LMFDB - Embedded newform 98.10.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,10,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("98.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.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:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 7165x^{4} + 16168x^{3} + 12807408x^{2} - 32180328x - 5372164 $ x^6 - 2x^5 - 7165x^4 + 16168x^3 + 12807408x^2 - 32180328*x - 5372164
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-61.3733$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} -143.106 q^{3} +256.000 q^{4} -474.347 q^{5} -2289.70 q^{6} +4096.00 q^{8} +796.313 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} -143.106 q^{3} +256.000 q^{4} -474.347 q^{5} -2289.70 q^{6} +4096.00 q^{8} +796.313 q^{9} -7589.55 q^{10} +10931.4 q^{11} -36635.1 q^{12} -64961.9 q^{13} +67881.8 q^{15} +65536.0 q^{16} -79631.4 q^{17} +12741.0 q^{18} -708069. q^{19} -121433. q^{20} +174902. q^{22} +1.94871e6 q^{23} -586162. q^{24} -1.72812e6 q^{25} -1.03939e6 q^{26} +2.70280e6 q^{27} +5.39846e6 q^{29} +1.08611e6 q^{30} -3.79389e6 q^{31} +1.04858e6 q^{32} -1.56434e6 q^{33} -1.27410e6 q^{34} +203856. q^{36} -4.06185e6 q^{37} -1.13291e7 q^{38} +9.29643e6 q^{39} -1.94292e6 q^{40} +1.51857e7 q^{41} +2.47532e7 q^{43} +2.79843e6 q^{44} -377729. q^{45} +3.11793e7 q^{46} +4.69758e7 q^{47} -9.37859e6 q^{48} -2.76499e7 q^{50} +1.13957e7 q^{51} -1.66302e7 q^{52} +5.18076e7 q^{53} +4.32448e7 q^{54} -5.18526e6 q^{55} +1.01329e8 q^{57} +8.63754e7 q^{58} +5.43631e7 q^{59} +1.73778e7 q^{60} +1.50378e8 q^{61} -6.07023e7 q^{62} +1.67772e7 q^{64} +3.08145e7 q^{65} -2.50295e7 q^{66} -1.53353e8 q^{67} -2.03856e7 q^{68} -2.78871e8 q^{69} +3.07635e8 q^{71} +3.26170e6 q^{72} -2.58970e8 q^{73} -6.49896e7 q^{74} +2.47304e8 q^{75} -1.81266e8 q^{76} +1.48743e8 q^{78} +2.27387e8 q^{79} -3.10868e7 q^{80} -4.02460e8 q^{81} +2.42972e8 q^{82} -4.55012e8 q^{83} +3.77729e7 q^{85} +3.96052e8 q^{86} -7.72552e8 q^{87} +4.47749e7 q^{88} +8.80524e8 q^{89} -6.04366e6 q^{90} +4.98869e8 q^{92} +5.42929e8 q^{93} +7.51613e8 q^{94} +3.35870e8 q^{95} -1.50057e8 q^{96} +1.78479e8 q^{97} +8.70479e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 96 q^{2} + 1536 q^{4} + 24576 q^{8} + 72550 q^{9}+O(q^{10}) $ 6 * q + 96 * q^2 + 1536 * q^4 + 24576 * q^8 + 72550 * q^9	$ 6 q + 96 q^{2} + 1536 q^{4} + 24576 q^{8} + 72550 q^{9} + 110664 q^{11} - 522728 q^{15} + 393216 q^{16} + 1160800 q^{18} + 1770624 q^{22} + 243384 q^{23} + 17125446 q^{25} + 10463640 q^{29} - 8363648 q^{30} + 6291456 q^{32} + 18572800 q^{36} + 24332568 q^{37} + 42635880 q^{39} + 74758584 q^{43} + 28329984 q^{44} + 3894144 q^{46} + 274007136 q^{50} + 260246248 q^{51} + 137815308 q^{53} + 449663960 q^{57} + 167418240 q^{58} - 133818368 q^{60} + 100663296 q^{64} + 565976460 q^{65} - 202943376 q^{67} + 614292768 q^{71} + 297164800 q^{72} + 389321088 q^{74} + 682174080 q^{78} - 182370096 q^{79} - 432881842 q^{81} + 2070495732 q^{85} + 1196137344 q^{86} + 453279744 q^{88} + 62306304 q^{92} + 190722192 q^{93} - 1311555480 q^{95} + 5322586792 q^{99}+O(q^{100}) $ 6 * q + 96 * q^2 + 1536 * q^4 + 24576 * q^8 + 72550 * q^9 + 110664 * q^11 - 522728 * q^15 + 393216 * q^16 + 1160800 * q^18 + 1770624 * q^22 + 243384 * q^23 + 17125446 * q^25 + 10463640 * q^29 - 8363648 * q^30 + 6291456 * q^32 + 18572800 * q^36 + 24332568 * q^37 + 42635880 * q^39 + 74758584 * q^43 + 28329984 * q^44 + 3894144 * q^46 + 274007136 * q^50 + 260246248 * q^51 + 137815308 * q^53 + 449663960 * q^57 + 167418240 * q^58 - 133818368 * q^60 + 100663296 * q^64 + 565976460 * q^65 - 202943376 * q^67 + 614292768 * q^71 + 297164800 * q^72 + 389321088 * q^74 + 682174080 * q^78 - 182370096 * q^79 - 432881842 * q^81 + 2070495732 * q^85 + 1196137344 * q^86 + 453279744 * q^88 + 62306304 * q^92 + 190722192 * q^93 - 1311555480 * q^95 + 5322586792 * 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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−143.106	−1.02003	−0.510014	−	0.860166i	$-0.670360\pi$
$3$	−143.106	−1.02003	−0.510014	+	0.860166i	$0.670360\pi$
$4$	256.000	0.500000
$5$	−474.347	−0.339415	−0.169707	−	0.985494i	$-0.554282\pi$
$5$	−474.347	−0.339415	−0.169707	+	0.985494i	$0.554282\pi$
$6$	−2289.70	−0.721269
$7$	0	0
$7$	0	0
$8$	4096.00	0.353553
$9$	796.313	0.0404569
$10$	−7589.55	−0.240003
$11$	10931.4	0.225116	0.112558	−	0.993645i	$-0.464096\pi$
$11$	10931.4	0.225116	0.112558	+	0.993645i	$0.464096\pi$
$12$	−36635.1	−0.510014
$13$	−64961.9	−0.630832	−0.315416	−	0.948954i	$-0.602144\pi$
$13$	−64961.9	−0.630832	−0.315416	+	0.948954i	$0.602144\pi$
$14$	0	0
$15$	67881.8	0.346213
$16$	65536.0	0.250000
$17$	−79631.4	−0.231241	−0.115620	−	0.993293i	$-0.536886\pi$
$17$	−79631.4	−0.231241	−0.115620	+	0.993293i	$0.536886\pi$
$18$	12741.0	0.0286074
$19$	−708069.	−1.24648	−0.623239	−	0.782032i	$-0.714183\pi$
$19$	−708069.	−1.24648	−0.623239	+	0.782032i	$0.714183\pi$
$20$	−121433.	−0.169707
$21$	0	0
$22$	174902.	0.159181
$23$	1.94871e6	1.45201	0.726007	−	0.687687i	$-0.241374\pi$
$23$	1.94871e6	1.45201	0.726007	+	0.687687i	$0.241374\pi$
$24$	−586162.	−0.360634
$25$	−1.72812e6	−0.884798
$26$	−1.03939e6	−0.446065
$27$	2.70280e6	0.978761
$28$	0	0
$29$	5.39846e6	1.41736	0.708678	−	0.705532i	$-0.249292\pi$
$29$	5.39846e6	1.41736	0.708678	+	0.705532i	$0.249292\pi$
$30$	1.08611e6	0.244809
$31$	−3.79389e6	−0.737832	−0.368916	−	0.929463i	$-0.620271\pi$
$31$	−3.79389e6	−0.737832	−0.368916	+	0.929463i	$0.620271\pi$
$32$	1.04858e6	0.176777
$33$	−1.56434e6	−0.229625
$34$	−1.27410e6	−0.163512
$35$	0	0
$36$	203856.	0.0202285
$37$	−4.06185e6	−0.356300	−0.178150	−	0.984003i	$-0.557011\pi$
$37$	−4.06185e6	−0.356300	−0.178150	+	0.984003i	$0.557011\pi$
$38$	−1.13291e7	−0.881392
$39$	9.29643e6	0.643466
$40$	−1.94292e6	−0.120001
$41$	1.51857e7	0.839284	0.419642	−	0.907690i	$-0.362156\pi$
$41$	1.51857e7	0.839284	0.419642	+	0.907690i	$0.362156\pi$
$42$	0	0
$43$	2.47532e7	1.10414	0.552070	−	0.833798i	$-0.313838\pi$
$43$	2.47532e7	1.10414	0.552070	+	0.833798i	$0.313838\pi$
$44$	2.79843e6	0.112558
$45$	−377729.	−0.0137317
$46$	3.11793e7	1.02673
$47$	4.69758e7	1.40422	0.702108	−	0.712070i	$-0.252242\pi$
$47$	4.69758e7	1.40422	0.702108	+	0.712070i	$0.252242\pi$
$48$	−9.37859e6	−0.255007
$49$	0	0
$50$	−2.76499e7	−0.625646
$51$	1.13957e7	0.235872
$52$	−1.66302e7	−0.315416
$53$	5.18076e7	0.901886	0.450943	−	0.892553i	$-0.351088\pi$
$53$	5.18076e7	0.901886	0.450943	+	0.892553i	$0.351088\pi$
$54$	4.32448e7	0.692088
$55$	−5.18526e6	−0.0764079
$56$	0	0
$57$	1.01329e8	1.27144
$58$	8.63754e7	1.00222
$59$	5.43631e7	0.584077	0.292038	−	0.956407i	$-0.405666\pi$
$59$	5.43631e7	0.584077	0.292038	+	0.956407i	$0.405666\pi$
$60$	1.73778e7	0.173106
$61$	1.50378e8	1.39059	0.695296	−	0.718724i	$-0.255273\pi$
$61$	1.50378e8	1.39059	0.695296	+	0.718724i	$0.255273\pi$
$62$	−6.07023e7	−0.521726
$63$	0	0
$64$	1.67772e7	0.125000
$65$	3.08145e7	0.214114
$66$	−2.50295e7	−0.162369
$67$	−1.53353e8	−0.929726	−0.464863	−	0.885383i	$-0.653896\pi$
$67$	−1.53353e8	−0.929726	−0.464863	+	0.885383i	$0.653896\pi$
$68$	−2.03856e7	−0.115620
$69$	−2.78871e8	−1.48110
$70$	0	0
$71$	3.07635e8	1.43672	0.718361	−	0.695670i	$-0.244892\pi$
$71$	3.07635e8	1.43672	0.718361	+	0.695670i	$0.244892\pi$
$72$	3.26170e6	0.0143037
$73$	−2.58970e8	−1.06732	−0.533662	−	0.845698i	$-0.679185\pi$
$73$	−2.58970e8	−1.06732	−0.533662	+	0.845698i	$0.679185\pi$
$74$	−6.49896e7	−0.251942
$75$	2.47304e8	0.902518
$76$	−1.81266e8	−0.623239
$77$	0	0
$78$	1.48743e8	0.454999
$79$	2.27387e8	0.656817	0.328409	−	0.944536i	$-0.393488\pi$
$79$	2.27387e8	0.656817	0.328409	+	0.944536i	$0.393488\pi$
$80$	−3.10868e7	−0.0848537
$81$	−4.02460e8	−1.03882
$82$	2.42972e8	0.593463
$83$	−4.55012e8	−1.05238	−0.526188	−	0.850368i	$-0.676379\pi$
$83$	−4.55012e8	−1.05238	−0.526188	+	0.850368i	$0.676379\pi$
$84$	0	0
$85$	3.77729e7	0.0784865
$86$	3.96052e8	0.780745
$87$	−7.72552e8	−1.44574
$88$	4.47749e7	0.0795907
$89$	8.80524e8	1.48760	0.743800	−	0.668402i	$-0.233022\pi$
$89$	8.80524e8	1.48760	0.743800	+	0.668402i	$0.233022\pi$
$90$	−6.04366e6	−0.00970976
$91$	0	0
$92$	4.98869e8	0.726007
$93$	5.42929e8	0.752609
$94$	7.51613e8	0.992931
$95$	3.35870e8	0.423073
$96$	−1.50057e8	−0.180317
$97$	1.78479e8	0.204699	0.102349	−	0.994749i	$-0.467364\pi$
$97$	1.78479e8	0.204699	0.102349	+	0.994749i	$0.467364\pi$
$98$	0	0
$99$	8.70479e6	0.00910752
$100$	−4.42399e8	−0.442399
$101$	−2.92368e8	−0.279565	−0.139783	−	0.990182i	$-0.544640\pi$
$101$	−2.92368e8	−0.279565	−0.139783	+	0.990182i	$0.544640\pi$
$102$	1.82332e8	0.166787
$103$	7.34489e8	0.643011	0.321505	−	0.946908i	$-0.395811\pi$
$103$	7.34489e8	0.643011	0.321505	+	0.946908i	$0.395811\pi$
$104$	−2.66084e8	−0.223033
$105$	0	0
$106$	8.28921e8	0.637730
$107$	−8.60254e8	−0.634453	−0.317227	−	0.948350i	$-0.602752\pi$
$107$	−8.60254e8	−0.634453	−0.317227	+	0.948350i	$0.602752\pi$
$108$	6.91916e8	0.489380
$109$	2.63793e9	1.78996	0.894981	−	0.446104i	$-0.147189\pi$
$109$	2.63793e9	1.78996	0.894981	+	0.446104i	$0.147189\pi$
$110$	−8.29641e7	−0.0540285
$111$	5.81275e8	0.363436
$112$	0	0
$113$	−3.19349e8	−0.184252	−0.0921262	−	0.995747i	$-0.529366\pi$
$113$	−3.19349e8	−0.184252	−0.0921262	+	0.995747i	$0.529366\pi$
$114$	1.62126e9	0.899045
$115$	−9.24362e8	−0.492835
$116$	1.38201e9	0.708678
$117$	−5.17300e7	−0.0255215
$118$	8.69809e8	0.413005
$119$	0	0
$120$	2.78044e8	0.122405
$121$	−2.23845e9	−0.949323
$122$	2.40605e9	0.983297
$123$	−2.17317e9	−0.856093
$124$	−9.71237e8	−0.368916
$125$	1.74619e9	0.639728
$126$	0	0
$127$	2.68274e7	0.00915085	0.00457542	−	0.999990i	$-0.498544\pi$
$127$	2.68274e7	0.00915085	0.00457542	+	0.999990i	$0.498544\pi$
$128$	2.68435e8	0.0883883
$129$	−3.54234e9	−1.12625
$130$	4.93031e8	0.151401
$131$	−2.91442e9	−0.864633	−0.432317	−	0.901722i	$-0.642304\pi$
$131$	−2.91442e9	−0.864633	−0.432317	+	0.901722i	$0.642304\pi$
$132$	−4.00472e8	−0.114813
$133$	0	0
$134$	−2.45364e9	−0.657416
$135$	−1.28206e9	−0.332206
$136$	−3.26170e8	−0.0817559
$137$	−4.25031e9	−1.03081	−0.515405	−	0.856947i	$-0.672358\pi$
$137$	−4.25031e9	−1.03081	−0.515405	+	0.856947i	$0.672358\pi$
$138$	−4.46194e9	−1.04729
$139$	6.13097e9	1.39304	0.696519	−	0.717538i	$-0.254731\pi$
$139$	6.13097e9	1.39304	0.696519	+	0.717538i	$0.254731\pi$
$140$	0	0
$141$	−6.72252e9	−1.43234
$142$	4.92216e9	1.01592
$143$	−7.10122e8	−0.142011
$144$	5.21872e7	0.0101142
$145$	−2.56074e9	−0.481072
$146$	−4.14352e9	−0.754712
$147$	0	0
$148$	−1.03983e9	−0.178150
$149$	−1.01658e10	−1.68968	−0.844839	−	0.535020i	$-0.820304\pi$
$149$	−1.01658e10	−1.68968	−0.844839	+	0.535020i	$0.820304\pi$
$150$	3.95687e9	0.638177
$151$	−1.11772e10	−1.74959	−0.874796	−	0.484491i	$-0.839005\pi$
$151$	−1.11772e10	−1.74959	−0.874796	+	0.484491i	$0.839005\pi$
$152$	−2.90025e9	−0.440696
$153$	−6.34115e7	−0.00935528
$154$	0	0
$155$	1.79962e9	0.250431
$156$	2.37989e9	0.321733
$157$	7.75337e9	1.01846	0.509228	−	0.860632i	$-0.329931\pi$
$157$	7.75337e9	1.01846	0.509228	+	0.860632i	$0.329931\pi$
$158$	3.63820e9	0.464440
$159$	−7.41397e9	−0.919949
$160$	−4.97389e8	−0.0600006
$161$	0	0
$162$	−6.43936e9	−0.734557
$163$	−8.29824e9	−0.920750	−0.460375	−	0.887724i	$-0.652285\pi$
$163$	−8.29824e9	−0.920750	−0.460375	+	0.887724i	$0.652285\pi$
$164$	3.88755e9	0.419642
$165$	7.42041e8	0.0779382
$166$	−7.28019e9	−0.744142
$167$	−4.65724e8	−0.0463345	−0.0231672	−	0.999732i	$-0.507375\pi$
$167$	−4.65724e8	−0.0463345	−0.0231672	+	0.999732i	$0.507375\pi$
$168$	0	0
$169$	−6.38445e9	−0.602051
$170$	6.04366e8	0.0554983
$171$	−5.63845e8	−0.0504286
$172$	6.33683e9	0.552070
$173$	1.58962e10	1.34923	0.674614	−	0.738170i	$-0.264310\pi$
$173$	1.58962e10	1.34923	0.674614	+	0.738170i	$0.264310\pi$
$174$	−1.23608e10	−1.02229
$175$	0	0
$176$	7.16398e8	0.0562791
$177$	−7.77968e9	−0.595775
$178$	1.40884e10	1.05189
$179$	−9.58336e9	−0.697717	−0.348858	−	0.937175i	$-0.613431\pi$
$179$	−9.58336e9	−0.697717	−0.348858	+	0.937175i	$0.613431\pi$
$180$	−9.66986e7	−0.00686584
$181$	1.70867e10	1.18333	0.591663	−	0.806185i	$-0.298472\pi$
$181$	1.70867e10	1.18333	0.591663	+	0.806185i	$0.298472\pi$
$182$	0	0
$183$	−2.15200e10	−1.41844
$184$	7.98190e9	0.513365
$185$	1.92673e9	0.120934
$186$	8.68686e9	0.532175
$187$	−8.70479e8	−0.0520560
$188$	1.20258e10	0.702108
$189$	0	0
$190$	5.37392e9	0.299158
$191$	1.63607e8	0.00889512	0.00444756	−	0.999990i	$-0.498584\pi$
$191$	1.63607e8	0.00889512	0.00444756	+	0.999990i	$0.498584\pi$
$192$	−2.40092e9	−0.127503
$193$	2.13018e10	1.10512	0.552558	−	0.833475i	$-0.313652\pi$
$193$	2.13018e10	1.10512	0.552558	+	0.833475i	$0.313652\pi$
$194$	2.85567e9	0.144744
$195$	−4.40973e9	−0.218402
$196$	0	0
$197$	8.77150e9	0.414931	0.207465	−	0.978242i	$-0.433479\pi$
$197$	8.77150e9	0.414931	0.207465	+	0.978242i	$0.433479\pi$
$198$	1.39277e8	0.00643999
$199$	−3.12398e10	−1.41211	−0.706056	−	0.708156i	$-0.749527\pi$
$199$	−3.12398e10	−1.41211	−0.706056	+	0.708156i	$0.749527\pi$
$200$	−7.07838e9	−0.312823
$201$	2.19457e10	0.948347
$202$	−4.67788e9	−0.197682
$203$	0	0
$204$	2.91730e9	0.117936
$205$	−7.20331e9	−0.284865
$206$	1.17518e10	0.454677
$207$	1.55178e9	0.0587440
$208$	−4.25734e9	−0.157708
$209$	−7.74016e9	−0.280603
$210$	0	0
$211$	4.63585e10	1.61012	0.805061	−	0.593192i	$-0.202133\pi$
$211$	4.63585e10	1.61012	0.805061	+	0.593192i	$0.202133\pi$
$212$	1.32627e10	0.450943
$213$	−4.40244e10	−1.46550
$214$	−1.37641e10	−0.448626
$215$	−1.17416e10	−0.374761
$216$	1.10707e10	0.346044
$217$	0	0
$218$	4.22069e10	1.26569
$219$	3.70601e10	1.08870
$220$	−1.32743e9	−0.0382039
$221$	5.17300e9	0.145874
$222$	9.30040e9	0.256988
$223$	−1.21315e10	−0.328505	−0.164253	−	0.986418i	$-0.552521\pi$
$223$	−1.21315e10	−0.328505	−0.164253	+	0.986418i	$0.552521\pi$
$224$	0	0
$225$	−1.37613e9	−0.0357962
$226$	−5.10959e9	−0.130286
$227$	−3.79090e10	−0.947602	−0.473801	−	0.880632i	$-0.657118\pi$
$227$	−3.79090e10	−0.947602	−0.473801	+	0.880632i	$0.657118\pi$
$228$	2.59402e10	0.635721
$229$	9.29606e9	0.223377	0.111689	−	0.993743i	$-0.464374\pi$
$229$	9.29606e9	0.223377	0.111689	+	0.993743i	$0.464374\pi$
$230$	−1.47898e10	−0.348487
$231$	0	0
$232$	2.21121e10	0.501111
$233$	3.72959e10	0.829010	0.414505	−	0.910047i	$-0.363955\pi$
$233$	3.72959e10	0.829010	0.414505	+	0.910047i	$0.363955\pi$
$234$	−8.27681e8	−0.0180464
$235$	−2.22828e10	−0.476612
$236$	1.39169e10	0.292038
$237$	−3.25405e10	−0.669972
$238$	0	0
$239$	5.93728e10	1.17706	0.588528	−	0.808477i	$-0.299708\pi$
$239$	5.93728e10	1.17706	0.588528	+	0.808477i	$0.299708\pi$
$240$	4.44870e9	0.0865532
$241$	5.82571e10	1.11243	0.556214	−	0.831039i	$-0.312253\pi$
$241$	5.82571e10	1.11243	0.556214	+	0.831039i	$0.312253\pi$
$242$	−3.58152e10	−0.671272
$243$	4.39529e9	0.0808648
$244$	3.84967e10	0.695296
$245$	0	0
$246$	−3.47707e10	−0.605349
$247$	4.59975e10	0.786317
$248$	−1.55398e10	−0.260863
$249$	6.51149e10	1.07345
$250$	2.79390e10	0.452356
$251$	−3.20706e10	−0.510007	−0.255003	−	0.966940i	$-0.582077\pi$
$251$	−3.20706e10	−0.510007	−0.255003	+	0.966940i	$0.582077\pi$
$252$	0	0
$253$	2.13020e10	0.326872
$254$	4.29238e8	0.00647063
$255$	−5.40552e9	−0.0800584
$256$	4.29497e9	0.0625000
$257$	1.28831e11	1.84213	0.921067	−	0.389405i	$-0.127319\pi$
$257$	1.28831e11	1.84213	0.921067	+	0.389405i	$0.127319\pi$
$258$	−5.66774e10	−0.796381
$259$	0	0
$260$	7.88850e9	0.107057
$261$	4.29887e9	0.0573419
$262$	−4.66308e10	−0.611388
$263$	−1.64719e10	−0.212296	−0.106148	−	0.994350i	$-0.533852\pi$
$263$	−1.64719e10	−0.212296	−0.106148	+	0.994350i	$0.533852\pi$
$264$	−6.40755e9	−0.0811847
$265$	−2.45748e10	−0.306114
$266$	0	0
$267$	−1.26008e11	−1.51739
$268$	−3.92583e10	−0.464863
$269$	8.49310e10	0.988965	0.494482	−	0.869188i	$-0.335358\pi$
$269$	8.49310e10	0.988965	0.494482	+	0.869188i	$0.335358\pi$
$270$	−2.05130e10	−0.234905
$271$	−7.20132e9	−0.0811055	−0.0405528	−	0.999177i	$-0.512912\pi$
$271$	−7.20132e9	−0.0811055	−0.0405528	+	0.999177i	$0.512912\pi$
$272$	−5.21872e9	−0.0578101
$273$	0	0
$274$	−6.80050e10	−0.728893
$275$	−1.88907e10	−0.199182
$276$	−7.13911e10	−0.740548
$277$	1.34429e10	0.137194	0.0685970	−	0.997644i	$-0.478148\pi$
$277$	1.34429e10	0.137194	0.0685970	+	0.997644i	$0.478148\pi$
$278$	9.80956e10	0.985026
$279$	−3.02113e9	−0.0298504
$280$	0	0
$281$	1.20215e11	1.15022	0.575108	−	0.818077i	$-0.304960\pi$
$281$	1.20215e11	1.15022	0.575108	+	0.818077i	$0.304960\pi$
$282$	−1.07560e11	−1.01282
$283$	1.62973e11	1.51034	0.755172	−	0.655527i	$-0.227554\pi$
$283$	1.62973e11	1.51034	0.755172	+	0.655527i	$0.227554\pi$
$284$	7.87545e10	0.718361
$285$	−4.80650e10	−0.431546
$286$	−1.13620e10	−0.100417
$287$	0	0
$288$	8.34995e8	0.00715184
$289$	−1.12247e11	−0.946528
$290$	−4.09719e10	−0.340169
$291$	−2.55414e10	−0.208798
$292$	−6.62963e10	−0.533662
$293$	6.53971e9	0.0518387	0.0259194	−	0.999664i	$-0.491749\pi$
$293$	6.53971e9	0.0518387	0.0259194	+	0.999664i	$0.491749\pi$
$294$	0	0
$295$	−2.57869e10	−0.198244
$296$	−1.66373e10	−0.125971
$297$	2.95453e10	0.220335
$298$	−1.62653e11	−1.19478
$299$	−1.26592e11	−0.915977
$300$	6.33099e10	0.451259
$301$	0	0
$302$	−1.78835e11	−1.23715
$303$	4.18395e10	0.285164
$304$	−4.64040e10	−0.311619
$305$	−7.13312e10	−0.471987
$306$	−1.01458e9	−0.00661518
$307$	5.92298e10	0.380555	0.190278	−	0.981730i	$-0.439061\pi$
$307$	5.92298e10	0.380555	0.190278	+	0.981730i	$0.439061\pi$
$308$	0	0
$309$	−1.05110e11	−0.655889
$310$	2.87939e10	0.177082
$311$	9.96027e10	0.603739	0.301870	−	0.953349i	$-0.402389\pi$
$311$	9.96027e10	0.603739	0.301870	+	0.953349i	$0.402389\pi$
$312$	3.80782e10	0.227500
$313$	−2.68182e11	−1.57935	−0.789677	−	0.613522i	$-0.789752\pi$
$313$	−2.68182e11	−1.57935	−0.789677	+	0.613522i	$0.789752\pi$
$314$	1.24054e11	0.720157
$315$	0	0
$316$	5.82112e10	0.328409
$317$	2.40883e11	1.33980	0.669900	−	0.742451i	$-0.266337\pi$
$317$	2.40883e11	1.33980	0.669900	+	0.742451i	$0.266337\pi$
$318$	−1.18624e11	−0.650502
$319$	5.90126e10	0.319070
$320$	−7.95822e9	−0.0424269
$321$	1.23107e11	0.647160
$322$	0	0
$323$	5.63845e10	0.288236
$324$	−1.03030e11	−0.519410
$325$	1.12262e11	0.558158
$326$	−1.32772e11	−0.651069
$327$	−3.77503e11	−1.82581
$328$	6.22008e10	0.296732
$329$	0	0
$330$	1.18727e10	0.0551106
$331$	−6.42244e10	−0.294086	−0.147043	−	0.989130i	$-0.546976\pi$
$331$	−6.42244e10	−0.294086	−0.147043	+	0.989130i	$0.546976\pi$
$332$	−1.16483e11	−0.526188
$333$	−3.23451e9	−0.0144148
$334$	−7.45158e9	−0.0327634
$335$	7.27424e10	0.315563
$336$	0	0
$337$	−1.77107e11	−0.747999	−0.374000	−	0.927429i	$-0.622014\pi$
$337$	−1.77107e11	−0.747999	−0.374000	+	0.927429i	$0.622014\pi$
$338$	−1.02151e11	−0.425714
$339$	4.57008e10	0.187943
$340$	9.66986e9	0.0392432
$341$	−4.14724e10	−0.166098
$342$	−9.02152e9	−0.0356584
$343$	0	0
$344$	1.01389e11	0.390372
$345$	1.32282e11	0.502706
$346$	2.54339e11	0.954049
$347$	3.70366e11	1.37135	0.685676	−	0.727907i	$-0.259507\pi$
$347$	3.70366e11	1.37135	0.685676	+	0.727907i	$0.259507\pi$
$348$	−1.97773e11	−0.722872
$349$	−1.67459e11	−0.604219	−0.302109	−	0.953273i	$-0.597691\pi$
$349$	−1.67459e11	−0.604219	−0.302109	+	0.953273i	$0.597691\pi$
$350$	0	0
$351$	−1.75579e11	−0.617433
$352$	1.14624e10	0.0397953
$353$	−3.95218e11	−1.35472	−0.677361	−	0.735651i	$-0.736876\pi$
$353$	−3.95218e11	−1.35472	−0.677361	+	0.735651i	$0.736876\pi$
$354$	−1.24475e11	−0.421276
$355$	−1.45926e11	−0.487645
$356$	2.25414e11	0.743800
$357$	0	0
$358$	−1.53334e11	−0.493360
$359$	−3.98350e11	−1.26573	−0.632863	−	0.774264i	$-0.718120\pi$
$359$	−3.98350e11	−1.26573	−0.632863	+	0.774264i	$0.718120\pi$
$360$	−1.54718e9	−0.00485488
$361$	1.78674e11	0.553705
$362$	2.73387e11	0.836738
$363$	3.20336e11	0.968336
$364$	0	0
$365$	1.22842e11	0.362266
$366$	−3.44319e11	−1.00299
$367$	3.28613e11	0.945556	0.472778	−	0.881182i	$-0.343251\pi$
$367$	3.28613e11	0.945556	0.472778	+	0.881182i	$0.343251\pi$
$368$	1.27710e11	0.363004
$369$	1.20926e10	0.0339548
$370$	3.08276e10	0.0855130
$371$	0	0
$372$	1.38990e11	0.376305
$373$	1.10852e11	0.296521	0.148260	−	0.988948i	$-0.452633\pi$
$373$	1.10852e11	0.296521	0.148260	+	0.988948i	$0.452633\pi$
$374$	−1.39277e10	−0.0368092
$375$	−2.49890e11	−0.652541
$376$	1.92413e11	0.496466
$377$	−3.50694e11	−0.894114
$378$	0	0
$379$	−5.61446e11	−1.39776	−0.698878	−	0.715241i	$-0.746317\pi$
$379$	−5.61446e11	−1.39776	−0.698878	+	0.715241i	$0.746317\pi$
$380$	8.59828e10	0.211536
$381$	−3.83916e9	−0.00933412
$382$	2.61771e9	0.00628980
$383$	7.73633e11	1.83713	0.918566	−	0.395267i	$-0.129348\pi$
$383$	7.73633e11	1.83713	0.918566	+	0.395267i	$0.129348\pi$
$384$	−3.84147e10	−0.0901586
$385$	0	0
$386$	3.40828e11	0.781435
$387$	1.97113e10	0.0446701
$388$	4.56907e10	0.102349
$389$	−5.91513e10	−0.130976	−0.0654879	−	0.997853i	$-0.520860\pi$
$389$	−5.91513e10	−0.130976	−0.0654879	+	0.997853i	$0.520860\pi$
$390$	−7.05557e10	−0.154434
$391$	−1.55178e11	−0.335765
$392$	0	0
$393$	4.17072e11	0.881950
$394$	1.40344e11	0.293400
$395$	−1.07861e11	−0.222934
$396$	2.22843e9	0.00455376
$397$	4.17298e11	0.843120	0.421560	−	0.906800i	$-0.361483\pi$
$397$	4.17298e11	0.843120	0.421560	+	0.906800i	$0.361483\pi$
$398$	−4.99836e11	−0.998514
$399$	0	0
$400$	−1.13254e11	−0.221199
$401$	2.44698e11	0.472585	0.236293	−	0.971682i	$-0.424068\pi$
$401$	2.44698e11	0.472585	0.236293	+	0.971682i	$0.424068\pi$
$402$	3.51131e11	0.670582
$403$	2.46459e11	0.465448
$404$	−7.48461e10	−0.139783
$405$	1.90906e11	0.352591
$406$	0	0
$407$	−4.44016e10	−0.0802091
$408$	4.66769e10	0.0833933
$409$	−2.21356e11	−0.391144	−0.195572	−	0.980689i	$-0.562656\pi$
$409$	−2.21356e11	−0.391144	−0.195572	+	0.980689i	$0.562656\pi$
$410$	−1.15253e11	−0.201430
$411$	6.08245e11	1.05145
$412$	1.88029e11	0.321505
$413$	0	0
$414$	2.48285e10	0.0415383
$415$	2.15833e11	0.357192
$416$	−6.81175e10	−0.111516
$417$	−8.77379e11	−1.42094
$418$	−1.23843e11	−0.198416
$419$	−6.86922e11	−1.08879	−0.544395	−	0.838829i	$-0.683241\pi$
$419$	−6.86922e11	−1.08879	−0.544395	+	0.838829i	$0.683241\pi$
$420$	0	0
$421$	8.26071e11	1.28159	0.640793	−	0.767714i	$-0.278606\pi$
$421$	8.26071e11	1.28159	0.640793	+	0.767714i	$0.278606\pi$
$422$	7.41736e11	1.13853
$423$	3.74075e10	0.0568103
$424$	2.12204e11	0.318865
$425$	1.37613e11	0.204601
$426$	−7.04390e11	−1.03626
$427$	0	0
$428$	−2.20225e11	−0.317227
$429$	1.01623e11	0.144855
$430$	−1.87866e11	−0.264996
$431$	−1.67951e11	−0.234441	−0.117221	−	0.993106i	$-0.537398\pi$
$431$	−1.67951e11	−0.234441	−0.117221	+	0.993106i	$0.537398\pi$
$432$	1.77131e11	0.244690
$433$	−1.18681e12	−1.62250	−0.811249	−	0.584701i	$-0.801212\pi$
$433$	−1.18681e12	−1.62250	−0.811249	+	0.584701i	$0.801212\pi$
$434$	0	0
$435$	3.66458e11	0.490707
$436$	6.75310e11	0.894981
$437$	−1.37982e12	−1.80990
$438$	5.92962e11	0.769828
$439$	−1.13578e12	−1.45950	−0.729749	−	0.683715i	$-0.760363\pi$
$439$	−1.13578e12	−1.45950	−0.729749	+	0.683715i	$0.760363\pi$
$440$	−2.12388e10	−0.0270143
$441$	0	0
$442$	8.27681e10	0.103148
$443$	−8.85219e11	−1.09203	−0.546014	−	0.837776i	$-0.683855\pi$
$443$	−8.85219e11	−1.09203	−0.546014	+	0.837776i	$0.683855\pi$
$444$	1.48806e11	0.181718
$445$	−4.17674e11	−0.504914
$446$	−1.94104e11	−0.232288
$447$	1.45479e12	1.72352
$448$	0	0
$449$	1.29277e12	1.50111	0.750555	−	0.660808i	$-0.229786\pi$
$449$	1.29277e12	1.50111	0.750555	+	0.660808i	$0.229786\pi$
$450$	−2.20180e10	−0.0253117
$451$	1.66001e11	0.188937
$452$	−8.17534e10	−0.0921262
$453$	1.59952e12	1.78463
$454$	−6.06544e11	−0.670055
$455$	0	0
$456$	4.15043e11	0.449522
$457$	7.90262e11	0.847517	0.423758	−	0.905775i	$-0.360711\pi$
$457$	7.90262e11	0.847517	0.423758	+	0.905775i	$0.360711\pi$
$458$	1.48737e11	0.157952
$459$	−2.15227e11	−0.226329
$460$	−2.36637e11	−0.246418
$461$	−6.98259e10	−0.0720049	−0.0360025	−	0.999352i	$-0.511462\pi$
$461$	−6.98259e10	−0.0720049	−0.0360025	+	0.999352i	$0.511462\pi$
$462$	0	0
$463$	2.12109e11	0.214509	0.107254	−	0.994232i	$-0.465794\pi$
$463$	2.12109e11	0.214509	0.107254	+	0.994232i	$0.465794\pi$
$464$	3.53794e11	0.354339
$465$	−2.57536e11	−0.255447
$466$	5.96735e11	0.586198
$467$	7.71373e11	0.750479	0.375239	−	0.926928i	$-0.377561\pi$
$467$	7.71373e11	0.750479	0.375239	+	0.926928i	$0.377561\pi$
$468$	−1.32429e10	−0.0127608
$469$	0	0
$470$	−3.56525e11	−0.337016
$471$	−1.10955e12	−1.03885
$472$	2.22671e11	0.206502
$473$	2.70587e11	0.248560
$474$	−5.20648e11	−0.473742
$475$	1.22363e12	1.10288
$476$	0	0
$477$	4.12551e10	0.0364875
$478$	9.49965e11	0.832304
$479$	−7.61804e11	−0.661201	−0.330601	−	0.943771i	$-0.607251\pi$
$479$	−7.61804e11	−0.661201	−0.330601	+	0.943771i	$0.607251\pi$
$480$	7.11793e10	0.0612023
$481$	2.63865e11	0.224766
$482$	9.32114e11	0.786606
$483$	0	0
$484$	−5.73044e11	−0.474661
$485$	−8.46610e10	−0.0694778
$486$	7.03247e10	0.0571801
$487$	1.00175e12	0.807007	0.403503	−	0.914978i	$-0.367792\pi$
$487$	1.00175e12	0.807007	0.403503	+	0.914978i	$0.367792\pi$
$488$	6.15948e11	0.491648
$489$	1.18753e12	0.939191
$490$	0	0
$491$	−1.69916e12	−1.31937	−0.659686	−	0.751541i	$-0.729311\pi$
$491$	−1.69916e12	−1.31937	−0.659686	+	0.751541i	$0.729311\pi$
$492$	−5.56332e11	−0.428046
$493$	−4.29887e11	−0.327750
$494$	7.35960e11	0.556010
$495$	−4.12909e9	−0.00309123
$496$	−2.48637e11	−0.184458
$497$	0	0
$498$	1.04184e12	0.759046
$499$	−1.19292e12	−0.861311	−0.430655	−	0.902516i	$-0.641718\pi$
$499$	−1.19292e12	−0.861311	−0.430655	+	0.902516i	$0.641718\pi$
$500$	4.47024e11	0.319864
$501$	6.66478e10	0.0472625
$502$	−5.13130e11	−0.360629
$503$	−6.26154e10	−0.0436140	−0.0218070	−	0.999762i	$-0.506942\pi$
$503$	−6.26154e10	−0.0436140	−0.0218070	+	0.999762i	$0.506942\pi$
$504$	0	0
$505$	1.38684e11	0.0948886
$506$	3.40832e11	0.231134
$507$	9.13653e11	0.614109
$508$	6.86781e9	0.00457542
$509$	−1.51259e11	−0.0998827	−0.0499413	−	0.998752i	$-0.515903\pi$
$509$	−1.51259e11	−0.0998827	−0.0499413	+	0.998752i	$0.515903\pi$
$510$	−8.64884e10	−0.0566098
$511$	0	0
$512$	6.87195e10	0.0441942
$513$	−1.91377e12	−1.22000
$514$	2.06129e12	1.30258
$515$	−3.48403e11	−0.218247
$516$	−9.06838e11	−0.563127
$517$	5.13510e11	0.316112
$518$	0	0
$519$	−2.27484e12	−1.37625
$520$	1.26216e11	0.0757006
$521$	−3.95351e11	−0.235079	−0.117539	−	0.993068i	$-0.537501\pi$
$521$	−3.95351e11	−0.235079	−0.117539	+	0.993068i	$0.537501\pi$
$522$	6.87819e10	0.0405468
$523$	−3.35119e12	−1.95858	−0.979289	−	0.202465i	$-0.935105\pi$
$523$	−3.35119e12	−1.95858	−0.979289	+	0.202465i	$0.935105\pi$
$524$	−7.46093e11	−0.432317
$525$	0	0
$526$	−2.63550e11	−0.150116
$527$	3.02113e11	0.170617
$528$	−1.02521e11	−0.0574063
$529$	1.99630e12	1.10835
$530$	−3.93196e11	−0.216455
$531$	4.32900e10	0.0236299
$532$	0	0
$533$	−9.86495e11	−0.529447
$534$	−2.01613e12	−1.07296
$535$	4.08059e11	0.215343
$536$	−6.28133e11	−0.328708
$537$	1.37144e12	0.711690
$538$	1.35890e12	0.699304
$539$	0	0
$540$	−3.28208e11	−0.166103
$541$	3.15478e12	1.58337	0.791684	−	0.610931i	$-0.209205\pi$
$541$	3.15478e12	1.58337	0.791684	+	0.610931i	$0.209205\pi$
$542$	−1.15221e11	−0.0573503
$543$	−2.44521e12	−1.20703
$544$	−8.34995e10	−0.0408779
$545$	−1.25129e12	−0.607540
$546$	0	0
$547$	−1.93469e12	−0.923993	−0.461997	−	0.886882i	$-0.652867\pi$
$547$	−1.93469e12	−0.923993	−0.461997	+	0.886882i	$0.652867\pi$
$548$	−1.08808e12	−0.515405
$549$	1.19748e11	0.0562590
$550$	−3.02251e11	−0.140843
$551$	−3.82248e12	−1.76670
$552$	−1.14226e12	−0.523646
$553$	0	0
$554$	2.15087e11	0.0970108
$555$	−2.75726e11	−0.123356
$556$	1.56953e12	0.696519
$557$	−2.75837e12	−1.21424	−0.607120	−	0.794610i	$-0.707675\pi$
$557$	−2.75837e12	−1.21424	−0.607120	+	0.794610i	$0.707675\pi$
$558$	−4.83381e10	−0.0211074
$559$	−1.60802e12	−0.696526
$560$	0	0
$561$	1.24571e11	0.0530986
$562$	1.92344e12	0.813326
$563$	−1.33949e11	−0.0561891	−0.0280946	−	0.999605i	$-0.508944\pi$
$563$	−1.33949e11	−0.0561891	−0.0280946	+	0.999605i	$0.508944\pi$
$564$	−1.72097e12	−0.716170
$565$	1.51482e11	0.0625380
$566$	2.60756e12	1.06797
$567$	0	0
$568$	1.26007e12	0.507958
$569$	−4.00617e12	−1.60223	−0.801113	−	0.598513i	$-0.795758\pi$
$569$	−4.00617e12	−1.60223	−0.801113	+	0.598513i	$0.795758\pi$
$570$	−7.69040e11	−0.305149
$571$	−4.89470e11	−0.192692	−0.0963461	−	0.995348i	$-0.530716\pi$
$571$	−4.89470e11	−0.192692	−0.0963461	+	0.995348i	$0.530716\pi$
$572$	−1.81791e11	−0.0710053
$573$	−2.34132e10	−0.00907328
$574$	0	0
$575$	−3.36760e12	−1.28474
$576$	1.33599e10	0.00505711
$577$	2.81679e12	1.05795	0.528973	−	0.848638i	$-0.322577\pi$
$577$	2.81679e12	1.05795	0.528973	+	0.848638i	$0.322577\pi$
$578$	−1.79595e12	−0.669296
$579$	−3.04841e12	−1.12725
$580$	−6.55550e11	−0.240536
$581$	0	0
$582$	−4.08663e11	−0.147643
$583$	5.66327e11	0.203029
$584$	−1.06074e12	−0.377356
$585$	2.45380e10	0.00866238
$586$	1.04635e11	0.0366555
$587$	4.96674e12	1.72663	0.863316	−	0.504663i	$-0.168383\pi$
$587$	4.96674e12	1.72663	0.863316	+	0.504663i	$0.168383\pi$
$588$	0	0
$589$	2.68634e12	0.919691
$590$	−4.12591e11	−0.140180
$591$	−1.25525e12	−0.423241
$592$	−2.66197e11	−0.0890751
$593$	3.03376e12	1.00748	0.503738	−	0.863856i	$-0.331958\pi$
$593$	3.03376e12	1.00748	0.503738	+	0.863856i	$0.331958\pi$
$594$	4.72724e11	0.155800
$595$	0	0
$596$	−2.60245e12	−0.844839
$597$	4.47060e12	1.44039
$598$	−2.02547e12	−0.647693
$599$	−2.58910e12	−0.821728	−0.410864	−	0.911697i	$-0.634773\pi$
$599$	−2.58910e12	−0.821728	−0.410864	+	0.911697i	$0.634773\pi$
$600$	1.01296e12	0.319088
$601$	−6.11026e12	−1.91040	−0.955200	−	0.295960i	$-0.904360\pi$
$601$	−6.11026e12	−1.91040	−0.955200	+	0.295960i	$0.904360\pi$
$602$	0	0
$603$	−1.22117e11	−0.0376139
$604$	−2.86136e12	−0.874796
$605$	1.06180e12	0.322214
$606$	6.69433e11	0.201642
$607$	−2.85460e12	−0.853486	−0.426743	−	0.904373i	$-0.640339\pi$
$607$	−2.85460e12	−0.853486	−0.426743	+	0.904373i	$0.640339\pi$
$608$	−7.42464e11	−0.220348
$609$	0	0
$610$	−1.14130e12	−0.333746
$611$	−3.05164e12	−0.885825
$612$	−1.62333e10	−0.00467764
$613$	6.38939e12	1.82763	0.913813	−	0.406134i	$-0.133123\pi$
$613$	6.38939e12	1.82763	0.913813	+	0.406134i	$0.133123\pi$
$614$	9.47677e11	0.269093
$615$	1.03084e12	0.290571
$616$	0	0
$617$	2.49727e12	0.693716	0.346858	−	0.937918i	$-0.387249\pi$
$617$	2.49727e12	0.693716	0.346858	+	0.937918i	$0.387249\pi$
$618$	−1.68176e12	−0.463783
$619$	5.63167e12	1.54180	0.770902	−	0.636953i	$-0.219806\pi$
$619$	5.63167e12	1.54180	0.770902	+	0.636953i	$0.219806\pi$
$620$	4.60703e11	0.125216
$621$	5.26696e12	1.42117
$622$	1.59364e12	0.426908
$623$	0	0
$624$	6.09251e11	0.160867
$625$	2.54694e12	0.667664
$626$	−4.29091e12	−1.11677
$627$	1.10766e12	0.286222
$628$	1.98486e12	0.509228
$629$	3.23451e11	0.0823911
$630$	0	0
$631$	4.25383e12	1.06819	0.534094	−	0.845425i	$-0.320653\pi$
$631$	4.25383e12	1.06819	0.534094	+	0.845425i	$0.320653\pi$
$632$	9.31379e11	0.232220
$633$	−6.63418e12	−1.64237
$634$	3.85413e12	0.947382
$635$	−1.27255e10	−0.00310593
$636$	−1.89798e12	−0.459975
$637$	0	0
$638$	9.44201e11	0.225617
$639$	2.44974e11	0.0581254
$640$	−1.27331e11	−0.0300003
$641$	7.15877e12	1.67485	0.837427	−	0.546549i	$-0.184059\pi$
$641$	7.15877e12	1.67485	0.837427	+	0.546549i	$0.184059\pi$
$642$	1.96972e12	0.457611
$643$	−1.31085e12	−0.302414	−0.151207	−	0.988502i	$-0.548316\pi$
$643$	−1.31085e12	−0.302414	−0.151207	+	0.988502i	$0.548316\pi$
$644$	0	0
$645$	1.68030e12	0.382267
$646$	9.02152e11	0.203814
$647$	4.69942e12	1.05433	0.527164	−	0.849764i	$-0.323255\pi$
$647$	4.69942e12	1.05433	0.527164	+	0.849764i	$0.323255\pi$
$648$	−1.64848e12	−0.367278
$649$	5.94263e11	0.131485
$650$	1.79619e12	0.394678
$651$	0	0
$652$	−2.12435e12	−0.460375
$653$	2.03525e11	0.0438035	0.0219018	−	0.999760i	$-0.493028\pi$
$653$	2.03525e11	0.0438035	0.0219018	+	0.999760i	$0.493028\pi$
$654$	−6.04005e12	−1.29104
$655$	1.38245e12	0.293469
$656$	9.95213e11	0.209821
$657$	−2.06221e11	−0.0431807
$658$	0	0
$659$	2.92909e12	0.604990	0.302495	−	0.953151i	$-0.402180\pi$
$659$	2.92909e12	0.604990	0.302495	+	0.953151i	$0.402180\pi$
$660$	1.89963e11	0.0389691
$661$	8.02824e12	1.63574	0.817869	−	0.575404i	$-0.195155\pi$
$661$	8.02824e12	1.63574	0.817869	+	0.575404i	$0.195155\pi$
$662$	−1.02759e12	−0.207950
$663$	−7.40288e11	−0.148795
$664$	−1.86373e12	−0.372071
$665$	0	0
$666$	−5.17521e10	−0.0101928
$667$	1.05200e13	2.05802
$668$	−1.19225e11	−0.0231672
$669$	1.73609e12	0.335085
$670$	1.16388e12	0.223137
$671$	1.64383e12	0.313045
$672$	0	0
$673$	9.13805e12	1.71706	0.858531	−	0.512762i	$-0.171378\pi$
$673$	9.13805e12	1.71706	0.858531	+	0.512762i	$0.171378\pi$
$674$	−2.83371e12	−0.528915
$675$	−4.67076e12	−0.866005
$676$	−1.63442e12	−0.301026
$677$	1.01820e13	1.86287	0.931436	−	0.363906i	$-0.118557\pi$
$677$	1.01820e13	1.86287	0.931436	+	0.363906i	$0.118557\pi$
$678$	7.31213e11	0.132895
$679$	0	0
$680$	1.54718e11	0.0277492
$681$	5.42500e12	0.966580
$682$	−6.63559e11	−0.117449
$683$	−4.54453e12	−0.799090	−0.399545	−	0.916714i	$-0.630832\pi$
$683$	−4.54453e12	−0.799090	−0.399545	+	0.916714i	$0.630832\pi$
$684$	−1.44344e11	−0.0252143
$685$	2.01612e12	0.349872
$686$	0	0
$687$	−1.33032e12	−0.227851
$688$	1.62223e12	0.276035
$689$	−3.36552e12	−0.568939
$690$	2.11651e12	0.355467
$691$	−3.79134e12	−0.632618	−0.316309	−	0.948656i	$-0.602444\pi$
$691$	−3.79134e12	−0.632618	−0.316309	+	0.948656i	$0.602444\pi$
$692$	4.06942e12	0.674614
$693$	0	0
$694$	5.92586e12	0.969692
$695$	−2.90821e12	−0.472818
$696$	−3.16437e12	−0.511147
$697$	−1.20926e12	−0.194076
$698$	−2.67934e12	−0.427247
$699$	−5.33727e12	−0.845613
$700$	0	0
$701$	−1.57151e12	−0.245802	−0.122901	−	0.992419i	$-0.539220\pi$
$701$	−1.57151e12	−0.245802	−0.122901	+	0.992419i	$0.539220\pi$
$702$	−2.80926e12	−0.436591
$703$	2.87607e12	0.444120
$704$	1.83398e11	0.0281396
$705$	3.18881e12	0.486158
$706$	−6.32348e12	−0.957933
$707$	0	0
$708$	−1.99160e12	−0.297887
$709$	7.89156e12	1.17288	0.586442	−	0.809992i	$-0.300528\pi$
$709$	7.89156e12	1.17288	0.586442	+	0.809992i	$0.300528\pi$
$710$	−2.33481e12	−0.344817
$711$	1.81072e11	0.0265728
$712$	3.60663e12	0.525946
$713$	−7.39318e12	−1.07134
$714$	0	0
$715$	3.36844e11	0.0482005
$716$	−2.45334e12	−0.348858
$717$	−8.49660e12	−1.20063
$718$	−6.37359e12	−0.895003
$719$	−1.16080e13	−1.61986	−0.809930	−	0.586527i	$-0.800495\pi$
$719$	−1.16080e13	−1.61986	−0.809930	+	0.586527i	$0.800495\pi$
$720$	−2.47548e10	−0.00343292
$721$	0	0
$722$	2.85878e12	0.391529
$723$	−8.33694e12	−1.13471
$724$	4.37419e12	0.591663
$725$	−9.32919e12	−1.25407
$726$	5.12538e12	0.684717
$727$	−1.45587e12	−0.193294	−0.0966469	−	0.995319i	$-0.530812\pi$
$727$	−1.45587e12	−0.193294	−0.0966469	+	0.995319i	$0.530812\pi$
$728$	0	0
$729$	7.29263e12	0.956336
$730$	1.96546e12	0.256161
$731$	−1.97113e12	−0.255322
$732$	−5.50911e12	−0.709221
$733$	5.18207e12	0.663034	0.331517	−	0.943449i	$-0.392440\pi$
$733$	5.18207e12	0.663034	0.331517	+	0.943449i	$0.392440\pi$
$734$	5.25781e12	0.668609
$735$	0	0
$736$	2.04337e12	0.256682
$737$	−1.67636e12	−0.209297
$738$	1.93482e11	0.0240097
$739$	2.90528e12	0.358334	0.179167	−	0.983819i	$-0.442660\pi$
$739$	2.90528e12	0.358334	0.179167	+	0.983819i	$0.442660\pi$
$740$	4.93242e11	0.0604668
$741$	−6.58252e12	−0.802066
$742$	0	0
$743$	−8.79352e12	−1.05855	−0.529277	−	0.848449i	$-0.677537\pi$
$743$	−8.79352e12	−1.05855	−0.529277	+	0.848449i	$0.677537\pi$
$744$	2.22384e12	0.266088
$745$	4.82212e12	0.573502
$746$	1.77364e12	0.209672
$747$	−3.62332e11	−0.0425759
$748$	−2.22843e11	−0.0260280
$749$	0	0
$750$	−3.99824e12	−0.461416
$751$	3.36742e12	0.386294	0.193147	−	0.981170i	$-0.438131\pi$
$751$	3.36742e12	0.386294	0.193147	+	0.981170i	$0.438131\pi$
$752$	3.07861e12	0.351054
$753$	4.58950e12	0.520221
$754$	−5.61111e12	−0.632234
$755$	5.30187e12	0.593838
$756$	0	0
$757$	−8.88376e12	−0.983253	−0.491627	−	0.870806i	$-0.663597\pi$
$757$	−8.88376e12	−0.983253	−0.491627	+	0.870806i	$0.663597\pi$
$758$	−8.98313e12	−0.988363
$759$	−3.04844e12	−0.333419
$760$	1.37572e12	0.149579
$761$	−6.41718e12	−0.693607	−0.346803	−	0.937938i	$-0.612733\pi$
$761$	−6.41718e12	−0.693607	−0.346803	+	0.937938i	$0.612733\pi$
$762$	−6.14265e10	−0.00660022
$763$	0	0
$764$	4.18834e10	0.00444756
$765$	3.00790e10	0.00317532
$766$	1.23781e13	1.29905
$767$	−3.53153e12	−0.368454
$768$	−6.14635e11	−0.0637517
$769$	−1.22742e13	−1.26569	−0.632843	−	0.774280i	$-0.718112\pi$
$769$	−1.22742e13	−1.26569	−0.632843	+	0.774280i	$0.718112\pi$
$770$	0	0
$771$	−1.84365e13	−1.87903
$772$	5.45325e12	0.552558
$773$	−4.03376e12	−0.406352	−0.203176	−	0.979142i	$-0.565126\pi$
$773$	−4.03376e12	−0.406352	−0.203176	+	0.979142i	$0.565126\pi$
$774$	3.15381e11	0.0315865
$775$	6.55630e12	0.652832
$776$	7.31051e11	0.0723719
$777$	0	0
$778$	−9.46421e11	−0.0926139
$779$	−1.07526e13	−1.04615
$780$	−1.12889e12	−0.109201
$781$	3.36287e12	0.323430
$782$	−2.48285e12	−0.237421
$783$	1.45910e13	1.38725
$784$	0	0
$785$	−3.67779e12	−0.345679
$786$	6.67314e12	0.623633
$787$	1.92483e13	1.78857	0.894285	−	0.447497i	$-0.147685\pi$
$787$	1.92483e13	1.78857	0.894285	+	0.447497i	$0.147685\pi$
$788$	2.24550e12	0.207465
$789$	2.35722e12	0.216548
$790$	−1.72577e12	−0.157638
$791$	0	0
$792$	3.56548e10	0.00321999
$793$	−9.76883e12	−0.877229
$794$	6.67677e12	0.596176
$795$	3.51679e12	0.312245
$796$	−7.99738e12	−0.706056
$797$	1.67346e13	1.46911	0.734553	−	0.678551i	$-0.237392\pi$
$797$	1.67346e13	1.46911	0.734553	+	0.678551i	$0.237392\pi$
$798$	0	0
$799$	−3.74075e12	−0.324712
$800$	−1.81207e12	−0.156412
$801$	7.01173e11	0.0601837
$802$	3.91516e12	0.334168
$803$	−2.83089e12	−0.240272
$804$	5.61810e12	0.474173
$805$	0	0
$806$	3.94334e12	0.329121
$807$	−1.21541e13	−1.00877
$808$	−1.19754e12	−0.0988412
$809$	−2.37363e12	−0.194825	−0.0974124	−	0.995244i	$-0.531057\pi$
$809$	−2.37363e12	−0.194825	−0.0974124	+	0.995244i	$0.531057\pi$
$810$	3.05449e12	0.249320
$811$	5.15898e12	0.418765	0.209382	−	0.977834i	$-0.432855\pi$
$811$	5.15898e12	0.418765	0.209382	+	0.977834i	$0.432855\pi$
$812$	0	0
$813$	1.03055e12	0.0827299
$814$	−7.10425e11	−0.0567164
$815$	3.93624e12	0.312516
$816$	7.46830e11	0.0589679
$817$	−1.75270e13	−1.37628
$818$	−3.54170e12	−0.276580
$819$	0	0
$820$	−1.84405e12	−0.142433
$821$	6.56725e12	0.504475	0.252237	−	0.967665i	$-0.418834\pi$
$821$	6.56725e12	0.504475	0.252237	+	0.967665i	$0.418834\pi$
$822$	9.73193e12	0.743491
$823$	3.86923e12	0.293985	0.146992	−	0.989138i	$-0.453041\pi$
$823$	3.86923e12	0.293985	0.146992	+	0.989138i	$0.453041\pi$
$824$	3.00847e12	0.227339
$825$	2.70337e12	0.203172
$826$	0	0
$827$	−5.32429e12	−0.395810	−0.197905	−	0.980221i	$-0.563414\pi$
$827$	−5.32429e12	−0.395810	−0.197905	+	0.980221i	$0.563414\pi$
$828$	3.97256e11	0.0293720
$829$	−1.09886e13	−0.808069	−0.404034	−	0.914744i	$-0.632392\pi$
$829$	−1.09886e13	−0.808069	−0.404034	+	0.914744i	$0.632392\pi$
$830$	3.45333e12	0.252573
$831$	−1.92376e12	−0.139942
$832$	−1.08988e12	−0.0788540
$833$	0	0
$834$	−1.40381e13	−1.00475
$835$	2.20915e11	0.0157266
$836$	−1.98148e12	−0.140301
$837$	−1.02541e13	−0.722161
$838$	−1.09907e13	−0.769891
$839$	−6.50828e11	−0.0453458	−0.0226729	−	0.999743i	$-0.507218\pi$
$839$	−6.50828e11	−0.0453458	−0.0226729	+	0.999743i	$0.507218\pi$
$840$	0	0
$841$	1.46363e13	1.00890
$842$	1.32171e13	0.906218
$843$	−1.72035e13	−1.17325
$844$	1.18678e13	0.805061
$845$	3.02844e12	0.204345
$846$	5.98520e11	0.0401709
$847$	0	0
$848$	3.39526e12	0.225472
$849$	−2.33223e13	−1.54059
$850$	2.20180e12	0.144675
$851$	−7.91535e12	−0.517353
$852$	−1.12702e13	−0.732749
$853$	2.03197e13	1.31415	0.657076	−	0.753824i	$-0.271793\pi$
$853$	2.03197e13	1.31415	0.657076	+	0.753824i	$0.271793\pi$
$854$	0	0
$855$	2.67458e11	0.0171162
$856$	−3.52360e12	−0.224313
$857$	−1.52383e13	−0.964988	−0.482494	−	0.875899i	$-0.660269\pi$
$857$	−1.52383e13	−0.964988	−0.482494	+	0.875899i	$0.660269\pi$
$858$	1.62596e12	0.102428
$859$	−1.80059e13	−1.12836	−0.564178	−	0.825653i	$-0.690807\pi$
$859$	−1.80059e13	−1.12836	−0.564178	+	0.825653i	$0.690807\pi$
$860$	−3.00585e12	−0.187381
$861$	0	0
$862$	−2.68721e12	−0.165775
$863$	−2.43124e13	−1.49203	−0.746017	−	0.665927i	$-0.768036\pi$
$863$	−2.43124e13	−1.49203	−0.746017	+	0.665927i	$0.768036\pi$
$864$	2.83409e12	0.173022
$865$	−7.54031e12	−0.457948
$866$	−1.89889e13	−1.14728
$867$	1.60632e13	0.965485
$868$	0	0
$869$	2.48566e12	0.147860
$870$	5.86332e12	0.346982
$871$	9.96209e12	0.586501
$872$	1.08050e13	0.632847
$873$	1.42125e11	0.00828147
$874$	−2.20771e13	−1.27979
$875$	0	0
$876$	9.48740e12	0.544350
$877$	3.50274e13	1.99944	0.999722	−	0.0235752i	$-0.00750493\pi$
$877$	3.50274e13	1.99944	0.999722	+	0.0235752i	$0.00750493\pi$
$878$	−1.81725e13	−1.03202
$879$	−9.35871e11	−0.0528769
$880$	−3.39821e11	−0.0191020
$881$	−4.60815e12	−0.257712	−0.128856	−	0.991663i	$-0.541131\pi$
$881$	−4.60815e12	−0.257712	−0.128856	+	0.991663i	$0.541131\pi$
$882$	0	0
$883$	−9.40362e12	−0.520561	−0.260281	−	0.965533i	$-0.583815\pi$
$883$	−9.40362e12	−0.520561	−0.260281	+	0.965533i	$0.583815\pi$
$884$	1.32429e12	0.0729369
$885$	3.69027e12	0.202215
$886$	−1.41635e13	−0.772181
$887$	2.23764e13	1.21376	0.606881	−	0.794793i	$-0.292421\pi$
$887$	2.23764e13	1.21376	0.606881	+	0.794793i	$0.292421\pi$
$888$	2.38090e12	0.128494
$889$	0	0
$890$	−6.68278e12	−0.357028
$891$	−4.39944e12	−0.233856
$892$	−3.10566e12	−0.164253
$893$	−3.32621e13	−1.75032
$894$	2.32766e13	1.21871
$895$	4.54583e12	0.236815
$896$	0	0
$897$	1.81160e13	0.934322
$898$	2.06843e13	1.06145
$899$	−2.04812e13	−1.04577
$900$	−3.52288e11	−0.0178981
$901$	−4.12551e12	−0.208553
$902$	2.65601e12	0.133598
$903$	0	0
$904$	−1.30805e12	−0.0651430
$905$	−8.10502e12	−0.401639
$906$	2.55924e13	1.26193
$907$	2.60662e13	1.27892	0.639461	−	0.768823i	$-0.279157\pi$
$907$	2.60662e13	1.27892	0.639461	+	0.768823i	$0.279157\pi$
$908$	−9.70470e12	−0.473801
$909$	−2.32816e11	−0.0113103
$910$	0	0
$911$	−2.27125e12	−0.109253	−0.0546264	−	0.998507i	$-0.517397\pi$
$911$	−2.27125e12	−0.109253	−0.0546264	+	0.998507i	$0.517397\pi$
$912$	6.64069e12	0.317860
$913$	−4.97390e12	−0.236907
$914$	1.26442e13	0.599285
$915$	1.02079e13	0.481440
$916$	2.37979e12	0.111689
$917$	0	0
$918$	−3.44364e12	−0.160039
$919$	2.25126e13	1.04113	0.520567	−	0.853821i	$-0.325721\pi$
$919$	2.25126e13	1.04113	0.520567	+	0.853821i	$0.325721\pi$
$920$	−3.78619e12	−0.174244
$921$	−8.47614e12	−0.388177
$922$	−1.11721e12	−0.0509152
$923$	−1.99845e13	−0.906330
$924$	0	0
$925$	7.01937e12	0.315254
$926$	3.39375e12	0.151681
$927$	5.84884e11	0.0260142
$928$	5.66070e12	0.250556
$929$	2.72479e13	1.20022	0.600112	−	0.799916i	$-0.295123\pi$
$929$	2.72479e13	1.20022	0.600112	+	0.799916i	$0.295123\pi$
$930$	−4.12058e12	−0.180628
$931$	0	0
$932$	9.54776e12	0.414505
$933$	−1.42537e13	−0.615831
$934$	1.23420e13	0.530669
$935$	4.12909e11	0.0176686
$936$	−2.11886e11	−0.00902322
$937$	−2.68200e13	−1.13666	−0.568330	−	0.822800i	$-0.692410\pi$
$937$	−2.68200e13	−1.13666	−0.568330	+	0.822800i	$0.692410\pi$
$938$	0	0
$939$	3.83784e13	1.61099
$940$	−5.70441e12	−0.238306
$941$	2.69039e13	1.11857	0.559284	−	0.828976i	$-0.311076\pi$
$941$	2.69039e13	1.11857	0.559284	+	0.828976i	$0.311076\pi$
$942$	−1.77529e13	−0.734580
$943$	2.95925e13	1.21865
$944$	3.56274e12	0.146019
$945$	0	0
$946$	4.32939e12	0.175758
$947$	1.49678e13	0.604761	0.302380	−	0.953187i	$-0.402219\pi$
$947$	1.49678e13	0.604761	0.302380	+	0.953187i	$0.402219\pi$
$948$	−8.33037e12	−0.334986
$949$	1.68232e13	0.673302
$950$	1.95780e13	0.779854
$951$	−3.44718e13	−1.36663
$952$	0	0
$953$	−2.66506e13	−1.04662	−0.523310	−	0.852142i	$-0.675303\pi$
$953$	−2.66506e13	−1.04662	−0.523310	+	0.852142i	$0.675303\pi$
$954$	6.60081e11	0.0258006
$955$	−7.76065e10	−0.00301914
$956$	1.51994e13	0.588528
$957$	−8.44505e12	−0.325461
$958$	−1.21889e13	−0.467540
$959$	0	0
$960$	1.13887e12	0.0432766
$961$	−1.20460e13	−0.455604
$962$	4.22185e12	0.158933
$963$	−6.85032e11	−0.0256680
$964$	1.49138e13	0.556214
$965$	−1.01044e13	−0.375093
$966$	0	0
$967$	−8.87439e12	−0.326377	−0.163188	−	0.986595i	$-0.552178\pi$
$967$	−8.87439e12	−0.326377	−0.163188	+	0.986595i	$0.552178\pi$
$968$	−9.16870e12	−0.335636
$969$	−8.06895e12	−0.294009
$970$	−1.35458e12	−0.0491282
$971$	4.26335e13	1.53909	0.769545	−	0.638592i	$-0.220483\pi$
$971$	4.26335e13	1.53909	0.769545	+	0.638592i	$0.220483\pi$
$972$	1.12520e12	0.0404324
$973$	0	0
$974$	1.60279e13	0.570640
$975$	−1.60654e13	−0.569337
$976$	9.85516e12	0.347648
$977$	2.87339e13	1.00895	0.504474	−	0.863427i	$-0.331686\pi$
$977$	2.87339e13	1.00895	0.504474	+	0.863427i	$0.331686\pi$
$978$	1.90004e13	0.664108
$979$	9.62533e12	0.334883
$980$	0	0
$981$	2.10062e12	0.0724163
$982$	−2.71866e13	−0.932937
$983$	−4.27084e12	−0.145889	−0.0729445	−	0.997336i	$-0.523240\pi$
$983$	−4.27084e12	−0.145889	−0.0729445	+	0.997336i	$0.523240\pi$
$984$	−8.90131e12	−0.302674
$985$	−4.16073e12	−0.140834
$986$	−6.87819e12	−0.231754
$987$	0	0
$988$	1.17754e13	0.393159
$989$	4.82368e13	1.60323
$990$	−6.60654e10	−0.00218583
$991$	1.15432e13	0.380185	0.190093	−	0.981766i	$-0.439121\pi$
$991$	1.15432e13	0.380185	0.190093	+	0.981766i	$0.439121\pi$
$992$	−3.97819e12	−0.130432
$993$	9.19090e12	0.299976
$994$	0	0
$995$	1.48185e13	0.479292
$996$	1.66694e13	0.536727
$997$	−3.62805e13	−1.16291	−0.581453	−	0.813580i	$-0.697516\pi$
$997$	−3.62805e13	−1.16291	−0.581453	+	0.813580i	$0.697516\pi$
$998$	−1.90868e13	−0.609039
$999$	−1.09784e13	−0.348733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.l.1.2	✓	6
7.2	even	3		98.10.c.n.67.5		12
7.3	odd	6		98.10.c.n.79.2		12
7.4	even	3		98.10.c.n.79.5		12
7.5	odd	6		98.10.c.n.67.2		12
7.6	odd	2	inner	98.10.a.l.1.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.l.1.2	✓	6	1.1	even	1	trivial
98.10.a.l.1.5	yes	6	7.6	odd	2	inner
98.10.c.n.67.2		12	7.5	odd	6
98.10.c.n.67.5		12	7.2	even	3
98.10.c.n.79.2		12	7.3	odd	6
98.10.c.n.79.5		12	7.4	even	3

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -143.106 q^{3} +256.000 q^{4} -474.347 q^{5} -2289.70 q^{6} +4096.00 q^{8} +796.313 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} -143.106 q^{3} +256.000 q^{4} -474.347 q^{5} -2289.70 q^{6} +4096.00 q^{8} +796.313 q^{9} -7589.55 q^{10} +10931.4 q^{11} -36635.1 q^{12} -64961.9 q^{13} +67881.8 q^{15} +65536.0 q^{16} -79631.4 q^{17} +12741.0 q^{18} -708069. q^{19} -121433. q^{20} +174902. q^{22} +1.94871e6 q^{23} -586162. q^{24} -1.72812e6 q^{25} -1.03939e6 q^{26} +2.70280e6 q^{27} +5.39846e6 q^{29} +1.08611e6 q^{30} -3.79389e6 q^{31} +1.04858e6 q^{32} -1.56434e6 q^{33} -1.27410e6 q^{34} +203856. q^{36} -4.06185e6 q^{37} -1.13291e7 q^{38} +9.29643e6 q^{39} -1.94292e6 q^{40} +1.51857e7 q^{41} +2.47532e7 q^{43} +2.79843e6 q^{44} -377729. q^{45} +3.11793e7 q^{46} +4.69758e7 q^{47} -9.37859e6 q^{48} -2.76499e7 q^{50} +1.13957e7 q^{51} -1.66302e7 q^{52} +5.18076e7 q^{53} +4.32448e7 q^{54} -5.18526e6 q^{55} +1.01329e8 q^{57} +8.63754e7 q^{58} +5.43631e7 q^{59} +1.73778e7 q^{60} +1.50378e8 q^{61} -6.07023e7 q^{62} +1.67772e7 q^{64} +3.08145e7 q^{65} -2.50295e7 q^{66} -1.53353e8 q^{67} -2.03856e7 q^{68} -2.78871e8 q^{69} +3.07635e8 q^{71} +3.26170e6 q^{72} -2.58970e8 q^{73} -6.49896e7 q^{74} +2.47304e8 q^{75} -1.81266e8 q^{76} +1.48743e8 q^{78} +2.27387e8 q^{79} -3.10868e7 q^{80} -4.02460e8 q^{81} +2.42972e8 q^{82} -4.55012e8 q^{83} +3.77729e7 q^{85} +3.96052e8 q^{86} -7.72552e8 q^{87} +4.47749e7 q^{88} +8.80524e8 q^{89} -6.04366e6 q^{90} +4.98869e8 q^{92} +5.42929e8 q^{93} +7.51613e8 q^{94} +3.35870e8 q^{95} -1.50057e8 q^{96} +1.78479e8 q^{97} +8.70479e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 96 q^{2} + 1536 q^{4} + 24576 q^{8} + 72550 q^{9}+O(q^{10}) \) 6 * q + 96 * q^2 + 1536 * q^4 + 24576 * q^8 + 72550 * q^9	\( 6 q + 96 q^{2} + 1536 q^{4} + 24576 q^{8} + 72550 q^{9} + 110664 q^{11} - 522728 q^{15} + 393216 q^{16} + 1160800 q^{18} + 1770624 q^{22} + 243384 q^{23} + 17125446 q^{25} + 10463640 q^{29} - 8363648 q^{30} + 6291456 q^{32} + 18572800 q^{36} + 24332568 q^{37} + 42635880 q^{39} + 74758584 q^{43} + 28329984 q^{44} + 3894144 q^{46} + 274007136 q^{50} + 260246248 q^{51} + 137815308 q^{53} + 449663960 q^{57} + 167418240 q^{58} - 133818368 q^{60} + 100663296 q^{64} + 565976460 q^{65} - 202943376 q^{67} + 614292768 q^{71} + 297164800 q^{72} + 389321088 q^{74} + 682174080 q^{78} - 182370096 q^{79} - 432881842 q^{81} + 2070495732 q^{85} + 1196137344 q^{86} + 453279744 q^{88} + 62306304 q^{92} + 190722192 q^{93} - 1311555480 q^{95} + 5322586792 q^{99}+O(q^{100}) \) 6 * q + 96 * q^2 + 1536 * q^4 + 24576 * q^8 + 72550 * q^9 + 110664 * q^11 - 522728 * q^15 + 393216 * q^16 + 1160800 * q^18 + 1770624 * q^22 + 243384 * q^23 + 17125446 * q^25 + 10463640 * q^29 - 8363648 * q^30 + 6291456 * q^32 + 18572800 * q^36 + 24332568 * q^37 + 42635880 * q^39 + 74758584 * q^43 + 28329984 * q^44 + 3894144 * q^46 + 274007136 * q^50 + 260246248 * q^51 + 137815308 * q^53 + 449663960 * q^57 + 167418240 * q^58 - 133818368 * q^60 + 100663296 * q^64 + 565976460 * q^65 - 202943376 * q^67 + 614292768 * q^71 + 297164800 * q^72 + 389321088 * q^74 + 682174080 * q^78 - 182370096 * q^79 - 432881842 * q^81 + 2070495732 * q^85 + 1196137344 * q^86 + 453279744 * q^88 + 62306304 * q^92 + 190722192 * q^93 - 1311555480 * q^95 + 5322586792 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more