LMFDB - Embedded newform 98.10.a.f.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(1,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [2,32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$50.4735119441$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{106}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 106 $ x^2 - 106
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$10.2956$ 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)

$f(q)$	$=$	\(q+16.0000 q^{2} +123.548 q^{3} +256.000 q^{4} -1276.66 q^{5} +1976.76 q^{6} +4096.00 q^{8} -4419.00 q^{9} -20426.5 q^{10} -27644.0 q^{11} +31628.2 q^{12} +83312.2 q^{13} -157728. q^{15} +65536.0 q^{16} -554234. q^{17} -70704.0 q^{18} +343503. q^{19} -326824. q^{20} -442304. q^{22} -535704. q^{23} +506051. q^{24} -323269. q^{25} +1.33300e6 q^{26} -2.97774e6 q^{27} -2.59101e6 q^{29} -2.52365e6 q^{30} -6.09724e6 q^{31} +1.04858e6 q^{32} -3.41535e6 q^{33} -8.86775e6 q^{34} -1.13126e6 q^{36} -1.78079e7 q^{37} +5.49605e6 q^{38} +1.02930e7 q^{39} -5.22919e6 q^{40} +3.05338e7 q^{41} -8.75976e6 q^{43} -7.07686e6 q^{44} +5.64155e6 q^{45} -8.57126e6 q^{46} +2.72730e7 q^{47} +8.09681e6 q^{48} -5.17230e6 q^{50} -6.84743e7 q^{51} +2.13279e7 q^{52} -8.34885e7 q^{53} -4.76439e7 q^{54} +3.52919e7 q^{55} +4.24390e7 q^{57} -4.14561e7 q^{58} +8.15475e7 q^{59} -4.03784e7 q^{60} +4.98442e7 q^{61} -9.75558e7 q^{62} +1.67772e7 q^{64} -1.06361e8 q^{65} -5.46456e7 q^{66} -1.85493e8 q^{67} -1.41884e8 q^{68} -6.61849e7 q^{69} +3.70271e8 q^{71} -1.81002e7 q^{72} -2.46011e8 q^{73} -2.84927e8 q^{74} -3.99391e7 q^{75} +8.79369e7 q^{76} +1.64688e8 q^{78} -5.19907e8 q^{79} -8.36671e7 q^{80} -2.80914e8 q^{81} +4.88541e8 q^{82} -2.98889e8 q^{83} +7.07568e8 q^{85} -1.40156e8 q^{86} -3.20112e8 q^{87} -1.13230e8 q^{88} +2.97527e8 q^{89} +9.02648e7 q^{90} -1.37140e8 q^{92} -7.53299e8 q^{93} +4.36367e8 q^{94} -4.38536e8 q^{95} +1.29549e8 q^{96} +7.80734e8 q^{97} +1.22159e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32 q^{2} + 512 q^{4} + 8192 q^{8} - 8838 q^{9} - 55288 q^{11} - 315456 q^{15} + 131072 q^{16} - 141408 q^{18} - 884608 q^{22} - 1071408 q^{23} - 646538 q^{25} - 5182012 q^{29} - 5047296 q^{30} + 2097152 q^{32}+ \cdots + 244317672 q^{99}+O(q^{100}) $ 2 * q + 32 * q^2 + 512 * q^4 + 8192 * q^8 - 8838 * q^9 - 55288 * q^11 - 315456 * q^15 + 131072 * q^16 - 141408 * q^18 - 884608 * q^22 - 1071408 * q^23 - 646538 * q^25 - 5182012 * q^29 - 5047296 * q^30 + 2097152 * q^32 - 2262528 * q^36 - 35615820 * q^37 + 20586048 * q^39 - 17519512 * q^43 - 14153728 * q^44 - 17142528 * q^46 - 10344608 * q^50 - 136948608 * q^51 - 166976980 * q^53 + 84878016 * q^57 - 82912192 * q^58 - 80756736 * q^60 + 33554432 * q^64 - 212722496 * q^65 - 370985848 * q^67 + 740541344 * q^71 - 36200448 * q^72 - 569853120 * q^74 + 329376768 * q^78 - 1039814512 * q^79 - 561827502 * q^81 + 1415135616 * q^85 - 280312192 * q^86 - 226459648 * q^88 - 274280448 * q^92 - 1506597504 * q^93 - 877072832 * q^95 + 244317672 * q^99

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
$3$	123.548	0.880620	0.440310	−	0.897846i	$-0.354869\pi$
$3$	123.548	0.880620	0.440310	+	0.897846i	$0.354869\pi$
$4$	256.000	0.500000
$5$	−1276.66	−0.913502	−0.456751	−	0.889595i	$-0.650987\pi$
$5$	−1276.66	−0.913502	−0.456751	+	0.889595i	$0.650987\pi$
$6$	1976.76	0.622692
$7$	0	0
$7$	0	0
$8$	4096.00	0.353553
$9$	−4419.00	−0.224508
$10$	−20426.5	−0.645944
$11$	−27644.0	−0.569290	−0.284645	−	0.958633i	$-0.591876\pi$
$11$	−27644.0	−0.569290	−0.284645	+	0.958633i	$0.591876\pi$
$12$	31628.2	0.440310
$13$	83312.2	0.809028	0.404514	−	0.914532i	$-0.367441\pi$
$13$	83312.2	0.809028	0.404514	+	0.914532i	$0.367441\pi$
$14$	0	0
$15$	−157728.	−0.804448
$16$	65536.0	0.250000
$17$	−554234.	−1.60943	−0.804717	−	0.593658i	$-0.797683\pi$
$17$	−554234.	−1.60943	−0.804717	+	0.593658i	$0.797683\pi$
$18$	−70704.0	−0.158751
$19$	343503.	0.604700	0.302350	−	0.953197i	$-0.402229\pi$
$19$	343503.	0.604700	0.302350	+	0.953197i	$0.402229\pi$
$20$	−326824.	−0.456751
$21$	0	0
$22$	−442304.	−0.402549
$23$	−535704.	−0.399162	−0.199581	−	0.979881i	$-0.563958\pi$
$23$	−535704.	−0.399162	−0.199581	+	0.979881i	$0.563958\pi$
$24$	506051.	0.311346
$25$	−323269.	−0.165514
$26$	1.33300e6	0.572069
$27$	−2.97774e6	−1.07833
$28$	0	0
$29$	−2.59101e6	−0.680264	−0.340132	−	0.940378i	$-0.610472\pi$
$29$	−2.59101e6	−0.680264	−0.340132	+	0.940378i	$0.610472\pi$
$30$	−2.52365e6	−0.568831
$31$	−6.09724e6	−1.18578	−0.592892	−	0.805282i	$-0.702014\pi$
$31$	−6.09724e6	−1.18578	−0.592892	+	0.805282i	$0.702014\pi$
$32$	1.04858e6	0.176777
$33$	−3.41535e6	−0.501328
$34$	−8.86775e6	−1.13804
$35$	0	0
$36$	−1.13126e6	−0.112254
$37$	−1.78079e7	−1.56209	−0.781043	−	0.624477i	$-0.785312\pi$
$37$	−1.78079e7	−1.56209	−0.781043	+	0.624477i	$0.785312\pi$
$38$	5.49605e6	0.427587
$39$	1.02930e7	0.712446
$40$	−5.22919e6	−0.322972
$41$	3.05338e7	1.68754	0.843769	−	0.536707i	$-0.180332\pi$
$41$	3.05338e7	1.68754	0.843769	+	0.536707i	$0.180332\pi$
$42$	0	0
$43$	−8.75976e6	−0.390736	−0.195368	−	0.980730i	$-0.562590\pi$
$43$	−8.75976e6	−0.390736	−0.195368	+	0.980730i	$0.562590\pi$
$44$	−7.07686e6	−0.284645
$45$	5.64155e6	0.205089
$46$	−8.57126e6	−0.282250
$47$	2.72730e7	0.815252	0.407626	−	0.913149i	$-0.366357\pi$
$47$	2.72730e7	0.815252	0.407626	+	0.913149i	$0.366357\pi$
$48$	8.09681e6	0.220155
$49$	0	0
$50$	−5.17230e6	−0.117036
$51$	−6.84743e7	−1.41730
$52$	2.13279e7	0.404514
$53$	−8.34885e7	−1.45340	−0.726700	−	0.686955i	$-0.758947\pi$
$53$	−8.34885e7	−1.45340	−0.726700	+	0.686955i	$0.758947\pi$
$54$	−4.76439e7	−0.762492
$55$	3.52919e7	0.520048
$56$	0	0
$57$	4.24390e7	0.532511
$58$	−4.14561e7	−0.481019
$59$	8.15475e7	0.876147	0.438073	−	0.898939i	$-0.355661\pi$
$59$	8.15475e7	0.876147	0.438073	+	0.898939i	$0.355661\pi$
$60$	−4.03784e7	−0.402224
$61$	4.98442e7	0.460925	0.230463	−	0.973081i	$-0.425976\pi$
$61$	4.98442e7	0.460925	0.230463	+	0.973081i	$0.425976\pi$
$62$	−9.75558e7	−0.838476
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−1.06361e8	−0.739049
$66$	−5.46456e7	−0.354493
$67$	−1.85493e8	−1.12458	−0.562290	−	0.826940i	$-0.690080\pi$
$67$	−1.85493e8	−1.12458	−0.562290	+	0.826940i	$0.690080\pi$
$68$	−1.41884e8	−0.804717
$69$	−6.61849e7	−0.351510
$70$	0	0
$71$	3.70271e8	1.72925	0.864623	−	0.502421i	$-0.167557\pi$
$71$	3.70271e8	1.72925	0.864623	+	0.502421i	$0.167557\pi$
$72$	−1.81002e7	−0.0793757
$73$	−2.46011e8	−1.01391	−0.506957	−	0.861972i	$-0.669230\pi$
$73$	−2.46011e8	−1.01391	−0.506957	+	0.861972i	$0.669230\pi$
$74$	−2.84927e8	−1.10456
$75$	−3.99391e7	−0.145755
$76$	8.79369e7	0.302350
$77$	0	0
$78$	1.64688e8	0.503776
$79$	−5.19907e8	−1.50177	−0.750886	−	0.660432i	$-0.770373\pi$
$79$	−5.19907e8	−1.50177	−0.750886	+	0.660432i	$0.770373\pi$
$80$	−8.36671e7	−0.228376
$81$	−2.80914e8	−0.725087
$82$	4.88541e8	1.19327
$83$	−2.98889e8	−0.691287	−0.345643	−	0.938366i	$-0.612339\pi$
$83$	−2.98889e8	−0.691287	−0.345643	+	0.938366i	$0.612339\pi$
$84$	0	0
$85$	7.07568e8	1.47022
$86$	−1.40156e8	−0.276292
$87$	−3.20112e8	−0.599054
$88$	−1.13230e8	−0.201275
$89$	2.97527e8	0.502656	0.251328	−	0.967902i	$-0.419133\pi$
$89$	2.97527e8	0.502656	0.251328	+	0.967902i	$0.419133\pi$
$90$	9.02648e7	0.145020
$91$	0	0
$92$	−1.37140e8	−0.199581
$93$	−7.53299e8	−1.04422
$94$	4.36367e8	0.576470
$95$	−4.38536e8	−0.552395
$96$	1.29549e8	0.155673
$97$	7.80734e8	0.895427	0.447713	−	0.894177i	$-0.352238\pi$
$97$	7.80734e8	0.895427	0.447713	+	0.894177i	$0.352238\pi$
$98$	0	0
$99$	1.22159e8	0.127810
$100$	−8.27569e7	−0.0827569
$101$	1.30232e9	1.24529	0.622646	−	0.782504i	$-0.286058\pi$
$101$	1.30232e9	1.24529	0.622646	+	0.782504i	$0.286058\pi$
$102$	−1.09559e9	−1.00218
$103$	−2.14949e9	−1.88177	−0.940887	−	0.338720i	$-0.890006\pi$
$103$	−2.14949e9	−1.88177	−0.940887	+	0.338720i	$0.890006\pi$
$104$	3.41247e8	0.286035
$105$	0	0
$106$	−1.33582e9	−1.02771
$107$	−8.34888e8	−0.615745	−0.307873	−	0.951428i	$-0.599617\pi$
$107$	−8.34888e8	−0.615745	−0.307873	+	0.951428i	$0.599617\pi$
$108$	−7.62302e8	−0.539163
$109$	1.02563e9	0.695937	0.347969	−	0.937506i	$-0.386872\pi$
$109$	1.02563e9	0.695937	0.347969	+	0.937506i	$0.386872\pi$
$110$	5.64671e8	0.367729
$111$	−2.20012e9	−1.37560
$112$	0	0
$113$	−4.65902e8	−0.268808	−0.134404	−	0.990927i	$-0.542912\pi$
$113$	−4.65902e8	−0.268808	−0.134404	+	0.990927i	$0.542912\pi$
$114$	6.79024e8	0.376542
$115$	6.83911e8	0.364636
$116$	−6.63298e8	−0.340132
$117$	−3.68157e8	−0.181634
$118$	1.30476e9	0.619529
$119$	0	0
$120$	−6.46054e8	−0.284415
$121$	−1.59376e9	−0.675909
$122$	7.97508e8	0.325923
$123$	3.77238e9	1.48608
$124$	−1.56089e9	−0.592892
$125$	2.90618e9	1.06470
$126$	0	0
$127$	−7.84044e8	−0.267438	−0.133719	−	0.991019i	$-0.542692\pi$
$127$	−7.84044e8	−0.267438	−0.133719	+	0.991019i	$0.542692\pi$
$128$	2.68435e8	0.0883883
$129$	−1.08225e9	−0.344090
$130$	−1.70178e9	−0.522587
$131$	5.77364e9	1.71289	0.856444	−	0.516240i	$-0.172669\pi$
$131$	5.77364e9	1.71289	0.856444	+	0.516240i	$0.172669\pi$
$132$	−8.74329e8	−0.250664
$133$	0	0
$134$	−2.96789e9	−0.795199
$135$	3.80156e9	0.985054
$136$	−2.27014e9	−0.569021
$137$	7.17672e9	1.74054	0.870269	−	0.492576i	$-0.163945\pi$
$137$	7.17672e9	1.74054	0.870269	+	0.492576i	$0.163945\pi$
$138$	−1.05896e9	−0.248555
$139$	−3.11320e9	−0.707359	−0.353679	−	0.935367i	$-0.615070\pi$
$139$	−3.11320e9	−0.707359	−0.353679	+	0.935367i	$0.615070\pi$
$140$	0	0
$141$	3.36951e9	0.717927
$142$	5.92433e9	1.22276
$143$	−2.30308e9	−0.460572
$144$	−2.89604e8	−0.0561271
$145$	3.30783e9	0.621423
$146$	−3.93617e9	−0.716945
$147$	0	0
$148$	−4.55882e9	−0.781043
$149$	6.87070e9	1.14199	0.570996	−	0.820953i	$-0.306557\pi$
$149$	6.87070e9	1.14199	0.570996	+	0.820953i	$0.306557\pi$
$150$	−6.39026e8	−0.103064
$151$	9.06756e9	1.41936	0.709682	−	0.704522i	$-0.248838\pi$
$151$	9.06756e9	1.41936	0.709682	+	0.704522i	$0.248838\pi$
$152$	1.40699e9	0.213794
$153$	2.44916e9	0.361332
$154$	0	0
$155$	7.78409e9	1.08322
$156$	2.63501e9	0.356223
$157$	−3.35488e9	−0.440686	−0.220343	−	0.975422i	$-0.570718\pi$
$157$	−3.35488e9	−0.440686	−0.220343	+	0.975422i	$0.570718\pi$
$158$	−8.31852e9	−1.06191
$159$	−1.03148e10	−1.27989
$160$	−1.33867e9	−0.161486
$161$	0	0
$162$	−4.49462e9	−0.512714
$163$	6.57962e9	0.730056	0.365028	−	0.930996i	$-0.381059\pi$
$163$	6.57962e9	0.730056	0.365028	+	0.930996i	$0.381059\pi$
$164$	7.81665e9	0.843769
$165$	4.36023e9	0.457965
$166$	−4.78222e9	−0.488814
$167$	3.22471e8	0.0320824	0.0160412	−	0.999871i	$-0.494894\pi$
$167$	3.22471e8	0.0320824	0.0160412	+	0.999871i	$0.494894\pi$
$168$	0	0
$169$	−3.66357e9	−0.345473
$170$	1.13211e10	1.03960
$171$	−1.51794e9	−0.135760
$172$	−2.24250e9	−0.195368
$173$	−1.67229e9	−0.141940	−0.0709699	−	0.997478i	$-0.522609\pi$
$173$	−1.67229e9	−0.141940	−0.0709699	+	0.997478i	$0.522609\pi$
$174$	−5.12180e9	−0.423595
$175$	0	0
$176$	−1.81168e9	−0.142323
$177$	1.00750e10	0.771552
$178$	4.76043e9	0.355432
$179$	8.42902e9	0.613675	0.306838	−	0.951762i	$-0.400729\pi$
$179$	8.42902e9	0.613675	0.306838	+	0.951762i	$0.400729\pi$
$180$	1.44424e9	0.102544
$181$	2.02316e10	1.40113	0.700563	−	0.713591i	$-0.252932\pi$
$181$	2.02316e10	1.40113	0.700563	+	0.713591i	$0.252932\pi$
$182$	0	0
$183$	6.15813e9	0.405900
$184$	−2.19424e9	−0.141125
$185$	2.27346e10	1.42697
$186$	−1.20528e10	−0.738378
$187$	1.53213e10	0.916235
$188$	6.98188e9	0.407626
$189$	0	0
$190$	−7.01658e9	−0.390602
$191$	−1.78228e10	−0.969004	−0.484502	−	0.874790i	$-0.660999\pi$
$191$	−1.78228e10	−0.969004	−0.484502	+	0.874790i	$0.660999\pi$
$192$	2.07278e9	0.110077
$193$	1.54567e10	0.801881	0.400940	−	0.916104i	$-0.368683\pi$
$193$	1.54567e10	0.801881	0.400940	+	0.916104i	$0.368683\pi$
$194$	1.24917e10	0.633162
$195$	−1.31407e10	−0.650821
$196$	0	0
$197$	2.03655e10	0.963376	0.481688	−	0.876343i	$-0.340024\pi$
$197$	2.03655e10	0.963376	0.481688	+	0.876343i	$0.340024\pi$
$198$	1.95454e9	0.0903757
$199$	−2.77025e10	−1.25222	−0.626109	−	0.779735i	$-0.715354\pi$
$199$	−2.77025e10	−1.25222	−0.626109	+	0.779735i	$0.715354\pi$
$200$	−1.32411e9	−0.0585179
$201$	−2.29172e10	−0.990328
$202$	2.08371e10	0.880554
$203$	0	0
$204$	−1.75294e10	−0.708650
$205$	−3.89812e10	−1.54157
$206$	−3.43918e10	−1.33062
$207$	2.36728e9	0.0896153
$208$	5.45995e9	0.202257
$209$	−9.49581e9	−0.344250
$210$	0	0
$211$	−1.30691e10	−0.453914	−0.226957	−	0.973905i	$-0.572878\pi$
$211$	−1.30691e10	−0.453914	−0.226957	+	0.973905i	$0.572878\pi$
$212$	−2.13731e10	−0.726700
$213$	4.57460e10	1.52281
$214$	−1.33582e10	−0.435398
$215$	1.11832e10	0.356939
$216$	−1.21968e10	−0.381246
$217$	0	0
$218$	1.64100e10	0.492102
$219$	−3.03940e10	−0.892872
$220$	9.03474e9	0.260024
$221$	−4.61745e10	−1.30208
$222$	−3.52020e10	−0.972700
$223$	−4.18178e10	−1.13237	−0.566187	−	0.824277i	$-0.691582\pi$
$223$	−4.18178e10	−1.13237	−0.566187	+	0.824277i	$0.691582\pi$
$224$	0	0
$225$	1.42853e9	0.0371592
$226$	−7.45444e9	−0.190076
$227$	−5.61223e10	−1.40288	−0.701438	−	0.712731i	$-0.747458\pi$
$227$	−5.61223e10	−1.40288	−0.701438	+	0.712731i	$0.747458\pi$
$228$	1.08644e10	0.266255
$229$	−4.49082e9	−0.107911	−0.0539556	−	0.998543i	$-0.517183\pi$
$229$	−4.49082e9	−0.107911	−0.0539556	+	0.998543i	$0.517183\pi$
$230$	1.09426e10	0.257836
$231$	0	0
$232$	−1.06128e10	−0.240510
$233$	−6.44663e10	−1.43295	−0.716475	−	0.697613i	$-0.754245\pi$
$233$	−6.44663e10	−1.43295	−0.716475	+	0.697613i	$0.754245\pi$
$234$	−5.89051e9	−0.128434
$235$	−3.48182e10	−0.744735
$236$	2.08762e10	0.438073
$237$	−6.42333e10	−1.32249
$238$	0	0
$239$	−1.23198e9	−0.0244238	−0.0122119	−	0.999925i	$-0.503887\pi$
$239$	−1.23198e9	−0.0244238	−0.0122119	+	0.999925i	$0.503887\pi$
$240$	−1.03369e10	−0.201112
$241$	−8.88350e9	−0.169632	−0.0848160	−	0.996397i	$-0.527030\pi$
$241$	−8.88350e9	−0.169632	−0.0848160	+	0.996397i	$0.527030\pi$
$242$	−2.55001e10	−0.477940
$243$	2.39047e10	0.439800
$244$	1.27601e10	0.230463
$245$	0	0
$246$	6.03580e10	1.05082
$247$	2.86180e10	0.489219
$248$	−2.49743e10	−0.419238
$249$	−3.69270e10	−0.608761
$250$	4.64988e10	0.752856
$251$	9.92817e10	1.57884	0.789419	−	0.613855i	$-0.210382\pi$
$251$	9.92817e10	1.57884	0.789419	+	0.613855i	$0.210382\pi$
$252$	0	0
$253$	1.48090e10	0.227239
$254$	−1.25447e10	−0.189108
$255$	8.74183e10	1.29471
$256$	4.29497e9	0.0625000
$257$	−5.56657e10	−0.795955	−0.397977	−	0.917395i	$-0.630288\pi$
$257$	−5.56657e10	−0.795955	−0.397977	+	0.917395i	$0.630288\pi$
$258$	−1.73159e10	−0.243309
$259$	0	0
$260$	−2.72285e10	−0.369525
$261$	1.14497e10	0.152725
$262$	9.23783e10	1.21119
$263$	−9.97727e10	−1.28591	−0.642955	−	0.765904i	$-0.722292\pi$
$263$	−9.97727e10	−1.28591	−0.642955	+	0.765904i	$0.722292\pi$
$264$	−1.39893e10	−0.177246
$265$	1.06586e11	1.32768
$266$	0	0
$267$	3.67587e10	0.442649
$268$	−4.74862e10	−0.562290
$269$	−1.97349e10	−0.229800	−0.114900	−	0.993377i	$-0.536655\pi$
$269$	−1.97349e10	−0.229800	−0.114900	+	0.993377i	$0.536655\pi$
$270$	6.08250e10	0.696538
$271$	5.88440e10	0.662735	0.331368	−	0.943502i	$-0.392490\pi$
$271$	5.88440e10	0.662735	0.331368	+	0.943502i	$0.392490\pi$
$272$	−3.63223e10	−0.402359
$273$	0	0
$274$	1.14828e11	1.23075
$275$	8.93645e9	0.0942254
$276$	−1.69433e10	−0.175755
$277$	−4.19495e10	−0.428122	−0.214061	−	0.976820i	$-0.568669\pi$
$277$	−4.19495e10	−0.428122	−0.214061	+	0.976820i	$0.568669\pi$
$278$	−4.98111e10	−0.500178
$279$	2.69437e10	0.266218
$280$	0	0
$281$	2.62716e10	0.251367	0.125684	−	0.992070i	$-0.459888\pi$
$281$	2.62716e10	0.251367	0.125684	+	0.992070i	$0.459888\pi$
$282$	5.39121e10	0.507651
$283$	−1.23717e11	−1.14654	−0.573271	−	0.819366i	$-0.694326\pi$
$283$	−1.23717e11	−1.14654	−0.573271	+	0.819366i	$0.694326\pi$
$284$	9.47893e10	0.864623
$285$	−5.41801e10	−0.486450
$286$	−3.68493e10	−0.325674
$287$	0	0
$288$	−4.63366e9	−0.0396879
$289$	1.88588e11	1.59028
$290$	5.29253e10	0.439412
$291$	9.64577e10	0.788531
$292$	−6.29787e10	−0.506957
$293$	3.33848e10	0.264633	0.132316	−	0.991208i	$-0.457758\pi$
$293$	3.33848e10	0.264633	0.132316	+	0.991208i	$0.457758\pi$
$294$	0	0
$295$	−1.04108e11	−0.800362
$296$	−7.29412e10	−0.552281
$297$	8.23167e10	0.613881
$298$	1.09931e11	0.807510
$299$	−4.46307e10	−0.322934
$300$	−1.02244e10	−0.0728773
$301$	0	0
$302$	1.45081e11	1.00364
$303$	1.60898e11	1.09663
$304$	2.25118e10	0.151175
$305$	−6.36340e10	−0.421056
$306$	3.91866e10	0.255500
$307$	−2.32773e11	−1.49558	−0.747791	−	0.663935i	$-0.768885\pi$
$307$	−2.32773e11	−1.49558	−0.747791	+	0.663935i	$0.768885\pi$
$308$	0	0
$309$	−2.65564e11	−1.65713
$310$	1.24545e11	0.765949
$311$	7.62815e9	0.0462378	0.0231189	−	0.999733i	$-0.492640\pi$
$311$	7.62815e9	0.0462378	0.0231189	+	0.999733i	$0.492640\pi$
$312$	4.21602e10	0.251888
$313$	1.69667e11	0.999188	0.499594	−	0.866260i	$-0.333483\pi$
$313$	1.69667e11	0.999188	0.499594	+	0.866260i	$0.333483\pi$
$314$	−5.36781e10	−0.311612
$315$	0	0
$316$	−1.33096e11	−0.750886
$317$	−8.60051e10	−0.478363	−0.239182	−	0.970975i	$-0.576879\pi$
$317$	−8.60051e10	−0.478363	−0.239182	+	0.970975i	$0.576879\pi$
$318$	−1.65037e11	−0.905021
$319$	7.16258e10	0.387268
$320$	−2.14188e10	−0.114188
$321$	−1.03148e11	−0.542237
$322$	0	0
$323$	−1.90381e11	−0.973225
$324$	−7.19139e10	−0.362544
$325$	−2.69323e10	−0.133905
$326$	1.05274e11	0.516228
$327$	1.26714e11	0.612856
$328$	1.25066e11	0.596635
$329$	0	0
$330$	6.97637e10	0.323830
$331$	3.59276e11	1.64514	0.822568	−	0.568667i	$-0.192541\pi$
$331$	3.59276e11	1.64514	0.822568	+	0.568667i	$0.192541\pi$
$332$	−7.65155e10	−0.345643
$333$	7.86932e10	0.350702
$334$	5.15954e9	0.0226857
$335$	2.36811e11	1.02731
$336$	0	0
$337$	−2.23831e11	−0.945335	−0.472668	−	0.881241i	$-0.656709\pi$
$337$	−2.23831e11	−0.945335	−0.472668	+	0.881241i	$0.656709\pi$
$338$	−5.86171e10	−0.244286
$339$	−5.75611e10	−0.236718
$340$	1.81137e11	0.735111
$341$	1.68552e11	0.675055
$342$	−2.42871e10	−0.0959970
$343$	0	0
$344$	−3.58800e10	−0.138146
$345$	8.44955e10	0.321106
$346$	−2.67566e10	−0.100367
$347$	1.24895e11	0.462449	0.231224	−	0.972900i	$-0.425727\pi$
$347$	1.24895e11	0.462449	0.231224	+	0.972900i	$0.425727\pi$
$348$	−8.19488e10	−0.299527
$349$	−4.14076e9	−0.0149405	−0.00747025	−	0.999972i	$-0.502378\pi$
$349$	−4.14076e9	−0.0149405	−0.00747025	+	0.999972i	$0.502378\pi$
$350$	0	0
$351$	−2.48082e11	−0.872397
$352$	−2.89868e10	−0.100637
$353$	−1.72793e11	−0.592297	−0.296149	−	0.955142i	$-0.595702\pi$
$353$	−1.72793e11	−0.592297	−0.296149	+	0.955142i	$0.595702\pi$
$354$	1.61200e11	0.545570
$355$	−4.72709e11	−1.57967
$356$	7.61669e10	0.251328
$357$	0	0
$358$	1.34864e11	0.433934
$359$	−2.15079e10	−0.0683397	−0.0341699	−	0.999416i	$-0.510879\pi$
$359$	−2.15079e10	−0.0683397	−0.0341699	+	0.999416i	$0.510879\pi$
$360$	2.31078e10	0.0725099
$361$	−2.04693e11	−0.634338
$362$	3.23706e11	0.990745
$363$	−1.96905e11	−0.595219
$364$	0	0
$365$	3.14071e11	0.926212
$366$	9.85301e10	0.287015
$367$	5.48596e11	1.57854	0.789270	−	0.614047i	$-0.210459\pi$
$367$	5.48596e11	1.57854	0.789270	+	0.614047i	$0.210459\pi$
$368$	−3.51079e10	−0.0997906
$369$	−1.34929e11	−0.378866
$370$	3.63754e11	1.00902
$371$	0	0
$372$	−1.92844e11	−0.522112
$373$	−1.26024e11	−0.337104	−0.168552	−	0.985693i	$-0.553909\pi$
$373$	−1.26024e11	−0.337104	−0.168552	+	0.985693i	$0.553909\pi$
$374$	2.45140e11	0.647876
$375$	3.59051e11	0.937596
$376$	1.11710e11	0.288235
$377$	−2.15863e11	−0.550353
$378$	0	0
$379$	−5.31002e10	−0.132197	−0.0660983	−	0.997813i	$-0.521055\pi$
$379$	−5.31002e10	−0.132197	−0.0660983	+	0.997813i	$0.521055\pi$
$380$	−1.12265e11	−0.276197
$381$	−9.68667e10	−0.235512
$382$	−2.85165e11	−0.685189
$383$	−6.22690e11	−1.47869	−0.739346	−	0.673326i	$-0.764865\pi$
$383$	−6.22690e11	−1.47869	−0.739346	+	0.673326i	$0.764865\pi$
$384$	3.31645e10	0.0778365
$385$	0	0
$386$	2.47308e11	0.567015
$387$	3.87094e10	0.0877236
$388$	1.99868e11	0.447713
$389$	−2.37879e11	−0.526724	−0.263362	−	0.964697i	$-0.584831\pi$
$389$	−2.37879e11	−0.526724	−0.263362	+	0.964697i	$0.584831\pi$
$390$	−2.10251e11	−0.460200
$391$	2.96906e11	0.642426
$392$	0	0
$393$	7.13319e11	1.50840
$394$	3.25847e11	0.681210
$395$	6.63744e11	1.37187
$396$	3.12727e10	0.0639052
$397$	1.69545e11	0.342554	0.171277	−	0.985223i	$-0.445211\pi$
$397$	1.69545e11	0.342554	0.171277	+	0.985223i	$0.445211\pi$
$398$	−4.43240e11	−0.885453
$399$	0	0
$400$	−2.11858e10	−0.0413784
$401$	−9.03546e11	−1.74502	−0.872510	−	0.488596i	$-0.837509\pi$
$401$	−9.03546e11	−1.74502	−0.872510	+	0.488596i	$0.837509\pi$
$402$	−3.66675e11	−0.700268
$403$	−5.07974e11	−0.959333
$404$	3.33393e11	0.622646
$405$	3.58631e11	0.662369
$406$	0	0
$407$	4.92282e11	0.889281
$408$	−2.80471e11	−0.501091
$409$	−1.04510e12	−1.84673	−0.923363	−	0.383927i	$-0.874571\pi$
$409$	−1.04510e12	−1.84673	−0.923363	+	0.383927i	$0.874571\pi$
$410$	−6.23699e11	−1.09005
$411$	8.86667e11	1.53275
$412$	−5.50269e11	−0.940887
$413$	0	0
$414$	3.78764e10	0.0633676
$415$	3.81579e11	0.631492
$416$	8.73592e10	0.143017
$417$	−3.84628e11	−0.622914
$418$	−1.51933e11	−0.243421
$419$	−4.17508e11	−0.661761	−0.330881	−	0.943673i	$-0.607346\pi$
$419$	−4.17508e11	−0.661761	−0.330881	+	0.943673i	$0.607346\pi$
$420$	0	0
$421$	1.67897e11	0.260480	0.130240	−	0.991482i	$-0.458425\pi$
$421$	1.67897e11	0.260480	0.130240	+	0.991482i	$0.458425\pi$
$422$	−2.09105e11	−0.320966
$423$	−1.20519e11	−0.183031
$424$	−3.41969e11	−0.513855
$425$	1.79167e11	0.266384
$426$	7.31937e11	1.07679
$427$	0	0
$428$	−2.13731e11	−0.307873
$429$	−2.84540e11	−0.405589
$430$	1.78931e11	0.252394
$431$	−1.60399e11	−0.223900	−0.111950	−	0.993714i	$-0.535710\pi$
$431$	−1.60399e11	−0.223900	−0.111950	+	0.993714i	$0.535710\pi$
$432$	−1.95149e11	−0.269582
$433$	4.44852e10	0.0608163	0.0304081	−	0.999538i	$-0.490319\pi$
$433$	4.44852e10	0.0608163	0.0304081	+	0.999538i	$0.490319\pi$
$434$	0	0
$435$	4.08674e11	0.547237
$436$	2.62560e11	0.347969
$437$	−1.84016e11	−0.241373
$438$	−4.86304e11	−0.631356
$439$	−5.75085e11	−0.738995	−0.369498	−	0.929232i	$-0.620470\pi$
$439$	−5.75085e11	−0.738995	−0.369498	+	0.929232i	$0.620470\pi$
$440$	1.44556e11	0.183865
$441$	0	0
$442$	−7.38792e11	−0.920708
$443$	−8.29838e11	−1.02371	−0.511855	−	0.859072i	$-0.671041\pi$
$443$	−8.29838e11	−1.02371	−0.511855	+	0.859072i	$0.671041\pi$
$444$	−5.63232e11	−0.687802
$445$	−3.79840e11	−0.459178
$446$	−6.69085e11	−0.800709
$447$	8.48858e11	1.00566
$448$	0	0
$449$	8.23705e11	0.956452	0.478226	−	0.878237i	$-0.341280\pi$
$449$	8.23705e11	0.956452	0.478226	+	0.878237i	$0.341280\pi$
$450$	2.28564e10	0.0262755
$451$	−8.44076e11	−0.960699
$452$	−1.19271e11	−0.134404
$453$	1.12027e12	1.24992
$454$	−8.97957e11	−0.991983
$455$	0	0
$456$	1.73830e11	0.188271
$457$	−1.59828e12	−1.71408	−0.857039	−	0.515252i	$-0.827698\pi$
$457$	−1.59828e12	−1.71408	−0.857039	+	0.515252i	$0.827698\pi$
$458$	−7.18532e10	−0.0763047
$459$	1.65037e12	1.73550
$460$	1.75081e11	0.182318
$461$	−1.27501e12	−1.31480	−0.657402	−	0.753540i	$-0.728345\pi$
$461$	−1.27501e12	−1.31480	−0.657402	+	0.753540i	$0.728345\pi$
$462$	0	0
$463$	−3.13766e11	−0.317316	−0.158658	−	0.987334i	$-0.550717\pi$
$463$	−3.13766e11	−0.317316	−0.158658	+	0.987334i	$0.550717\pi$
$464$	−1.69804e11	−0.170066
$465$	9.61705e11	0.953902
$466$	−1.03146e12	−1.01325
$467$	9.41486e11	0.915984	0.457992	−	0.888956i	$-0.348569\pi$
$467$	9.41486e11	0.915984	0.457992	+	0.888956i	$0.348569\pi$
$468$	−9.42481e10	−0.0908169
$469$	0	0
$470$	−5.57092e11	−0.526607
$471$	−4.14488e11	−0.388077
$472$	3.34019e11	0.309765
$473$	2.42155e11	0.222442
$474$	−1.02773e12	−0.935142
$475$	−1.11044e11	−0.100086
$476$	0	0
$477$	3.68936e11	0.326301
$478$	−1.97117e10	−0.0172702
$479$	7.10040e11	0.616273	0.308137	−	0.951342i	$-0.400295\pi$
$479$	7.10040e11	0.616273	0.308137	+	0.951342i	$0.400295\pi$
$480$	−1.65390e11	−0.142208
$481$	−1.48362e12	−1.26377
$482$	−1.42136e11	−0.119948
$483$	0	0
$484$	−4.08002e11	−0.337954
$485$	−9.96730e11	−0.817974
$486$	3.82475e11	0.310986
$487$	1.21863e12	0.981729	0.490864	−	0.871236i	$-0.336681\pi$
$487$	1.21863e12	0.981729	0.490864	+	0.871236i	$0.336681\pi$
$488$	2.04162e11	0.162962
$489$	8.12896e11	0.642902
$490$	0	0
$491$	−5.76219e10	−0.0447426	−0.0223713	−	0.999750i	$-0.507122\pi$
$491$	−5.76219e10	−0.0447426	−0.0223713	+	0.999750i	$0.507122\pi$
$492$	9.65728e11	0.743040
$493$	1.43602e12	1.09484
$494$	4.57889e11	0.345930
$495$	−1.55955e11	−0.116755
$496$	−3.99589e11	−0.296446
$497$	0	0
$498$	−5.90832e11	−0.430459
$499$	2.38874e12	1.72471	0.862357	−	0.506300i	$-0.168987\pi$
$499$	2.38874e12	1.72471	0.862357	+	0.506300i	$0.168987\pi$
$500$	7.43981e11	0.532350
$501$	3.98406e10	0.0282524
$502$	1.58851e12	1.11641
$503$	1.80042e12	1.25406	0.627030	−	0.778995i	$-0.284270\pi$
$503$	1.80042e12	1.25406	0.627030	+	0.778995i	$0.284270\pi$
$504$	0	0
$505$	−1.66261e12	−1.13758
$506$	2.36944e11	0.160682
$507$	−4.52625e11	−0.304231
$508$	−2.00715e11	−0.133719
$509$	−1.32860e12	−0.877335	−0.438668	−	0.898649i	$-0.644549\pi$
$509$	−1.32860e12	−0.877335	−0.438668	+	0.898649i	$0.644549\pi$
$510$	1.39869e12	0.915496
$511$	0	0
$512$	6.87195e10	0.0441942
$513$	−1.02286e12	−0.652064
$514$	−8.90651e11	−0.562825
$515$	2.74416e12	1.71901
$516$	−2.77055e11	−0.172045
$517$	−7.53934e11	−0.464115
$518$	0	0
$519$	−2.06607e11	−0.124995
$520$	−4.35656e11	−0.261293
$521$	−2.19083e12	−1.30268	−0.651341	−	0.758785i	$-0.725793\pi$
$521$	−2.19083e12	−1.30268	−0.651341	+	0.758785i	$0.725793\pi$
$522$	1.83194e11	0.107993
$523$	−5.08236e11	−0.297035	−0.148518	−	0.988910i	$-0.547450\pi$
$523$	−5.08236e11	−0.297035	−0.148518	+	0.988910i	$0.547450\pi$
$524$	1.47805e12	0.856444
$525$	0	0
$526$	−1.59636e12	−0.909276
$527$	3.37930e12	1.90844
$528$	−2.23828e11	−0.125332
$529$	−1.51417e12	−0.840669
$530$	1.70538e12	0.938815
$531$	−3.60359e11	−0.196702
$532$	0	0
$533$	2.54384e12	1.36527
$534$	5.88140e11	0.313000
$535$	1.06587e12	0.562485
$536$	−7.59779e11	−0.397599
$537$	1.04139e12	0.540415
$538$	−3.15758e11	−0.162493
$539$	0	0
$540$	9.73199e11	0.492527
$541$	1.00015e12	0.501968	0.250984	−	0.967991i	$-0.419246\pi$
$541$	1.00015e12	0.501968	0.250984	+	0.967991i	$0.419246\pi$
$542$	9.41504e11	0.468625
$543$	2.49957e12	1.23386
$544$	−5.81157e11	−0.284511
$545$	−1.30937e12	−0.635740
$546$	0	0
$547$	−3.35970e12	−1.60457	−0.802283	−	0.596944i	$-0.796381\pi$
$547$	−3.35970e12	−1.60457	−0.802283	+	0.596944i	$0.796381\pi$
$548$	1.83724e12	0.870269
$549$	−2.20262e11	−0.103482
$550$	1.42983e11	0.0666274
$551$	−8.90019e11	−0.411355
$552$	−2.71093e11	−0.124278
$553$	0	0
$554$	−6.71191e11	−0.302728
$555$	2.80881e12	1.25662
$556$	−7.96978e11	−0.353679
$557$	1.39008e11	0.0611913	0.0305957	−	0.999532i	$-0.490260\pi$
$557$	1.39008e11	0.0611913	0.0305957	+	0.999532i	$0.490260\pi$
$558$	4.31099e11	0.188245
$559$	−7.29795e11	−0.316117
$560$	0	0
$561$	1.89290e12	0.806855
$562$	4.20346e11	0.177743
$563$	−3.88167e12	−1.62829	−0.814143	−	0.580664i	$-0.802793\pi$
$563$	−3.88167e12	−1.62829	−0.814143	+	0.580664i	$0.802793\pi$
$564$	8.62594e11	0.358964
$565$	5.94798e11	0.245557
$566$	−1.97947e12	−0.810728
$567$	0	0
$568$	1.51663e12	0.611381
$569$	1.24560e12	0.498164	0.249082	−	0.968482i	$-0.419871\pi$
$569$	1.24560e12	0.498164	0.249082	+	0.968482i	$0.419871\pi$
$570$	−8.66882e11	−0.343972
$571$	−2.56587e12	−1.01012	−0.505059	−	0.863085i	$-0.668529\pi$
$571$	−2.56587e12	−1.01012	−0.505059	+	0.863085i	$0.668529\pi$
$572$	−5.89589e11	−0.230286
$573$	−2.20196e12	−0.853324
$574$	0	0
$575$	1.73176e11	0.0660669
$576$	−7.41385e10	−0.0280636
$577$	3.78810e12	1.42276	0.711378	−	0.702810i	$-0.248072\pi$
$577$	3.78810e12	1.42276	0.711378	+	0.702810i	$0.248072\pi$
$578$	3.01741e12	1.12450
$579$	1.90964e12	0.706152
$580$	8.46804e11	0.310711
$581$	0	0
$582$	1.54332e12	0.557575
$583$	2.30796e12	0.827407
$584$	−1.00766e12	−0.358473
$585$	4.70010e11	0.165923
$586$	5.34156e11	0.187124
$587$	−2.25752e12	−0.784802	−0.392401	−	0.919794i	$-0.628355\pi$
$587$	−2.25752e12	−0.784802	−0.392401	+	0.919794i	$0.628355\pi$
$588$	0	0
$589$	−2.09442e12	−0.717043
$590$	−1.66573e12	−0.565941
$591$	2.51610e12	0.848369
$592$	−1.16706e12	−0.390522
$593$	−4.52765e12	−1.50358	−0.751790	−	0.659402i	$-0.770809\pi$
$593$	−4.52765e12	−1.50358	−0.751790	+	0.659402i	$0.770809\pi$
$594$	1.31707e12	0.434079
$595$	0	0
$596$	1.75890e12	0.570996
$597$	−3.42258e12	−1.10273
$598$	−7.14091e11	−0.228349
$599$	3.89624e12	1.23659	0.618293	−	0.785947i	$-0.287824\pi$
$599$	3.89624e12	1.23659	0.618293	+	0.785947i	$0.287824\pi$
$600$	−1.63591e11	−0.0515321
$601$	4.27283e12	1.33592	0.667960	−	0.744197i	$-0.267168\pi$
$601$	4.27283e12	1.33592	0.667960	+	0.744197i	$0.267168\pi$
$602$	0	0
$603$	8.19693e11	0.252478
$604$	2.32129e12	0.709682
$605$	2.03468e12	0.617444
$606$	2.57437e12	0.775433
$607$	4.84102e12	1.44740	0.723699	−	0.690116i	$-0.242441\pi$
$607$	4.84102e12	1.44740	0.723699	+	0.690116i	$0.242441\pi$
$608$	3.60189e11	0.106897
$609$	0	0
$610$	−1.01814e12	−0.297732
$611$	2.27217e12	0.659562
$612$	6.26985e11	0.180666
$613$	−6.72388e12	−1.92330	−0.961652	−	0.274274i	$-0.911563\pi$
$613$	−6.72388e12	−1.92330	−0.961652	+	0.274274i	$0.911563\pi$
$614$	−3.72437e12	−1.05754
$615$	−4.81603e12	−1.35754
$616$	0	0
$617$	8.50617e11	0.236293	0.118146	−	0.992996i	$-0.462305\pi$
$617$	8.50617e11	0.236293	0.118146	+	0.992996i	$0.462305\pi$
$618$	−4.24902e12	−1.17177
$619$	−5.97444e12	−1.63565	−0.817823	−	0.575469i	$-0.804819\pi$
$619$	−5.97444e12	−1.63565	−0.817823	+	0.575469i	$0.804819\pi$
$620$	1.99273e12	0.541608
$621$	1.59519e12	0.430427
$622$	1.22050e11	0.0326951
$623$	0	0
$624$	6.74564e11	0.178112
$625$	−3.07881e12	−0.807091
$626$	2.71467e12	0.706533
$627$	−1.17318e12	−0.303153
$628$	−8.58850e11	−0.220343
$629$	9.86976e12	2.51408
$630$	0	0
$631$	−5.96909e12	−1.49891	−0.749455	−	0.662055i	$-0.769685\pi$
$631$	−5.96909e12	−1.49891	−0.749455	+	0.662055i	$0.769685\pi$
$632$	−2.12954e12	−0.530957
$633$	−1.61465e12	−0.399726
$634$	−1.37608e12	−0.338254
$635$	1.00096e12	0.244306
$636$	−2.64059e12	−0.639947
$637$	0	0
$638$	1.14601e12	0.273840
$639$	−1.63623e12	−0.388230
$640$	−3.42700e11	−0.0807430
$641$	−4.21558e12	−0.986272	−0.493136	−	0.869952i	$-0.664149\pi$
$641$	−4.21558e12	−0.986272	−0.493136	+	0.869952i	$0.664149\pi$
$642$	−1.65037e12	−0.383420
$643$	5.53403e12	1.27671	0.638354	−	0.769743i	$-0.279615\pi$
$643$	5.53403e12	1.27671	0.638354	+	0.769743i	$0.279615\pi$
$644$	0	0
$645$	1.38166e12	0.314327
$646$	−3.04610e12	−0.688174
$647$	2.51909e12	0.565165	0.282582	−	0.959243i	$-0.408809\pi$
$647$	2.51909e12	0.565165	0.282582	+	0.959243i	$0.408809\pi$
$648$	−1.15062e12	−0.256357
$649$	−2.25430e12	−0.498782
$650$	−4.30916e11	−0.0946853
$651$	0	0
$652$	1.68438e12	0.365028
$653$	−7.60345e12	−1.63645	−0.818223	−	0.574901i	$-0.805040\pi$
$653$	−7.60345e12	−1.63645	−0.818223	+	0.574901i	$0.805040\pi$
$654$	2.02742e12	0.433355
$655$	−7.37097e12	−1.56473
$656$	2.00106e12	0.421884
$657$	1.08712e12	0.227632
$658$	0	0
$659$	−4.45281e12	−0.919708	−0.459854	−	0.887994i	$-0.652098\pi$
$659$	−4.45281e12	−0.919708	−0.459854	+	0.887994i	$0.652098\pi$
$660$	1.11622e12	0.228982
$661$	5.31348e12	1.08261	0.541305	−	0.840826i	$-0.317930\pi$
$661$	5.31348e12	1.08261	0.541305	+	0.840826i	$0.317930\pi$
$662$	5.74841e12	1.16329
$663$	−5.70475e12	−1.14664
$664$	−1.22425e12	−0.244407
$665$	0	0
$666$	1.25909e12	0.247984
$667$	1.38801e12	0.271536
$668$	8.25527e10	0.0160412
$669$	−5.16649e12	−0.997191
$670$	3.78898e12	0.726416
$671$	−1.37789e12	−0.262400
$672$	0	0
$673$	−2.03778e12	−0.382904	−0.191452	−	0.981502i	$-0.561320\pi$
$673$	−2.03778e12	−0.382904	−0.191452	+	0.981502i	$0.561320\pi$
$674$	−3.58130e12	−0.668453
$675$	9.62612e11	0.178478
$676$	−9.37874e11	−0.172737
$677$	1.00898e13	1.84601	0.923004	−	0.384790i	$-0.125726\pi$
$677$	1.00898e13	1.84601	0.923004	+	0.384790i	$0.125726\pi$
$678$	−9.20977e11	−0.167385
$679$	0	0
$680$	2.89820e12	0.519802
$681$	−6.93377e12	−1.23540
$682$	2.69683e12	0.477336
$683$	9.29076e12	1.63365	0.816823	−	0.576888i	$-0.195733\pi$
$683$	9.29076e12	1.63365	0.816823	+	0.576888i	$0.195733\pi$
$684$	−3.88593e11	−0.0678801
$685$	−9.16222e12	−1.58999
$686$	0	0
$687$	−5.54830e11	−0.0950287
$688$	−5.74079e11	−0.0976841
$689$	−6.95561e12	−1.17584
$690$	1.35193e12	0.227056
$691$	−6.85546e12	−1.14389	−0.571947	−	0.820291i	$-0.693812\pi$
$691$	−6.85546e12	−1.14389	−0.571947	+	0.820291i	$0.693812\pi$
$692$	−4.28106e11	−0.0709699
$693$	0	0
$694$	1.99833e12	0.327001
$695$	3.97449e12	0.646174
$696$	−1.31118e12	−0.211798
$697$	−1.69229e13	−2.71598
$698$	−6.62521e10	−0.0105645
$699$	−7.96465e12	−1.26188
$700$	0	0
$701$	2.51709e12	0.393702	0.196851	−	0.980433i	$-0.436928\pi$
$701$	2.51709e12	0.393702	0.196851	+	0.980433i	$0.436928\pi$
$702$	−3.96932e12	−0.616878
$703$	−6.11708e12	−0.944594
$704$	−4.63789e11	−0.0711613
$705$	−4.30171e12	−0.655828
$706$	−2.76469e12	−0.418817
$707$	0	0
$708$	2.57920e12	0.385776
$709$	−6.59233e12	−0.979785	−0.489892	−	0.871783i	$-0.662964\pi$
$709$	−6.59233e12	−0.979785	−0.489892	+	0.871783i	$0.662964\pi$
$710$	−7.56335e12	−1.11700
$711$	2.29747e12	0.337160
$712$	1.21867e12	0.177716
$713$	3.26631e12	0.473320
$714$	0	0
$715$	2.94025e12	0.420734
$716$	2.15783e12	0.306838
$717$	−1.52208e11	−0.0215081
$718$	−3.44127e11	−0.0483235
$719$	7.89215e11	0.110132	0.0550662	−	0.998483i	$-0.482463\pi$
$719$	7.89215e11	0.110132	0.0550662	+	0.998483i	$0.482463\pi$
$720$	3.69725e11	0.0512722
$721$	0	0
$722$	−3.27509e12	−0.448545
$723$	−1.09754e12	−0.149381
$724$	5.17929e12	0.700563
$725$	8.37592e11	0.112593
$726$	−3.15048e12	−0.420883
$727$	4.67869e12	0.621183	0.310592	−	0.950543i	$-0.399473\pi$
$727$	4.67869e12	0.621183	0.310592	+	0.950543i	$0.399473\pi$
$728$	0	0
$729$	8.48259e12	1.11238
$730$	5.02514e12	0.654931
$731$	4.85496e12	0.628865
$732$	1.57648e12	0.202950
$733$	7.38248e12	0.944571	0.472285	−	0.881446i	$-0.343429\pi$
$733$	7.38248e12	0.944571	0.472285	+	0.881446i	$0.343429\pi$
$734$	8.77754e12	1.11620
$735$	0	0
$736$	−5.61726e11	−0.0705626
$737$	5.12777e12	0.640213
$738$	−2.15886e12	−0.267899
$739$	−3.72777e12	−0.459780	−0.229890	−	0.973217i	$-0.573837\pi$
$739$	−3.72777e12	−0.459780	−0.229890	+	0.973217i	$0.573837\pi$
$740$	5.82006e12	0.713485
$741$	3.53569e12	0.430816
$742$	0	0
$743$	8.63062e12	1.03894	0.519472	−	0.854487i	$-0.326129\pi$
$743$	8.63062e12	1.03894	0.519472	+	0.854487i	$0.326129\pi$
$744$	−3.08551e12	−0.369189
$745$	−8.77154e12	−1.04321
$746$	−2.01639e12	−0.238368
$747$	1.32079e12	0.155200
$748$	3.92224e12	0.458118
$749$	0	0
$750$	5.74482e12	0.662980
$751$	1.71581e13	1.96829	0.984146	−	0.177359i	$-0.0567555\pi$
$751$	1.71581e13	1.96829	0.984146	+	0.177359i	$0.0567555\pi$
$752$	1.78736e12	0.203813
$753$	1.22660e13	1.39036
$754$	−3.45380e12	−0.389158
$755$	−1.15762e13	−1.29659
$756$	0	0
$757$	−6.69732e12	−0.741258	−0.370629	−	0.928781i	$-0.620858\pi$
$757$	−6.69732e12	−0.741258	−0.370629	+	0.928781i	$0.620858\pi$
$758$	−8.49604e11	−0.0934770
$759$	1.82962e12	0.200111
$760$	−1.79625e12	−0.195301
$761$	−3.08096e12	−0.333008	−0.166504	−	0.986041i	$-0.553248\pi$
$761$	−3.08096e12	−0.333008	−0.166504	+	0.986041i	$0.553248\pi$
$762$	−1.54987e12	−0.166532
$763$	0	0
$764$	−4.56263e12	−0.484502
$765$	−3.12674e12	−0.330077
$766$	−9.96305e12	−1.04559
$767$	6.79391e12	0.708827
$768$	5.30633e11	0.0550387
$769$	3.26639e11	0.0336821	0.0168410	−	0.999858i	$-0.494639\pi$
$769$	3.26639e11	0.0336821	0.0168410	+	0.999858i	$0.494639\pi$
$770$	0	0
$771$	−6.87736e12	−0.700934
$772$	3.95692e12	0.400940
$773$	1.96236e13	1.97684	0.988421	−	0.151736i	$-0.0484865\pi$
$773$	1.96236e13	1.97684	0.988421	+	0.151736i	$0.0484865\pi$
$774$	6.19350e11	0.0620300
$775$	1.97105e12	0.196263
$776$	3.19789e12	0.316581
$777$	0	0
$778$	−3.80607e12	−0.372450
$779$	1.04885e13	1.02045
$780$	−3.36401e12	−0.325411
$781$	−1.02358e13	−0.984443
$782$	4.75049e12	0.454264
$783$	7.71535e12	0.733547
$784$	0	0
$785$	4.28304e12	0.402567
$786$	1.14131e13	1.06660
$787$	1.46792e13	1.36400	0.682001	−	0.731351i	$-0.261110\pi$
$787$	1.46792e13	1.36400	0.682001	+	0.731351i	$0.261110\pi$
$788$	5.21356e12	0.481688
$789$	−1.23267e13	−1.13240
$790$	1.06199e13	0.970060
$791$	0	0
$792$	5.00363e11	0.0451878
$793$	4.15263e12	0.372902
$794$	2.71273e12	0.242222
$795$	1.31685e13	1.16919
$796$	−7.09184e12	−0.626109
$797$	−9.49591e12	−0.833632	−0.416816	−	0.908991i	$-0.636854\pi$
$797$	−9.49591e12	−0.833632	−0.416816	+	0.908991i	$0.636854\pi$
$798$	0	0
$799$	−1.51156e13	−1.31209
$800$	−3.38972e11	−0.0292590
$801$	−1.31477e12	−0.112851
$802$	−1.44567e13	−1.23392
$803$	6.80072e12	0.577211
$804$	−5.86680e12	−0.495164
$805$	0	0
$806$	−8.12759e12	−0.678351
$807$	−2.43820e12	−0.202366
$808$	5.33429e12	0.440277
$809$	1.44737e13	1.18799	0.593993	−	0.804470i	$-0.297551\pi$
$809$	1.44737e13	1.18799	0.593993	+	0.804470i	$0.297551\pi$
$810$	5.73809e12	0.468366
$811$	7.11471e12	0.577516	0.288758	−	0.957402i	$-0.406758\pi$
$811$	7.11471e12	0.577516	0.288758	+	0.957402i	$0.406758\pi$
$812$	0	0
$813$	7.27003e12	0.583618
$814$	7.87651e12	0.628817
$815$	−8.39992e12	−0.666908
$816$	−4.48753e12	−0.354325
$817$	−3.00901e12	−0.236278
$818$	−1.67216e13	−1.30583
$819$	0	0
$820$	−9.97919e12	−0.770785
$821$	7.47018e12	0.573835	0.286918	−	0.957955i	$-0.407369\pi$
$821$	7.47018e12	0.573835	0.286918	+	0.957955i	$0.407369\pi$
$822$	1.41867e13	1.08382
$823$	1.58484e13	1.20417	0.602085	−	0.798432i	$-0.294337\pi$
$823$	1.58484e13	1.20417	0.602085	+	0.798432i	$0.294337\pi$
$824$	−8.80430e12	−0.665308
$825$	1.10408e12	0.0829767
$826$	0	0
$827$	2.27588e12	0.169190	0.0845948	−	0.996415i	$-0.473040\pi$
$827$	2.27588e12	0.169190	0.0845948	+	0.996415i	$0.473040\pi$
$828$	6.06023e11	0.0448077
$829$	−1.27889e13	−0.940453	−0.470226	−	0.882546i	$-0.655828\pi$
$829$	−1.27889e13	−0.940453	−0.470226	+	0.882546i	$0.655828\pi$
$830$	6.10526e12	0.446532
$831$	−5.18275e12	−0.377013
$832$	1.39775e12	0.101129
$833$	0	0
$834$	−6.15404e12	−0.440467
$835$	−4.11686e11	−0.0293074
$836$	−2.43093e12	−0.172125
$837$	1.81560e13	1.27866
$838$	−6.68012e12	−0.467936
$839$	1.07948e13	0.752119	0.376060	−	0.926595i	$-0.377279\pi$
$839$	1.07948e13	0.752119	0.376060	+	0.926595i	$0.377279\pi$
$840$	0	0
$841$	−7.79383e12	−0.537241
$842$	2.68636e12	0.184187
$843$	3.24580e12	0.221359
$844$	−3.34568e12	−0.226957
$845$	4.67713e12	0.315591
$846$	−1.92831e12	−0.129422
$847$	0	0
$848$	−5.47150e12	−0.363350
$849$	−1.52849e13	−1.00967
$850$	2.86667e12	0.188362
$851$	9.53977e12	0.623526
$852$	1.17110e13	0.761404
$853$	−1.76557e13	−1.14187	−0.570933	−	0.820997i	$-0.693418\pi$
$853$	−1.76557e13	−1.14187	−0.570933	+	0.820997i	$0.693418\pi$
$854$	0	0
$855$	1.93789e12	0.124017
$856$	−3.41970e12	−0.217699
$857$	−1.64326e13	−1.04062	−0.520309	−	0.853978i	$-0.674183\pi$
$857$	−1.64326e13	−1.04062	−0.520309	+	0.853978i	$0.674183\pi$
$858$	−4.55265e12	−0.286795
$859$	8.44024e11	0.0528914	0.0264457	−	0.999650i	$-0.491581\pi$
$859$	8.44024e11	0.0528914	0.0264457	+	0.999650i	$0.491581\pi$
$860$	2.86290e12	0.178469
$861$	0	0
$862$	−2.56639e12	−0.158321
$863$	−2.46263e12	−0.151130	−0.0755649	−	0.997141i	$-0.524076\pi$
$863$	−2.46263e12	−0.151130	−0.0755649	+	0.997141i	$0.524076\pi$
$864$	−3.12239e12	−0.190623
$865$	2.13494e12	0.129662
$866$	7.11763e11	0.0430036
$867$	2.32996e13	1.40043
$868$	0	0
$869$	1.43723e13	0.854944
$870$	6.53879e12	0.386955
$871$	−1.54538e13	−0.909818
$872$	4.20097e12	0.246051
$873$	−3.45006e12	−0.201031
$874$	−2.94426e12	−0.170677
$875$	0	0
$876$	−7.78086e12	−0.446436
$877$	3.00332e12	0.171437	0.0857184	−	0.996319i	$-0.472681\pi$
$877$	3.00332e12	0.171437	0.0857184	+	0.996319i	$0.472681\pi$
$878$	−9.20136e12	−0.522549
$879$	4.12461e12	0.233041
$880$	2.31289e12	0.130012
$881$	−4.67820e11	−0.0261630	−0.0130815	−	0.999914i	$-0.504164\pi$
$881$	−4.67820e11	−0.0261630	−0.0130815	+	0.999914i	$0.504164\pi$
$882$	0	0
$883$	−9.28272e12	−0.513869	−0.256934	−	0.966429i	$-0.582712\pi$
$883$	−9.28272e12	−0.513869	−0.256934	+	0.966429i	$0.582712\pi$
$884$	−1.18207e13	−0.651039
$885$	−1.28623e13	−0.704815
$886$	−1.32774e13	−0.723872
$887$	9.97831e12	0.541253	0.270627	−	0.962684i	$-0.412769\pi$
$887$	9.97831e12	0.541253	0.270627	+	0.962684i	$0.412769\pi$
$888$	−9.01171e12	−0.486350
$889$	0	0
$890$	−6.07744e12	−0.324688
$891$	7.76558e12	0.412785
$892$	−1.07054e13	−0.566187
$893$	9.36835e12	0.492983
$894$	1.35817e13	0.711109
$895$	−1.07610e13	−0.560594
$896$	0	0
$897$	−5.51401e12	−0.284382
$898$	1.31793e13	0.676313
$899$	1.57980e13	0.806646
$900$	3.65703e11	0.0185796
$901$	4.62722e13	2.33915
$902$	−1.35052e13	−0.679317
$903$	0	0
$904$	−1.90834e12	−0.0950379
$905$	−2.58289e13	−1.27993
$906$	1.79244e13	0.883827
$907$	−1.03996e12	−0.0510249	−0.0255124	−	0.999675i	$-0.508122\pi$
$907$	−1.03996e12	−0.0510249	−0.0255124	+	0.999675i	$0.508122\pi$
$908$	−1.43673e13	−0.701438
$909$	−5.75494e12	−0.279578
$910$	0	0
$911$	2.92798e13	1.40843	0.704215	−	0.709986i	$-0.251299\pi$
$911$	2.92798e13	1.40843	0.704215	+	0.709986i	$0.251299\pi$
$912$	2.78128e12	0.133128
$913$	8.26248e12	0.393543
$914$	−2.55725e13	−1.21204
$915$	−7.86183e12	−0.370791
$916$	−1.14965e12	−0.0539556
$917$	0	0
$918$	2.64059e13	1.22718
$919$	−1.31519e13	−0.608231	−0.304115	−	0.952635i	$-0.598361\pi$
$919$	−1.31519e13	−0.608231	−0.304115	+	0.952635i	$0.598361\pi$
$920$	2.80130e12	0.128918
$921$	−2.87585e13	−1.31704
$922$	−2.04002e13	−0.929706
$923$	3.08481e13	1.39901
$924$	0	0
$925$	5.75675e12	0.258547
$926$	−5.02026e12	−0.224376
$927$	9.49859e12	0.422474
$928$	−2.71687e12	−0.120255
$929$	−3.36952e13	−1.48422	−0.742108	−	0.670280i	$-0.766174\pi$
$929$	−3.36952e13	−1.48422	−0.742108	+	0.670280i	$0.766174\pi$
$930$	1.53873e13	0.674510
$931$	0	0
$932$	−1.65034e13	−0.716475
$933$	9.42439e11	0.0407180
$934$	1.50638e13	0.647699
$935$	−1.95600e13	−0.836983
$936$	−1.50797e12	−0.0642172
$937$	−1.90556e13	−0.807598	−0.403799	−	0.914848i	$-0.632311\pi$
$937$	−1.90556e13	−0.807598	−0.403799	+	0.914848i	$0.632311\pi$
$938$	0	0
$939$	2.09619e13	0.879905
$940$	−8.91347e12	−0.372367
$941$	1.67435e13	0.696134	0.348067	−	0.937470i	$-0.386838\pi$
$941$	1.67435e13	0.696134	0.348067	+	0.937470i	$0.386838\pi$
$942$	−6.63180e12	−0.274412
$943$	−1.63571e13	−0.673601
$944$	5.34430e12	0.219037
$945$	0	0
$946$	3.87448e12	0.157291
$947$	−2.34965e13	−0.949355	−0.474677	−	0.880160i	$-0.657435\pi$
$947$	−2.34965e13	−0.949355	−0.474677	+	0.880160i	$0.657435\pi$
$948$	−1.64437e13	−0.661245
$949$	−2.04957e13	−0.820285
$950$	−1.77670e12	−0.0707716
$951$	−1.06257e13	−0.421256
$952$	0	0
$953$	2.77607e13	1.09022	0.545108	−	0.838366i	$-0.316489\pi$
$953$	2.77607e13	1.09022	0.545108	+	0.838366i	$0.316489\pi$
$954$	5.90297e12	0.230729
$955$	2.27536e13	0.885187
$956$	−3.15387e11	−0.0122119
$957$	8.84919e12	0.341036
$958$	1.13606e13	0.435771
$959$	0	0
$960$	−2.64624e12	−0.100556
$961$	1.07367e13	0.406083
$962$	−2.37379e13	−0.893622
$963$	3.68937e12	0.138240
$964$	−2.27418e12	−0.0848160
$965$	−1.97330e13	−0.732520
$966$	0	0
$967$	−1.72985e13	−0.636193	−0.318097	−	0.948058i	$-0.603044\pi$
$967$	−1.72985e13	−0.636193	−0.318097	+	0.948058i	$0.603044\pi$
$968$	−6.52803e12	−0.238970
$969$	−2.35212e13	−0.857041
$970$	−1.59477e13	−0.578395
$971$	−1.21004e13	−0.436832	−0.218416	−	0.975856i	$-0.570089\pi$
$971$	−1.21004e13	−0.436832	−0.218416	+	0.975856i	$0.570089\pi$
$972$	6.11961e12	0.219900
$973$	0	0
$974$	1.94981e13	0.694187
$975$	−3.32742e12	−0.117920
$976$	3.26659e12	0.115231
$977$	−2.99686e13	−1.05230	−0.526151	−	0.850391i	$-0.676365\pi$
$977$	−2.99686e13	−1.05230	−0.526151	+	0.850391i	$0.676365\pi$
$978$	1.30063e13	0.454601
$979$	−8.22483e12	−0.286157
$980$	0	0
$981$	−4.53225e12	−0.156244
$982$	−9.21950e11	−0.0316378
$983$	7.63647e11	0.0260857	0.0130428	−	0.999915i	$-0.495848\pi$
$983$	7.63647e11	0.0260857	0.0130428	+	0.999915i	$0.495848\pi$
$984$	1.54516e13	0.525408
$985$	−2.59997e13	−0.880046
$986$	2.29764e13	0.774169
$987$	0	0
$988$	7.32622e12	0.244610
$989$	4.69264e12	0.155967
$990$	−2.49528e12	−0.0825584
$991$	−4.14811e13	−1.36621	−0.683107	−	0.730318i	$-0.739372\pi$
$991$	−4.14811e13	−1.36621	−0.683107	+	0.730318i	$0.739372\pi$
$992$	−6.39342e12	−0.209619
$993$	4.43876e13	1.44874
$994$	0	0
$995$	3.53666e13	1.14390
$996$	−9.45331e12	−0.304381
$997$	5.09261e13	1.63235	0.816173	−	0.577808i	$-0.196092\pi$
$997$	5.09261e13	1.63235	0.816173	+	0.577808i	$0.196092\pi$
$998$	3.82199e13	1.21956
$999$	5.30274e13	1.68444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.f.1.2	yes	2
7.2	even	3		98.10.c.g.67.1		4
7.3	odd	6		98.10.c.g.79.2		4
7.4	even	3		98.10.c.g.79.1		4
7.5	odd	6		98.10.c.g.67.2		4
7.6	odd	2	inner	98.10.a.f.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.f.1.1	✓	2	7.6	odd	2	inner
98.10.a.f.1.2	yes	2	1.1	even	1	trivial
98.10.c.g.67.1		4	7.2	even	3
98.10.c.g.67.2		4	7.5	odd	6
98.10.c.g.79.1		4	7.4	even	3
98.10.c.g.79.2		4	7.3	odd	6

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +123.548 q^{3} +256.000 q^{4} -1276.66 q^{5} +1976.76 q^{6} +4096.00 q^{8} -4419.00 q^{9} -20426.5 q^{10} -27644.0 q^{11} +31628.2 q^{12} +83312.2 q^{13} -157728. q^{15} +65536.0 q^{16} -554234. q^{17} -70704.0 q^{18} +343503. q^{19} -326824. q^{20} -442304. q^{22} -535704. q^{23} +506051. q^{24} -323269. q^{25} +1.33300e6 q^{26} -2.97774e6 q^{27} -2.59101e6 q^{29} -2.52365e6 q^{30} -6.09724e6 q^{31} +1.04858e6 q^{32} -3.41535e6 q^{33} -8.86775e6 q^{34} -1.13126e6 q^{36} -1.78079e7 q^{37} +5.49605e6 q^{38} +1.02930e7 q^{39} -5.22919e6 q^{40} +3.05338e7 q^{41} -8.75976e6 q^{43} -7.07686e6 q^{44} +5.64155e6 q^{45} -8.57126e6 q^{46} +2.72730e7 q^{47} +8.09681e6 q^{48} -5.17230e6 q^{50} -6.84743e7 q^{51} +2.13279e7 q^{52} -8.34885e7 q^{53} -4.76439e7 q^{54} +3.52919e7 q^{55} +4.24390e7 q^{57} -4.14561e7 q^{58} +8.15475e7 q^{59} -4.03784e7 q^{60} +4.98442e7 q^{61} -9.75558e7 q^{62} +1.67772e7 q^{64} -1.06361e8 q^{65} -5.46456e7 q^{66} -1.85493e8 q^{67} -1.41884e8 q^{68} -6.61849e7 q^{69} +3.70271e8 q^{71} -1.81002e7 q^{72} -2.46011e8 q^{73} -2.84927e8 q^{74} -3.99391e7 q^{75} +8.79369e7 q^{76} +1.64688e8 q^{78} -5.19907e8 q^{79} -8.36671e7 q^{80} -2.80914e8 q^{81} +4.88541e8 q^{82} -2.98889e8 q^{83} +7.07568e8 q^{85} -1.40156e8 q^{86} -3.20112e8 q^{87} -1.13230e8 q^{88} +2.97527e8 q^{89} +9.02648e7 q^{90} -1.37140e8 q^{92} -7.53299e8 q^{93} +4.36367e8 q^{94} -4.38536e8 q^{95} +1.29549e8 q^{96} +7.80734e8 q^{97} +1.22159e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{2} + 512 q^{4} + 8192 q^{8} - 8838 q^{9} - 55288 q^{11} - 315456 q^{15} + 131072 q^{16} - 141408 q^{18} - 884608 q^{22} - 1071408 q^{23} - 646538 q^{25} - 5182012 q^{29} - 5047296 q^{30} + 2097152 q^{32}+ \cdots + 244317672 q^{99}+O(q^{100}) \) 2 * q + 32 * q^2 + 512 * q^4 + 8192 * q^8 - 8838 * q^9 - 55288 * q^11 - 315456 * q^15 + 131072 * q^16 - 141408 * q^18 - 884608 * q^22 - 1071408 * q^23 - 646538 * q^25 - 5182012 * q^29 - 5047296 * q^30 + 2097152 * q^32 - 2262528 * q^36 - 35615820 * q^37 + 20586048 * q^39 - 17519512 * q^43 - 14153728 * q^44 - 17142528 * q^46 - 10344608 * q^50 - 136948608 * q^51 - 166976980 * q^53 + 84878016 * q^57 - 82912192 * q^58 - 80756736 * q^60 + 33554432 * q^64 - 212722496 * q^65 - 370985848 * q^67 + 740541344 * q^71 - 36200448 * q^72 - 569853120 * q^74 + 329376768 * q^78 - 1039814512 * q^79 - 561827502 * q^81 + 1415135616 * q^85 - 280312192 * q^86 - 226459648 * q^88 - 274280448 * q^92 - 1506597504 * q^93 - 877072832 * q^95 + 244317672 * q^99

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