.23444e6	−0.286190
$739$	−2.60064e6	−0.175174	−0.0875870	−	0.996157i	$-0.527916\pi$
$739$	−2.60064e6	−0.175174	−0.0875870	+	0.996157i	$0.527916\pi$
$740$	−5.12836e6	−0.344270
$741$	1.72510e7	1.15417
$742$	0	0
$743$	−2.29585e7	−1.52571	−0.762854	−	0.646571i	$-0.776203\pi$
$743$	−2.29585e7	−1.52571	−0.762854	+	0.646571i	$0.776203\pi$
$744$	−2.60993e6	−0.172861
$745$	−1.75471e7	−1.15828
$746$	8.95839e6	0.589363
$747$	−7.11121e6	−0.466275
$748$	−2.02763e6	−0.132506
$749$	0	0
$750$	6.83831e6	0.443911
$751$	4.60318e6	0.297823	0.148911	−	0.988851i	$-0.452423\pi$
$751$	4.60318e6	0.297823	0.148911	+	0.988851i	$0.452423\pi$
$752$	−3.45416e6	−0.222740
$753$	4.33180e6	0.278407
$754$	−522814.	−0.0334903
$755$	4.06591e6	0.259592
$756$	0	0
$757$	4.78695e6	0.303612	0.151806	−	0.988410i	$-0.451491\pi$
$757$	4.78695e6	0.303612	0.151806	+	0.988410i	$0.451491\pi$
$758$	−1.70169e7	−1.07574
$759$	718033.	0.0452418
$760$	7.62948e6	0.479138
$761$	−2.28441e7	−1.42992	−0.714962	−	0.699164i	$-0.753556\pi$
$761$	−2.28441e7	−1.42992	−0.714962	+	0.699164i	$0.753556\pi$
$762$	−1.23665e7	−0.771544
$763$	0	0
$764$	−3.88135e6	−0.240574
$765$	−5.50815e6	−0.340292
$766$	−6.47533e6	−0.398740
$767$	2.29155e7	1.40651
$768$	589824.	0.0360844
$769$	1.02787e7	0.626793	0.313397	−	0.949622i	$-0.398533\pi$
$769$	1.02787e7	0.626793	0.313397	+	0.949622i	$0.398533\pi$
$770$	0	0
$771$	−297798.	−0.0180420
$772$	−9.30439e6	−0.561882
$773$	1.38227e7	0.832038	0.416019	−	0.909356i	$-0.363425\pi$
$773$	1.38227e7	0.832038	0.416019	+	0.909356i	$0.363425\pi$
$774$	−3.97797e6	−0.238676
$775$	4.18076e6	0.250035
$776$	2.69961e6	0.160933
$777$	0	0
$778$	−5.41262e6	−0.320596
$779$	3.31990e7	1.96012
$780$	5.09918e6	0.300098
$781$	288201.	0.0169071
$782$	−5.28753e6	−0.309198
$783$	126275.	0.00736060
$784$	0	0
$785$	−2.16893e7	−1.25624
$786$	1.30058e7	0.750897
$787$	736248.	0.0423728	0.0211864	−	0.999776i	$-0.493256\pi$
$787$	736248.	0.0423728	0.0211864	+	0.999776i	$0.493256\pi$
$788$	1.19827e7	0.687444
$789$	4.01580e6	0.229657
$790$	−1.85058e7	−1.05497
$791$	0	0
$792$	−453371.	−0.0256827
$793$	552699.	0.0312108
$794$	1.71222e6	0.0963850
$795$	4.08748e6	0.229371
$796$	1.16111e7	0.649516
$797$	−3.29571e7	−1.83782	−0.918912	−	0.394464i	$-0.870930\pi$
$797$	−3.29571e7	−1.83782	−0.918912	+	0.394464i	$0.870930\pi$
$798$	0	0
$799$	−1.95516e7	−1.08347
$800$	−944820.	−0.0521944
$801$	5.59709e6	0.308234
$802$	−472913.	−0.0259624
$803$	895389.	0.0490030
$804$	6.68159e6	0.364535
$805$	0	0
$806$	1.36761e7	0.741526
$807$	1.75368e7	0.947911
$808$	−1.14223e7	−0.615498
$809$	−1.09629e7	−0.588918	−0.294459	−	0.955664i	$-0.595139\pi$
$809$	−1.09629e7	−0.588918	−0.294459	+	0.955664i	$0.595139\pi$
$810$	−1.23160e6	−0.0659566
$811$	−2.77365e7	−1.48081	−0.740406	−	0.672160i	$-0.765367\pi$
$811$	−2.77365e7	−1.48081	−0.740406	+	0.672160i	$0.765367\pi$
$812$	0	0
$813$	871857.	0.0462614
$814$	−2.38928e6	−0.126388
$815$	−2.85812e7	−1.50726
$816$	3.33859e6	0.175524
$817$	3.11882e7	1.63469
$818$	−4.83897e6	−0.252854
$819$	0	0
$820$	9.81322e6	0.509656
$821$	1.25487e7	0.649743	0.324872	−	0.945758i	$-0.394679\pi$
$821$	1.25487e7	0.649743	0.324872	+	0.945758i	$0.394679\pi$
$822$	−1.09666e7	−0.566098
$823$	2.88571e7	1.48509	0.742545	−	0.669796i	$-0.233618\pi$
$823$	2.88571e7	1.48509	0.742545	+	0.669796i	$0.233618\pi$
$824$	−2.25447e6	−0.115672
$825$	726240.	0.0371489
$826$	0	0
$827$	−2.83888e7	−1.44339	−0.721694	−	0.692213i	$-0.756636\pi$
$827$	−2.83888e7	−1.44339	−0.721694	+	0.692213i	$0.756636\pi$
$828$	−1.18227e6	−0.0599297
$829$	2.40584e7	1.21585	0.607926	−	0.793994i	$-0.292002\pi$
$829$	2.40584e7	1.21585	0.607926	+	0.793994i	$0.292002\pi$
$830$	1.64801e7	0.830355
$831$	1.47311e7	0.740001
$832$	−3.09070e6	−0.154792
$833$	0	0
$834$	−4.67053e6	−0.232515
$835$	−5.99686e6	−0.297651
$836$	3.55454e6	0.175901
$837$	−3.30320e6	−0.162975
$838$	−1.65037e7	−0.811842
$839$	−2.99511e6	−0.146895	−0.0734477	−	0.997299i	$-0.523400\pi$
$839$	−2.99511e6	−0.146895	−0.0734477	+	0.997299i	$0.523400\pi$
$840$	0	0
$841$	−2.04811e7	−0.998537
$842$	1.24950e7	0.607372
$843$	−1.61602e7	−0.783211
$844$	1.30355e7	0.629899
$845$	−9.29551e6	−0.447849
$846$	−4.37167e6	−0.210001
$847$	0	0
$848$	−2.47749e6	−0.118310
$849$	1.15243e7	0.548712
$850$	−5.34797e6	−0.253888
$851$	−6.23061e6	−0.294922
$852$	−474537.	−0.0223960
$853$	1.46234e6	0.0688137	0.0344069	−	0.999408i	$-0.489046\pi$
$853$	1.46234e6	0.0688137	0.0344069	+	0.999408i	$0.489046\pi$
$854$	0	0
$855$	9.65606e6	0.451736
$856$	5.75750e6	0.268565
$857$	1.66909e7	0.776295	0.388148	−	0.921597i	$-0.373115\pi$
$857$	1.66909e7	0.776295	0.388148	+	0.921597i	$0.373115\pi$
$858$	2.37568e6	0.110172
$859$	3.01647e7	1.39481	0.697406	−	0.716676i	$-0.254337\pi$
$859$	3.01647e7	1.39481	0.697406	+	0.716676i	$0.254337\pi$
$860$	9.21886e6	0.425041
$861$	0	0
$862$	4.45834e6	0.204364
$863$	−2.88352e7	−1.31794	−0.658970	−	0.752169i	$-0.729008\pi$
$863$	−2.88352e7	−1.31794	−0.658970	+	0.752169i	$0.729008\pi$
$864$	746496.	0.0340207
$865$	−6.68921e6	−0.303973
$866$	−1.06455e6	−0.0482361
$867$	6.11871e6	0.276447
$868$	0	0
$869$	−8.62175e6	−0.387298
$870$	−292640.	−0.0131080
$871$	−3.50118e7	−1.56376
$872$	1.18402e7	0.527310
$873$	3.41669e6	0.151730
$874$	9.26931e6	0.410458
$875$	0	0
$876$	−1.47430e6	−0.0649120
$877$	3.15732e7	1.38618	0.693090	−	0.720851i	$-0.256249\pi$
$877$	3.15732e7	1.38618	0.693090	+	0.720851i	$0.256249\pi$
$878$	−9.84188e6	−0.430865
$879$	2.97733e6	0.129973
$880$	1.05068e6	0.0457365
$881$	1.42247e7	0.617452	0.308726	−	0.951151i	$-0.400097\pi$
$881$	1.42247e7	0.617452	0.308726	+	0.951151i	$0.400097\pi$
$882$	0	0
$883$	−9.42179e6	−0.406660	−0.203330	−	0.979110i	$-0.565176\pi$
$883$	−9.42179e6	−0.406660	−0.203330	+	0.979110i	$0.565176\pi$
$884$	−1.74943e7	−0.752950
$885$	1.28267e7	0.550501
$886$	−4.84323e6	−0.207277
$887$	1.50474e7	0.642174	0.321087	−	0.947050i	$-0.395952\pi$
$887$	1.50474e7	0.642174	0.321087	+	0.947050i	$0.395952\pi$
$888$	3.93405e6	0.167420
$889$	0	0
$890$	−1.29711e7	−0.548912
$891$	−573798.	−0.0242139
$892$	5.37399e6	0.226144
$893$	3.42749e7	1.43829
$894$	1.34607e7	0.563279
$895$	1.39207e7	0.580904
$896$	0	0
$897$	6.19516e6	0.257082
$898$	−1.46535e7	−0.606388
$899$	−784869.	−0.0323890
$900$	−1.19579e6	−0.0492094
$901$	−1.40234e7	−0.575494
$902$	4.57193e6	0.187104
$903$	0	0
$904$	−1.46096e7	−0.594589
$905$	−1.30300e7	−0.528838
$906$	−3.11903e6	−0.126241
$907$	−1.87480e7	−0.756725	−0.378362	−	0.925658i	$-0.623513\pi$
$907$	−1.87480e7	−0.756725	−0.378362	+	0.925658i	$0.623513\pi$
$908$	1.03554e6	0.0416823
$909$	−1.44564e7	−0.580297
$910$	0	0
$911$	1.49384e7	0.596358	0.298179	−	0.954510i	$-0.403621\pi$
$911$	1.49384e7	0.596358	0.298179	+	0.954510i	$0.403621\pi$
$912$	−5.85271e6	−0.233007
$913$	7.67798e6	0.304839
$914$	−3.49547e7	−1.38401
$915$	309367.	0.0122158
$916$	−1.20126e7	−0.473041
$917$	0	0
$918$	4.22540e6	0.165486
$919$	4.21133e7	1.64487	0.822434	−	0.568861i	$-0.192616\pi$
$919$	4.21133e7	1.64487	0.822434	+	0.568861i	$0.192616\pi$
$920$	2.73989e6	0.106724
$921$	−4.98679e6	−0.193719
$922$	−4.93905e6	−0.191345
$923$	2.48659e6	0.0960727
$924$	0	0
$925$	−6.30183e6	−0.242166
$926$	−1.63106e7	−0.625088
$927$	−2.85332e6	−0.109056
$928$	177374.	0.00676114
$929$	−5.87883e6	−0.223487	−0.111743	−	0.993737i	$-0.535643\pi$
$929$	−5.87883e6	−0.223487	−0.111743	+	0.993737i	$0.535643\pi$
$930$	7.65508e6	0.290230
$931$	0	0
$932$	−2.21948e7	−0.836974
$933$	−1.58333e7	−0.595480
$934$	−2.10008e7	−0.787715
$935$	5.94716e6	0.222475
$936$	−3.91167e6	−0.145939
$937$	−1.42337e7	−0.529625	−0.264813	−	0.964300i	$-0.585310\pi$
$937$	−1.42337e7	−0.529625	−0.264813	+	0.964300i	$0.585310\pi$
$938$	0	0
$939$	−2.10437e7	−0.778859
$940$	1.01312e7	0.373975
$941$	3.24512e7	1.19469	0.597347	−	0.801983i	$-0.296222\pi$
$941$	3.24512e7	1.19469	0.597347	+	0.801983i	$0.296222\pi$
$942$	1.66382e7	0.610914
$943$	1.19224e7	0.436601
$944$	−7.77451e6	−0.283951
$945$	0	0
$946$	4.29502e6	0.156041
$947$	−2.60957e7	−0.945570	−0.472785	−	0.881178i	$-0.656751\pi$
$947$	−2.60957e7	−0.945570	−0.472785	+	0.881178i	$0.656751\pi$
$948$	1.41961e7	0.513036
$949$	7.72538e6	0.278455
$950$	9.37526e6	0.337034
$951$	−8.70653e6	−0.312172
$952$	0	0
$953$	2.98631e7	1.06513	0.532565	−	0.846389i	$-0.321228\pi$
$953$	2.98631e7	1.06513	0.532565	+	0.846389i	$0.321228\pi$
$954$	−3.13558e6	−0.111544
$955$	1.13842e7	0.403920
$956$	−2.57451e6	−0.0911064
$957$	−136339.	−0.00481218
$958$	−6.74827e6	−0.237563
$959$	0	0
$960$	−1.72999e6	−0.0605850
$961$	−8.09799e6	−0.282858
$962$	−2.06146e7	−0.718186
$963$	7.28683e6	0.253205
$964$	2.05571e7	0.712473
$965$	2.72903e7	0.943388
$966$	0	0
$967$	6.83038e6	0.234898	0.117449	−	0.993079i	$-0.462528\pi$
$967$	6.83038e6	0.234898	0.117449	+	0.993079i	$0.462528\pi$
$968$	−9.81776e6	−0.336763
$969$	−3.31281e7	−1.13341
$970$	−7.91811e6	−0.270204
$971$	−8.99328e6	−0.306105	−0.153052	−	0.988218i	$-0.548910\pi$
$971$	−8.99328e6	−0.306105	−0.153052	+	0.988218i	$0.548910\pi$
$972$	944784.	0.0320750
$973$	0	0
$974$	1.75808e7	0.593801
$975$	6.26597e6	0.211094
$976$	−187513.	−0.00630096
$977$	−2.94394e7	−0.986718	−0.493359	−	0.869826i	$-0.664231\pi$
$977$	−2.94394e7	−0.986718	−0.493359	+	0.869826i	$0.664231\pi$
$978$	2.19252e7	0.732986
$979$	−6.04318e6	−0.201516
$980$	0	0
$981$	1.49852e7	0.497153
$982$	8.54329e6	0.282713
$983$	−3.96261e7	−1.30797	−0.653984	−	0.756508i	$-0.726904\pi$
$983$	−3.96261e7	−1.30797	−0.653984	+	0.756508i	$0.726904\pi$
$984$	−7.52790e6	−0.247848
$985$	−3.51458e7	−1.15421
$986$	1.00399e6	0.0328880
$987$	0	0
$988$	3.06684e7	0.999537
$989$	1.12003e7	0.364115
$990$	1.32976e6	0.0431208
$991$	5.34988e7	1.73045	0.865226	−	0.501382i	$-0.167175\pi$
$991$	5.34988e7	1.73045	0.865226	+	0.501382i	$0.167175\pi$
$992$	−4.63988e6	−0.149702
$993$	−2.95028e6	−0.0949488
$994$	0	0
$995$	−3.40560e7	−1.09053
$996$	−1.26421e7	−0.403806
$997$	3.76239e7	1.19874	0.599371	−	0.800471i	$-0.295417\pi$
$997$	3.76239e7	1.19874	0.599371	+	0.800471i	$0.295417\pi$
$998$	−7.73756e6	−0.245911
$999$	4.97904e6	0.157845

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.6.a.t.1.1	✓	2	7.6	odd	2
294.6.a.u.1.2	yes	2	1.1	even	1	trivial
294.6.e.u.67.1		4	7.2	even	3
294.6.e.u.79.1		4	7.4	even	3
294.6.e.v.67.2		4	7.5	odd	6
294.6.e.v.79.2		4	7.3	odd	6
882.6.a.z.1.2		2	21.20	even	2
882.6.a.bj.1.1		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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -46.9289 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -46.9289 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} -187.716 q^{10} -87.4558 q^{11} +144.000 q^{12} -754.566 q^{13} -422.360 q^{15} +256.000 q^{16} +1449.04 q^{17} +324.000 q^{18} -2540.24 q^{19} -750.863 q^{20} -349.823 q^{22} -912.248 q^{23} +576.000 q^{24} -922.675 q^{25} -3018.26 q^{26} +729.000 q^{27} +173.217 q^{29} -1689.44 q^{30} -4531.13 q^{31} +1024.00 q^{32} -787.103 q^{33} +5796.16 q^{34} +1296.00 q^{36} +6829.96 q^{37} -10161.0 q^{38} -6791.09 q^{39} -3003.45 q^{40} -13069.3 q^{41} -12277.7 q^{43} -1399.29 q^{44} -3801.24 q^{45} -3648.99 q^{46} -13492.8 q^{47} +2304.00 q^{48} -3690.70 q^{50} +13041.4 q^{51} -12073.0 q^{52} -9677.70 q^{53} +2916.00 q^{54} +4104.21 q^{55} -22862.1 q^{57} +692.868 q^{58} -30369.2 q^{59} -6757.77 q^{60} -732.473 q^{61} -18124.5 q^{62} +4096.00 q^{64} +35411.0 q^{65} -3148.41 q^{66} +46399.9 q^{67} +23184.6 q^{68} -8210.23 q^{69} -3295.39 q^{71} +5184.00 q^{72} -10238.2 q^{73} +27319.8 q^{74} -8304.08 q^{75} -40643.8 q^{76} -27164.4 q^{78} +98584.0 q^{79} -12013.8 q^{80} +6561.00 q^{81} -52277.1 q^{82} -87792.7 q^{83} -68001.9 q^{85} -49110.8 q^{86} +1558.95 q^{87} -5597.17 q^{88} +69099.8 q^{89} -15205.0 q^{90} -14596.0 q^{92} -40780.2 q^{93} -53971.2 q^{94} +119211. q^{95} +9216.00 q^{96} +42181.4 q^{97} -7083.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} + 128 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q + 8 * q^2 + 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 + 128 * q^8 + 162 * q^9	\( 2 q + 8 q^{2} + 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} + 128 q^{8} + 162 q^{9} - 432 q^{10} - 124 q^{11} + 288 q^{12} - 720 q^{13} - 972 q^{15} + 512 q^{16} - 612 q^{17} + 648 q^{18} - 2088 q^{19} - 1728 q^{20} - 496 q^{22} + 772 q^{23} + 1152 q^{24} - 318 q^{25} - 2880 q^{26} + 1458 q^{27} - 4592 q^{29} - 3888 q^{30} - 9792 q^{31} + 2048 q^{32} - 1116 q^{33} - 2448 q^{34} + 2592 q^{36} - 5992 q^{37} - 8352 q^{38} - 6480 q^{39} - 6912 q^{40} - 20196 q^{41} - 1136 q^{43} - 1984 q^{44} - 8748 q^{45} + 3088 q^{46} - 36936 q^{47} + 4608 q^{48} - 1272 q^{50} - 5508 q^{51} - 11520 q^{52} - 16708 q^{53} + 5832 q^{54} + 6336 q^{55} - 18792 q^{57} - 18368 q^{58} - 74592 q^{59} - 15552 q^{60} + 18648 q^{61} - 39168 q^{62} + 8192 q^{64} + 33300 q^{65} - 4464 q^{66} + 67344 q^{67} - 9792 q^{68} + 6948 q^{69} + 76548 q^{71} + 10368 q^{72} - 47304 q^{73} - 23968 q^{74} - 2862 q^{75} - 33408 q^{76} - 25920 q^{78} + 140656 q^{79} - 27648 q^{80} + 13122 q^{81} - 80784 q^{82} - 94104 q^{83} + 57868 q^{85} - 4544 q^{86} - 41328 q^{87} - 7936 q^{88} + 17604 q^{89} - 34992 q^{90} + 12352 q^{92} - 88128 q^{93} - 147744 q^{94} + 91592 q^{95} + 18432 q^{96} - 85176 q^{97} - 10044 q^{99}+O(q^{100}) \) 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 - 612 * q^17 + 648 * q^18 - 2088 * q^19 - 1728 * q^20 - 496 * q^22 + 772 * q^23 + 1152 * q^24 - 318 * q^25 - 2880 * q^26 + 1458 * q^27 - 4592 * q^29 - 3888 * q^30 - 9792 * q^31 + 2048 * q^32 - 1116 * q^33 - 2448 * q^34 + 2592 * q^36 - 5992 * q^37 - 8352 * q^38 - 6480 * q^39 - 6912 * q^40 - 20196 * q^41 - 1136 * q^43 - 1984 * q^44 - 8748 * q^45 + 3088 * q^46 - 36936 * q^47 + 4608 * q^48 - 1272 * q^50 - 5508 * q^51 - 11520 * q^52 - 16708 * q^53 + 5832 * q^54 + 6336 * q^55 - 18792 * q^57 - 18368 * q^58 - 74592 * q^59 - 15552 * q^60 + 18648 * q^61 - 39168 * q^62 + 8192 * q^64 + 33300 * q^65 - 4464 * q^66 + 67344 * q^67 - 9792 * q^68 + 6948 * q^69 + 76548 * q^71 + 10368 * q^72 - 47304 * q^73 - 23968 * q^74 - 2862 * q^75 - 33408 * q^76 - 25920 * q^78 + 140656 * q^79 - 27648 * q^80 + 13122 * q^81 - 80784 * q^82 - 94104 * q^83 + 57868 * q^85 - 4544 * q^86 - 41328 * q^87 - 7936 * q^88 + 17604 * q^89 - 34992 * q^90 + 12352 * q^92 - 88128 * q^93 - 147744 * q^94 + 91592 * q^95 + 18432 * q^96 - 85176 * q^97 - 10044 * q^99

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