LMFDB - Embedded newform 98.10.a.l.1.3

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			1.3
Root			$61.1162$ 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)

$f(q)$	$=$	$q+16.0000 q^{2} -121.370 q^{3} +256.000 q^{4} -2666.02 q^{5} -1941.92 q^{6} +4096.00 q^{8} -4952.27 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} -121.370 q^{3} +256.000 q^{4} -2666.02 q^{5} -1941.92 q^{6} +4096.00 q^{8} -4952.27 q^{9} -42656.3 q^{10} -18893.1 q^{11} -31070.8 q^{12} -96063.7 q^{13} +323575. q^{15} +65536.0 q^{16} -573992. q^{17} -79236.3 q^{18} -87739.9 q^{19} -682500. q^{20} -302289. q^{22} -1.50035e6 q^{23} -497132. q^{24} +5.15452e6 q^{25} -1.53702e6 q^{26} +2.98999e6 q^{27} -1.78997e6 q^{29} +5.17720e6 q^{30} +9.66130e6 q^{31} +1.04858e6 q^{32} +2.29306e6 q^{33} -9.18388e6 q^{34} -1.26778e6 q^{36} -3.09681e6 q^{37} -1.40384e6 q^{38} +1.16593e7 q^{39} -1.09200e7 q^{40} -1.17852e7 q^{41} +3.60280e7 q^{43} -4.83663e6 q^{44} +1.32028e7 q^{45} -2.40056e7 q^{46} -5.91997e6 q^{47} -7.95412e6 q^{48} +8.24723e7 q^{50} +6.96656e7 q^{51} -2.45923e7 q^{52} -3.00313e7 q^{53} +4.78398e7 q^{54} +5.03692e7 q^{55} +1.06490e7 q^{57} -2.86396e7 q^{58} +1.43321e8 q^{59} +8.28352e7 q^{60} -1.50645e8 q^{61} +1.54581e8 q^{62} +1.67772e7 q^{64} +2.56107e8 q^{65} +3.66889e7 q^{66} +9.94910e7 q^{67} -1.46942e8 q^{68} +1.82097e8 q^{69} -2.01373e8 q^{71} -2.02845e7 q^{72} -4.65676e7 q^{73} -4.95489e7 q^{74} -6.25605e8 q^{75} -2.24614e7 q^{76} +1.86548e8 q^{78} -2.53222e8 q^{79} -1.74720e8 q^{80} -2.65420e8 q^{81} -1.88564e8 q^{82} +3.16834e8 q^{83} +1.53027e9 q^{85} +5.76448e8 q^{86} +2.17250e8 q^{87} -7.73860e7 q^{88} -8.40622e8 q^{89} +2.11245e8 q^{90} -3.84089e8 q^{92} -1.17259e9 q^{93} -9.47195e7 q^{94} +2.33916e8 q^{95} -1.27266e8 q^{96} +2.72768e8 q^{97} +9.35636e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−121.370	−0.865100	−0.432550	−	0.901610i	$-0.642386\pi$
$3$	−121.370	−0.865100	−0.432550	+	0.901610i	$0.642386\pi$
$4$	256.000	0.500000
$5$	−2666.02	−1.90765	−0.953823	−	0.300370i	$-0.902890\pi$
$5$	−2666.02	−1.90765	−0.953823	+	0.300370i	$0.902890\pi$
$6$	−1941.92	−0.611718
$7$	0	0
$7$	0	0
$8$	4096.00	0.353553
$9$	−4952.27	−0.251601
$10$	−42656.3	−1.34891
$11$	−18893.1	−0.389077	−0.194538	−	0.980895i	$-0.562321\pi$
$11$	−18893.1	−0.389077	−0.194538	+	0.980895i	$0.562321\pi$
$12$	−31070.8	−0.432550
$13$	−96063.7	−0.932856	−0.466428	−	0.884559i	$-0.654459\pi$
$13$	−96063.7	−0.932856	−0.466428	+	0.884559i	$0.654459\pi$
$14$	0	0
$15$	323575.	1.65031
$16$	65536.0	0.250000
$17$	−573992.	−1.66681	−0.833405	−	0.552663i	$-0.813612\pi$
$17$	−573992.	−1.66681	−0.833405	+	0.552663i	$0.813612\pi$
$18$	−79236.3	−0.177909
$19$	−87739.9	−0.154456	−0.0772282	−	0.997013i	$-0.524607\pi$
$19$	−87739.9	−0.154456	−0.0772282	+	0.997013i	$0.524607\pi$
$20$	−682500.	−0.953823
$21$	0	0
$22$	−302289.	−0.275119
$23$	−1.50035e6	−1.11793	−0.558967	−	0.829190i	$-0.688802\pi$
$23$	−1.50035e6	−1.11793	−0.558967	+	0.829190i	$0.688802\pi$
$24$	−497132.	−0.305859
$25$	5.15452e6	2.63911
$26$	−1.53702e6	−0.659628
$27$	2.98999e6	1.08276
$28$	0	0
$29$	−1.78997e6	−0.469955	−0.234977	−	0.972001i	$-0.575502\pi$
$29$	−1.78997e6	−0.469955	−0.234977	+	0.972001i	$0.575502\pi$
$30$	5.17720e6	1.16694
$31$	9.66130e6	1.87892	0.939459	−	0.342661i	$-0.111328\pi$
$31$	9.66130e6	1.87892	0.939459	+	0.342661i	$0.111328\pi$
$32$	1.04858e6	0.176777
$33$	2.29306e6	0.336591
$34$	−9.18388e6	−1.17861
$35$	0	0
$36$	−1.26778e6	−0.125801
$37$	−3.09681e6	−0.271648	−0.135824	−	0.990733i	$-0.543368\pi$
$37$	−3.09681e6	−0.271648	−0.135824	+	0.990733i	$0.543368\pi$
$38$	−1.40384e6	−0.109217
$39$	1.16593e7	0.807014
$40$	−1.09200e7	−0.674455
$41$	−1.17852e7	−0.651345	−0.325673	−	0.945483i	$-0.605591\pi$
$41$	−1.17852e7	−0.651345	−0.325673	+	0.945483i	$0.605591\pi$
$42$	0	0
$43$	3.60280e7	1.60706	0.803530	−	0.595264i	$-0.202953\pi$
$43$	3.60280e7	1.60706	0.803530	+	0.595264i	$0.202953\pi$
$44$	−4.83663e6	−0.194538
$45$	1.32028e7	0.479966
$46$	−2.40056e7	−0.790499
$47$	−5.91997e6	−0.176962	−0.0884808	−	0.996078i	$-0.528201\pi$
$47$	−5.91997e6	−0.176962	−0.0884808	+	0.996078i	$0.528201\pi$
$48$	−7.95412e6	−0.216275
$49$	0	0
$50$	8.24723e7	1.86613
$51$	6.96656e7	1.44196
$52$	−2.45923e7	−0.466428
$53$	−3.00313e7	−0.522797	−0.261399	−	0.965231i	$-0.584184\pi$
$53$	−3.00313e7	−0.522797	−0.261399	+	0.965231i	$0.584184\pi$
$54$	4.78398e7	0.765628
$55$	5.03692e7	0.742221
$56$	0	0
$57$	1.06490e7	0.133620
$58$	−2.86396e7	−0.332308
$59$	1.43321e8	1.53984	0.769922	−	0.638138i	$-0.220295\pi$
$59$	1.43321e8	1.53984	0.769922	+	0.638138i	$0.220295\pi$
$60$	8.28352e7	0.825153
$61$	−1.50645e8	−1.39307	−0.696533	−	0.717525i	$-0.745275\pi$
$61$	−1.50645e8	−1.39307	−0.696533	+	0.717525i	$0.745275\pi$
$62$	1.54581e8	1.32860
$63$	0	0
$64$	1.67772e7	0.125000
$65$	2.56107e8	1.77956
$66$	3.66889e7	0.238005
$67$	9.94910e7	0.603180	0.301590	−	0.953438i	$-0.402483\pi$
$67$	9.94910e7	0.603180	0.301590	+	0.953438i	$0.402483\pi$
$68$	−1.46942e8	−0.833405
$69$	1.82097e8	0.967126
$70$	0	0
$71$	−2.01373e8	−0.940455	−0.470228	−	0.882545i	$-0.655828\pi$
$71$	−2.01373e8	−0.940455	−0.470228	+	0.882545i	$0.655828\pi$
$72$	−2.02845e7	−0.0889545
$73$	−4.65676e7	−0.191925	−0.0959624	−	0.995385i	$-0.530593\pi$
$73$	−4.65676e7	−0.191925	−0.0959624	+	0.995385i	$0.530593\pi$
$74$	−4.95489e7	−0.192084
$75$	−6.25605e8	−2.28310
$76$	−2.24614e7	−0.0772282
$77$	0	0
$78$	1.86548e8	0.570645
$79$	−2.53222e8	−0.731441	−0.365721	−	0.930725i	$-0.619177\pi$
$79$	−2.53222e8	−0.731441	−0.365721	+	0.930725i	$0.619177\pi$
$80$	−1.74720e8	−0.476911
$81$	−2.65420e8	−0.685095
$82$	−1.88564e8	−0.460571
$83$	3.16834e8	0.732793	0.366396	−	0.930459i	$-0.380591\pi$
$83$	3.16834e8	0.732793	0.366396	+	0.930459i	$0.380591\pi$
$84$	0	0
$85$	1.53027e9	3.17968
$86$	5.76448e8	1.13636
$87$	2.17250e8	0.406558
$88$	−7.73860e7	−0.137559
$89$	−8.40622e8	−1.42019	−0.710094	−	0.704107i	$-0.751348\pi$
$89$	−8.40622e8	−1.42019	−0.710094	+	0.704107i	$0.751348\pi$
$90$	2.11245e8	0.339387
$91$	0	0
$92$	−3.84089e8	−0.558967
$93$	−1.17259e9	−1.62545
$94$	−9.47195e7	−0.125131
$95$	2.33916e8	0.294648
$96$	−1.27266e8	−0.152930
$97$	2.72768e8	0.312839	0.156419	−	0.987691i	$-0.450005\pi$
$97$	2.72768e8	0.312839	0.156419	+	0.987691i	$0.450005\pi$
$98$	0	0
$99$	9.35636e7	0.0978923
$100$	1.31956e9	1.31956
$101$	3.71664e8	0.355390	0.177695	−	0.984086i	$-0.443136\pi$
$101$	3.71664e8	0.355390	0.177695	+	0.984086i	$0.443136\pi$
$102$	1.11465e9	1.01962
$103$	9.96912e8	0.872749	0.436375	−	0.899765i	$-0.356262\pi$
$103$	9.96912e8	0.872749	0.436375	+	0.899765i	$0.356262\pi$
$104$	−3.93477e8	−0.329814
$105$	0	0
$106$	−4.80501e8	−0.369673
$107$	2.65373e9	1.95717	0.978586	−	0.205838i	$-0.0659922\pi$
$107$	2.65373e9	1.95717	0.978586	+	0.205838i	$0.0659922\pi$
$108$	7.65437e8	0.541380
$109$	−9.88172e8	−0.670523	−0.335261	−	0.942125i	$-0.608825\pi$
$109$	−9.88172e8	−0.670523	−0.335261	+	0.942125i	$0.608825\pi$
$110$	8.05908e8	0.524829
$111$	3.75860e8	0.235003
$112$	0	0
$113$	6.67601e8	0.385180	0.192590	−	0.981279i	$-0.438311\pi$
$113$	6.67601e8	0.385180	0.192590	+	0.981279i	$0.438311\pi$
$114$	1.70384e8	0.0944839
$115$	3.99995e9	2.13262
$116$	−4.58233e8	−0.234977
$117$	4.75734e8	0.234708
$118$	2.29314e9	1.08883
$119$	0	0
$120$	1.32536e9	0.583471
$121$	−2.00100e9	−0.848619
$122$	−2.41033e9	−0.985046
$123$	1.43038e9	0.563479
$124$	2.47329e9	0.939459
$125$	−8.53496e9	−3.12685
$126$	0	0
$127$	−3.51915e9	−1.20039	−0.600193	−	0.799856i	$-0.704909\pi$
$127$	−3.51915e9	−1.20039	−0.600193	+	0.799856i	$0.704909\pi$
$128$	2.68435e8	0.0883883
$129$	−4.37273e9	−1.39027
$130$	4.09772e9	1.25834
$131$	−3.80260e9	−1.12813	−0.564066	−	0.825730i	$-0.690764\pi$
$131$	−3.80260e9	−1.12813	−0.564066	+	0.825730i	$0.690764\pi$
$132$	5.87022e8	0.168295
$133$	0	0
$134$	1.59186e9	0.426513
$135$	−7.97136e9	−2.06552
$136$	−2.35107e9	−0.589306
$137$	−7.54296e9	−1.82936	−0.914680	−	0.404178i	$-0.867557\pi$
$137$	−7.54296e9	−1.82936	−0.914680	+	0.404178i	$0.867557\pi$
$138$	2.91356e9	0.683861
$139$	−1.04500e9	−0.237437	−0.118718	−	0.992928i	$-0.537879\pi$
$139$	−1.04500e9	−0.237437	−0.118718	+	0.992928i	$0.537879\pi$
$140$	0	0
$141$	7.18508e8	0.153090
$142$	−3.22196e9	−0.665002
$143$	1.81494e9	0.362953
$144$	−3.24552e8	−0.0629003
$145$	4.77210e9	0.896507
$146$	−7.45082e8	−0.135711
$147$	0	0
$148$	−7.92783e8	−0.135824
$149$	−3.66644e8	−0.0609406	−0.0304703	−	0.999536i	$-0.509700\pi$
$149$	−3.66644e8	−0.0609406	−0.0304703	+	0.999536i	$0.509700\pi$
$150$	−1.00097e10	−1.61439
$151$	5.38005e9	0.842151	0.421076	−	0.907025i	$-0.361653\pi$
$151$	5.38005e9	0.842151	0.421076	+	0.907025i	$0.361653\pi$
$152$	−3.59383e8	−0.0546086
$153$	2.84257e9	0.419372
$154$	0	0
$155$	−2.57572e10	−3.58431
$156$	2.98477e9	0.403507
$157$	8.37138e9	1.09964	0.549818	−	0.835285i	$-0.314697\pi$
$157$	8.37138e9	1.09964	0.549818	+	0.835285i	$0.314697\pi$
$158$	−4.05155e9	−0.517207
$159$	3.64491e9	0.452272
$160$	−2.79552e9	−0.337227
$161$	0	0
$162$	−4.24672e9	−0.484436
$163$	−7.31500e9	−0.811652	−0.405826	−	0.913950i	$-0.633016\pi$
$163$	−7.31500e9	−0.811652	−0.405826	+	0.913950i	$0.633016\pi$
$164$	−3.01702e9	−0.325673
$165$	−6.11332e9	−0.642095
$166$	5.06935e9	0.518163
$167$	5.33639e9	0.530913	0.265457	−	0.964123i	$-0.414477\pi$
$167$	5.33639e9	0.530913	0.265457	+	0.964123i	$0.414477\pi$
$168$	0	0
$169$	−1.37626e9	−0.129780
$170$	2.44844e10	2.24837
$171$	4.34512e8	0.0388615
$172$	9.22317e9	0.803530
$173$	4.48514e9	0.380687	0.190344	−	0.981718i	$-0.439040\pi$
$173$	4.48514e9	0.380687	0.190344	+	0.981718i	$0.439040\pi$
$174$	3.47599e9	0.287480
$175$	0	0
$176$	−1.23818e9	−0.0972692
$177$	−1.73949e10	−1.33212
$178$	−1.34500e10	−1.00422
$179$	−6.76276e9	−0.492363	−0.246181	−	0.969224i	$-0.579176\pi$
$179$	−6.76276e9	−0.492363	−0.246181	+	0.969224i	$0.579176\pi$
$180$	3.37993e9	0.239983
$181$	4.06637e9	0.281613	0.140807	−	0.990037i	$-0.455030\pi$
$181$	4.06637e9	0.281613	0.140807	+	0.990037i	$0.455030\pi$
$182$	0	0
$183$	1.82839e10	1.20514
$184$	−6.14542e9	−0.395250
$185$	8.25614e9	0.518208
$186$	−1.87615e10	−1.14937
$187$	1.08445e10	0.648517
$188$	−1.51551e9	−0.0884808
$189$	0	0
$190$	3.74266e9	0.208348
$191$	−1.12743e10	−0.612968	−0.306484	−	0.951876i	$-0.599153\pi$
$191$	−1.12743e10	−0.612968	−0.306484	+	0.951876i	$0.599153\pi$
$192$	−2.03625e9	−0.108138
$193$	−2.30111e10	−1.19379	−0.596896	−	0.802318i	$-0.703600\pi$
$193$	−2.30111e10	−1.19379	−0.596896	+	0.802318i	$0.703600\pi$
$194$	4.36429e9	0.221210
$195$	−3.10838e10	−1.53950
$196$	0	0
$197$	1.63377e10	0.772844	0.386422	−	0.922322i	$-0.373711\pi$
$197$	1.63377e10	0.772844	0.386422	+	0.922322i	$0.373711\pi$
$198$	1.49702e9	0.0692203
$199$	−2.41457e9	−0.109144	−0.0545722	−	0.998510i	$-0.517380\pi$
$199$	−2.41457e9	−0.109144	−0.0545722	+	0.998510i	$0.517380\pi$
$200$	2.11129e10	0.933067
$201$	−1.20752e10	−0.521812
$202$	5.94663e9	0.251298
$203$	0	0
$204$	1.78344e10	0.720979
$205$	3.14196e10	1.24254
$206$	1.59506e10	0.617127
$207$	7.43013e9	0.281274
$208$	−6.29563e9	−0.233214
$209$	1.65768e9	0.0600954
$210$	0	0
$211$	1.58653e10	0.551034	0.275517	−	0.961296i	$-0.411151\pi$
$211$	1.58653e10	0.551034	0.275517	+	0.961296i	$0.411151\pi$
$212$	−7.68802e9	−0.261399
$213$	2.44407e10	0.813588
$214$	4.24596e10	1.38393
$215$	−9.60512e10	−3.06570
$216$	1.22470e10	0.382814
$217$	0	0
$218$	−1.58108e10	−0.474131
$219$	5.65192e9	0.166034
$220$	1.28945e10	0.371110
$221$	5.51399e10	1.55489
$222$	6.01377e9	0.166172
$223$	−3.21097e10	−0.869489	−0.434745	−	0.900554i	$-0.643161\pi$
$223$	−3.21097e10	−0.869489	−0.434745	+	0.900554i	$0.643161\pi$
$224$	0	0
$225$	−2.55266e10	−0.664004
$226$	1.06816e10	0.272364
$227$	−4.56740e9	−0.114170	−0.0570851	−	0.998369i	$-0.518181\pi$
$227$	−4.56740e9	−0.114170	−0.0570851	+	0.998369i	$0.518181\pi$
$228$	2.72615e9	0.0668102
$229$	1.32210e10	0.317690	0.158845	−	0.987304i	$-0.449223\pi$
$229$	1.32210e10	0.317690	0.158845	+	0.987304i	$0.449223\pi$
$230$	6.39992e10	1.50799
$231$	0	0
$232$	−7.33174e9	−0.166154
$233$	4.87335e10	1.08324	0.541622	−	0.840622i	$-0.317810\pi$
$233$	4.87335e10	1.08324	0.541622	+	0.840622i	$0.317810\pi$
$234$	7.61174e9	0.165963
$235$	1.57827e10	0.337580
$236$	3.66903e10	0.769922
$237$	3.07336e10	0.632770
$238$	0	0
$239$	7.16988e10	1.42142	0.710708	−	0.703487i	$-0.248375\pi$
$239$	7.16988e10	1.42142	0.710708	+	0.703487i	$0.248375\pi$
$240$	2.12058e10	0.412576
$241$	6.39036e10	1.22025	0.610125	−	0.792305i	$-0.291119\pi$
$241$	6.39036e10	1.22025	0.610125	+	0.792305i	$0.291119\pi$
$242$	−3.20160e10	−0.600064
$243$	−2.66379e10	−0.490085
$244$	−3.85652e10	−0.696533
$245$	0	0
$246$	2.28860e10	0.398440
$247$	8.42863e9	0.144086
$248$	3.95727e10	0.664298
$249$	−3.84543e10	−0.633939
$250$	−1.36559e11	−2.21101
$251$	9.92465e10	1.57828	0.789139	−	0.614215i	$-0.210527\pi$
$251$	9.92465e10	1.57828	0.789139	+	0.614215i	$0.210527\pi$
$252$	0	0
$253$	2.83462e10	0.434963
$254$	−5.63063e10	−0.848801
$255$	−1.85730e11	−2.75074
$256$	4.29497e9	0.0625000
$257$	1.30024e10	0.185919	0.0929593	−	0.995670i	$-0.470367\pi$
$257$	1.30024e10	0.185919	0.0929593	+	0.995670i	$0.470367\pi$
$258$	−6.99636e10	−0.983068
$259$	0	0
$260$	6.55635e10	0.889779
$261$	8.86444e9	0.118241
$262$	−6.08416e10	−0.797710
$263$	3.28330e10	0.423165	0.211582	−	0.977360i	$-0.432138\pi$
$263$	3.28330e10	0.423165	0.211582	+	0.977360i	$0.432138\pi$
$264$	9.39236e9	0.119003
$265$	8.00640e10	0.997312
$266$	0	0
$267$	1.02026e11	1.22861
$268$	2.54697e10	0.301590
$269$	7.30259e10	0.850338	0.425169	−	0.905114i	$-0.360215\pi$
$269$	7.30259e10	0.850338	0.425169	+	0.905114i	$0.360215\pi$
$270$	−1.27542e11	−1.46055
$271$	8.83287e10	0.994809	0.497405	−	0.867519i	$-0.334286\pi$
$271$	8.83287e10	0.994809	0.497405	+	0.867519i	$0.334286\pi$
$272$	−3.76172e10	−0.416702
$273$	0	0
$274$	−1.20687e11	−1.29355
$275$	−9.73846e10	−1.02682
$276$	4.66170e10	0.483563
$277$	−1.17475e11	−1.19891	−0.599455	−	0.800408i	$-0.704616\pi$
$277$	−1.17475e11	−1.19891	−0.599455	+	0.800408i	$0.704616\pi$
$278$	−1.67199e10	−0.167893
$279$	−4.78454e10	−0.472738
$280$	0	0
$281$	−3.51607e10	−0.336418	−0.168209	−	0.985751i	$-0.553798\pi$
$281$	−3.51607e10	−0.336418	−0.168209	+	0.985751i	$0.553798\pi$
$282$	1.14961e10	0.108251
$283$	5.03459e10	0.466579	0.233290	−	0.972407i	$-0.425051\pi$
$283$	5.03459e10	0.466579	0.233290	+	0.972407i	$0.425051\pi$
$284$	−5.15514e10	−0.470228
$285$	−2.83904e10	−0.254900
$286$	2.90390e10	0.256646
$287$	0	0
$288$	−5.19283e9	−0.0444773
$289$	2.10879e11	1.77825
$290$	7.63536e10	0.633926
$291$	−3.31059e10	−0.270637
$292$	−1.19213e10	−0.0959624
$293$	1.70340e11	1.35024	0.675121	−	0.737707i	$-0.264091\pi$
$293$	1.70340e11	1.35024	0.675121	+	0.737707i	$0.264091\pi$
$294$	0	0
$295$	−3.82097e11	−2.93748
$296$	−1.26845e10	−0.0960421
$297$	−5.64900e10	−0.421277
$298$	−5.86630e9	−0.0430915
$299$	1.44129e11	1.04287
$300$	−1.60155e11	−1.14155
$301$	0	0
$302$	8.60808e10	0.595491
$303$	−4.51090e10	−0.307448
$304$	−5.75012e9	−0.0386141
$305$	4.01623e11	2.65748
$306$	4.54810e10	0.296540
$307$	−5.25886e10	−0.337885	−0.168943	−	0.985626i	$-0.554035\pi$
$307$	−5.25886e10	−0.337885	−0.168943	+	0.985626i	$0.554035\pi$
$308$	0	0
$309$	−1.20995e11	−0.755016
$310$	−4.12115e11	−2.53449
$311$	−6.08603e10	−0.368903	−0.184451	−	0.982842i	$-0.559051\pi$
$311$	−6.08603e10	−0.368903	−0.184451	+	0.982842i	$0.559051\pi$
$312$	4.77564e10	0.285322
$313$	1.88490e11	1.11004	0.555019	−	0.831838i	$-0.312711\pi$
$313$	1.88490e11	1.11004	0.555019	+	0.831838i	$0.312711\pi$
$314$	1.33942e11	0.777560
$315$	0	0
$316$	−6.48248e10	−0.365721
$317$	−1.91983e10	−0.106782	−0.0533908	−	0.998574i	$-0.517003\pi$
$317$	−1.91983e10	−0.106782	−0.0533908	+	0.998574i	$0.517003\pi$
$318$	5.83185e10	0.319805
$319$	3.38181e10	0.182848
$320$	−4.47283e10	−0.238456
$321$	−3.22083e11	−1.69315
$322$	0	0
$323$	5.03621e10	0.257450
$324$	−6.79475e10	−0.342548
$325$	−4.95162e11	−2.46191
$326$	−1.17040e11	−0.573925
$327$	1.19935e11	0.580069
$328$	−4.82724e10	−0.230285
$329$	0	0
$330$	−9.78132e10	−0.454030
$331$	3.10516e11	1.42186	0.710931	−	0.703262i	$-0.248274\pi$
$331$	3.10516e11	1.42186	0.710931	+	0.703262i	$0.248274\pi$
$332$	8.11096e10	0.366396
$333$	1.53362e10	0.0683470
$334$	8.53823e10	0.375412
$335$	−2.65245e11	−1.15065
$336$	0	0
$337$	3.29977e11	1.39363	0.696817	−	0.717249i	$-0.254599\pi$
$337$	3.29977e11	1.39363	0.696817	+	0.717249i	$0.254599\pi$
$338$	−2.20201e10	−0.0917687
$339$	−8.10269e10	−0.333220
$340$	3.91750e11	1.58984
$341$	−1.82532e11	−0.731044
$342$	6.95219e9	0.0274792
$343$	0	0
$344$	1.47571e11	0.568181
$345$	−4.85475e11	−1.84493
$346$	7.17622e10	0.269187
$347$	−3.55666e11	−1.31692	−0.658460	−	0.752615i	$-0.728792\pi$
$347$	−3.55666e11	−1.31692	−0.658460	+	0.752615i	$0.728792\pi$
$348$	5.56159e10	0.203279
$349$	−2.61881e11	−0.944907	−0.472454	−	0.881356i	$-0.656632\pi$
$349$	−2.61881e11	−0.944907	−0.472454	+	0.881356i	$0.656632\pi$
$350$	0	0
$351$	−2.87229e11	−1.01006
$352$	−1.98108e10	−0.0687797
$353$	−1.14752e11	−0.393347	−0.196673	−	0.980469i	$-0.563014\pi$
$353$	−1.14752e11	−0.393347	−0.196673	+	0.980469i	$0.563014\pi$
$354$	−2.78319e11	−0.941951
$355$	5.36863e11	1.79406
$356$	−2.15199e11	−0.710094
$357$	0	0
$358$	−1.08204e11	−0.348153
$359$	1.85010e11	0.587854	0.293927	−	0.955828i	$-0.405038\pi$
$359$	1.85010e11	0.587854	0.293927	+	0.955828i	$0.405038\pi$
$360$	5.40788e10	0.169694
$361$	−3.14989e11	−0.976143
$362$	6.50619e10	0.199131
$363$	2.42862e11	0.734141
$364$	0	0
$365$	1.24150e11	0.366125
$366$	2.92542e11	0.852164
$367$	1.64535e11	0.473435	0.236717	−	0.971579i	$-0.423928\pi$
$367$	1.64535e11	0.473435	0.236717	+	0.971579i	$0.423928\pi$
$368$	−9.83268e10	−0.279484
$369$	5.83637e10	0.163879
$370$	1.32098e11	0.366429
$371$	0	0
$372$	−3.00184e11	−0.812726
$373$	−6.36122e10	−0.170157	−0.0850787	−	0.996374i	$-0.527114\pi$
$373$	−6.36122e10	−0.170157	−0.0850787	+	0.996374i	$0.527114\pi$
$374$	1.73512e11	0.458571
$375$	1.03589e12	2.70504
$376$	−2.42482e10	−0.0625654
$377$	1.71952e11	0.438400
$378$	0	0
$379$	−7.53720e10	−0.187644	−0.0938218	−	0.995589i	$-0.529908\pi$
$379$	−7.53720e10	−0.187644	−0.0938218	+	0.995589i	$0.529908\pi$
$380$	5.98825e10	0.147324
$381$	4.27120e11	1.03845
$382$	−1.80388e11	−0.433434
$383$	−3.91555e11	−0.929820	−0.464910	−	0.885358i	$-0.653913\pi$
$383$	−3.91555e11	−0.929820	−0.464910	+	0.885358i	$0.653913\pi$
$384$	−3.25801e10	−0.0764648
$385$	0	0
$386$	−3.68177e11	−0.844139
$387$	−1.78420e11	−0.404339
$388$	6.98286e10	0.156419
$389$	−4.06368e11	−0.899800	−0.449900	−	0.893079i	$-0.648540\pi$
$389$	−4.06368e11	−0.899800	−0.449900	+	0.893079i	$0.648540\pi$
$390$	−4.97341e11	−1.08859
$391$	8.61188e11	1.86338
$392$	0	0
$393$	4.61523e11	0.975948
$394$	2.61402e11	0.546483
$395$	6.75094e11	1.39533
$396$	2.39523e10	0.0489461
$397$	−2.48023e11	−0.501111	−0.250555	−	0.968102i	$-0.580613\pi$
$397$	−2.48023e11	−0.501111	−0.250555	+	0.968102i	$0.580613\pi$
$398$	−3.86332e10	−0.0771768
$399$	0	0
$400$	3.37806e11	0.659778
$401$	5.26496e11	1.01682	0.508412	−	0.861114i	$-0.330233\pi$
$401$	5.26496e11	1.01682	0.508412	+	0.861114i	$0.330233\pi$
$402$	−1.93204e11	−0.368976
$403$	−9.28101e11	−1.75276
$404$	9.51461e10	0.177695
$405$	7.07614e11	1.30692
$406$	0	0
$407$	5.85082e10	0.105692
$408$	2.85350e11	0.509809
$409$	−7.76353e11	−1.37184	−0.685921	−	0.727676i	$-0.740601\pi$
$409$	−7.76353e11	−1.37184	−0.685921	+	0.727676i	$0.740601\pi$
$410$	5.02714e11	0.878606
$411$	9.15491e11	1.58258
$412$	2.55210e11	0.436375
$413$	0	0
$414$	1.18882e11	0.198891
$415$	−8.44686e11	−1.39791
$416$	−1.00730e11	−0.164907
$417$	1.26831e11	0.205407
$418$	2.65228e10	0.0424939
$419$	−8.55309e11	−1.35569	−0.677844	−	0.735205i	$-0.737086\pi$
$419$	−8.55309e11	−1.35569	−0.677844	+	0.735205i	$0.737086\pi$
$420$	0	0
$421$	8.48099e11	1.31576	0.657881	−	0.753122i	$-0.271453\pi$
$421$	8.48099e11	1.31576	0.657881	+	0.753122i	$0.271453\pi$
$422$	2.53845e11	0.389640
$423$	2.93173e10	0.0445238
$424$	−1.23008e11	−0.184837
$425$	−2.95865e12	−4.39890
$426$	3.91050e11	0.575294
$427$	0	0
$428$	6.79354e11	0.978586
$429$	−2.20280e11	−0.313990
$430$	−1.53682e12	−2.16778
$431$	−2.34728e11	−0.327656	−0.163828	−	0.986489i	$-0.552384\pi$
$431$	−2.34728e11	−0.327656	−0.163828	+	0.986489i	$0.552384\pi$
$432$	1.95952e11	0.270690
$433$	−2.27943e11	−0.311624	−0.155812	−	0.987787i	$-0.549799\pi$
$433$	−2.27943e11	−0.311624	−0.155812	+	0.987787i	$0.549799\pi$
$434$	0	0
$435$	−5.79191e11	−0.775568
$436$	−2.52972e11	−0.335261
$437$	1.31640e11	0.172672
$438$	9.04308e10	0.117404
$439$	−7.34118e11	−0.943356	−0.471678	−	0.881771i	$-0.656352\pi$
$439$	−7.34118e11	−0.943356	−0.471678	+	0.881771i	$0.656352\pi$
$440$	2.06312e11	0.262415
$441$	0	0
$442$	8.82238e11	1.09947
$443$	1.34400e12	1.65799	0.828996	−	0.559254i	$-0.188912\pi$
$443$	1.34400e12	1.65799	0.828996	+	0.559254i	$0.188912\pi$
$444$	9.62203e10	0.117501
$445$	2.24111e12	2.70922
$446$	−5.13755e11	−0.614822
$447$	4.44997e10	0.0527197
$448$	0	0
$449$	−3.61013e11	−0.419193	−0.209597	−	0.977788i	$-0.567215\pi$
$449$	−3.61013e11	−0.419193	−0.209597	+	0.977788i	$0.567215\pi$
$450$	−4.08425e11	−0.469522
$451$	2.22659e11	0.253423
$452$	1.70906e11	0.192590
$453$	−6.52978e11	−0.728546
$454$	−7.30784e10	−0.0807305
$455$	0	0
$456$	4.36184e10	0.0472419
$457$	8.48179e11	0.909630	0.454815	−	0.890586i	$-0.349705\pi$
$457$	8.48179e11	0.909630	0.454815	+	0.890586i	$0.349705\pi$
$458$	2.11536e11	0.224641
$459$	−1.71623e12	−1.80476
$460$	1.02399e12	1.06631
$461$	−2.08658e11	−0.215170	−0.107585	−	0.994196i	$-0.534312\pi$
$461$	−2.08658e11	−0.215170	−0.107585	+	0.994196i	$0.534312\pi$
$462$	0	0
$463$	−5.84855e11	−0.591471	−0.295736	−	0.955270i	$-0.595565\pi$
$463$	−5.84855e11	−0.591471	−0.295736	+	0.955270i	$0.595565\pi$
$464$	−1.17308e11	−0.117489
$465$	3.12615e12	3.10079
$466$	7.79736e11	0.765969
$467$	1.32692e12	1.29098	0.645488	−	0.763770i	$-0.276654\pi$
$467$	1.32692e12	1.29098	0.645488	+	0.763770i	$0.276654\pi$
$468$	1.21788e11	0.117354
$469$	0	0
$470$	2.52524e11	0.238705
$471$	−1.01604e12	−0.951295
$472$	5.87044e11	0.544417
$473$	−6.80679e11	−0.625270
$474$	4.91738e11	0.447436
$475$	−4.52257e11	−0.407628
$476$	0	0
$477$	1.48723e11	0.131536
$478$	1.14718e12	1.00509
$479$	1.82534e11	0.158429	0.0792144	−	0.996858i	$-0.474759\pi$
$479$	1.82534e11	0.158429	0.0792144	+	0.996858i	$0.474759\pi$
$480$	3.39293e11	0.291735
$481$	2.97491e11	0.253408
$482$	1.02246e12	0.862847
$483$	0	0
$484$	−5.12256e11	−0.424310
$485$	−7.27204e11	−0.596785
$486$	−4.26206e11	−0.346542
$487$	1.73623e12	1.39871	0.699354	−	0.714776i	$-0.253471\pi$
$487$	1.73623e12	1.39871	0.699354	+	0.714776i	$0.253471\pi$
$488$	−6.17044e11	−0.492523
$489$	8.87823e11	0.702161
$490$	0	0
$491$	1.43457e12	1.11392	0.556962	−	0.830538i	$-0.311967\pi$
$491$	1.43457e12	1.11392	0.556962	+	0.830538i	$0.311967\pi$
$492$	3.66177e11	0.281739
$493$	1.02743e12	0.783325
$494$	1.34858e11	0.101884
$495$	−2.49442e11	−0.186744
$496$	6.33163e11	0.469730
$497$	0	0
$498$	−6.15268e11	−0.448263
$499$	−2.00302e11	−0.144622	−0.0723108	−	0.997382i	$-0.523037\pi$
$499$	−2.00302e11	−0.144622	−0.0723108	+	0.997382i	$0.523037\pi$
$500$	−2.18495e12	−1.56342
$501$	−6.47679e11	−0.459293
$502$	1.58794e12	1.11601
$503$	−2.58160e12	−1.79818	−0.899090	−	0.437764i	$-0.855771\pi$
$503$	−2.58160e12	−1.79818	−0.899090	+	0.437764i	$0.855771\pi$
$504$	0	0
$505$	−9.90863e11	−0.677958
$506$	4.53539e11	0.307565
$507$	1.67037e11	0.112273
$508$	−9.00902e11	−0.600193
$509$	1.63704e12	1.08101	0.540503	−	0.841342i	$-0.318234\pi$
$509$	1.63704e12	1.08101	0.540503	+	0.841342i	$0.318234\pi$
$510$	−2.97167e12	−1.94507
$511$	0	0
$512$	6.87195e10	0.0441942
$513$	−2.62341e11	−0.167239
$514$	2.08038e11	0.131464
$515$	−2.65778e12	−1.66490
$516$	−1.11942e12	−0.695134
$517$	1.11846e11	0.0688517
$518$	0	0
$519$	−5.44362e11	−0.329333
$520$	1.04902e12	0.629169
$521$	−9.60425e11	−0.571076	−0.285538	−	0.958367i	$-0.592172\pi$
$521$	−9.60425e11	−0.571076	−0.285538	+	0.958367i	$0.592172\pi$
$522$	1.41831e11	0.0836092
$523$	1.67089e12	0.976542	0.488271	−	0.872692i	$-0.337628\pi$
$523$	1.67089e12	0.976542	0.488271	+	0.872692i	$0.337628\pi$
$524$	−9.73466e11	−0.564066
$525$	0	0
$526$	5.25328e11	0.299223
$527$	−5.54551e12	−3.13180
$528$	1.50278e11	0.0841476
$529$	4.49889e11	0.249779
$530$	1.28102e12	0.705206
$531$	−7.09766e11	−0.387427
$532$	0	0
$533$	1.13213e12	0.607611
$534$	1.63242e12	0.868755
$535$	−7.07487e12	−3.73359
$536$	4.07515e11	0.213256
$537$	8.20798e11	0.425943
$538$	1.16841e12	0.601280
$539$	0	0
$540$	−2.04067e12	−1.03276
$541$	2.10233e12	1.05515	0.527575	−	0.849509i	$-0.323101\pi$
$541$	2.10233e12	1.05515	0.527575	+	0.849509i	$0.323101\pi$
$542$	1.41326e12	0.703436
$543$	−4.93536e11	−0.243624
$544$	−6.01875e11	−0.294653
$545$	2.63448e12	1.27912
$546$	0	0
$547$	1.37451e11	0.0656455	0.0328228	−	0.999461i	$-0.489550\pi$
$547$	1.37451e11	0.0656455	0.0328228	+	0.999461i	$0.489550\pi$
$548$	−1.93100e12	−0.914680
$549$	7.46037e11	0.350497
$550$	−1.55815e12	−0.726070
$551$	1.57052e11	0.0725875
$552$	7.45871e11	0.341931
$553$	0	0
$554$	−1.87960e12	−0.847758
$555$	−1.00205e12	−0.448302
$556$	−2.67519e11	−0.118718
$557$	6.11765e11	0.269300	0.134650	−	0.990893i	$-0.457009\pi$
$557$	6.11765e11	0.269300	0.134650	+	0.990893i	$0.457009\pi$
$558$	−7.65526e11	−0.334277
$559$	−3.46098e12	−1.49915
$560$	0	0
$561$	−1.31620e12	−0.561032
$562$	−5.62572e11	−0.237884
$563$	1.57297e12	0.659831	0.329916	−	0.944010i	$-0.392980\pi$
$563$	1.57297e12	0.659831	0.329916	+	0.944010i	$0.392980\pi$
$564$	1.83938e11	0.0765448
$565$	−1.77984e12	−0.734788
$566$	8.05535e11	0.329921
$567$	0	0
$568$	−8.24823e11	−0.332501
$569$	3.23825e11	0.129511	0.0647554	−	0.997901i	$-0.479373\pi$
$569$	3.23825e11	0.129511	0.0647554	+	0.997901i	$0.479373\pi$
$570$	−4.54247e11	−0.180242
$571$	1.38751e12	0.546227	0.273113	−	0.961982i	$-0.411947\pi$
$571$	1.38751e12	0.546227	0.273113	+	0.961982i	$0.411947\pi$
$572$	4.64624e11	0.181476
$573$	1.36836e12	0.530279
$574$	0	0
$575$	−7.73356e12	−2.95036
$576$	−8.30853e10	−0.0314502
$577$	−4.43500e11	−0.166572	−0.0832862	−	0.996526i	$-0.526542\pi$
$577$	−4.43500e11	−0.166572	−0.0832862	+	0.996526i	$0.526542\pi$
$578$	3.37407e12	1.25742
$579$	2.79286e12	1.03275
$580$	1.22166e12	0.448253
$581$	0	0
$582$	−5.29694e11	−0.191369
$583$	5.67384e11	0.203408
$584$	−1.90741e11	−0.0678557
$585$	−1.26831e12	−0.447739
$586$	2.72544e12	0.954766
$587$	3.22961e12	1.12274	0.561369	−	0.827565i	$-0.310275\pi$
$587$	3.22961e12	1.12274	0.561369	+	0.827565i	$0.310275\pi$
$588$	0	0
$589$	−8.47682e11	−0.290211
$590$	−6.11355e12	−2.07711
$591$	−1.98290e12	−0.668587
$592$	−2.02952e11	−0.0679120
$593$	−2.78675e12	−0.925449	−0.462724	−	0.886502i	$-0.653128\pi$
$593$	−2.78675e12	−0.925449	−0.462724	+	0.886502i	$0.653128\pi$
$594$	−9.03841e11	−0.297888
$595$	0	0
$596$	−9.38609e10	−0.0304703
$597$	2.93057e11	0.0944209
$598$	2.30606e12	0.737422
$599$	8.96148e11	0.284419	0.142210	−	0.989837i	$-0.454579\pi$
$599$	8.96148e11	0.284419	0.142210	+	0.989837i	$0.454579\pi$
$600$	−2.56248e12	−0.807197
$601$	−2.34296e12	−0.732536	−0.366268	−	0.930509i	$-0.619365\pi$
$601$	−2.34296e12	−0.732536	−0.366268	+	0.930509i	$0.619365\pi$
$602$	0	0
$603$	−4.92706e11	−0.151761
$604$	1.37729e12	0.421076
$605$	5.33470e12	1.61886
$606$	−7.21744e11	−0.217398
$607$	1.47062e12	0.439696	0.219848	−	0.975534i	$-0.429444\pi$
$607$	1.47062e12	0.439696	0.219848	+	0.975534i	$0.429444\pi$
$608$	−9.20020e10	−0.0273043
$609$	0	0
$610$	6.42597e12	1.87912
$611$	5.68694e11	0.165080
$612$	7.27697e11	0.209686
$613$	−1.17641e12	−0.336500	−0.168250	−	0.985744i	$-0.553812\pi$
$613$	−1.17641e12	−0.336500	−0.168250	+	0.985744i	$0.553812\pi$
$614$	−8.41418e11	−0.238921
$615$	−3.81341e12	−1.07492
$616$	0	0
$617$	6.76956e12	1.88052	0.940259	−	0.340461i	$-0.110583\pi$
$617$	6.76956e12	1.88052	0.940259	+	0.340461i	$0.110583\pi$
$618$	−1.93593e12	−0.533877
$619$	−5.89037e12	−1.61263	−0.806315	−	0.591486i	$-0.798542\pi$
$619$	−5.89037e12	−1.61263	−0.806315	+	0.591486i	$0.798542\pi$
$620$	−6.59384e12	−1.79216
$621$	−4.48602e12	−1.21046
$622$	−9.73764e11	−0.260854
$623$	0	0
$624$	7.64102e11	0.201753
$625$	1.26869e13	3.32580
$626$	3.01583e12	0.784915
$627$	−2.01193e11	−0.0519886
$628$	2.14307e12	0.549818
$629$	1.77754e12	0.452786
$630$	0	0
$631$	2.08173e12	0.522748	0.261374	−	0.965238i	$-0.415824\pi$
$631$	2.08173e12	0.522748	0.261374	+	0.965238i	$0.415824\pi$
$632$	−1.03720e12	−0.258603
$633$	−1.92558e12	−0.476700
$634$	−3.07173e11	−0.0755059
$635$	9.38210e12	2.28991
$636$	9.33097e11	0.226136
$637$	0	0
$638$	5.41090e11	0.129293
$639$	9.97252e11	0.236620
$640$	−7.15653e11	−0.168614
$641$	−2.05937e12	−0.481808	−0.240904	−	0.970549i	$-0.577444\pi$
$641$	−2.05937e12	−0.481808	−0.240904	+	0.970549i	$0.577444\pi$
$642$	−5.15333e12	−1.19724
$643$	3.54773e12	0.818468	0.409234	−	0.912429i	$-0.365796\pi$
$643$	3.54773e12	0.818468	0.409234	+	0.912429i	$0.365796\pi$
$644$	0	0
$645$	1.16578e13	2.65214
$646$	8.05793e11	0.182044
$647$	9.70649e11	0.217767	0.108884	−	0.994054i	$-0.465272\pi$
$647$	9.70649e11	0.217767	0.108884	+	0.994054i	$0.465272\pi$
$648$	−1.08716e12	−0.242218
$649$	−2.70778e12	−0.599118
$650$	−7.92259e12	−1.74083
$651$	0	0
$652$	−1.87264e12	−0.405826
$653$	−3.85104e12	−0.828835	−0.414418	−	0.910087i	$-0.636015\pi$
$653$	−3.85104e12	−0.828835	−0.414418	+	0.910087i	$0.636015\pi$
$654$	1.91895e12	0.410171
$655$	1.01378e13	2.15208
$656$	−7.72358e11	−0.162836
$657$	2.30615e11	0.0482886
$658$	0	0
$659$	−6.97320e12	−1.44028	−0.720141	−	0.693827i	$-0.755923\pi$
$659$	−6.97320e12	−1.44028	−0.720141	+	0.693827i	$0.755923\pi$
$660$	−1.56501e12	−0.321048
$661$	−3.78855e12	−0.771910	−0.385955	−	0.922518i	$-0.626128\pi$
$661$	−3.78855e12	−0.771910	−0.385955	+	0.922518i	$0.626128\pi$
$662$	4.96825e12	1.00541
$663$	−6.69234e12	−1.34514
$664$	1.29775e12	0.259081
$665$	0	0
$666$	2.45380e11	0.0483287
$667$	2.68558e12	0.525379
$668$	1.36612e12	0.265457
$669$	3.89716e12	0.752195
$670$	−4.24391e12	−0.813636
$671$	2.84615e12	0.542010
$672$	0	0
$673$	5.11087e12	0.960344	0.480172	−	0.877174i	$-0.340574\pi$
$673$	5.11087e12	0.960344	0.480172	+	0.877174i	$0.340574\pi$
$674$	5.27963e12	0.985449
$675$	1.54119e13	2.85753
$676$	−3.52322e11	−0.0648902
$677$	5.62747e12	1.02959	0.514795	−	0.857314i	$-0.327868\pi$
$677$	5.62747e12	1.02959	0.514795	+	0.857314i	$0.327868\pi$
$678$	−1.29643e12	−0.235622
$679$	0	0
$680$	6.26800e12	1.12419
$681$	5.54346e11	0.0987687
$682$	−2.92051e12	−0.516926
$683$	2.40559e12	0.422988	0.211494	−	0.977379i	$-0.432167\pi$
$683$	2.40559e12	0.422988	0.211494	+	0.977379i	$0.432167\pi$
$684$	1.11235e11	0.0194307
$685$	2.01097e13	3.48977
$686$	0	0
$687$	−1.60463e12	−0.274834
$688$	2.36113e12	0.401765
$689$	2.88492e12	0.487694
$690$	−7.76760e12	−1.30457
$691$	2.14525e12	0.357953	0.178976	−	0.983853i	$-0.442721\pi$
$691$	2.14525e12	0.357953	0.178976	+	0.983853i	$0.442721\pi$
$692$	1.14820e12	0.190344
$693$	0	0
$694$	−5.69065e12	−0.931203
$695$	2.78597e12	0.452945
$696$	8.89854e11	0.143740
$697$	6.76464e12	1.08567
$698$	−4.19009e12	−0.668150
$699$	−5.91480e12	−0.937114
$700$	0	0
$701$	3.57696e12	0.559478	0.279739	−	0.960076i	$-0.409752\pi$
$701$	3.57696e12	0.559478	0.279739	+	0.960076i	$0.409752\pi$
$702$	−4.59567e12	−0.714220
$703$	2.71714e11	0.0419578
$704$	−3.16973e11	−0.0486346
$705$	−1.91555e12	−0.292041
$706$	−1.83604e12	−0.278138
$707$	0	0
$708$	−4.45311e12	−0.666060
$709$	5.06767e12	0.753183	0.376592	−	0.926379i	$-0.377096\pi$
$709$	5.06767e12	0.753183	0.376592	+	0.926379i	$0.377096\pi$
$710$	8.58981e12	1.26859
$711$	1.25402e12	0.184032
$712$	−3.44319e12	−0.502112
$713$	−1.44953e13	−2.10051
$714$	0	0
$715$	−4.83866e12	−0.692385
$716$	−1.73127e12	−0.246181
$717$	−8.70210e12	−1.22967
$718$	2.96015e12	0.415675
$719$	−1.38056e13	−1.92653	−0.963265	−	0.268553i	$-0.913455\pi$
$719$	−1.38056e13	−1.92653	−0.963265	+	0.268553i	$0.913455\pi$
$720$	8.65261e11	0.119992
$721$	0	0
$722$	−5.03983e12	−0.690237
$723$	−7.75600e12	−1.05564
$724$	1.04099e12	0.140807
$725$	−9.22645e12	−1.24026
$726$	3.88579e12	0.519116
$727$	1.39068e13	1.84638	0.923190	−	0.384343i	$-0.125572\pi$
$727$	1.39068e13	1.84638	0.923190	+	0.384343i	$0.125572\pi$
$728$	0	0
$729$	8.45730e12	1.10907
$730$	1.98640e12	0.258889
$731$	−2.06798e13	−2.67866
$732$	4.68067e12	0.602571
$733$	−6.93377e12	−0.887159	−0.443579	−	0.896235i	$-0.646292\pi$
$733$	−6.93377e12	−0.887159	−0.443579	+	0.896235i	$0.646292\pi$
$734$	2.63255e12	0.334769
$735$	0	0
$736$	−1.57323e12	−0.197625
$737$	−1.87969e12	−0.234684
$738$	9.33819e11	0.115880
$739$	−2.41835e12	−0.298277	−0.149138	−	0.988816i	$-0.547650\pi$
$739$	−2.41835e12	−0.298277	−0.149138	+	0.988816i	$0.547650\pi$
$740$	2.11357e12	0.259104
$741$	−1.02298e12	−0.124648
$742$	0	0
$743$	−1.07681e13	−1.29626	−0.648129	−	0.761531i	$-0.724448\pi$
$743$	−1.07681e13	−1.29626	−0.648129	+	0.761531i	$0.724448\pi$
$744$	−4.80294e12	−0.574684
$745$	9.77479e11	0.116253
$746$	−1.01780e12	−0.120319
$747$	−1.56905e12	−0.184372
$748$	2.77619e12	0.324258
$749$	0	0
$750$	1.65742e13	1.91275
$751$	−2.36270e11	−0.0271037	−0.0135519	−	0.999908i	$-0.504314\pi$
$751$	−2.36270e11	−0.0271037	−0.0135519	+	0.999908i	$0.504314\pi$
$752$	−3.87971e11	−0.0442404
$753$	−1.20456e13	−1.36537
$754$	2.75123e12	0.309995
$755$	−1.43433e13	−1.60653
$756$	0	0
$757$	9.94250e12	1.10043	0.550217	−	0.835022i	$-0.314545\pi$
$757$	9.94250e12	1.10043	0.550217	+	0.835022i	$0.314545\pi$
$758$	−1.20595e12	−0.132684
$759$	−3.44038e12	−0.376286
$760$	9.58120e11	0.104174
$761$	−1.20176e13	−1.29894	−0.649469	−	0.760388i	$-0.725009\pi$
$761$	−1.20176e13	−1.29894	−0.649469	+	0.760388i	$0.725009\pi$
$762$	6.83391e12	0.734298
$763$	0	0
$764$	−2.88621e12	−0.306484
$765$	−7.57832e12	−0.800012
$766$	−6.26489e12	−0.657482
$767$	−1.37680e13	−1.43645
$768$	−5.21281e11	−0.0540688
$769$	−8.18420e12	−0.843933	−0.421966	−	0.906611i	$-0.638660\pi$
$769$	−8.18420e12	−0.843933	−0.421966	+	0.906611i	$0.638660\pi$
$770$	0	0
$771$	−1.57810e12	−0.160838
$772$	−5.89083e12	−0.596896
$773$	8.99974e12	0.906613	0.453307	−	0.891355i	$-0.350244\pi$
$773$	8.99974e12	0.906613	0.453307	+	0.891355i	$0.350244\pi$
$774$	−2.85473e12	−0.285911
$775$	4.97993e13	4.95868
$776$	1.11726e12	0.110605
$777$	0	0
$778$	−6.50188e12	−0.636255
$779$	1.03404e12	0.100604
$780$	−7.95746e12	−0.769748
$781$	3.80455e12	0.365909
$782$	1.37790e13	1.31761
$783$	−5.35200e12	−0.508848
$784$	0	0
$785$	−2.23182e13	−2.09772
$786$	7.38436e12	0.690099
$787$	−1.54598e12	−0.143654	−0.0718270	−	0.997417i	$-0.522883\pi$
$787$	−1.54598e12	−0.143654	−0.0718270	+	0.997417i	$0.522883\pi$
$788$	4.18244e12	0.386422
$789$	−3.98495e12	−0.366080
$790$	1.08015e13	0.986648
$791$	0	0
$792$	3.83236e11	0.0346101
$793$	1.44716e13	1.29953
$794$	−3.96836e12	−0.354339
$795$	−9.71738e12	−0.862775
$796$	−6.18131e11	−0.0545722
$797$	6.94374e12	0.609581	0.304790	−	0.952419i	$-0.401414\pi$
$797$	6.94374e12	0.609581	0.304790	+	0.952419i	$0.401414\pi$
$798$	0	0
$799$	3.39802e12	0.294961
$800$	5.40490e12	0.466534
$801$	4.16299e12	0.357321
$802$	8.42394e12	0.719003
$803$	8.79805e11	0.0746735
$804$	−3.09126e12	−0.260906
$805$	0	0
$806$	−1.48496e13	−1.23939
$807$	−8.86316e12	−0.735627
$808$	1.52234e12	0.125649
$809$	1.20210e13	0.986669	0.493335	−	0.869840i	$-0.335778\pi$
$809$	1.20210e13	0.986669	0.493335	+	0.869840i	$0.335778\pi$
$810$	1.13218e13	0.924131
$811$	3.73568e11	0.0303232	0.0151616	−	0.999885i	$-0.495174\pi$
$811$	3.73568e11	0.0303232	0.0151616	+	0.999885i	$0.495174\pi$
$812$	0	0
$813$	−1.07205e13	−0.860610
$814$	9.36132e11	0.0747355
$815$	1.95019e13	1.54834
$816$	4.56560e12	0.360489
$817$	−3.16109e12	−0.248221
$818$	−1.24216e13	−0.970039
$819$	0	0
$820$	8.04343e12	0.621268
$821$	−1.11137e13	−0.853718	−0.426859	−	0.904318i	$-0.640380\pi$
$821$	−1.11137e13	−0.853718	−0.426859	+	0.904318i	$0.640380\pi$
$822$	1.46479e13	1.11905
$823$	−6.95373e12	−0.528346	−0.264173	−	0.964475i	$-0.585099\pi$
$823$	−6.95373e12	−0.528346	−0.264173	+	0.964475i	$0.585099\pi$
$824$	4.08335e12	0.308563
$825$	1.18196e13	0.888300
$826$	0	0
$827$	−2.17166e12	−0.161442	−0.0807211	−	0.996737i	$-0.525722\pi$
$827$	−2.17166e12	−0.161442	−0.0807211	+	0.996737i	$0.525722\pi$
$828$	1.90211e12	0.140637
$829$	−6.13605e12	−0.451226	−0.225613	−	0.974217i	$-0.572438\pi$
$829$	−6.13605e12	−0.451226	−0.225613	+	0.974217i	$0.572438\pi$
$830$	−1.35150e13	−0.988471
$831$	1.42580e13	1.03718
$832$	−1.61168e12	−0.116607
$833$	0	0
$834$	2.02930e12	0.145244
$835$	−1.42269e13	−1.01279
$836$	4.24365e11	0.0300477
$837$	2.88872e13	2.03442
$838$	−1.36849e13	−0.958617
$839$	−1.85233e13	−1.29059	−0.645297	−	0.763932i	$-0.723266\pi$
$839$	−1.85233e13	−1.29059	−0.645297	+	0.763932i	$0.723266\pi$
$840$	0	0
$841$	−1.13031e13	−0.779143
$842$	1.35696e13	0.930384
$843$	4.26747e12	0.291036
$844$	4.06153e12	0.275517
$845$	3.66912e12	0.247575
$846$	4.69077e11	0.0314831
$847$	0	0
$848$	−1.96813e12	−0.130699
$849$	−6.11050e12	−0.403638
$850$	−4.73384e13	−3.11049
$851$	4.64629e12	0.303685
$852$	6.25681e12	0.406794
$853$	−2.20104e13	−1.42350	−0.711750	−	0.702433i	$-0.752097\pi$
$853$	−2.20104e13	−1.42350	−0.711750	+	0.702433i	$0.752097\pi$
$854$	0	0
$855$	−1.15842e12	−0.0741339
$856$	1.08697e13	0.691965
$857$	5.77075e12	0.365442	0.182721	−	0.983165i	$-0.441509\pi$
$857$	5.77075e12	0.365442	0.182721	+	0.983165i	$0.441509\pi$
$858$	−3.52447e12	−0.222025
$859$	−1.26861e13	−0.794985	−0.397493	−	0.917605i	$-0.630120\pi$
$859$	−1.26861e13	−0.794985	−0.397493	+	0.917605i	$0.630120\pi$
$860$	−2.45891e13	−1.53285
$861$	0	0
$862$	−3.75566e12	−0.231688
$863$	−2.60879e13	−1.60100	−0.800498	−	0.599335i	$-0.795432\pi$
$863$	−2.60879e13	−1.60100	−0.800498	+	0.599335i	$0.795432\pi$
$864$	3.13523e12	0.191407
$865$	−1.19575e13	−0.726217
$866$	−3.64709e12	−0.220352
$867$	−2.55945e13	−1.53837
$868$	0	0
$869$	4.78414e12	0.284587
$870$	−9.26705e12	−0.548410
$871$	−9.55748e12	−0.562680
$872$	−4.04755e12	−0.237066
$873$	−1.35082e12	−0.0787106
$874$	2.10625e12	0.122098
$875$	0	0
$876$	1.44689e12	0.0830171
$877$	−1.06941e13	−0.610447	−0.305224	−	0.952281i	$-0.598731\pi$
$877$	−1.06941e13	−0.610447	−0.305224	+	0.952281i	$0.598731\pi$
$878$	−1.17459e13	−0.667054
$879$	−2.06742e13	−1.16810
$880$	3.30100e12	0.185555
$881$	2.77622e13	1.55261	0.776304	−	0.630359i	$-0.217092\pi$
$881$	2.77622e13	1.55261	0.776304	+	0.630359i	$0.217092\pi$
$882$	0	0
$883$	2.89461e13	1.60239	0.801193	−	0.598407i	$-0.204199\pi$
$883$	2.89461e13	1.60239	0.801193	+	0.598407i	$0.204199\pi$
$884$	1.41158e13	0.777446
$885$	4.63752e13	2.54121
$886$	2.15040e13	1.17238
$887$	−6.33688e12	−0.343732	−0.171866	−	0.985120i	$-0.554980\pi$
$887$	−6.33688e12	−0.343732	−0.171866	+	0.985120i	$0.554980\pi$
$888$	1.53952e12	0.0830861
$889$	0	0
$890$	3.58578e13	1.91570
$891$	5.01460e12	0.266555
$892$	−8.22008e12	−0.434745
$893$	5.19418e11	0.0273329
$894$	7.11995e11	0.0372785
$895$	1.80296e13	0.939254
$896$	0	0
$897$	−1.74930e13	−0.902189
$898$	−5.77621e12	−0.296414
$899$	−1.72935e13	−0.883006
$900$	−6.53480e12	−0.332002
$901$	1.72378e13	0.871403
$902$	3.56255e12	0.179197
$903$	0	0
$904$	2.73450e12	0.136182
$905$	−1.08410e13	−0.537219
$906$	−1.04476e13	−0.515159
$907$	2.68892e13	1.31930	0.659651	−	0.751572i	$-0.270704\pi$
$907$	2.68892e13	1.31930	0.659651	+	0.751572i	$0.270704\pi$
$908$	−1.16925e12	−0.0570851
$909$	−1.84058e12	−0.0894166
$910$	0	0
$911$	1.68170e13	0.808940	0.404470	−	0.914551i	$-0.367456\pi$
$911$	1.68170e13	0.808940	0.404470	+	0.914551i	$0.367456\pi$
$912$	6.97894e11	0.0334051
$913$	−5.98598e12	−0.285113
$914$	1.35709e13	0.643205
$915$	−4.87451e13	−2.29898
$916$	3.38457e12	0.158845
$917$	0	0
$918$	−2.74597e13	−1.27616
$919$	3.54064e13	1.63743	0.818713	−	0.574203i	$-0.194688\pi$
$919$	3.54064e13	1.63743	0.818713	+	0.574203i	$0.194688\pi$
$920$	1.63838e13	0.753996
$921$	6.38270e12	0.292305
$922$	−3.33854e12	−0.152148
$923$	1.93446e13	0.877309
$924$	0	0
$925$	−1.59626e13	−0.716910
$926$	−9.35768e12	−0.418233
$927$	−4.93698e12	−0.219585
$928$	−1.87692e12	−0.0830770
$929$	−2.58128e13	−1.13701	−0.568506	−	0.822679i	$-0.692478\pi$
$929$	−2.58128e13	−1.13701	−0.568506	+	0.822679i	$0.692478\pi$
$930$	5.00185e13	2.19259
$931$	0	0
$932$	1.24758e13	0.541622
$933$	7.38662e12	0.319138
$934$	2.12307e13	0.912859
$935$	−2.89115e13	−1.23714
$936$	1.94860e12	0.0829817
$937$	−2.58007e13	−1.09346	−0.546730	−	0.837309i	$-0.684128\pi$
$937$	−2.58007e13	−1.09346	−0.546730	+	0.837309i	$0.684128\pi$
$938$	0	0
$939$	−2.28770e13	−0.960294
$940$	4.04038e12	0.168790
$941$	3.33579e12	0.138690	0.0693451	−	0.997593i	$-0.477909\pi$
$941$	3.33579e12	0.138690	0.0693451	+	0.997593i	$0.477909\pi$
$942$	−1.62566e13	−0.672667
$943$	1.76820e13	0.728161
$944$	9.39271e12	0.384961
$945$	0	0
$946$	−1.08909e13	−0.442133
$947$	9.48940e12	0.383410	0.191705	−	0.981453i	$-0.438598\pi$
$947$	9.48940e12	0.383410	0.191705	+	0.981453i	$0.438598\pi$
$948$	7.86780e12	0.316385
$949$	4.47346e12	0.179038
$950$	−7.23611e12	−0.288237
$951$	2.33010e12	0.0923767
$952$	0	0
$953$	9.71866e12	0.381670	0.190835	−	0.981622i	$-0.438880\pi$
$953$	9.71866e12	0.381670	0.190835	+	0.981622i	$0.438880\pi$
$954$	2.37957e12	0.0930103
$955$	3.00573e13	1.16933
$956$	1.83549e13	0.710708
$957$	−4.10451e12	−0.158182
$958$	2.92055e12	0.112026
$959$	0	0
$960$	5.42869e12	0.206288
$961$	6.69011e13	2.53033
$962$	4.75986e12	0.179187
$963$	−1.31420e13	−0.492427
$964$	1.63593e13	0.610125
$965$	6.13479e13	2.27733
$966$	0	0
$967$	3.55171e13	1.30623	0.653113	−	0.757260i	$-0.273463\pi$
$967$	3.55171e13	1.30623	0.653113	+	0.757260i	$0.273463\pi$
$968$	−8.19609e12	−0.300032
$969$	−6.11245e12	−0.222720
$970$	−1.16353e13	−0.421991
$971$	−1.11011e13	−0.400756	−0.200378	−	0.979719i	$-0.564217\pi$
$971$	−1.11011e13	−0.400756	−0.200378	+	0.979719i	$0.564217\pi$
$972$	−6.81929e12	−0.245042
$973$	0	0
$974$	2.77797e13	0.989036
$975$	6.00979e13	2.12980
$976$	−9.87270e12	−0.348266
$977$	−2.94195e13	−1.03302	−0.516511	−	0.856280i	$-0.672770\pi$
$977$	−2.94195e13	−1.03302	−0.516511	+	0.856280i	$0.672770\pi$
$978$	1.42052e13	0.496503
$979$	1.58819e13	0.552562
$980$	0	0
$981$	4.89370e12	0.168704
$982$	2.29531e13	0.787663
$983$	4.45741e13	1.52262	0.761310	−	0.648388i	$-0.224556\pi$
$983$	4.45741e13	1.52262	0.761310	+	0.648388i	$0.224556\pi$
$984$	5.85883e12	0.199220
$985$	−4.35565e13	−1.47431
$986$	1.64389e13	0.553894
$987$	0	0
$988$	2.15773e12	0.0720428
$989$	−5.40545e13	−1.79659
$990$	−3.99107e12	−0.132048
$991$	−4.90305e13	−1.61486	−0.807430	−	0.589963i	$-0.799142\pi$
$991$	−4.90305e13	−1.61486	−0.807430	+	0.589963i	$0.799142\pi$
$992$	1.01306e13	0.332149
$993$	−3.76874e13	−1.23005
$994$	0	0
$995$	6.43729e12	0.208209
$996$	−9.84429e12	−0.316970
$997$	−4.94831e13	−1.58609	−0.793047	−	0.609160i	$-0.791507\pi$
$997$	−4.94831e13	−1.58609	−0.793047	+	0.609160i	$0.791507\pi$
$998$	−3.20484e12	−0.102263
$999$	−9.25942e12	−0.294130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.l.1.3	✓	6
7.2	even	3		98.10.c.n.67.4		12
7.3	odd	6		98.10.c.n.79.3		12
7.4	even	3		98.10.c.n.79.4		12
7.5	odd	6		98.10.c.n.67.3		12
7.6	odd	2	inner	98.10.a.l.1.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.l.1.3	✓	6	1.1	even	1	trivial
98.10.a.l.1.4	yes	6	7.6	odd	2	inner
98.10.c.n.67.3		12	7.5	odd	6
98.10.c.n.67.4		12	7.2	even	3
98.10.c.n.79.3		12	7.3	odd	6
98.10.c.n.79.4		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)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -121.370 q^{3} +256.000 q^{4} -2666.02 q^{5} -1941.92 q^{6} +4096.00 q^{8} -4952.27 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} -121.370 q^{3} +256.000 q^{4} -2666.02 q^{5} -1941.92 q^{6} +4096.00 q^{8} -4952.27 q^{9} -42656.3 q^{10} -18893.1 q^{11} -31070.8 q^{12} -96063.7 q^{13} +323575. q^{15} +65536.0 q^{16} -573992. q^{17} -79236.3 q^{18} -87739.9 q^{19} -682500. q^{20} -302289. q^{22} -1.50035e6 q^{23} -497132. q^{24} +5.15452e6 q^{25} -1.53702e6 q^{26} +2.98999e6 q^{27} -1.78997e6 q^{29} +5.17720e6 q^{30} +9.66130e6 q^{31} +1.04858e6 q^{32} +2.29306e6 q^{33} -9.18388e6 q^{34} -1.26778e6 q^{36} -3.09681e6 q^{37} -1.40384e6 q^{38} +1.16593e7 q^{39} -1.09200e7 q^{40} -1.17852e7 q^{41} +3.60280e7 q^{43} -4.83663e6 q^{44} +1.32028e7 q^{45} -2.40056e7 q^{46} -5.91997e6 q^{47} -7.95412e6 q^{48} +8.24723e7 q^{50} +6.96656e7 q^{51} -2.45923e7 q^{52} -3.00313e7 q^{53} +4.78398e7 q^{54} +5.03692e7 q^{55} +1.06490e7 q^{57} -2.86396e7 q^{58} +1.43321e8 q^{59} +8.28352e7 q^{60} -1.50645e8 q^{61} +1.54581e8 q^{62} +1.67772e7 q^{64} +2.56107e8 q^{65} +3.66889e7 q^{66} +9.94910e7 q^{67} -1.46942e8 q^{68} +1.82097e8 q^{69} -2.01373e8 q^{71} -2.02845e7 q^{72} -4.65676e7 q^{73} -4.95489e7 q^{74} -6.25605e8 q^{75} -2.24614e7 q^{76} +1.86548e8 q^{78} -2.53222e8 q^{79} -1.74720e8 q^{80} -2.65420e8 q^{81} -1.88564e8 q^{82} +3.16834e8 q^{83} +1.53027e9 q^{85} +5.76448e8 q^{86} +2.17250e8 q^{87} -7.73860e7 q^{88} -8.40622e8 q^{89} +2.11245e8 q^{90} -3.84089e8 q^{92} -1.17259e9 q^{93} -9.47195e7 q^{94} +2.33916e8 q^{95} -1.27266e8 q^{96} +2.72768e8 q^{97} +9.35636e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 96 q^{2} + 1536 q^{4} + 24576 q^{8} + 72550 q^{9}+O(q^{10}) \) 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

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