LMFDB - Embedded newform 63.10.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,10,Mod(1,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("63.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	63.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:	$32.4472576783$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{193}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 48 $ x^2 - x - 48
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$7.44622$ of defining polynomial
Character	$\chi$	$=$	63.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.8924 q^{2} -226.645 q^{4} +2438.78 q^{5} -2401.00 q^{7} -12477.5 q^{8} +O(q^{10})$	\(q+16.8924 q^{2} -226.645 q^{4} +2438.78 q^{5} -2401.00 q^{7} -12477.5 q^{8} +41197.0 q^{10} +28548.3 q^{11} +138149. q^{13} -40558.8 q^{14} -94733.5 q^{16} +101010. q^{17} -488928. q^{19} -552739. q^{20} +482250. q^{22} +140071. q^{23} +3.99453e6 q^{25} +2.33367e6 q^{26} +544175. q^{28} +6.31716e6 q^{29} -1.00903e6 q^{31} +4.78821e6 q^{32} +1.70630e6 q^{34} -5.85552e6 q^{35} +1.19206e7 q^{37} -8.25919e6 q^{38} -3.04300e7 q^{40} +2.15106e7 q^{41} +1.65957e7 q^{43} -6.47033e6 q^{44} +2.36615e6 q^{46} +2.67441e7 q^{47} +5.76480e6 q^{49} +6.74774e7 q^{50} -3.13108e7 q^{52} -3.74991e7 q^{53} +6.96230e7 q^{55} +2.99585e7 q^{56} +1.06712e8 q^{58} -1.81907e7 q^{59} -2.50111e7 q^{61} -1.70449e7 q^{62} +1.29388e8 q^{64} +3.36915e8 q^{65} -2.18572e8 q^{67} -2.28934e7 q^{68} -9.89140e7 q^{70} -3.12688e8 q^{71} -2.89038e8 q^{73} +2.01369e8 q^{74} +1.10813e8 q^{76} -6.85444e7 q^{77} +4.68685e8 q^{79} -2.31034e8 q^{80} +3.63366e8 q^{82} +7.75407e7 q^{83} +2.46341e8 q^{85} +2.80342e8 q^{86} -3.56212e8 q^{88} -3.37680e8 q^{89} -3.31695e8 q^{91} -3.17465e7 q^{92} +4.51773e8 q^{94} -1.19239e9 q^{95} -7.36733e8 q^{97} +9.73816e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} - 620 q^{4} + 2238 q^{5} - 4802 q^{7} - 2616 q^{8}+O(q^{10}) $ 2 * q + 6 * q^2 - 620 * q^4 + 2238 * q^5 - 4802 * q^7 - 2616 * q^8	\( 2 q + 6 q^{2} - 620 q^{4} + 2238 q^{5} - 4802 q^{7} - 2616 q^{8} + 43384 q^{10} - 35316 q^{11} - 26530 q^{13} - 14406 q^{14} - 752 q^{16} + 463920 q^{17} - 925426 q^{19} - 473760 q^{20} + 1177888 q^{22} - 778128 q^{23} + 2081722 q^{25} + 4127424 q^{26} + 1488620 q^{28} + 10003584 q^{29} + 2467260 q^{31} - 1284576 q^{32} - 2246676 q^{34} - 5373438 q^{35} + 30735552 q^{37} - 3504660 q^{38} - 32409984 q^{40} + 19103448 q^{41} + 4065100 q^{43} + 18650976 q^{44} + 12367584 q^{46} + 82195020 q^{47} + 11529602 q^{49} + 88312626 q^{50} + 33466384 q^{52} + 55189812 q^{53} + 82445816 q^{55} + 6281016 q^{56} + 66558004 q^{58} + 7069218 q^{59} + 44316386 q^{61} - 54910200 q^{62} + 147417152 q^{64} + 369979260 q^{65} - 241921336 q^{67} - 165645816 q^{68} - 104164984 q^{70} - 206493816 q^{71} - 499153188 q^{73} - 3571524 q^{74} + 282511768 q^{76} + 84793716 q^{77} + 468535096 q^{79} - 249904128 q^{80} + 389586092 q^{82} - 444023958 q^{83} + 173475060 q^{85} + 416830608 q^{86} - 986010816 q^{88} - 636267396 q^{89} + 63698530 q^{91} + 329431488 q^{92} - 152223192 q^{94} - 1104747984 q^{95} - 1632716064 q^{97} + 34588806 q^{98}+O(q^{100}) \) 2 * q + 6 * q^2 - 620 * q^4 + 2238 * q^5 - 4802 * q^7 - 2616 * q^8 + 43384 * q^10 - 35316 * q^11 - 26530 * q^13 - 14406 * q^14 - 752 * q^16 + 463920 * q^17 - 925426 * q^19 - 473760 * q^20 + 1177888 * q^22 - 778128 * q^23 + 2081722 * q^25 + 4127424 * q^26 + 1488620 * q^28 + 10003584 * q^29 + 2467260 * q^31 - 1284576 * q^32 - 2246676 * q^34 - 5373438 * q^35 + 30735552 * q^37 - 3504660 * q^38 - 32409984 * q^40 + 19103448 * q^41 + 4065100 * q^43 + 18650976 * q^44 + 12367584 * q^46 + 82195020 * q^47 + 11529602 * q^49 + 88312626 * q^50 + 33466384 * q^52 + 55189812 * q^53 + 82445816 * q^55 + 6281016 * q^56 + 66558004 * q^58 + 7069218 * q^59 + 44316386 * q^61 - 54910200 * q^62 + 147417152 * q^64 + 369979260 * q^65 - 241921336 * q^67 - 165645816 * q^68 - 104164984 * q^70 - 206493816 * q^71 - 499153188 * q^73 - 3571524 * q^74 + 282511768 * q^76 + 84793716 * q^77 + 468535096 * q^79 - 249904128 * q^80 + 389586092 * q^82 - 444023958 * q^83 + 173475060 * q^85 + 416830608 * q^86 - 986010816 * q^88 - 636267396 * q^89 + 63698530 * q^91 + 329431488 * q^92 - 152223192 * q^94 - 1104747984 * q^95 - 1632716064 * q^97 + 34588806 * q^98

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 $

$2$	16.8924	0.746548	0.373274	−	0.927721i	$-0.378235\pi$
$2$	16.8924	0.746548	0.373274	+	0.927721i	$0.378235\pi$
$3$	0	0
$3$	0	0
$4$	−226.645	−0.442667
$5$	2438.78	1.74505	0.872525	−	0.488569i	$-0.162481\pi$
$5$	2438.78	1.74505	0.872525	+	0.488569i	$0.162481\pi$
$6$	0	0
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−12477.5	−1.07702
$9$	0	0
$10$	41197.0	1.30276
$11$	28548.3	0.587912	0.293956	−	0.955819i	$-0.405028\pi$
$11$	28548.3	0.587912	0.293956	+	0.955819i	$0.405028\pi$
$12$	0	0
$13$	138149.	1.34153	0.670767	−	0.741668i	$-0.265965\pi$
$13$	138149.	1.34153	0.670767	+	0.741668i	$0.265965\pi$
$14$	−40558.8	−0.282168
$15$	0	0
$16$	−94733.5	−0.361380
$17$	101010.	0.293321	0.146661	−	0.989187i	$-0.453147\pi$
$17$	101010.	0.293321	0.146661	+	0.989187i	$0.453147\pi$
$18$	0	0
$19$	−488928.	−0.860704	−0.430352	−	0.902661i	$-0.641611\pi$
$19$	−488928.	−0.860704	−0.430352	+	0.902661i	$0.641611\pi$
$20$	−552739.	−0.772476
$21$	0	0
$22$	482250.	0.438905
$23$	140071.	0.104370	0.0521848	−	0.998637i	$-0.483382\pi$
$23$	140071.	0.104370	0.0521848	+	0.998637i	$0.483382\pi$
$24$	0	0
$25$	3.99453e6	2.04520
$26$	2.33367e6	1.00152
$27$	0	0
$28$	544175.	0.167312
$29$	6.31716e6	1.65856	0.829279	−	0.558835i	$-0.188751\pi$
$29$	6.31716e6	1.65856	0.829279	+	0.558835i	$0.188751\pi$
$30$	0	0
$31$	−1.00903e6	−0.196234	−0.0981172	−	0.995175i	$-0.531282\pi$
$31$	−1.00903e6	−0.196234	−0.0981172	+	0.995175i	$0.531282\pi$
$32$	4.78821e6	0.807232
$33$	0	0
$34$	1.70630e6	0.218978
$35$	−5.85552e6	−0.659567
$36$	0	0
$37$	1.19206e7	1.04566	0.522832	−	0.852436i	$-0.324876\pi$
$37$	1.19206e7	1.04566	0.522832	+	0.852436i	$0.324876\pi$
$38$	−8.25919e6	−0.642556
$39$	0	0
$40$	−3.04300e7	−1.87945
$41$	2.15106e7	1.18884	0.594422	−	0.804153i	$-0.297381\pi$
$41$	2.15106e7	1.18884	0.594422	+	0.804153i	$0.297381\pi$
$42$	0	0
$43$	1.65957e7	0.740265	0.370133	−	0.928979i	$-0.379312\pi$
$43$	1.65957e7	0.740265	0.370133	+	0.928979i	$0.379312\pi$
$44$	−6.47033e6	−0.260249
$45$	0	0
$46$	2.36615e6	0.0779169
$47$	2.67441e7	0.799443	0.399721	−	0.916637i	$-0.369107\pi$
$47$	2.67441e7	0.799443	0.399721	+	0.916637i	$0.369107\pi$
$48$	0	0
$49$	5.76480e6	0.142857
$50$	6.74774e7	1.52684
$51$	0	0
$52$	−3.13108e7	−0.593853
$53$	−3.74991e7	−0.652799	−0.326399	−	0.945232i	$-0.605835\pi$
$53$	−3.74991e7	−0.652799	−0.326399	+	0.945232i	$0.605835\pi$
$54$	0	0
$55$	6.96230e7	1.02594
$56$	2.99585e7	0.407075
$57$	0	0
$58$	1.06712e8	1.23819
$59$	−1.81907e7	−0.195441	−0.0977207	−	0.995214i	$-0.531155\pi$
$59$	−1.81907e7	−0.195441	−0.0977207	+	0.995214i	$0.531155\pi$
$60$	0	0
$61$	−2.50111e7	−0.231285	−0.115643	−	0.993291i	$-0.536893\pi$
$61$	−2.50111e7	−0.231285	−0.115643	+	0.993291i	$0.536893\pi$
$62$	−1.70449e7	−0.146498
$63$	0	0
$64$	1.29388e8	0.964017
$65$	3.36915e8	2.34105
$66$	0	0
$67$	−2.18572e8	−1.32513	−0.662564	−	0.749005i	$-0.730532\pi$
$67$	−2.18572e8	−1.32513	−0.662564	+	0.749005i	$0.730532\pi$
$68$	−2.28934e7	−0.129844
$69$	0	0
$70$	−9.89140e7	−0.492398
$71$	−3.12688e8	−1.46032	−0.730161	−	0.683275i	$-0.760555\pi$
$71$	−3.12688e8	−1.46032	−0.730161	+	0.683275i	$0.760555\pi$
$72$	0	0
$73$	−2.89038e8	−1.19125	−0.595624	−	0.803264i	$-0.703095\pi$
$73$	−2.89038e8	−1.19125	−0.595624	+	0.803264i	$0.703095\pi$
$74$	2.01369e8	0.780638
$75$	0	0
$76$	1.10813e8	0.381005
$77$	−6.85444e7	−0.222210
$78$	0	0
$79$	4.68685e8	1.35381	0.676907	−	0.736069i	$-0.263320\pi$
$79$	4.68685e8	1.35381	0.676907	+	0.736069i	$0.263320\pi$
$80$	−2.31034e8	−0.630626
$81$	0	0
$82$	3.63366e8	0.887529
$83$	7.75407e7	0.179341	0.0896703	−	0.995972i	$-0.471419\pi$
$83$	7.75407e7	0.179341	0.0896703	+	0.995972i	$0.471419\pi$
$84$	0	0
$85$	2.46341e8	0.511860
$86$	2.80342e8	0.552643
$87$	0	0
$88$	−3.56212e8	−0.633193
$89$	−3.37680e8	−0.570493	−0.285246	−	0.958454i	$-0.592075\pi$
$89$	−3.37680e8	−0.570493	−0.285246	+	0.958454i	$0.592075\pi$
$90$	0	0
$91$	−3.31695e8	−0.507052
$92$	−3.17465e7	−0.0462010
$93$	0	0
$94$	4.51773e8	0.596822
$95$	−1.19239e9	−1.50197
$96$	0	0
$97$	−7.36733e8	−0.844962	−0.422481	−	0.906372i	$-0.638841\pi$
$97$	−7.36733e8	−0.844962	−0.422481	+	0.906372i	$0.638841\pi$
$98$	9.73816e7	0.106650
$99$	0	0
$100$	−9.05342e8	−0.905342
$101$	−1.97428e8	−0.188783	−0.0943914	−	0.995535i	$-0.530091\pi$
$101$	−1.97428e8	−0.188783	−0.0943914	+	0.995535i	$0.530091\pi$
$102$	0	0
$103$	−1.27449e9	−1.11576	−0.557879	−	0.829922i	$-0.688385\pi$
$103$	−1.27449e9	−1.11576	−0.557879	+	0.829922i	$0.688385\pi$
$104$	−1.72375e9	−1.44486
$105$	0	0
$106$	−6.33451e8	−0.487345
$107$	−1.81937e9	−1.34182	−0.670908	−	0.741541i	$-0.734095\pi$
$107$	−1.81937e9	−1.34182	−0.670908	+	0.741541i	$0.734095\pi$
$108$	0	0
$109$	−2.31425e8	−0.157033	−0.0785167	−	0.996913i	$-0.525018\pi$
$109$	−2.31425e8	−0.157033	−0.0785167	+	0.996913i	$0.525018\pi$
$110$	1.17610e9	0.765911
$111$	0	0
$112$	2.27455e8	0.136589
$113$	1.51983e9	0.876885	0.438443	−	0.898759i	$-0.355530\pi$
$113$	1.51983e9	0.876885	0.438443	+	0.898759i	$0.355530\pi$
$114$	0	0
$115$	3.41604e8	0.182130
$116$	−1.43175e9	−0.734188
$117$	0	0
$118$	−3.07286e8	−0.145906
$119$	−2.42525e8	−0.110865
$120$	0	0
$121$	−1.54294e9	−0.654359
$122$	−4.22498e8	−0.172666
$123$	0	0
$124$	2.28691e8	0.0868665
$125$	4.97855e9	1.82393
$126$	0	0
$127$	4.20951e9	1.43587	0.717934	−	0.696111i	$-0.245088\pi$
$127$	4.20951e9	1.43587	0.717934	+	0.696111i	$0.245088\pi$
$128$	−2.65883e8	−0.0875478
$129$	0	0
$130$	5.69131e9	1.74770
$131$	4.12131e9	1.22268	0.611342	−	0.791367i	$-0.290630\pi$
$131$	4.12131e9	1.22268	0.611342	+	0.791367i	$0.290630\pi$
$132$	0	0
$133$	1.17392e9	0.325315
$134$	−3.69221e9	−0.989271
$135$	0	0
$136$	−1.26035e9	−0.315913
$137$	1.27942e9	0.310292	0.155146	−	0.987892i	$-0.450415\pi$
$137$	1.27942e9	0.310292	0.155146	+	0.987892i	$0.450415\pi$
$138$	0	0
$139$	−4.02340e9	−0.914170	−0.457085	−	0.889423i	$-0.651107\pi$
$139$	−4.02340e9	−0.914170	−0.457085	+	0.889423i	$0.651107\pi$
$140$	1.32713e9	0.291968
$141$	0	0
$142$	−5.28206e9	−1.09020
$143$	3.94391e9	0.788705
$144$	0	0
$145$	1.54062e10	2.89427
$146$	−4.88256e9	−0.889323
$147$	0	0
$148$	−2.70176e9	−0.462880
$149$	7.67785e8	0.127615	0.0638075	−	0.997962i	$-0.479676\pi$
$149$	7.67785e8	0.127615	0.0638075	+	0.997962i	$0.479676\pi$
$150$	0	0
$151$	−9.84752e9	−1.54145	−0.770727	−	0.637165i	$-0.780107\pi$
$151$	−9.84752e9	−1.54145	−0.770727	+	0.637165i	$0.780107\pi$
$152$	6.10061e9	0.926995
$153$	0	0
$154$	−1.15788e9	−0.165890
$155$	−2.46080e9	−0.342439
$156$	0	0
$157$	8.04096e9	1.05623	0.528116	−	0.849172i	$-0.322898\pi$
$157$	8.04096e9	1.05623	0.528116	+	0.849172i	$0.322898\pi$
$158$	7.91723e9	1.01069
$159$	0	0
$160$	1.16774e10	1.40866
$161$	−3.36311e8	−0.0394480
$162$	0	0
$163$	−9.07348e9	−1.00677	−0.503384	−	0.864063i	$-0.667912\pi$
$163$	−9.07348e9	−1.00677	−0.503384	+	0.864063i	$0.667912\pi$
$164$	−4.87527e9	−0.526262
$165$	0	0
$166$	1.30985e9	0.133886
$167$	8.83471e9	0.878958	0.439479	−	0.898253i	$-0.355163\pi$
$167$	8.83471e9	0.878958	0.439479	+	0.898253i	$0.355163\pi$
$168$	0	0
$169$	8.48058e9	0.799715
$170$	4.16130e9	0.382128
$171$	0	0
$172$	−3.76134e9	−0.327691
$173$	−7.89871e9	−0.670423	−0.335211	−	0.942143i	$-0.608808\pi$
$173$	−7.89871e9	−0.670423	−0.335211	+	0.942143i	$0.608808\pi$
$174$	0	0
$175$	−9.59087e9	−0.773013
$176$	−2.70448e9	−0.212460
$177$	0	0
$178$	−5.70424e9	−0.425900
$179$	−4.59871e9	−0.334810	−0.167405	−	0.985888i	$-0.553539\pi$
$179$	−4.59871e9	−0.334810	−0.167405	+	0.985888i	$0.553539\pi$
$180$	0	0
$181$	−6.70993e8	−0.0464691	−0.0232346	−	0.999730i	$-0.507396\pi$
$181$	−6.70993e8	−0.0464691	−0.0232346	+	0.999730i	$0.507396\pi$
$182$	−5.60314e9	−0.378539
$183$	0	0
$184$	−1.74774e9	−0.112408
$185$	2.90719e10	1.82474
$186$	0	0
$187$	2.88366e9	0.172447
$188$	−6.06142e9	−0.353887
$189$	0	0
$190$	−2.01424e10	−1.12129
$191$	−1.00686e10	−0.547416	−0.273708	−	0.961813i	$-0.588250\pi$
$191$	−1.00686e10	−0.547416	−0.273708	+	0.961813i	$0.588250\pi$
$192$	0	0
$193$	−1.97876e10	−1.02656	−0.513281	−	0.858221i	$-0.671570\pi$
$193$	−1.97876e10	−1.02656	−0.513281	+	0.858221i	$0.671570\pi$
$194$	−1.24452e10	−0.630805
$195$	0	0
$196$	−1.30657e9	−0.0632381
$197$	1.07508e10	0.508560	0.254280	−	0.967131i	$-0.418161\pi$
$197$	1.07508e10	0.508560	0.254280	+	0.967131i	$0.418161\pi$
$198$	0	0
$199$	−1.58060e9	−0.0714468	−0.0357234	−	0.999362i	$-0.511374\pi$
$199$	−1.58060e9	−0.0714468	−0.0357234	+	0.999362i	$0.511374\pi$
$200$	−4.98419e10	−2.20272
$201$	0	0
$202$	−3.33504e9	−0.140935
$203$	−1.51675e10	−0.626876
$204$	0	0
$205$	5.24596e10	2.07459
$206$	−2.15293e10	−0.832967
$207$	0	0
$208$	−1.30873e10	−0.484803
$209$	−1.39580e10	−0.506019
$210$	0	0
$211$	4.44247e10	1.54295	0.771477	−	0.636257i	$-0.219518\pi$
$211$	4.44247e10	1.54295	0.771477	+	0.636257i	$0.219518\pi$
$212$	8.49899e9	0.288972
$213$	0	0
$214$	−3.07335e10	−1.00173
$215$	4.04733e10	1.29180
$216$	0	0
$217$	2.42267e9	0.0741697
$218$	−3.90934e9	−0.117233
$219$	0	0
$220$	−1.57797e10	−0.454148
$221$	1.39544e10	0.393501
$222$	0	0
$223$	2.40745e10	0.651907	0.325954	−	0.945386i	$-0.394315\pi$
$223$	2.40745e10	0.651907	0.325954	+	0.945386i	$0.394315\pi$
$224$	−1.14965e10	−0.305105
$225$	0	0
$226$	2.56737e10	0.654636
$227$	1.71588e8	0.00428915	0.00214458	−	0.999998i	$-0.499317\pi$
$227$	1.71588e8	0.00428915	0.00214458	+	0.999998i	$0.499317\pi$
$228$	0	0
$229$	−1.11777e10	−0.268592	−0.134296	−	0.990941i	$-0.542877\pi$
$229$	−1.11777e10	−0.268592	−0.134296	+	0.990941i	$0.542877\pi$
$230$	5.77052e9	0.135969
$231$	0	0
$232$	−7.88225e10	−1.78630
$233$	−6.54487e9	−0.145479	−0.0727393	−	0.997351i	$-0.523174\pi$
$233$	−6.54487e9	−0.145479	−0.0727393	+	0.997351i	$0.523174\pi$
$234$	0	0
$235$	6.52230e10	1.39507
$236$	4.12285e9	0.0865154
$237$	0	0
$238$	−4.09683e9	−0.0827660
$239$	9.08610e9	0.180130	0.0900651	−	0.995936i	$-0.471292\pi$
$239$	9.08610e9	0.180130	0.0900651	+	0.995936i	$0.471292\pi$
$240$	0	0
$241$	−5.36400e10	−1.02426	−0.512132	−	0.858906i	$-0.671144\pi$
$241$	−5.36400e10	−1.02426	−0.512132	+	0.858906i	$0.671144\pi$
$242$	−2.60641e10	−0.488510
$243$	0	0
$244$	5.66865e9	0.102382
$245$	1.40591e10	0.249293
$246$	0	0
$247$	−6.75448e10	−1.15466
$248$	1.25902e10	0.211348
$249$	0	0
$250$	8.40999e10	1.36165
$251$	−3.92651e10	−0.624418	−0.312209	−	0.950013i	$-0.601069\pi$
$251$	−3.92651e10	−0.624418	−0.312209	+	0.950013i	$0.601069\pi$
$252$	0	0
$253$	3.99880e9	0.0613602
$254$	7.11089e10	1.07194
$255$	0	0
$256$	−7.07381e10	−1.02938
$257$	7.70786e9	0.110213	0.0551067	−	0.998480i	$-0.482450\pi$
$257$	7.70786e9	0.110213	0.0551067	+	0.998480i	$0.482450\pi$
$258$	0	0
$259$	−2.86215e10	−0.395224
$260$	−7.63601e10	−1.03630
$261$	0	0
$262$	6.96189e10	0.912791
$263$	−3.65878e10	−0.471559	−0.235779	−	0.971807i	$-0.575764\pi$
$263$	−3.65878e10	−0.471559	−0.235779	+	0.971807i	$0.575764\pi$
$264$	0	0
$265$	−9.14521e10	−1.13917
$266$	1.98303e10	0.242863
$267$	0	0
$268$	4.95383e10	0.586590
$269$	1.65478e11	1.92688	0.963442	−	0.267916i	$-0.0863349\pi$
$269$	1.65478e11	1.92688	0.963442	+	0.267916i	$0.0863349\pi$
$270$	0	0
$271$	5.47248e10	0.616343	0.308171	−	0.951331i	$-0.400283\pi$
$271$	5.47248e10	0.616343	0.308171	+	0.951331i	$0.400283\pi$
$272$	−9.56901e9	−0.106000
$273$	0	0
$274$	2.16125e10	0.231648
$275$	1.14037e11	1.20240
$276$	0	0
$277$	−2.55019e10	−0.260264	−0.130132	−	0.991497i	$-0.541540\pi$
$277$	−2.55019e10	−0.260264	−0.130132	+	0.991497i	$0.541540\pi$
$278$	−6.79651e10	−0.682472
$279$	0	0
$280$	7.30623e10	0.710367
$281$	2.44664e10	0.234095	0.117047	−	0.993126i	$-0.462657\pi$
$281$	2.44664e10	0.234095	0.117047	+	0.993126i	$0.462657\pi$
$282$	0	0
$283$	1.83938e11	1.70464	0.852318	−	0.523024i	$-0.175196\pi$
$283$	1.83938e11	1.70464	0.852318	+	0.523024i	$0.175196\pi$
$284$	7.08693e10	0.646436
$285$	0	0
$286$	6.66222e10	0.588806
$287$	−5.16469e10	−0.449341
$288$	0	0
$289$	−1.08385e11	−0.913963
$290$	2.60248e11	2.16071
$291$	0	0
$292$	6.55091e10	0.527325
$293$	−1.39840e11	−1.10848	−0.554241	−	0.832356i	$-0.686991\pi$
$293$	−1.39840e11	−1.10848	−0.554241	+	0.832356i	$0.686991\pi$
$294$	0	0
$295$	−4.43633e10	−0.341055
$296$	−1.48740e11	−1.12620
$297$	0	0
$298$	1.29698e10	0.0952706
$299$	1.93507e10	0.140015
$300$	0	0
$301$	−3.98463e10	−0.279794
$302$	−1.66349e11	−1.15077
$303$	0	0
$304$	4.63179e10	0.311041
$305$	−6.09966e10	−0.403605
$306$	0	0
$307$	−1.22633e11	−0.787922	−0.393961	−	0.919127i	$-0.628895\pi$
$307$	−1.22633e11	−0.787922	−0.393961	+	0.919127i	$0.628895\pi$
$308$	1.55353e10	0.0983650
$309$	0	0
$310$	−4.15689e10	−0.255647
$311$	1.44117e11	0.873564	0.436782	−	0.899567i	$-0.356118\pi$
$311$	1.44117e11	0.873564	0.436782	+	0.899567i	$0.356118\pi$
$312$	0	0
$313$	−2.74753e11	−1.61805	−0.809027	−	0.587771i	$-0.800006\pi$
$313$	−2.74753e11	−1.61805	−0.809027	+	0.587771i	$0.800006\pi$
$314$	1.35832e11	0.788528
$315$	0	0
$316$	−1.06225e11	−0.599288
$317$	1.23139e11	0.684904	0.342452	−	0.939535i	$-0.388743\pi$
$317$	1.23139e11	0.684904	0.342452	+	0.939535i	$0.388743\pi$
$318$	0	0
$319$	1.80344e11	0.975087
$320$	3.15550e11	1.68226
$321$	0	0
$322$	−5.68112e9	−0.0294498
$323$	−4.93865e10	−0.252463
$324$	0	0
$325$	5.51840e11	2.74371
$326$	−1.53273e11	−0.751601
$327$	0	0
$328$	−2.68399e11	−1.28041
$329$	−6.42126e10	−0.302161
$330$	0	0
$331$	3.37245e11	1.54426	0.772129	−	0.635466i	$-0.219192\pi$
$331$	3.37245e11	1.54426	0.772129	+	0.635466i	$0.219192\pi$
$332$	−1.75742e10	−0.0793881
$333$	0	0
$334$	1.49240e11	0.656184
$335$	−5.33049e11	−2.31242
$336$	0	0
$337$	−2.84144e11	−1.20006	−0.600032	−	0.799976i	$-0.704846\pi$
$337$	−2.84144e11	−1.20006	−0.600032	+	0.799976i	$0.704846\pi$
$338$	1.43258e11	0.597025
$339$	0	0
$340$	−5.58320e10	−0.226584
$341$	−2.88060e10	−0.115369
$342$	0	0
$343$	−1.38413e10	−0.0539949
$344$	−2.07073e11	−0.797280
$345$	0	0
$346$	−1.33429e11	−0.500503
$347$	−1.38776e11	−0.513846	−0.256923	−	0.966432i	$-0.582709\pi$
$347$	−1.38776e11	−0.513846	−0.256923	+	0.966432i	$0.582709\pi$
$348$	0	0
$349$	−1.52561e11	−0.550463	−0.275231	−	0.961378i	$-0.588754\pi$
$349$	−1.52561e11	−0.550463	−0.275231	+	0.961378i	$0.588754\pi$
$350$	−1.62013e11	−0.577091
$351$	0	0
$352$	1.36695e11	0.474582
$353$	−1.24628e11	−0.427199	−0.213599	−	0.976921i	$-0.568519\pi$
$353$	−1.24628e11	−0.427199	−0.213599	+	0.976921i	$0.568519\pi$
$354$	0	0
$355$	−7.62578e11	−2.54834
$356$	7.65336e10	0.252538
$357$	0	0
$358$	−7.76835e10	−0.249951
$359$	7.69379e10	0.244464	0.122232	−	0.992502i	$-0.460995\pi$
$359$	7.69379e10	0.244464	0.122232	+	0.992502i	$0.460995\pi$
$360$	0	0
$361$	−8.36371e10	−0.259189
$362$	−1.13347e10	−0.0346914
$363$	0	0
$364$	7.51772e10	0.224455
$365$	−7.04900e11	−2.07879
$366$	0	0
$367$	−4.36607e11	−1.25630	−0.628150	−	0.778092i	$-0.716187\pi$
$367$	−4.36607e11	−1.25630	−0.628150	+	0.778092i	$0.716187\pi$
$368$	−1.32695e10	−0.0377171
$369$	0	0
$370$	4.91095e11	1.36225
$371$	9.00353e10	0.246735
$372$	0	0
$373$	1.66545e11	0.445495	0.222747	−	0.974876i	$-0.428497\pi$
$373$	1.66545e11	0.445495	0.222747	+	0.974876i	$0.428497\pi$
$374$	4.87120e10	0.128740
$375$	0	0
$376$	−3.33700e11	−0.861015
$377$	8.72707e11	2.22501
$378$	0	0
$379$	4.10213e11	1.02125	0.510627	−	0.859803i	$-0.329413\pi$
$379$	4.10213e11	1.02125	0.510627	+	0.859803i	$0.329413\pi$
$380$	2.70249e11	0.664873
$381$	0	0
$382$	−1.70083e11	−0.408672
$383$	−7.01166e11	−1.66505	−0.832523	−	0.553990i	$-0.813105\pi$
$383$	−7.01166e11	−1.66505	−0.832523	+	0.553990i	$0.813105\pi$
$384$	0	0
$385$	−1.67165e11	−0.387768
$386$	−3.34261e11	−0.766377
$387$	0	0
$388$	1.66977e11	0.374037
$389$	−8.46752e11	−1.87492	−0.937461	−	0.348090i	$-0.886830\pi$
$389$	−8.46752e11	−1.87492	−0.937461	+	0.348090i	$0.886830\pi$
$390$	0	0
$391$	1.41486e10	0.0306138
$392$	−7.19304e10	−0.153860
$393$	0	0
$394$	1.81607e11	0.379665
$395$	1.14302e12	2.36247
$396$	0	0
$397$	8.75287e11	1.76845	0.884226	−	0.467059i	$-0.154687\pi$
$397$	8.75287e11	1.76845	0.884226	+	0.467059i	$0.154687\pi$
$398$	−2.67002e10	−0.0533385
$399$	0	0
$400$	−3.78416e11	−0.739094
$401$	2.47491e11	0.477980	0.238990	−	0.971022i	$-0.423184\pi$
$401$	2.47491e11	0.477980	0.238990	+	0.971022i	$0.423184\pi$
$402$	0	0
$403$	−1.39396e11	−0.263255
$404$	4.47461e10	0.0835679
$405$	0	0
$406$	−2.56216e11	−0.467993
$407$	3.40314e11	0.614759
$408$	0	0
$409$	−9.48426e10	−0.167590	−0.0837951	−	0.996483i	$-0.526704\pi$
$409$	−9.48426e10	−0.167590	−0.0837951	+	0.996483i	$0.526704\pi$
$410$	8.86172e11	1.54878
$411$	0	0
$412$	2.88858e11	0.493909
$413$	4.36760e10	0.0738699
$414$	0	0
$415$	1.89105e11	0.312958
$416$	6.61486e11	1.08293
$417$	0	0
$418$	−2.35786e11	−0.377767
$419$	−9.93237e11	−1.57431	−0.787154	−	0.616756i	$-0.788446\pi$
$419$	−9.93237e11	−1.57431	−0.787154	+	0.616756i	$0.788446\pi$
$420$	0	0
$421$	3.88328e11	0.602461	0.301230	−	0.953551i	$-0.402603\pi$
$421$	3.88328e11	0.602461	0.301230	+	0.953551i	$0.402603\pi$
$422$	7.50441e11	1.15189
$423$	0	0
$424$	4.67896e11	0.703077
$425$	4.03487e11	0.599901
$426$	0	0
$427$	6.00516e10	0.0874177
$428$	4.12351e11	0.593977
$429$	0	0
$430$	6.83693e11	0.964390
$431$	−2.08495e11	−0.291036	−0.145518	−	0.989356i	$-0.546485\pi$
$431$	−2.08495e11	−0.291036	−0.145518	+	0.989356i	$0.546485\pi$
$432$	0	0
$433$	−3.43270e11	−0.469289	−0.234645	−	0.972081i	$-0.575393\pi$
$433$	−3.43270e11	−0.469289	−0.234645	+	0.972081i	$0.575393\pi$
$434$	4.09249e10	0.0553712
$435$	0	0
$436$	5.24515e10	0.0695134
$437$	−6.84848e10	−0.0898314
$438$	0	0
$439$	5.98857e11	0.769543	0.384771	−	0.923012i	$-0.374280\pi$
$439$	5.98857e11	0.769543	0.384771	+	0.923012i	$0.374280\pi$
$440$	−8.68723e11	−1.10495
$441$	0	0
$442$	2.35724e11	0.293767
$443$	3.05169e11	0.376464	0.188232	−	0.982125i	$-0.439724\pi$
$443$	3.05169e11	0.376464	0.188232	+	0.982125i	$0.439724\pi$
$444$	0	0
$445$	−8.23528e11	−0.995539
$446$	4.06678e11	0.486680
$447$	0	0
$448$	−3.10661e11	−0.364364
$449$	−2.40802e11	−0.279610	−0.139805	−	0.990179i	$-0.544648\pi$
$449$	−2.40802e11	−0.279610	−0.139805	+	0.990179i	$0.544648\pi$
$450$	0	0
$451$	6.14090e11	0.698936
$452$	−3.44463e11	−0.388168
$453$	0	0
$454$	2.89855e9	0.00320206
$455$	−8.08932e11	−0.884832
$456$	0	0
$457$	2.36226e11	0.253341	0.126671	−	0.991945i	$-0.459571\pi$
$457$	2.36226e11	0.253341	0.126671	+	0.991945i	$0.459571\pi$
$458$	−1.88819e11	−0.200517
$459$	0	0
$460$	−7.74229e10	−0.0806230
$461$	1.17120e12	1.20775	0.603873	−	0.797081i	$-0.293624\pi$
$461$	1.17120e12	1.20775	0.603873	+	0.797081i	$0.293624\pi$
$462$	0	0
$463$	−1.78934e12	−1.80958	−0.904791	−	0.425856i	$-0.859973\pi$
$463$	−1.78934e12	−1.80958	−0.904791	+	0.425856i	$0.859973\pi$
$464$	−5.98446e11	−0.599369
$465$	0	0
$466$	−1.10559e11	−0.108607
$467$	3.81202e11	0.370877	0.185438	−	0.982656i	$-0.440630\pi$
$467$	3.81202e11	0.370877	0.185438	+	0.982656i	$0.440630\pi$
$468$	0	0
$469$	5.24791e11	0.500851
$470$	1.10178e12	1.04148
$471$	0	0
$472$	2.26975e11	0.210494
$473$	4.73778e11	0.435211
$474$	0	0
$475$	−1.95304e12	−1.76031
$476$	5.49671e10	0.0490762
$477$	0	0
$478$	1.53486e11	0.134476
$479$	1.71146e12	1.48545	0.742725	−	0.669597i	$-0.233533\pi$
$479$	1.71146e12	1.48545	0.742725	+	0.669597i	$0.233533\pi$
$480$	0	0
$481$	1.64682e12	1.40279
$482$	−9.06111e11	−0.764663
$483$	0	0
$484$	3.49701e11	0.289663
$485$	−1.79673e12	−1.47450
$486$	0	0
$487$	7.38713e11	0.595108	0.297554	−	0.954705i	$-0.403829\pi$
$487$	7.38713e11	0.595108	0.297554	+	0.954705i	$0.403829\pi$
$488$	3.12076e11	0.249099
$489$	0	0
$490$	2.37492e11	0.186109
$491$	−1.52117e12	−1.18116	−0.590582	−	0.806978i	$-0.701102\pi$
$491$	−1.52117e12	−1.18116	−0.590582	+	0.806978i	$0.701102\pi$
$492$	0	0
$493$	6.38095e11	0.486490
$494$	−1.14100e12	−0.862012
$495$	0	0
$496$	9.55887e10	0.0709151
$497$	7.50764e11	0.551950
$498$	0	0
$499$	−1.67720e12	−1.21097	−0.605484	−	0.795857i	$-0.707021\pi$
$499$	−1.67720e12	−1.21097	−0.605484	+	0.795857i	$0.707021\pi$
$500$	−1.12837e12	−0.807392
$501$	0	0
$502$	−6.63284e11	−0.466158
$503$	−2.93328e11	−0.204314	−0.102157	−	0.994768i	$-0.532574\pi$
$503$	−2.93328e11	−0.204314	−0.102157	+	0.994768i	$0.532574\pi$
$504$	0	0
$505$	−4.81484e11	−0.329436
$506$	6.75494e10	0.0458083
$507$	0	0
$508$	−9.54065e11	−0.635611
$509$	2.87498e12	1.89848	0.949238	−	0.314559i	$-0.101857\pi$
$509$	2.87498e12	1.89848	0.949238	+	0.314559i	$0.101857\pi$
$510$	0	0
$511$	6.93980e11	0.450249
$512$	−1.05881e12	−0.680930
$513$	0	0
$514$	1.30205e11	0.0822796
$515$	−3.10821e12	−1.94706
$516$	0	0
$517$	7.63497e11	0.470002
$518$	−4.83487e11	−0.295053
$519$	0	0
$520$	−4.20386e12	−2.52135
$521$	−1.69333e12	−1.00687	−0.503434	−	0.864034i	$-0.667930\pi$
$521$	−1.69333e12	−1.00687	−0.503434	+	0.864034i	$0.667930\pi$
$522$	0	0
$523$	9.48465e11	0.554324	0.277162	−	0.960823i	$-0.410606\pi$
$523$	9.48465e11	0.554324	0.277162	+	0.960823i	$0.410606\pi$
$524$	−9.34075e11	−0.541241
$525$	0	0
$526$	−6.18058e11	−0.352041
$527$	−1.01922e11	−0.0575597
$528$	0	0
$529$	−1.78153e12	−0.989107
$530$	−1.54485e12	−0.850442
$531$	0	0
$532$	−2.66063e11	−0.144006
$533$	2.97166e12	1.59488
$534$	0	0
$535$	−4.43704e12	−2.34154
$536$	2.72724e12	1.42719
$537$	0	0
$538$	2.79533e12	1.43851
$539$	1.64575e11	0.0839875
$540$	0	0
$541$	2.60488e12	1.30738	0.653688	−	0.756764i	$-0.273221\pi$
$541$	2.60488e12	1.30738	0.653688	+	0.756764i	$0.273221\pi$
$542$	9.24436e11	0.460129
$543$	0	0
$544$	4.83657e11	0.236778
$545$	−5.64396e11	−0.274031
$546$	0	0
$547$	2.01576e12	0.962711	0.481356	−	0.876525i	$-0.340145\pi$
$547$	2.01576e12	0.962711	0.481356	+	0.876525i	$0.340145\pi$
$548$	−2.89974e11	−0.137356
$549$	0	0
$550$	1.92636e12	0.897648
$551$	−3.08863e12	−1.42753
$552$	0	0
$553$	−1.12531e12	−0.511693
$554$	−4.30790e11	−0.194300
$555$	0	0
$556$	9.11886e11	0.404673
$557$	3.04194e12	1.33907	0.669534	−	0.742782i	$-0.266494\pi$
$557$	3.04194e12	1.33907	0.669534	+	0.742782i	$0.266494\pi$
$558$	0	0
$559$	2.29267e12	0.993091
$560$	5.54713e11	0.238354
$561$	0	0
$562$	4.13297e11	0.174763
$563$	−4.23912e12	−1.77823	−0.889115	−	0.457684i	$-0.848679\pi$
$563$	−4.23912e12	−1.77823	−0.889115	+	0.457684i	$0.848679\pi$
$564$	0	0
$565$	3.70654e12	1.53021
$566$	3.10716e12	1.27259
$567$	0	0
$568$	3.90157e12	1.57280
$569$	−1.34119e11	−0.0536397	−0.0268199	−	0.999640i	$-0.508538\pi$
$569$	−1.34119e11	−0.0536397	−0.0268199	+	0.999640i	$0.508538\pi$
$570$	0	0
$571$	−1.51210e11	−0.0595277	−0.0297638	−	0.999557i	$-0.509476\pi$
$571$	−1.51210e11	−0.0595277	−0.0297638	+	0.999557i	$0.509476\pi$
$572$	−8.93868e11	−0.349133
$573$	0	0
$574$	−8.72443e11	−0.335454
$575$	5.59520e11	0.213457
$576$	0	0
$577$	−1.84681e12	−0.693633	−0.346817	−	0.937933i	$-0.612737\pi$
$577$	−1.84681e12	−0.693633	−0.346817	+	0.937933i	$0.612737\pi$
$578$	−1.83089e12	−0.682317
$579$	0	0
$580$	−3.49174e12	−1.28120
$581$	−1.86175e11	−0.0677843
$582$	0	0
$583$	−1.07053e12	−0.383788
$584$	3.60648e12	1.28300
$585$	0	0
$586$	−2.36225e12	−0.827535
$587$	2.97730e12	1.03503	0.517513	−	0.855675i	$-0.326858\pi$
$587$	2.97730e12	1.03503	0.517513	+	0.855675i	$0.326858\pi$
$588$	0	0
$589$	4.93342e11	0.168900
$590$	−7.49404e11	−0.254614
$591$	0	0
$592$	−1.12928e12	−0.377881
$593$	−1.06093e12	−0.352322	−0.176161	−	0.984361i	$-0.556368\pi$
$593$	−1.06093e12	−0.352322	−0.176161	+	0.984361i	$0.556368\pi$
$594$	0	0
$595$	−5.91465e11	−0.193465
$596$	−1.74015e11	−0.0564909
$597$	0	0
$598$	3.26880e11	0.104528
$599$	4.53108e12	1.43807	0.719037	−	0.694972i	$-0.244583\pi$
$599$	4.53108e12	1.43807	0.719037	+	0.694972i	$0.244583\pi$
$600$	0	0
$601$	−1.05588e12	−0.330127	−0.165063	−	0.986283i	$-0.552783\pi$
$601$	−1.05588e12	−0.330127	−0.165063	+	0.986283i	$0.552783\pi$
$602$	−6.73101e11	−0.208880
$603$	0	0
$604$	2.23190e12	0.682351
$605$	−3.76290e12	−1.14189
$606$	0	0
$607$	−3.25042e12	−0.971831	−0.485916	−	0.874006i	$-0.661514\pi$
$607$	−3.25042e12	−0.971831	−0.485916	+	0.874006i	$0.661514\pi$
$608$	−2.34109e12	−0.694788
$609$	0	0
$610$	−1.03038e12	−0.301310
$611$	3.69466e12	1.07248
$612$	0	0
$613$	−2.48670e12	−0.711299	−0.355649	−	0.934619i	$-0.615740\pi$
$613$	−2.48670e12	−0.711299	−0.355649	+	0.934619i	$0.615740\pi$
$614$	−2.07156e12	−0.588221
$615$	0	0
$616$	8.55264e11	0.239325
$617$	4.06622e12	1.12956	0.564778	−	0.825243i	$-0.308962\pi$
$617$	4.06622e12	1.12956	0.564778	+	0.825243i	$0.308962\pi$
$618$	0	0
$619$	−4.24730e12	−1.16280	−0.581400	−	0.813618i	$-0.697495\pi$
$619$	−4.24730e12	−1.16280	−0.581400	+	0.813618i	$0.697495\pi$
$620$	5.57728e11	0.151586
$621$	0	0
$622$	2.43450e12	0.652157
$623$	8.10769e11	0.215626
$624$	0	0
$625$	4.33978e12	1.13765
$626$	−4.64125e12	−1.20796
$627$	0	0
$628$	−1.82245e12	−0.467559
$629$	1.20410e12	0.306715
$630$	0	0
$631$	1.44130e12	0.361929	0.180965	−	0.983490i	$-0.442078\pi$
$631$	1.44130e12	0.361929	0.180965	+	0.983490i	$0.442078\pi$
$632$	−5.84803e12	−1.45808
$633$	0	0
$634$	2.08012e12	0.511314
$635$	1.02661e13	2.50566
$636$	0	0
$637$	7.96400e11	0.191648
$638$	3.04645e12	0.727949
$639$	0	0
$640$	−6.48430e11	−0.152775
$641$	−6.00980e12	−1.40604	−0.703022	−	0.711168i	$-0.748167\pi$
$641$	−6.00980e12	−1.40604	−0.703022	+	0.711168i	$0.748167\pi$
$642$	0	0
$643$	2.09069e12	0.482327	0.241163	−	0.970485i	$-0.422471\pi$
$643$	2.09069e12	0.482327	0.241163	+	0.970485i	$0.422471\pi$
$644$	7.62234e10	0.0174623
$645$	0	0
$646$	−8.34259e11	−0.188475
$647$	1.34894e12	0.302638	0.151319	−	0.988485i	$-0.451648\pi$
$647$	1.34894e12	0.302638	0.151319	+	0.988485i	$0.451648\pi$
$648$	0	0
$649$	−5.19314e11	−0.114902
$650$	9.32192e12	2.04831
$651$	0	0
$652$	2.05646e12	0.445663
$653$	7.38295e12	1.58899	0.794494	−	0.607272i	$-0.207736\pi$
$653$	7.38295e12	1.58899	0.794494	+	0.607272i	$0.207736\pi$
$654$	0	0
$655$	1.00510e13	2.13364
$656$	−2.03777e12	−0.429624
$657$	0	0
$658$	−1.08471e12	−0.225578
$659$	−3.34345e12	−0.690574	−0.345287	−	0.938497i	$-0.612218\pi$
$659$	−3.34345e12	−0.690574	−0.345287	+	0.938497i	$0.612218\pi$
$660$	0	0
$661$	8.14808e12	1.66016	0.830078	−	0.557648i	$-0.188296\pi$
$661$	8.14808e12	1.66016	0.830078	+	0.557648i	$0.188296\pi$
$662$	5.69690e12	1.15286
$663$	0	0
$664$	−9.67516e11	−0.193153
$665$	2.86293e12	0.567692
$666$	0	0
$667$	8.84853e11	0.173103
$668$	−2.00235e12	−0.389085
$669$	0	0
$670$	−9.00451e12	−1.72633
$671$	−7.14023e11	−0.135976
$672$	0	0
$673$	−6.60403e12	−1.24091	−0.620457	−	0.784241i	$-0.713053\pi$
$673$	−6.60403e12	−1.24091	−0.620457	+	0.784241i	$0.713053\pi$
$674$	−4.79989e12	−0.895905
$675$	0	0
$676$	−1.92208e12	−0.354007
$677$	−3.16321e12	−0.578735	−0.289367	−	0.957218i	$-0.593445\pi$
$677$	−3.16321e12	−0.578735	−0.289367	+	0.957218i	$0.593445\pi$
$678$	0	0
$679$	1.76890e12	0.319366
$680$	−3.07373e12	−0.551283
$681$	0	0
$682$	−4.86603e11	−0.0861282
$683$	−7.85876e12	−1.38185	−0.690925	−	0.722927i	$-0.742796\pi$
$683$	−7.85876e12	−1.38185	−0.690925	+	0.722927i	$0.742796\pi$
$684$	0	0
$685$	3.12022e12	0.541475
$686$	−2.33813e11	−0.0403098
$687$	0	0
$688$	−1.57217e12	−0.267517
$689$	−5.18045e12	−0.875752
$690$	0	0
$691$	3.21525e12	0.536492	0.268246	−	0.963350i	$-0.413556\pi$
$691$	3.21525e12	0.536492	0.268246	+	0.963350i	$0.413556\pi$
$692$	1.79021e12	0.296774
$693$	0	0
$694$	−2.34427e12	−0.383611
$695$	−9.81221e12	−1.59527
$696$	0	0
$697$	2.17278e12	0.348713
$698$	−2.57712e12	−0.410947
$699$	0	0
$700$	2.17373e12	0.342187
$701$	6.07789e12	0.950652	0.475326	−	0.879810i	$-0.342330\pi$
$701$	6.07789e12	0.950652	0.475326	+	0.879810i	$0.342330\pi$
$702$	0	0
$703$	−5.82834e12	−0.900007
$704$	3.69381e12	0.566758
$705$	0	0
$706$	−2.10528e12	−0.318924
$707$	4.74025e11	0.0713532
$708$	0	0
$709$	−6.79921e12	−1.01053	−0.505266	−	0.862963i	$-0.668606\pi$
$709$	−6.79921e12	−1.01053	−0.505266	+	0.862963i	$0.668606\pi$
$710$	−1.28818e13	−1.90245
$711$	0	0
$712$	4.21341e12	0.614432
$713$	−1.41336e11	−0.0204809
$714$	0	0
$715$	9.61833e12	1.37633
$716$	1.04228e12	0.148209
$717$	0	0
$718$	1.29967e12	0.182504
$719$	−8.63238e11	−0.120462	−0.0602311	−	0.998184i	$-0.519184\pi$
$719$	−8.63238e11	−0.120462	−0.0602311	+	0.998184i	$0.519184\pi$
$720$	0	0
$721$	3.06006e12	0.421717
$722$	−1.41283e12	−0.193497
$723$	0	0
$724$	1.52078e11	0.0205703
$725$	2.52341e13	3.39208
$726$	0	0
$727$	−9.34730e12	−1.24103	−0.620514	−	0.784195i	$-0.713076\pi$
$727$	−9.34730e12	−1.24103	−0.620514	+	0.784195i	$0.713076\pi$
$728$	4.13873e12	0.546105
$729$	0	0
$730$	−1.19075e13	−1.55191
$731$	1.67633e12	0.217135
$732$	0	0
$733$	−1.12045e13	−1.43359	−0.716793	−	0.697286i	$-0.754391\pi$
$733$	−1.12045e13	−1.43359	−0.716793	+	0.697286i	$0.754391\pi$
$734$	−7.37536e12	−0.937887
$735$	0	0
$736$	6.70692e11	0.0842506
$737$	−6.23985e12	−0.779059
$738$	0	0
$739$	−4.55769e12	−0.562140	−0.281070	−	0.959687i	$-0.590689\pi$
$739$	−4.55769e12	−0.562140	−0.281070	+	0.959687i	$0.590689\pi$
$740$	−6.58900e12	−0.807750
$741$	0	0
$742$	1.52092e12	0.184199
$743$	−3.57016e12	−0.429772	−0.214886	−	0.976639i	$-0.568938\pi$
$743$	−3.57016e12	−0.429772	−0.214886	+	0.976639i	$0.568938\pi$
$744$	0	0
$745$	1.87246e12	0.222695
$746$	2.81336e12	0.332583
$747$	0	0
$748$	−6.53567e11	−0.0763366
$749$	4.36830e12	0.507159
$750$	0	0
$751$	−2.38313e12	−0.273380	−0.136690	−	0.990614i	$-0.543646\pi$
$751$	−2.38313e12	−0.273380	−0.136690	+	0.990614i	$0.543646\pi$
$752$	−2.53356e12	−0.288902
$753$	0	0
$754$	1.47422e13	1.66108
$755$	−2.40160e13	−2.68992
$756$	0	0
$757$	4.96674e12	0.549718	0.274859	−	0.961484i	$-0.411369\pi$
$757$	4.96674e12	0.549718	0.274859	+	0.961484i	$0.411369\pi$
$758$	6.92951e12	0.762414
$759$	0	0
$760$	1.48781e13	1.61765
$761$	−1.01660e13	−1.09880	−0.549401	−	0.835559i	$-0.685144\pi$
$761$	−1.01660e13	−1.09880	−0.549401	+	0.835559i	$0.685144\pi$
$762$	0	0
$763$	5.55652e11	0.0593530
$764$	2.28200e12	0.242323
$765$	0	0
$766$	−1.18444e13	−1.24304
$767$	−2.51303e12	−0.262191
$768$	0	0
$769$	−4.53519e12	−0.467656	−0.233828	−	0.972278i	$-0.575125\pi$
$769$	−4.53519e12	−0.467656	−0.233828	+	0.972278i	$0.575125\pi$
$770$	−2.82382e12	−0.289487
$771$	0	0
$772$	4.48476e12	0.454424
$773$	3.64760e12	0.367451	0.183725	−	0.982978i	$-0.441184\pi$
$773$	3.64760e12	0.367451	0.183725	+	0.982978i	$0.441184\pi$
$774$	0	0
$775$	−4.03059e12	−0.401339
$776$	9.19261e12	0.910041
$777$	0	0
$778$	−1.43037e13	−1.39972
$779$	−1.05171e13	−1.02324
$780$	0	0
$781$	−8.92670e12	−0.858542
$782$	2.39004e11	0.0228547
$783$	0	0
$784$	−5.46120e11	−0.0516256
$785$	1.96102e13	1.84318
$786$	0	0
$787$	−2.68084e12	−0.249106	−0.124553	−	0.992213i	$-0.539750\pi$
$787$	−2.68084e12	−0.249106	−0.124553	+	0.992213i	$0.539750\pi$
$788$	−2.43662e12	−0.225123
$789$	0	0
$790$	1.93084e13	1.76370
$791$	−3.64912e12	−0.331431
$792$	0	0
$793$	−3.45525e12	−0.310277
$794$	1.47857e13	1.32023
$795$	0	0
$796$	3.58235e11	0.0316271
$797$	9.88359e12	0.867665	0.433833	−	0.900994i	$-0.357161\pi$
$797$	9.88359e12	0.867665	0.433833	+	0.900994i	$0.357161\pi$
$798$	0	0
$799$	2.70142e12	0.234494
$800$	1.91267e13	1.65095
$801$	0	0
$802$	4.18073e12	0.356835
$803$	−8.25153e12	−0.700349
$804$	0	0
$805$	−8.20190e11	−0.0688388
$806$	−2.35474e12	−0.196533
$807$	0	0
$808$	2.46341e12	0.203323
$809$	−1.62405e13	−1.33300	−0.666502	−	0.745503i	$-0.732209\pi$
$809$	−1.62405e13	−1.33300	−0.666502	+	0.745503i	$0.732209\pi$
$810$	0	0
$811$	−2.28548e13	−1.85517	−0.927584	−	0.373614i	$-0.878118\pi$
$811$	−2.28548e13	−1.85517	−0.927584	+	0.373614i	$0.878118\pi$
$812$	3.43764e12	0.277497
$813$	0	0
$814$	5.74873e12	0.458947
$815$	−2.21282e13	−1.75686
$816$	0	0
$817$	−8.11410e12	−0.637149
$818$	−1.60212e12	−0.125114
$819$	0	0
$820$	−1.18897e13	−0.918353
$821$	−1.65900e13	−1.27439	−0.637193	−	0.770704i	$-0.719905\pi$
$821$	−1.65900e13	−1.27439	−0.637193	+	0.770704i	$0.719905\pi$
$822$	0	0
$823$	9.87616e12	0.750393	0.375197	−	0.926945i	$-0.377575\pi$
$823$	9.87616e12	0.750393	0.375197	+	0.926945i	$0.377575\pi$
$824$	1.59025e13	1.20169
$825$	0	0
$826$	7.37794e11	0.0551474
$827$	3.15367e12	0.234445	0.117223	−	0.993106i	$-0.462601\pi$
$827$	3.15367e12	0.234445	0.117223	+	0.993106i	$0.462601\pi$
$828$	0	0
$829$	2.02328e13	1.48785	0.743927	−	0.668261i	$-0.232961\pi$
$829$	2.02328e13	1.48785	0.743927	+	0.668261i	$0.232961\pi$
$830$	3.19444e12	0.233638
$831$	0	0
$832$	1.78748e13	1.29326
$833$	5.82302e11	0.0419030
$834$	0	0
$835$	2.15459e13	1.53383
$836$	3.16353e12	0.223998
$837$	0	0
$838$	−1.67782e13	−1.17530
$839$	2.38915e13	1.66462	0.832310	−	0.554311i	$-0.187018\pi$
$839$	2.38915e13	1.66462	0.832310	+	0.554311i	$0.187018\pi$
$840$	0	0
$841$	2.53993e13	1.75081
$842$	6.55980e12	0.449766
$843$	0	0
$844$	−1.00686e13	−0.683015
$845$	2.06823e13	1.39554
$846$	0	0
$847$	3.70461e12	0.247324
$848$	3.55242e12	0.235908
$849$	0	0
$850$	6.81588e12	0.447855
$851$	1.66974e12	0.109136
$852$	0	0
$853$	1.68078e13	1.08703	0.543514	−	0.839400i	$-0.317094\pi$
$853$	1.68078e13	1.08703	0.543514	+	0.839400i	$0.317094\pi$
$854$	1.01442e12	0.0652615
$855$	0	0
$856$	2.27012e13	1.44516
$857$	6.68278e12	0.423198	0.211599	−	0.977357i	$-0.432133\pi$
$857$	6.68278e12	0.423198	0.211599	+	0.977357i	$0.432133\pi$
$858$	0	0
$859$	2.04541e13	1.28177	0.640887	−	0.767635i	$-0.278567\pi$
$859$	2.04541e13	1.28177	0.640887	+	0.767635i	$0.278567\pi$
$860$	−9.17308e12	−0.571837
$861$	0	0
$862$	−3.52198e12	−0.217272
$863$	1.87505e13	1.15071	0.575353	−	0.817905i	$-0.304865\pi$
$863$	1.87505e13	1.15071	0.575353	+	0.817905i	$0.304865\pi$
$864$	0	0
$865$	−1.92632e13	−1.16992
$866$	−5.79867e12	−0.350347
$867$	0	0
$868$	−5.49088e11	−0.0328324
$869$	1.33801e13	0.795924
$870$	0	0
$871$	−3.01954e13	−1.77771
$872$	2.88762e12	0.169128
$873$	0	0
$874$	−1.15688e12	−0.0670634
$875$	−1.19535e13	−0.689380
$876$	0	0
$877$	2.02759e13	1.15740	0.578699	−	0.815542i	$-0.303561\pi$
$877$	2.02759e13	1.15740	0.578699	+	0.815542i	$0.303561\pi$
$878$	1.01162e13	0.574500
$879$	0	0
$880$	−6.59563e12	−0.370753
$881$	2.17613e13	1.21701	0.608505	−	0.793550i	$-0.291770\pi$
$881$	2.17613e13	1.21701	0.608505	+	0.793550i	$0.291770\pi$
$882$	0	0
$883$	−3.44540e13	−1.90729	−0.953645	−	0.300933i	$-0.902702\pi$
$883$	−3.44540e13	−1.90729	−0.953645	+	0.300933i	$0.902702\pi$
$884$	−3.16270e12	−0.174190
$885$	0	0
$886$	5.15505e12	0.281048
$887$	−5.98069e12	−0.324410	−0.162205	−	0.986757i	$-0.551861\pi$
$887$	−5.98069e12	−0.324410	−0.162205	+	0.986757i	$0.551861\pi$
$888$	0	0
$889$	−1.01070e13	−0.542707
$890$	−1.39114e13	−0.743217
$891$	0	0
$892$	−5.45638e12	−0.288578
$893$	−1.30759e13	−0.688084
$894$	0	0
$895$	−1.12153e13	−0.584260
$896$	6.38384e11	0.0330900
$897$	0	0
$898$	−4.06774e12	−0.208742
$899$	−6.37418e12	−0.325466
$900$	0	0
$901$	−3.78778e12	−0.191480
$902$	1.03735e13	0.521789
$903$	0	0
$904$	−1.89637e13	−0.944422
$905$	−1.63641e12	−0.0810910
$906$	0	0
$907$	−2.51683e12	−0.123487	−0.0617434	−	0.998092i	$-0.519666\pi$
$907$	−2.51683e12	−0.123487	−0.0617434	+	0.998092i	$0.519666\pi$
$908$	−3.88897e10	−0.00189867
$909$	0	0
$910$	−1.36648e13	−0.660569
$911$	−3.96021e13	−1.90496	−0.952478	−	0.304607i	$-0.901475\pi$
$911$	−3.96021e13	−1.90496	−0.952478	+	0.304607i	$0.901475\pi$
$912$	0	0
$913$	2.21365e12	0.105437
$914$	3.99044e12	0.189131
$915$	0	0
$916$	2.53338e12	0.118897
$917$	−9.89525e12	−0.462131
$918$	0	0
$919$	−4.00850e13	−1.85380	−0.926899	−	0.375310i	$-0.877536\pi$
$919$	−4.00850e13	−1.85380	−0.926899	+	0.375310i	$0.877536\pi$
$920$	−4.26237e12	−0.196158
$921$	0	0
$922$	1.97844e13	0.901640
$923$	−4.31975e13	−1.95907
$924$	0	0
$925$	4.76174e13	2.13859
$926$	−3.02263e13	−1.35094
$927$	0	0
$928$	3.02479e13	1.33884
$929$	8.38470e12	0.369332	0.184666	−	0.982801i	$-0.440880\pi$
$929$	8.38470e12	0.369332	0.184666	+	0.982801i	$0.440880\pi$
$930$	0	0
$931$	−2.81857e12	−0.122958
$932$	1.48336e12	0.0643986
$933$	0	0
$934$	6.43944e12	0.276877
$935$	7.03261e12	0.300929
$936$	0	0
$937$	2.33983e12	0.0991645	0.0495822	−	0.998770i	$-0.484211\pi$
$937$	2.33983e12	0.0991645	0.0495822	+	0.998770i	$0.484211\pi$
$938$	8.86501e12	0.373909
$939$	0	0
$940$	−1.47825e13	−0.617550
$941$	6.45893e12	0.268539	0.134270	−	0.990945i	$-0.457131\pi$
$941$	6.45893e12	0.268539	0.134270	+	0.990945i	$0.457131\pi$
$942$	0	0
$943$	3.01302e12	0.124079
$944$	1.72327e12	0.0706285
$945$	0	0
$946$	8.00327e12	0.324906
$947$	2.43323e13	0.983123	0.491561	−	0.870843i	$-0.336426\pi$
$947$	2.43323e13	0.983123	0.491561	+	0.870843i	$0.336426\pi$
$948$	0	0
$949$	−3.99302e13	−1.59810
$950$	−3.29916e13	−1.31416
$951$	0	0
$952$	3.02611e12	0.119404
$953$	−2.50351e12	−0.0983177	−0.0491589	−	0.998791i	$-0.515654\pi$
$953$	−2.50351e12	−0.0983177	−0.0491589	+	0.998791i	$0.515654\pi$
$954$	0	0
$955$	−2.45551e13	−0.955269
$956$	−2.05932e12	−0.0797377
$957$	0	0
$958$	2.89108e13	1.10896
$959$	−3.07189e12	−0.117279
$960$	0	0
$961$	−2.54215e13	−0.961492
$962$	2.78188e13	1.04725
$963$	0	0
$964$	1.21573e13	0.453408
$965$	−4.82576e13	−1.79140
$966$	0	0
$967$	2.19887e13	0.808686	0.404343	−	0.914607i	$-0.367500\pi$
$967$	2.19887e13	0.808686	0.404343	+	0.914607i	$0.367500\pi$
$968$	1.92521e13	0.704757
$969$	0	0
$970$	−3.03512e13	−1.10079
$971$	9.07743e12	0.327700	0.163850	−	0.986485i	$-0.447609\pi$
$971$	9.07743e12	0.327700	0.163850	+	0.986485i	$0.447609\pi$
$972$	0	0
$973$	9.66019e12	0.345524
$974$	1.24787e13	0.444276
$975$	0	0
$976$	2.36939e12	0.0835818
$977$	−2.73152e13	−0.959134	−0.479567	−	0.877505i	$-0.659206\pi$
$977$	−2.73152e13	−0.959134	−0.479567	+	0.877505i	$0.659206\pi$
$978$	0	0
$979$	−9.64018e12	−0.335400
$980$	−3.18643e12	−0.110354
$981$	0	0
$982$	−2.56962e13	−0.881795
$983$	−1.07541e13	−0.367351	−0.183676	−	0.982987i	$-0.558800\pi$
$983$	−1.07541e13	−0.367351	−0.183676	+	0.982987i	$0.558800\pi$
$984$	0	0
$985$	2.62188e13	0.887464
$986$	1.07790e13	0.363188
$987$	0	0
$988$	1.53087e13	0.511131
$989$	2.32458e12	0.0772612
$990$	0	0
$991$	−2.06047e13	−0.678633	−0.339317	−	0.940672i	$-0.610196\pi$
$991$	−2.06047e13	−0.678633	−0.339317	+	0.940672i	$0.610196\pi$
$992$	−4.83144e12	−0.158407
$993$	0	0
$994$	1.26822e13	0.412057
$995$	−3.85474e12	−0.124678
$996$	0	0
$997$	2.30380e13	0.738444	0.369222	−	0.929341i	$-0.379624\pi$
$997$	2.30380e13	0.738444	0.369222	+	0.929341i	$0.379624\pi$
$998$	−2.83320e13	−0.904046
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.10.a.d.1.2		2
3.2	odd	2		7.10.a.a.1.1	✓	2
12.11	even	2		112.10.a.e.1.1		2
15.2	even	4		175.10.b.b.99.1		4
15.8	even	4		175.10.b.b.99.4		4
15.14	odd	2		175.10.a.b.1.2		2
21.2	odd	6		49.10.c.c.18.2		4
21.5	even	6		49.10.c.b.18.2		4
21.11	odd	6		49.10.c.c.30.2		4
21.17	even	6		49.10.c.b.30.2		4
21.20	even	2		49.10.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.a.1.1	✓	2	3.2	odd	2
49.10.a.b.1.1		2	21.20	even	2
49.10.c.b.18.2		4	21.5	even	6
49.10.c.b.30.2		4	21.17	even	6
49.10.c.c.18.2		4	21.2	odd	6
49.10.c.c.30.2		4	21.11	odd	6
63.10.a.d.1.2		2	1.1	even	1	trivial
112.10.a.e.1.1		2	12.11	even	2
175.10.a.b.1.2		2	15.14	odd	2
175.10.b.b.99.1		4	15.2	even	4
175.10.b.b.99.4		4	15.8	even	4

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	63.a (trivial)

\(f(q)\)	\(=\)	\(q+16.8924 q^{2} -226.645 q^{4} +2438.78 q^{5} -2401.00 q^{7} -12477.5 q^{8} +O(q^{10})\)	\(q+16.8924 q^{2} -226.645 q^{4} +2438.78 q^{5} -2401.00 q^{7} -12477.5 q^{8} +41197.0 q^{10} +28548.3 q^{11} +138149. q^{13} -40558.8 q^{14} -94733.5 q^{16} +101010. q^{17} -488928. q^{19} -552739. q^{20} +482250. q^{22} +140071. q^{23} +3.99453e6 q^{25} +2.33367e6 q^{26} +544175. q^{28} +6.31716e6 q^{29} -1.00903e6 q^{31} +4.78821e6 q^{32} +1.70630e6 q^{34} -5.85552e6 q^{35} +1.19206e7 q^{37} -8.25919e6 q^{38} -3.04300e7 q^{40} +2.15106e7 q^{41} +1.65957e7 q^{43} -6.47033e6 q^{44} +2.36615e6 q^{46} +2.67441e7 q^{47} +5.76480e6 q^{49} +6.74774e7 q^{50} -3.13108e7 q^{52} -3.74991e7 q^{53} +6.96230e7 q^{55} +2.99585e7 q^{56} +1.06712e8 q^{58} -1.81907e7 q^{59} -2.50111e7 q^{61} -1.70449e7 q^{62} +1.29388e8 q^{64} +3.36915e8 q^{65} -2.18572e8 q^{67} -2.28934e7 q^{68} -9.89140e7 q^{70} -3.12688e8 q^{71} -2.89038e8 q^{73} +2.01369e8 q^{74} +1.10813e8 q^{76} -6.85444e7 q^{77} +4.68685e8 q^{79} -2.31034e8 q^{80} +3.63366e8 q^{82} +7.75407e7 q^{83} +2.46341e8 q^{85} +2.80342e8 q^{86} -3.56212e8 q^{88} -3.37680e8 q^{89} -3.31695e8 q^{91} -3.17465e7 q^{92} +4.51773e8 q^{94} -1.19239e9 q^{95} -7.36733e8 q^{97} +9.73816e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} - 620 q^{4} + 2238 q^{5} - 4802 q^{7} - 2616 q^{8}+O(q^{10}) \) 2 * q + 6 * q^2 - 620 * q^4 + 2238 * q^5 - 4802 * q^7 - 2616 * q^8	\( 2 q + 6 q^{2} - 620 q^{4} + 2238 q^{5} - 4802 q^{7} - 2616 q^{8} + 43384 q^{10} - 35316 q^{11} - 26530 q^{13} - 14406 q^{14} - 752 q^{16} + 463920 q^{17} - 925426 q^{19} - 473760 q^{20} + 1177888 q^{22} - 778128 q^{23} + 2081722 q^{25} + 4127424 q^{26} + 1488620 q^{28} + 10003584 q^{29} + 2467260 q^{31} - 1284576 q^{32} - 2246676 q^{34} - 5373438 q^{35} + 30735552 q^{37} - 3504660 q^{38} - 32409984 q^{40} + 19103448 q^{41} + 4065100 q^{43} + 18650976 q^{44} + 12367584 q^{46} + 82195020 q^{47} + 11529602 q^{49} + 88312626 q^{50} + 33466384 q^{52} + 55189812 q^{53} + 82445816 q^{55} + 6281016 q^{56} + 66558004 q^{58} + 7069218 q^{59} + 44316386 q^{61} - 54910200 q^{62} + 147417152 q^{64} + 369979260 q^{65} - 241921336 q^{67} - 165645816 q^{68} - 104164984 q^{70} - 206493816 q^{71} - 499153188 q^{73} - 3571524 q^{74} + 282511768 q^{76} + 84793716 q^{77} + 468535096 q^{79} - 249904128 q^{80} + 389586092 q^{82} - 444023958 q^{83} + 173475060 q^{85} + 416830608 q^{86} - 986010816 q^{88} - 636267396 q^{89} + 63698530 q^{91} + 329431488 q^{92} - 152223192 q^{94} - 1104747984 q^{95} - 1632716064 q^{97} + 34588806 q^{98}+O(q^{100}) \) 2 * q + 6 * q^2 - 620 * q^4 + 2238 * q^5 - 4802 * q^7 - 2616 * q^8 + 43384 * q^10 - 35316 * q^11 - 26530 * q^13 - 14406 * q^14 - 752 * q^16 + 463920 * q^17 - 925426 * q^19 - 473760 * q^20 + 1177888 * q^22 - 778128 * q^23 + 2081722 * q^25 + 4127424 * q^26 + 1488620 * q^28 + 10003584 * q^29 + 2467260 * q^31 - 1284576 * q^32 - 2246676 * q^34 - 5373438 * q^35 + 30735552 * q^37 - 3504660 * q^38 - 32409984 * q^40 + 19103448 * q^41 + 4065100 * q^43 + 18650976 * q^44 + 12367584 * q^46 + 82195020 * q^47 + 11529602 * q^49 + 88312626 * q^50 + 33466384 * q^52 + 55189812 * q^53 + 82445816 * q^55 + 6281016 * q^56 + 66558004 * q^58 + 7069218 * q^59 + 44316386 * q^61 - 54910200 * q^62 + 147417152 * q^64 + 369979260 * q^65 - 241921336 * q^67 - 165645816 * q^68 - 104164984 * q^70 - 206493816 * q^71 - 499153188 * q^73 - 3571524 * q^74 + 282511768 * q^76 + 84793716 * q^77 + 468535096 * q^79 - 249904128 * q^80 + 389586092 * q^82 - 444023958 * q^83 + 173475060 * q^85 + 416830608 * q^86 - 986010816 * q^88 - 636267396 * q^89 + 63698530 * q^91 + 329431488 * q^92 - 152223192 * q^94 - 1104747984 * q^95 - 1632716064 * q^97 + 34588806 * q^98

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