LMFDB - Embedded newform 342.10.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,10,Mod(1,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, 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("342.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	342.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:	$176.142255968$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 $ x^4 - x^3 - 34433x^2 - 2723303x - 48270488
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-124.888$ of defining polynomial
Character	$\chi$	$=$	342.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +256.000 q^{4} -1263.95 q^{5} -3487.42 q^{7} +4096.00 q^{8} +O(q^{10})$	\(q+16.0000 q^{2} +256.000 q^{4} -1263.95 q^{5} -3487.42 q^{7} +4096.00 q^{8} -20223.2 q^{10} +49259.2 q^{11} -68065.3 q^{13} -55798.7 q^{14} +65536.0 q^{16} -505716. q^{17} +130321. q^{19} -323571. q^{20} +788147. q^{22} +585044. q^{23} -355562. q^{25} -1.08905e6 q^{26} -892779. q^{28} -2.62021e6 q^{29} +3.53093e6 q^{31} +1.04858e6 q^{32} -8.09145e6 q^{34} +4.40791e6 q^{35} +1.85431e7 q^{37} +2.08514e6 q^{38} -5.17713e6 q^{40} -2.18141e7 q^{41} -1.12704e7 q^{43} +1.26104e7 q^{44} +9.36070e6 q^{46} -1.54092e7 q^{47} -2.81915e7 q^{49} -5.68899e6 q^{50} -1.74247e7 q^{52} -7.05741e6 q^{53} -6.22611e7 q^{55} -1.42845e7 q^{56} -4.19234e7 q^{58} -2.90730e7 q^{59} +1.44284e8 q^{61} +5.64949e7 q^{62} +1.67772e7 q^{64} +8.60310e7 q^{65} +2.65266e7 q^{67} -1.29463e8 q^{68} +7.05266e7 q^{70} +4.27081e7 q^{71} +3.24644e8 q^{73} +2.96689e8 q^{74} +3.33622e7 q^{76} -1.71787e8 q^{77} -8.88210e7 q^{79} -8.28341e7 q^{80} -3.49026e8 q^{82} -6.29830e7 q^{83} +6.39198e8 q^{85} -1.80326e8 q^{86} +2.01766e8 q^{88} +4.54329e7 q^{89} +2.37372e8 q^{91} +1.49771e8 q^{92} -2.46547e8 q^{94} -1.64719e8 q^{95} +1.64830e9 q^{97} -4.51064e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8}+O(q^{10}) $ 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8} + 22320 q^{10} + 104249 q^{11} + 120486 q^{13} + 196912 q^{14} + 262144 q^{16} + 412139 q^{17} + 521284 q^{19} + 357120 q^{20} + 1667984 q^{22} - 3010300 q^{23} + 9760585 q^{25} + 1927776 q^{26} + 3150592 q^{28} - 6153240 q^{29} + 12774024 q^{31} + 4194304 q^{32} + 6594224 q^{34} - 9823425 q^{35} + 20506048 q^{37} + 8340544 q^{38} + 5713920 q^{40} - 11620300 q^{41} + 7698327 q^{43} + 26687744 q^{44} - 48164800 q^{46} + 31581083 q^{47} + 18970383 q^{49} + 156169360 q^{50} + 30844416 q^{52} - 72549422 q^{53} + 21332505 q^{55} + 50409472 q^{56} - 98451840 q^{58} + 149234120 q^{59} + 129004373 q^{61} + 204384384 q^{62} + 67108864 q^{64} - 124691700 q^{65} + 132595266 q^{67} + 105507584 q^{68} - 157174800 q^{70} + 47138482 q^{71} - 39332795 q^{73} + 328096768 q^{74} + 133448704 q^{76} + 165933719 q^{77} - 307010840 q^{79} + 91422720 q^{80} - 185924800 q^{82} + 746568232 q^{83} - 105005985 q^{85} + 123173232 q^{86} + 427003904 q^{88} - 286943482 q^{89} + 3155781114 q^{91} - 770636800 q^{92} + 505297328 q^{94} + 181797795 q^{95} + 793519958 q^{97} + 303526128 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8 + 22320 * q^10 + 104249 * q^11 + 120486 * q^13 + 196912 * q^14 + 262144 * q^16 + 412139 * q^17 + 521284 * q^19 + 357120 * q^20 + 1667984 * q^22 - 3010300 * q^23 + 9760585 * q^25 + 1927776 * q^26 + 3150592 * q^28 - 6153240 * q^29 + 12774024 * q^31 + 4194304 * q^32 + 6594224 * q^34 - 9823425 * q^35 + 20506048 * q^37 + 8340544 * q^38 + 5713920 * q^40 - 11620300 * q^41 + 7698327 * q^43 + 26687744 * q^44 - 48164800 * q^46 + 31581083 * q^47 + 18970383 * q^49 + 156169360 * q^50 + 30844416 * q^52 - 72549422 * q^53 + 21332505 * q^55 + 50409472 * q^56 - 98451840 * q^58 + 149234120 * q^59 + 129004373 * q^61 + 204384384 * q^62 + 67108864 * q^64 - 124691700 * q^65 + 132595266 * q^67 + 105507584 * q^68 - 157174800 * q^70 + 47138482 * q^71 - 39332795 * q^73 + 328096768 * q^74 + 133448704 * q^76 + 165933719 * q^77 - 307010840 * q^79 + 91422720 * q^80 - 185924800 * q^82 + 746568232 * q^83 - 105005985 * q^85 + 123173232 * q^86 + 427003904 * q^88 - 286943482 * q^89 + 3155781114 * q^91 - 770636800 * q^92 + 505297328 * q^94 + 181797795 * q^95 + 793519958 * q^97 + 303526128 * 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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	0	0
$3$	0	0
$4$	256.000	0.500000
$5$	−1263.95	−0.904407	−0.452204	−	0.891915i	$-0.649362\pi$
$5$	−1263.95	−0.904407	−0.452204	+	0.891915i	$0.649362\pi$
$6$	0	0
$7$	−3487.42	−0.548988	−0.274494	−	0.961589i	$-0.588510\pi$
$7$	−3487.42	−0.548988	−0.274494	+	0.961589i	$0.588510\pi$
$8$	4096.00	0.353553
$9$	0	0
$10$	−20223.2	−0.639512
$11$	49259.2	1.01443	0.507213	−	0.861821i	$-0.330676\pi$
$11$	49259.2	1.01443	0.507213	+	0.861821i	$0.330676\pi$
$12$	0	0
$13$	−68065.3	−0.660969	−0.330484	−	0.943811i	$-0.607212\pi$
$13$	−68065.3	−0.660969	−0.330484	+	0.943811i	$0.607212\pi$
$14$	−55798.7	−0.388193
$15$	0	0
$16$	65536.0	0.250000
$17$	−505716.	−1.46854	−0.734271	−	0.678857i	$-0.762476\pi$
$17$	−505716.	−1.46854	−0.734271	+	0.678857i	$0.762476\pi$
$18$	0	0
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	−323571.	−0.452204
$21$	0	0
$22$	788147.	0.717307
$23$	585044.	0.435926	0.217963	−	0.975957i	$-0.430059\pi$
$23$	585044.	0.435926	0.217963	+	0.975957i	$0.430059\pi$
$24$	0	0
$25$	−355562.	−0.182048
$26$	−1.08905e6	−0.467375
$27$	0	0
$28$	−892779.	−0.274494
$29$	−2.62021e6	−0.687932	−0.343966	−	0.938982i	$-0.611771\pi$
$29$	−2.62021e6	−0.687932	−0.343966	+	0.938982i	$0.611771\pi$
$30$	0	0
$31$	3.53093e6	0.686691	0.343345	−	0.939209i	$-0.388440\pi$
$31$	3.53093e6	0.686691	0.343345	+	0.939209i	$0.388440\pi$
$32$	1.04858e6	0.176777
$33$	0	0
$34$	−8.09145e6	−1.03842
$35$	4.40791e6	0.496509
$36$	0	0
$37$	1.85431e7	1.62657	0.813287	−	0.581863i	$-0.197676\pi$
$37$	1.85431e7	1.62657	0.813287	+	0.581863i	$0.197676\pi$
$38$	2.08514e6	0.162221
$39$	0	0
$40$	−5.17713e6	−0.319756
$41$	−2.18141e7	−1.20562	−0.602811	−	0.797884i	$-0.705953\pi$
$41$	−2.18141e7	−1.20562	−0.602811	+	0.797884i	$0.705953\pi$
$42$	0	0
$43$	−1.12704e7	−0.502725	−0.251362	−	0.967893i	$-0.580879\pi$
$43$	−1.12704e7	−0.502725	−0.251362	+	0.967893i	$0.580879\pi$
$44$	1.26104e7	0.507213
$45$	0	0
$46$	9.36070e6	0.308246
$47$	−1.54092e7	−0.460616	−0.230308	−	0.973118i	$-0.573973\pi$
$47$	−1.54092e7	−0.460616	−0.230308	+	0.973118i	$0.573973\pi$
$48$	0	0
$49$	−2.81915e7	−0.698612
$50$	−5.68899e6	−0.128727
$51$	0	0
$52$	−1.74247e7	−0.330484
$53$	−7.05741e6	−0.122858	−0.0614291	−	0.998111i	$-0.519566\pi$
$53$	−7.05741e6	−0.122858	−0.0614291	+	0.998111i	$0.519566\pi$
$54$	0	0
$55$	−6.22611e7	−0.917454
$56$	−1.42845e7	−0.194097
$57$	0	0
$58$	−4.19234e7	−0.486442
$59$	−2.90730e7	−0.312360	−0.156180	−	0.987729i	$-0.549918\pi$
$59$	−2.90730e7	−0.312360	−0.156180	+	0.987729i	$0.549918\pi$
$60$	0	0
$61$	1.44284e8	1.33424	0.667121	−	0.744949i	$-0.267526\pi$
$61$	1.44284e8	1.33424	0.667121	+	0.744949i	$0.267526\pi$
$62$	5.64949e7	0.485564
$63$	0	0
$64$	1.67772e7	0.125000
$65$	8.60310e7	0.597785
$66$	0	0
$67$	2.65266e7	0.160822	0.0804110	−	0.996762i	$-0.474377\pi$
$67$	2.65266e7	0.160822	0.0804110	+	0.996762i	$0.474377\pi$
$68$	−1.29463e8	−0.734271
$69$	0	0
$70$	7.05266e7	0.351085
$71$	4.27081e7	0.199456	0.0997281	−	0.995015i	$-0.468203\pi$
$71$	4.27081e7	0.199456	0.0997281	+	0.995015i	$0.468203\pi$
$72$	0	0
$73$	3.24644e8	1.33800	0.668998	−	0.743264i	$-0.266723\pi$
$73$	3.24644e8	1.33800	0.668998	+	0.743264i	$0.266723\pi$
$74$	2.96689e8	1.15016
$75$	0	0
$76$	3.33622e7	0.114708
$77$	−1.71787e8	−0.556908
$78$	0	0
$79$	−8.88210e7	−0.256563	−0.128281	−	0.991738i	$-0.540946\pi$
$79$	−8.88210e7	−0.256563	−0.128281	+	0.991738i	$0.540946\pi$
$80$	−8.28341e7	−0.226102
$81$	0	0
$82$	−3.49026e8	−0.852503
$83$	−6.29830e7	−0.145671	−0.0728353	−	0.997344i	$-0.523205\pi$
$83$	−6.29830e7	−0.145671	−0.0728353	+	0.997344i	$0.523205\pi$
$84$	0	0
$85$	6.39198e8	1.32816
$86$	−1.80326e8	−0.355480
$87$	0	0
$88$	2.01766e8	0.358654
$89$	4.54329e7	0.0767565	0.0383783	−	0.999263i	$-0.487781\pi$
$89$	4.54329e7	0.0767565	0.0383783	+	0.999263i	$0.487781\pi$
$90$	0	0
$91$	2.37372e8	0.362864
$92$	1.49771e8	0.217963
$93$	0	0
$94$	−2.46547e8	−0.325705
$95$	−1.64719e8	−0.207485
$96$	0	0
$97$	1.64830e9	1.89044	0.945219	−	0.326438i	$-0.105848\pi$
$97$	1.64830e9	1.89044	0.945219	+	0.326438i	$0.105848\pi$
$98$	−4.51064e8	−0.493994
$99$	0	0
$100$	−9.10238e7	−0.0910238
$101$	8.97226e8	0.857938	0.428969	−	0.903319i	$-0.358877\pi$
$101$	8.97226e8	0.857938	0.428969	+	0.903319i	$0.358877\pi$
$102$	0	0
$103$	1.67622e9	1.46745	0.733726	−	0.679445i	$-0.237779\pi$
$103$	1.67622e9	1.46745	0.733726	+	0.679445i	$0.237779\pi$
$104$	−2.78796e8	−0.233688
$105$	0	0
$106$	−1.12919e8	−0.0868738
$107$	−3.08053e8	−0.227195	−0.113597	−	0.993527i	$-0.536237\pi$
$107$	−3.08053e8	−0.227195	−0.113597	+	0.993527i	$0.536237\pi$
$108$	0	0
$109$	−1.79569e8	−0.121846	−0.0609230	−	0.998142i	$-0.519404\pi$
$109$	−1.79569e8	−0.121846	−0.0609230	+	0.998142i	$0.519404\pi$
$110$	−9.96177e8	−0.648738
$111$	0	0
$112$	−2.28551e8	−0.137247
$113$	2.30787e9	1.33155	0.665776	−	0.746152i	$-0.268101\pi$
$113$	2.30787e9	1.33155	0.665776	+	0.746152i	$0.268101\pi$
$114$	0	0
$115$	−7.39465e8	−0.394255
$116$	−6.70775e8	−0.343966
$117$	0	0
$118$	−4.65168e8	−0.220872
$119$	1.76364e9	0.806212
$120$	0	0
$121$	6.85222e7	0.0290601
$122$	2.30855e9	0.943452
$123$	0	0
$124$	9.03918e8	0.343345
$125$	2.91806e9	1.06905
$126$	0	0
$127$	−4.51313e9	−1.53943	−0.769717	−	0.638385i	$-0.779603\pi$
$127$	−4.51313e9	−1.53943	−0.769717	+	0.638385i	$0.779603\pi$
$128$	2.68435e8	0.0883883
$129$	0	0
$130$	1.37650e9	0.422698
$131$	2.53716e9	0.752708	0.376354	−	0.926476i	$-0.377178\pi$
$131$	2.53716e9	0.752708	0.376354	+	0.926476i	$0.377178\pi$
$132$	0	0
$133$	−4.54484e8	−0.125946
$134$	4.24426e8	0.113718
$135$	0	0
$136$	−2.07141e9	−0.519208
$137$	−4.04090e9	−0.980021	−0.490010	−	0.871717i	$-0.663007\pi$
$137$	−4.04090e9	−0.980021	−0.490010	+	0.871717i	$0.663007\pi$
$138$	0	0
$139$	−1.86522e9	−0.423803	−0.211901	−	0.977291i	$-0.567966\pi$
$139$	−1.86522e9	−0.423803	−0.211901	+	0.977291i	$0.567966\pi$
$140$	1.12843e9	0.248254
$141$	0	0
$142$	6.83329e8	0.141037
$143$	−3.35284e9	−0.670504
$144$	0	0
$145$	3.31181e9	0.622171
$146$	5.19431e9	0.946106
$147$	0	0
$148$	4.74702e9	0.813287
$149$	7.60481e9	1.26401	0.632004	−	0.774965i	$-0.282232\pi$
$149$	7.60481e9	1.26401	0.632004	+	0.774965i	$0.282232\pi$
$150$	0	0
$151$	1.74653e9	0.273388	0.136694	−	0.990613i	$-0.456352\pi$
$151$	1.74653e9	0.273388	0.136694	+	0.990613i	$0.456352\pi$
$152$	5.33795e8	0.0811107
$153$	0	0
$154$	−2.74860e9	−0.393793
$155$	−4.46291e9	−0.621048
$156$	0	0
$157$	1.06564e10	1.39979	0.699893	−	0.714248i	$-0.253231\pi$
$157$	1.06564e10	1.39979	0.699893	+	0.714248i	$0.253231\pi$
$158$	−1.42114e9	−0.181417
$159$	0	0
$160$	−1.32535e9	−0.159878
$161$	−2.04029e9	−0.239318
$162$	0	0
$163$	9.11348e9	1.01121	0.505603	−	0.862766i	$-0.331270\pi$
$163$	9.11348e9	1.01121	0.505603	+	0.862766i	$0.331270\pi$
$164$	−5.58442e9	−0.602811
$165$	0	0
$166$	−1.00773e9	−0.103005
$167$	−1.15546e10	−1.14956	−0.574778	−	0.818309i	$-0.694912\pi$
$167$	−1.15546e10	−1.14956	−0.574778	+	0.818309i	$0.694912\pi$
$168$	0	0
$169$	−5.97161e9	−0.563120
$170$	1.02272e10	0.939151
$171$	0	0
$172$	−2.88522e9	−0.251362
$173$	2.52786e9	0.214558	0.107279	−	0.994229i	$-0.465786\pi$
$173$	2.52786e9	0.214558	0.107279	+	0.994229i	$0.465786\pi$
$174$	0	0
$175$	1.23999e9	0.0999419
$176$	3.22825e9	0.253606
$177$	0	0
$178$	7.26926e8	0.0542751
$179$	1.73068e10	1.26002	0.630009	−	0.776588i	$-0.283051\pi$
$179$	1.73068e10	1.26002	0.630009	+	0.776588i	$0.283051\pi$
$180$	0	0
$181$	1.08688e10	0.752711	0.376355	−	0.926475i	$-0.377177\pi$
$181$	1.08688e10	0.752711	0.376355	+	0.926475i	$0.377177\pi$
$182$	3.79796e9	0.256583
$183$	0	0
$184$	2.39634e9	0.154123
$185$	−2.34375e10	−1.47108
$186$	0	0
$187$	−2.49112e10	−1.48973
$188$	−3.94475e9	−0.230308
$189$	0	0
$190$	−2.63550e9	−0.146714
$191$	5.33871e9	0.290259	0.145130	−	0.989413i	$-0.453640\pi$
$191$	5.33871e9	0.290259	0.145130	+	0.989413i	$0.453640\pi$
$192$	0	0
$193$	2.75948e10	1.43159	0.715797	−	0.698309i	$-0.246064\pi$
$193$	2.75948e10	1.43159	0.715797	+	0.698309i	$0.246064\pi$
$194$	2.63727e10	1.33674
$195$	0	0
$196$	−7.21703e9	−0.349306
$197$	9.61053e9	0.454621	0.227310	−	0.973822i	$-0.427007\pi$
$197$	9.61053e9	0.454621	0.227310	+	0.973822i	$0.427007\pi$
$198$	0	0
$199$	2.88815e10	1.30551	0.652756	−	0.757568i	$-0.273612\pi$
$199$	2.88815e10	1.30551	0.652756	+	0.757568i	$0.273612\pi$
$200$	−1.45638e9	−0.0643635
$201$	0	0
$202$	1.43556e10	0.606654
$203$	9.13778e9	0.377666
$204$	0	0
$205$	2.75719e10	1.09037
$206$	2.68196e10	1.03765
$207$	0	0
$208$	−4.46073e9	−0.165242
$209$	6.41951e9	0.232725
$210$	0	0
$211$	2.26589e10	0.786986	0.393493	−	0.919328i	$-0.371267\pi$
$211$	2.26589e10	0.786986	0.393493	+	0.919328i	$0.371267\pi$
$212$	−1.80670e9	−0.0614291
$213$	0	0
$214$	−4.92884e9	−0.160651
$215$	1.42452e10	0.454668
$216$	0	0
$217$	−1.23138e10	−0.376985
$218$	−2.87310e9	−0.0861581
$219$	0	0
$220$	−1.59388e10	−0.458727
$221$	3.44217e10	0.970660
$222$	0	0
$223$	−5.84566e10	−1.58293	−0.791465	−	0.611214i	$-0.790681\pi$
$223$	−5.84566e10	−1.58293	−0.791465	+	0.611214i	$0.790681\pi$
$224$	−3.65682e9	−0.0970483
$225$	0	0
$226$	3.69259e10	0.941549
$227$	4.82187e9	0.120531	0.0602656	−	0.998182i	$-0.480805\pi$
$227$	4.82187e9	0.120531	0.0602656	+	0.998182i	$0.480805\pi$
$228$	0	0
$229$	−7.15833e9	−0.172009	−0.0860046	−	0.996295i	$-0.527410\pi$
$229$	−7.15833e9	−0.172009	−0.0860046	+	0.996295i	$0.527410\pi$
$230$	−1.18314e10	−0.278780
$231$	0	0
$232$	−1.07324e10	−0.243221
$233$	−4.52737e10	−1.00634	−0.503169	−	0.864188i	$-0.667833\pi$
$233$	−4.52737e10	−1.00634	−0.503169	+	0.864188i	$0.667833\pi$
$234$	0	0
$235$	1.94764e10	0.416585
$236$	−7.44268e9	−0.156180
$237$	0	0
$238$	2.82183e10	0.570078
$239$	7.05422e10	1.39849	0.699244	−	0.714883i	$-0.253520\pi$
$239$	7.05422e10	1.39849	0.699244	+	0.714883i	$0.253520\pi$
$240$	0	0
$241$	7.83138e10	1.49542	0.747708	−	0.664028i	$-0.231154\pi$
$241$	7.83138e10	1.49542	0.747708	+	0.664028i	$0.231154\pi$
$242$	1.09635e9	0.0205486
$243$	0	0
$244$	3.69368e10	0.667121
$245$	3.56326e10	0.631830
$246$	0	0
$247$	−8.87034e9	−0.151637
$248$	1.44627e10	0.242782
$249$	0	0
$250$	4.66889e10	0.755934
$251$	−1.03661e11	−1.64848	−0.824240	−	0.566241i	$-0.808397\pi$
$251$	−1.03661e11	−1.64848	−0.824240	+	0.566241i	$0.808397\pi$
$252$	0	0
$253$	2.88188e10	0.442215
$254$	−7.22101e10	−1.08854
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−1.07294e11	−1.53419	−0.767093	−	0.641536i	$-0.778297\pi$
$257$	−1.07294e11	−1.53419	−0.767093	+	0.641536i	$0.778297\pi$
$258$	0	0
$259$	−6.46674e10	−0.892969
$260$	2.20239e10	0.298892
$261$	0	0
$262$	4.05945e10	0.532245
$263$	1.18240e11	1.52393	0.761963	−	0.647620i	$-0.224236\pi$
$263$	1.18240e11	1.52393	0.761963	+	0.647620i	$0.224236\pi$
$264$	0	0
$265$	8.92019e9	0.111114
$266$	−7.27174e9	−0.0890576
$267$	0	0
$268$	6.79082e9	0.0804110
$269$	−1.08142e11	−1.25924	−0.629620	−	0.776903i	$-0.716789\pi$
$269$	−1.08142e11	−1.25924	−0.629620	+	0.776903i	$0.716789\pi$
$270$	0	0
$271$	−1.22183e11	−1.37609	−0.688047	−	0.725667i	$-0.741532\pi$
$271$	−1.22183e11	−1.37609	−0.688047	+	0.725667i	$0.741532\pi$
$272$	−3.31426e10	−0.367135
$273$	0	0
$274$	−6.46544e10	−0.692979
$275$	−1.75147e10	−0.184674
$276$	0	0
$277$	1.18944e11	1.21390	0.606951	−	0.794740i	$-0.292393\pi$
$277$	1.18944e11	1.21390	0.606951	+	0.794740i	$0.292393\pi$
$278$	−2.98436e10	−0.299674
$279$	0	0
$280$	1.80548e10	0.175542
$281$	4.73680e10	0.453218	0.226609	−	0.973986i	$-0.427236\pi$
$281$	4.73680e10	0.453218	0.226609	+	0.973986i	$0.427236\pi$
$282$	0	0
$283$	1.59829e11	1.48121	0.740603	−	0.671943i	$-0.234540\pi$
$283$	1.59829e11	1.48121	0.740603	+	0.671943i	$0.234540\pi$
$284$	1.09333e10	0.0997281
$285$	0	0
$286$	−5.36455e10	−0.474118
$287$	7.60750e10	0.661871
$288$	0	0
$289$	1.37161e11	1.15662
$290$	5.29890e10	0.439941
$291$	0	0
$292$	8.31089e10	0.668998
$293$	−1.32731e11	−1.05212	−0.526062	−	0.850446i	$-0.676332\pi$
$293$	−1.32731e11	−1.05212	−0.526062	+	0.850446i	$0.676332\pi$
$294$	0	0
$295$	3.67467e10	0.282501
$296$	7.59524e10	0.575081
$297$	0	0
$298$	1.21677e11	0.893789
$299$	−3.98212e10	−0.288134
$300$	0	0
$301$	3.93045e10	0.275990
$302$	2.79444e10	0.193314
$303$	0	0
$304$	8.54072e9	0.0573539
$305$	−1.82368e11	−1.20670
$306$	0	0
$307$	2.41951e11	1.55455	0.777274	−	0.629162i	$-0.216602\pi$
$307$	2.41951e11	1.55455	0.777274	+	0.629162i	$0.216602\pi$
$308$	−4.39776e10	−0.278454
$309$	0	0
$310$	−7.14065e10	−0.439147
$311$	1.75276e11	1.06243	0.531217	−	0.847236i	$-0.321735\pi$
$311$	1.75276e11	1.06243	0.531217	+	0.847236i	$0.321735\pi$
$312$	0	0
$313$	−2.56460e11	−1.51032	−0.755161	−	0.655539i	$-0.772442\pi$
$313$	−2.56460e11	−1.51032	−0.755161	+	0.655539i	$0.772442\pi$
$314$	1.70502e11	0.989798
$315$	0	0
$316$	−2.27382e10	−0.128281
$317$	2.91020e10	0.161866	0.0809331	−	0.996720i	$-0.474210\pi$
$317$	2.91020e10	0.161866	0.0809331	+	0.996720i	$0.474210\pi$
$318$	0	0
$319$	−1.29070e11	−0.697856
$320$	−2.12055e10	−0.113051
$321$	0	0
$322$	−3.26447e10	−0.169224
$323$	−6.59054e10	−0.336907
$324$	0	0
$325$	2.42014e10	0.120328
$326$	1.45816e11	0.715031
$327$	0	0
$328$	−8.93508e10	−0.426251
$329$	5.37382e10	0.252873
$330$	0	0
$331$	−1.45683e11	−0.667088	−0.333544	−	0.942734i	$-0.608245\pi$
$331$	−1.45683e11	−0.667088	−0.333544	+	0.942734i	$0.608245\pi$
$332$	−1.61236e10	−0.0728353
$333$	0	0
$334$	−1.84873e11	−0.812859
$335$	−3.35283e10	−0.145449
$336$	0	0
$337$	−4.16729e10	−0.176002	−0.0880012	−	0.996120i	$-0.528048\pi$
$337$	−4.16729e10	−0.176002	−0.0880012	+	0.996120i	$0.528048\pi$
$338$	−9.55457e10	−0.398186
$339$	0	0
$340$	1.63635e11	0.664080
$341$	1.73931e11	0.696597
$342$	0	0
$343$	2.39045e11	0.932518
$344$	−4.61635e10	−0.177740
$345$	0	0
$346$	4.04457e10	0.151716
$347$	5.79909e10	0.214722	0.107361	−	0.994220i	$-0.465760\pi$
$347$	5.79909e10	0.214722	0.107361	+	0.994220i	$0.465760\pi$
$348$	0	0
$349$	−1.06762e11	−0.385214	−0.192607	−	0.981276i	$-0.561694\pi$
$349$	−1.06762e11	−0.385214	−0.192607	+	0.981276i	$0.561694\pi$
$350$	1.98399e10	0.0706696
$351$	0	0
$352$	5.16520e10	0.179327
$353$	4.27202e11	1.46436	0.732180	−	0.681112i	$-0.238503\pi$
$353$	4.27202e11	1.46436	0.732180	+	0.681112i	$0.238503\pi$
$354$	0	0
$355$	−5.39808e10	−0.180390
$356$	1.16308e10	0.0383783
$357$	0	0
$358$	2.76908e11	0.890968
$359$	−4.29892e11	−1.36595	−0.682975	−	0.730442i	$-0.739314\pi$
$359$	−4.29892e11	−1.36595	−0.682975	+	0.730442i	$0.739314\pi$
$360$	0	0
$361$	1.69836e10	0.0526316
$362$	1.73901e11	0.532247
$363$	0	0
$364$	6.07673e10	0.181432
$365$	−4.10333e11	−1.21009
$366$	0	0
$367$	1.40582e11	0.404512	0.202256	−	0.979333i	$-0.435173\pi$
$367$	1.40582e11	0.404512	0.202256	+	0.979333i	$0.435173\pi$
$368$	3.83414e10	0.108982
$369$	0	0
$370$	−3.74999e11	−1.04021
$371$	2.46121e10	0.0674476
$372$	0	0
$373$	4.31647e11	1.15462	0.577310	−	0.816525i	$-0.304102\pi$
$373$	4.31647e11	1.15462	0.577310	+	0.816525i	$0.304102\pi$
$374$	−3.98579e11	−1.05340
$375$	0	0
$376$	−6.31160e10	−0.162852
$377$	1.78346e11	0.454702
$378$	0	0
$379$	7.16332e11	1.78336	0.891678	−	0.452670i	$-0.149528\pi$
$379$	7.16332e11	1.78336	0.891678	+	0.452670i	$0.149528\pi$
$380$	−4.21680e10	−0.103743
$381$	0	0
$382$	8.54194e10	0.205244
$383$	1.03271e11	0.245236	0.122618	−	0.992454i	$-0.460871\pi$
$383$	1.03271e11	0.245236	0.122618	+	0.992454i	$0.460871\pi$
$384$	0	0
$385$	2.17130e11	0.503671
$386$	4.41517e11	1.01229
$387$	0	0
$388$	4.21964e11	0.945219
$389$	3.49935e11	0.774845	0.387422	−	0.921902i	$-0.373366\pi$
$389$	3.49935e11	0.774845	0.387422	+	0.921902i	$0.373366\pi$
$390$	0	0
$391$	−2.95866e11	−0.640176
$392$	−1.15473e11	−0.246997
$393$	0	0
$394$	1.53769e11	0.321466
$395$	1.12265e11	0.232037
$396$	0	0
$397$	−2.83640e11	−0.573073	−0.286536	−	0.958069i	$-0.592504\pi$
$397$	−2.83640e11	−0.573073	−0.286536	+	0.958069i	$0.592504\pi$
$398$	4.62104e11	0.923137
$399$	0	0
$400$	−2.33021e10	−0.0455119
$401$	9.94065e11	1.91984	0.959920	−	0.280275i	$-0.0904256\pi$
$401$	9.94065e11	1.91984	0.959920	+	0.280275i	$0.0904256\pi$
$402$	0	0
$403$	−2.40334e11	−0.453881
$404$	2.29690e11	0.428969
$405$	0	0
$406$	1.46204e11	0.267051
$407$	9.13417e11	1.65004
$408$	0	0
$409$	2.41111e11	0.426051	0.213026	−	0.977047i	$-0.431668\pi$
$409$	2.41111e11	0.426051	0.213026	+	0.977047i	$0.431668\pi$
$410$	4.41151e11	0.771010
$411$	0	0
$412$	4.29113e11	0.733726
$413$	1.01390e11	0.171482
$414$	0	0
$415$	7.96072e10	0.131745
$416$	−7.13717e10	−0.116844
$417$	0	0
$418$	1.02712e11	0.164562
$419$	−7.03102e11	−1.11444	−0.557218	−	0.830366i	$-0.688131\pi$
$419$	−7.03102e11	−1.11444	−0.557218	+	0.830366i	$0.688131\pi$
$420$	0	0
$421$	−2.68270e11	−0.416200	−0.208100	−	0.978108i	$-0.566728\pi$
$421$	−2.68270e11	−0.416200	−0.208100	+	0.978108i	$0.566728\pi$
$422$	3.62542e11	0.556483
$423$	0	0
$424$	−2.89071e10	−0.0434369
$425$	1.79813e11	0.267344
$426$	0	0
$427$	−5.03180e11	−0.732483
$428$	−7.88615e10	−0.113597
$429$	0	0
$430$	2.27923e11	0.321499
$431$	−5.95908e10	−0.0831825	−0.0415912	−	0.999135i	$-0.513243\pi$
$431$	−5.95908e10	−0.0831825	−0.0415912	+	0.999135i	$0.513243\pi$
$432$	0	0
$433$	−1.16290e12	−1.58982	−0.794909	−	0.606729i	$-0.792481\pi$
$433$	−1.16290e12	−1.58982	−0.794909	+	0.606729i	$0.792481\pi$
$434$	−1.97021e11	−0.266569
$435$	0	0
$436$	−4.59696e10	−0.0609230
$437$	7.62435e10	0.100008
$438$	0	0
$439$	−1.32465e12	−1.70220	−0.851100	−	0.525004i	$-0.824064\pi$
$439$	−1.32465e12	−1.70220	−0.851100	+	0.525004i	$0.824064\pi$
$440$	−2.55021e11	−0.324369
$441$	0	0
$442$	5.50747e11	0.686360
$443$	−7.48682e11	−0.923593	−0.461797	−	0.886986i	$-0.652795\pi$
$443$	−7.48682e11	−0.923593	−0.461797	+	0.886986i	$0.652795\pi$
$444$	0	0
$445$	−5.74248e10	−0.0694192
$446$	−9.35306e11	−1.11930
$447$	0	0
$448$	−5.85091e10	−0.0686235
$449$	−8.07450e11	−0.937577	−0.468788	−	0.883310i	$-0.655309\pi$
$449$	−8.07450e11	−0.937577	−0.468788	+	0.883310i	$0.655309\pi$
$450$	0	0
$451$	−1.07455e12	−1.22301
$452$	5.90814e11	0.665776
$453$	0	0
$454$	7.71500e10	0.0852284
$455$	−3.00026e11	−0.328177
$456$	0	0
$457$	−2.09593e11	−0.224778	−0.112389	−	0.993664i	$-0.535850\pi$
$457$	−2.09593e11	−0.224778	−0.112389	+	0.993664i	$0.535850\pi$
$458$	−1.14533e11	−0.121629
$459$	0	0
$460$	−1.89303e11	−0.197127
$461$	−1.12823e12	−1.16343	−0.581717	−	0.813391i	$-0.697619\pi$
$461$	−1.12823e12	−1.16343	−0.581717	+	0.813391i	$0.697619\pi$
$462$	0	0
$463$	−9.75512e11	−0.986548	−0.493274	−	0.869874i	$-0.664200\pi$
$463$	−9.75512e11	−0.986548	−0.493274	+	0.869874i	$0.664200\pi$
$464$	−1.71718e11	−0.171983
$465$	0	0
$466$	−7.24379e11	−0.711589
$467$	5.15878e11	0.501904	0.250952	−	0.968000i	$-0.419256\pi$
$467$	5.15878e11	0.501904	0.250952	+	0.968000i	$0.419256\pi$
$468$	0	0
$469$	−9.25095e10	−0.0882894
$470$	3.11622e11	0.294570
$471$	0	0
$472$	−1.19083e11	−0.110436
$473$	−5.55170e11	−0.509977
$474$	0	0
$475$	−4.63372e10	−0.0417646
$476$	4.51492e11	0.403106
$477$	0	0
$478$	1.12868e12	0.988880
$479$	−1.89215e12	−1.64228	−0.821139	−	0.570728i	$-0.806661\pi$
$479$	−1.89215e12	−1.64228	−0.821139	+	0.570728i	$0.806661\pi$
$480$	0	0
$481$	−1.26214e12	−1.07511
$482$	1.25302e12	1.05742
$483$	0	0
$484$	1.75417e10	0.0145300
$485$	−2.08336e12	−1.70973
$486$	0	0
$487$	1.35254e12	1.08960	0.544802	−	0.838565i	$-0.316605\pi$
$487$	1.35254e12	1.08960	0.544802	+	0.838565i	$0.316605\pi$
$488$	5.90989e11	0.471726
$489$	0	0
$490$	5.70122e11	0.446771
$491$	−9.23267e11	−0.716903	−0.358452	−	0.933548i	$-0.616695\pi$
$491$	−9.23267e11	−0.716903	−0.358452	+	0.933548i	$0.616695\pi$
$492$	0	0
$493$	1.32508e12	1.01026
$494$	−1.41925e11	−0.107223
$495$	0	0
$496$	2.31403e11	0.171673
$497$	−1.48941e11	−0.109499
$498$	0	0
$499$	1.98116e12	1.43043	0.715214	−	0.698905i	$-0.246329\pi$
$499$	1.98116e12	1.43043	0.715214	+	0.698905i	$0.246329\pi$
$500$	7.47023e11	0.534526
$501$	0	0
$502$	−1.65858e12	−1.16565
$503$	−2.56937e12	−1.78966	−0.894830	−	0.446406i	$-0.852704\pi$
$503$	−2.56937e12	−1.78966	−0.894830	+	0.446406i	$0.852704\pi$
$504$	0	0
$505$	−1.13405e12	−0.775925
$506$	4.61101e11	0.312693
$507$	0	0
$508$	−1.15536e12	−0.769717
$509$	−1.56900e11	−0.103608	−0.0518040	−	0.998657i	$-0.516497\pi$
$509$	−1.56900e11	−0.103608	−0.0518040	+	0.998657i	$0.516497\pi$
$510$	0	0
$511$	−1.13217e12	−0.734544
$512$	6.87195e10	0.0441942
$513$	0	0
$514$	−1.71671e12	−1.08483
$515$	−2.11866e12	−1.32717
$516$	0	0
$517$	−7.59044e11	−0.467261
$518$	−1.03468e12	−0.631424
$519$	0	0
$520$	3.52383e11	0.211349
$521$	1.30379e12	0.775241	0.387621	−	0.921819i	$-0.373297\pi$
$521$	1.30379e12	0.775241	0.387621	+	0.921819i	$0.373297\pi$
$522$	0	0
$523$	2.30458e12	1.34690	0.673449	−	0.739234i	$-0.264812\pi$
$523$	2.30458e12	1.34690	0.673449	+	0.739234i	$0.264812\pi$
$524$	6.49513e11	0.376354
$525$	0	0
$526$	1.89184e12	1.07758
$527$	−1.78565e12	−1.00843
$528$	0	0
$529$	−1.45888e12	−0.809968
$530$	1.42723e11	0.0785693
$531$	0	0
$532$	−1.16348e11	−0.0629732
$533$	1.48479e12	0.796878
$534$	0	0
$535$	3.89362e11	0.205476
$536$	1.08653e11	0.0568592
$537$	0	0
$538$	−1.73027e12	−0.890417
$539$	−1.38869e12	−0.708691
$540$	0	0
$541$	5.93525e11	0.297887	0.148943	−	0.988846i	$-0.452413\pi$
$541$	5.93525e11	0.297887	0.148943	+	0.988846i	$0.452413\pi$
$542$	−1.95492e12	−0.973045
$543$	0	0
$544$	−5.30281e11	−0.259604
$545$	2.26965e11	0.110198
$546$	0	0
$547$	−2.57843e12	−1.23144	−0.615719	−	0.787966i	$-0.711134\pi$
$547$	−2.57843e12	−1.23144	−0.615719	+	0.787966i	$0.711134\pi$
$548$	−1.03447e12	−0.490010
$549$	0	0
$550$	−2.80235e11	−0.130584
$551$	−3.41469e11	−0.157822
$552$	0	0
$553$	3.09756e11	0.140850
$554$	1.90310e12	0.858358
$555$	0	0
$556$	−4.77497e11	−0.211901
$557$	3.49163e12	1.53702	0.768510	−	0.639838i	$-0.220999\pi$
$557$	3.49163e12	1.53702	0.768510	+	0.639838i	$0.220999\pi$
$558$	0	0
$559$	7.67122e11	0.332285
$560$	2.88877e11	0.124127
$561$	0	0
$562$	7.57888e11	0.320473
$563$	1.40676e12	0.590109	0.295054	−	0.955480i	$-0.404662\pi$
$563$	1.40676e12	0.590109	0.295054	+	0.955480i	$0.404662\pi$
$564$	0	0
$565$	−2.91702e12	−1.20427
$566$	2.55726e12	1.04737
$567$	0	0
$568$	1.74932e11	0.0705184
$569$	−2.81635e12	−1.12637	−0.563185	−	0.826331i	$-0.690424\pi$
$569$	−2.81635e12	−1.12637	−0.563185	+	0.826331i	$0.690424\pi$
$570$	0	0
$571$	−1.85246e11	−0.0729266	−0.0364633	−	0.999335i	$-0.511609\pi$
$571$	−1.85246e11	−0.0729266	−0.0364633	+	0.999335i	$0.511609\pi$
$572$	−8.58328e11	−0.335252
$573$	0	0
$574$	1.21720e12	0.468014
$575$	−2.08019e11	−0.0793593
$576$	0	0
$577$	−2.36440e12	−0.888034	−0.444017	−	0.896018i	$-0.646447\pi$
$577$	−2.36440e12	−0.888034	−0.444017	+	0.896018i	$0.646447\pi$
$578$	2.19457e12	0.817850
$579$	0	0
$580$	8.47824e11	0.311085
$581$	2.19648e11	0.0799714
$582$	0	0
$583$	−3.47642e11	−0.124630
$584$	1.32974e12	0.473053
$585$	0	0
$586$	−2.12369e12	−0.743964
$587$	−8.75403e11	−0.304324	−0.152162	−	0.988356i	$-0.548624\pi$
$587$	−8.75403e11	−0.304324	−0.152162	+	0.988356i	$0.548624\pi$
$588$	0	0
$589$	4.60154e11	0.157538
$590$	5.87947e11	0.199758
$591$	0	0
$592$	1.21524e12	0.406643
$593$	2.10579e12	0.699307	0.349654	−	0.936879i	$-0.386299\pi$
$593$	2.10579e12	0.699307	0.349654	+	0.936879i	$0.386299\pi$
$594$	0	0
$595$	−2.22915e12	−0.729144
$596$	1.94683e12	0.632004
$597$	0	0
$598$	−6.37139e11	−0.203741
$599$	−5.86647e12	−1.86190	−0.930950	−	0.365147i	$-0.881019\pi$
$599$	−5.86647e12	−1.86190	−0.930950	+	0.365147i	$0.881019\pi$
$600$	0	0
$601$	−8.97472e11	−0.280599	−0.140299	−	0.990109i	$-0.544807\pi$
$601$	−8.97472e11	−0.280599	−0.140299	+	0.990109i	$0.544807\pi$
$602$	6.28872e11	0.195154
$603$	0	0
$604$	4.47111e11	0.136694
$605$	−8.66084e10	−0.0262822
$606$	0	0
$607$	−4.20534e12	−1.25734	−0.628669	−	0.777673i	$-0.716400\pi$
$607$	−4.20534e12	−1.25734	−0.628669	+	0.777673i	$0.716400\pi$
$608$	1.36651e11	0.0405554
$609$	0	0
$610$	−2.91788e12	−0.853265
$611$	1.04883e12	0.304453
$612$	0	0
$613$	4.66333e12	1.33390	0.666951	−	0.745102i	$-0.267599\pi$
$613$	4.66333e12	1.33390	0.666951	+	0.745102i	$0.267599\pi$
$614$	3.87121e12	1.09923
$615$	0	0
$616$	−7.03641e11	−0.196897
$617$	−3.80910e12	−1.05813	−0.529065	−	0.848581i	$-0.677457\pi$
$617$	−3.80910e12	−1.05813	−0.529065	+	0.848581i	$0.677457\pi$
$618$	0	0
$619$	−3.62001e12	−0.991063	−0.495532	−	0.868590i	$-0.665027\pi$
$619$	−3.62001e12	−0.991063	−0.495532	+	0.868590i	$0.665027\pi$
$620$	−1.14250e12	−0.310524
$621$	0	0
$622$	2.80442e12	0.751254
$623$	−1.58443e11	−0.0421384
$624$	0	0
$625$	−2.99382e12	−0.784811
$626$	−4.10336e12	−1.06796
$627$	0	0
$628$	2.72804e12	0.699893
$629$	−9.37752e12	−2.38869
$630$	0	0
$631$	−7.16358e11	−0.179886	−0.0899431	−	0.995947i	$-0.528669\pi$
$631$	−7.16358e11	−0.179886	−0.0899431	+	0.995947i	$0.528669\pi$
$632$	−3.63811e11	−0.0907086
$633$	0	0
$634$	4.65632e11	0.114457
$635$	5.70436e12	1.39228
$636$	0	0
$637$	1.91887e12	0.461761
$638$	−2.06511e12	−0.493459
$639$	0	0
$640$	−3.39288e11	−0.0799391
$641$	4.92458e12	1.15215	0.576074	−	0.817397i	$-0.304584\pi$
$641$	4.92458e12	1.15215	0.576074	+	0.817397i	$0.304584\pi$
$642$	0	0
$643$	3.16432e12	0.730013	0.365007	−	0.931005i	$-0.381067\pi$
$643$	3.16432e12	0.730013	0.365007	+	0.931005i	$0.381067\pi$
$644$	−5.22315e11	−0.119659
$645$	0	0
$646$	−1.05449e12	−0.238229
$647$	−8.63261e12	−1.93675	−0.968374	−	0.249504i	$-0.919732\pi$
$647$	−8.63261e12	−1.93675	−0.968374	+	0.249504i	$0.919732\pi$
$648$	0	0
$649$	−1.43211e12	−0.316866
$650$	3.87223e11	0.0850846
$651$	0	0
$652$	2.33305e12	0.505603
$653$	4.53346e12	0.975710	0.487855	−	0.872925i	$-0.337780\pi$
$653$	4.53346e12	0.975710	0.487855	+	0.872925i	$0.337780\pi$
$654$	0	0
$655$	−3.20684e12	−0.680755
$656$	−1.42961e12	−0.301405
$657$	0	0
$658$	8.59812e11	0.178808
$659$	−2.67609e12	−0.552734	−0.276367	−	0.961052i	$-0.589131\pi$
$659$	−2.67609e12	−0.552734	−0.276367	+	0.961052i	$0.589131\pi$
$660$	0	0
$661$	1.23915e12	0.252475	0.126238	−	0.992000i	$-0.459710\pi$
$661$	1.23915e12	0.252475	0.126238	+	0.992000i	$0.459710\pi$
$662$	−2.33093e12	−0.471703
$663$	0	0
$664$	−2.57978e11	−0.0515023
$665$	5.74444e11	0.113907
$666$	0	0
$667$	−1.53294e12	−0.299888
$668$	−2.95797e12	−0.574778
$669$	0	0
$670$	−5.36452e11	−0.102848
$671$	7.10733e12	1.35349
$672$	0	0
$673$	−5.79692e11	−0.108926	−0.0544628	−	0.998516i	$-0.517345\pi$
$673$	−5.79692e11	−0.108926	−0.0544628	+	0.998516i	$0.517345\pi$
$674$	−6.66766e11	−0.124453
$675$	0	0
$676$	−1.52873e12	−0.281560
$677$	−6.09981e12	−1.11601	−0.558004	−	0.829838i	$-0.688433\pi$
$677$	−6.09981e12	−1.11601	−0.558004	+	0.829838i	$0.688433\pi$
$678$	0	0
$679$	−5.74829e12	−1.03783
$680$	2.61816e12	0.469575
$681$	0	0
$682$	2.78289e12	0.492569
$683$	1.92035e12	0.337665	0.168833	−	0.985645i	$-0.446000\pi$
$683$	1.92035e12	0.337665	0.168833	+	0.985645i	$0.446000\pi$
$684$	0	0
$685$	5.10748e12	0.886338
$686$	3.82473e12	0.659389
$687$	0	0
$688$	−7.38615e11	−0.125681
$689$	4.80365e11	0.0812054
$690$	0	0
$691$	−1.22588e12	−0.204549	−0.102275	−	0.994756i	$-0.532612\pi$
$691$	−1.22588e12	−0.204549	−0.102275	+	0.994756i	$0.532612\pi$
$692$	6.47132e11	0.107279
$693$	0	0
$694$	9.27854e11	0.151832
$695$	2.35754e12	0.383290
$696$	0	0
$697$	1.10318e13	1.77051
$698$	−1.70819e12	−0.272388
$699$	0	0
$700$	3.17438e11	0.0499710
$701$	7.54657e10	0.0118037	0.00590186	−	0.999983i	$-0.498121\pi$
$701$	7.54657e10	0.0118037	0.00590186	+	0.999983i	$0.498121\pi$
$702$	0	0
$703$	2.41655e12	0.373162
$704$	8.26432e11	0.126803
$705$	0	0
$706$	6.83524e12	1.03546
$707$	−3.12900e12	−0.470997
$708$	0	0
$709$	−2.48251e12	−0.368964	−0.184482	−	0.982836i	$-0.559061\pi$
$709$	−2.48251e12	−0.368964	−0.184482	+	0.982836i	$0.559061\pi$
$710$	−8.63692e11	−0.127555
$711$	0	0
$712$	1.86093e11	0.0271375
$713$	2.06575e12	0.299347
$714$	0	0
$715$	4.23782e12	0.606409
$716$	4.43053e12	0.630009
$717$	0	0
$718$	−6.87828e12	−0.965872
$719$	5.21696e12	0.728010	0.364005	−	0.931397i	$-0.381409\pi$
$719$	5.21696e12	0.728010	0.364005	+	0.931397i	$0.381409\pi$
$720$	0	0
$721$	−5.84569e12	−0.805614
$722$	2.71737e11	0.0372161
$723$	0	0
$724$	2.78241e12	0.376355
$725$	9.31648e11	0.125236
$726$	0	0
$727$	1.23462e13	1.63919	0.819595	−	0.572944i	$-0.194199\pi$
$727$	1.23462e13	1.63919	0.819595	+	0.572944i	$0.194199\pi$
$728$	9.72277e11	0.128292
$729$	0	0
$730$	−6.56533e12	−0.855665
$731$	5.69961e12	0.738273
$732$	0	0
$733$	−7.23773e12	−0.926050	−0.463025	−	0.886345i	$-0.653236\pi$
$733$	−7.23773e12	−0.926050	−0.463025	+	0.886345i	$0.653236\pi$
$734$	2.24931e12	0.286033
$735$	0	0
$736$	6.13463e11	0.0770616
$737$	1.30668e12	0.163142
$738$	0	0
$739$	−1.58616e12	−0.195636	−0.0978179	−	0.995204i	$-0.531186\pi$
$739$	−1.58616e12	−0.195636	−0.0978179	+	0.995204i	$0.531186\pi$
$740$	−5.99999e12	−0.735542
$741$	0	0
$742$	3.93794e11	0.0476927
$743$	1.32982e13	1.60082	0.800408	−	0.599455i	$-0.204616\pi$
$743$	1.32982e13	1.60082	0.800408	+	0.599455i	$0.204616\pi$
$744$	0	0
$745$	−9.61208e12	−1.14318
$746$	6.90636e12	0.816440
$747$	0	0
$748$	−6.37726e12	−0.744864
$749$	1.07431e12	0.124727
$750$	0	0
$751$	−7.69495e12	−0.882726	−0.441363	−	0.897329i	$-0.645505\pi$
$751$	−7.69495e12	−0.882726	−0.441363	+	0.897329i	$0.645505\pi$
$752$	−1.00986e12	−0.115154
$753$	0	0
$754$	2.85353e12	0.321523
$755$	−2.20752e12	−0.247254
$756$	0	0
$757$	1.46042e13	1.61640	0.808198	−	0.588911i	$-0.200443\pi$
$757$	1.46042e13	1.61640	0.808198	+	0.588911i	$0.200443\pi$
$758$	1.14613e13	1.26102
$759$	0	0
$760$	−6.74689e11	−0.0733571
$761$	2.14254e12	0.231578	0.115789	−	0.993274i	$-0.463060\pi$
$761$	2.14254e12	0.231578	0.115789	+	0.993274i	$0.463060\pi$
$762$	0	0
$763$	6.26231e11	0.0668920
$764$	1.36671e12	0.145130
$765$	0	0
$766$	1.65234e12	0.173408
$767$	1.97886e12	0.206460
$768$	0	0
$769$	1.37576e13	1.41865	0.709326	−	0.704881i	$-0.249000\pi$
$769$	1.37576e13	1.41865	0.709326	+	0.704881i	$0.249000\pi$
$770$	3.47408e12	0.356149
$771$	0	0
$772$	7.06428e12	0.715797
$773$	−1.78934e13	−1.80254	−0.901270	−	0.433257i	$-0.857364\pi$
$773$	−1.78934e13	−1.80254	−0.901270	+	0.433257i	$0.857364\pi$
$774$	0	0
$775$	−1.25546e12	−0.125010
$776$	6.75142e12	0.668371
$777$	0	0
$778$	5.59897e12	0.547898
$779$	−2.84284e12	−0.276588
$780$	0	0
$781$	2.10377e12	0.202334
$782$	−4.73385e12	−0.452673
$783$	0	0
$784$	−1.84756e12	−0.174653
$785$	−1.34691e13	−1.26598
$786$	0	0
$787$	1.90983e13	1.77464	0.887318	−	0.461158i	$-0.152566\pi$
$787$	1.90983e13	1.77464	0.887318	+	0.461158i	$0.152566\pi$
$788$	2.46030e12	0.227310
$789$	0	0
$790$	1.79624e12	0.164075
$791$	−8.04850e12	−0.731006
$792$	0	0
$793$	−9.82076e12	−0.881893
$794$	−4.53823e12	−0.405224
$795$	0	0
$796$	7.39367e12	0.652756
$797$	4.39907e10	0.00386188	0.00193094	−	0.999998i	$-0.499385\pi$
$797$	4.39907e10	0.00386188	0.00193094	+	0.999998i	$0.499385\pi$
$798$	0	0
$799$	7.79267e12	0.676434
$800$	−3.72833e11	−0.0321818
$801$	0	0
$802$	1.59050e13	1.35753
$803$	1.59917e13	1.35730
$804$	0	0
$805$	2.57882e12	0.216441
$806$	−3.84534e12	−0.320943
$807$	0	0
$808$	3.67504e12	0.303327
$809$	1.85839e13	1.52535	0.762675	−	0.646782i	$-0.223886\pi$
$809$	1.85839e13	1.52535	0.762675	+	0.646782i	$0.223886\pi$
$810$	0	0
$811$	1.29810e13	1.05369	0.526847	−	0.849960i	$-0.323374\pi$
$811$	1.29810e13	1.05369	0.526847	+	0.849960i	$0.323374\pi$
$812$	2.33927e12	0.188833
$813$	0	0
$814$	1.46147e13	1.16675
$815$	−1.15190e13	−0.914543
$816$	0	0
$817$	−1.46877e12	−0.115333
$818$	3.85777e12	0.301264
$819$	0	0
$820$	7.05842e12	0.545186
$821$	4.47787e12	0.343975	0.171987	−	0.985099i	$-0.444981\pi$
$821$	4.47787e12	0.343975	0.171987	+	0.985099i	$0.444981\pi$
$822$	0	0
$823$	1.13315e13	0.860973	0.430487	−	0.902597i	$-0.358342\pi$
$823$	1.13315e13	0.860973	0.430487	+	0.902597i	$0.358342\pi$
$824$	6.86581e12	0.518823
$825$	0	0
$826$	1.62223e12	0.121256
$827$	1.46669e13	1.09034	0.545171	−	0.838325i	$-0.316465\pi$
$827$	1.46669e13	1.09034	0.545171	+	0.838325i	$0.316465\pi$
$828$	0	0
$829$	−2.45530e13	−1.80555	−0.902774	−	0.430115i	$-0.858473\pi$
$829$	−2.45530e13	−1.80555	−0.902774	+	0.430115i	$0.858473\pi$
$830$	1.27371e12	0.0931581
$831$	0	0
$832$	−1.14195e12	−0.0826211
$833$	1.42569e13	1.02594
$834$	0	0
$835$	1.46044e13	1.03967
$836$	1.64339e12	0.116363
$837$	0	0
$838$	−1.12496e13	−0.788025
$839$	−8.71743e12	−0.607379	−0.303689	−	0.952771i	$-0.598219\pi$
$839$	−8.71743e12	−0.607379	−0.303689	+	0.952771i	$0.598219\pi$
$840$	0	0
$841$	−7.64163e12	−0.526749
$842$	−4.29231e12	−0.294298
$843$	0	0
$844$	5.80067e12	0.393493
$845$	7.54780e12	0.509290
$846$	0	0
$847$	−2.38965e11	−0.0159536
$848$	−4.62514e11	−0.0307145
$849$	0	0
$850$	2.87701e12	0.189041
$851$	1.08485e13	0.709066
$852$	0	0
$853$	1.30680e12	0.0845159	0.0422580	−	0.999107i	$-0.486545\pi$
$853$	1.30680e12	0.0845159	0.0422580	+	0.999107i	$0.486545\pi$
$854$	−8.05087e12	−0.517944
$855$	0	0
$856$	−1.26178e12	−0.0803254
$857$	1.57408e12	0.0996811	0.0498405	−	0.998757i	$-0.484129\pi$
$857$	1.57408e12	0.0996811	0.0498405	+	0.998757i	$0.484129\pi$
$858$	0	0
$859$	1.39034e13	0.871265	0.435633	−	0.900125i	$-0.356525\pi$
$859$	1.39034e13	0.871265	0.435633	+	0.900125i	$0.356525\pi$
$860$	3.64676e12	0.227334
$861$	0	0
$862$	−9.53453e11	−0.0588189
$863$	−2.53344e11	−0.0155476	−0.00777378	−	0.999970i	$-0.502474\pi$
$863$	−2.53344e11	−0.0155476	−0.00777378	+	0.999970i	$0.502474\pi$
$864$	0	0
$865$	−3.19508e12	−0.194048
$866$	−1.86064e13	−1.12417
$867$	0	0
$868$	−3.15234e12	−0.188492
$869$	−4.37525e12	−0.260264
$870$	0	0
$871$	−1.80554e12	−0.106298
$872$	−7.35513e11	−0.0430791
$873$	0	0
$874$	1.21990e12	0.0707166
$875$	−1.01765e13	−0.586897
$876$	0	0
$877$	−4.95849e12	−0.283042	−0.141521	−	0.989935i	$-0.545199\pi$
$877$	−4.95849e12	−0.283042	−0.141521	+	0.989935i	$0.545199\pi$
$878$	−2.11944e13	−1.20364
$879$	0	0
$880$	−4.08034e12	−0.229364
$881$	1.32981e13	0.743702	0.371851	−	0.928292i	$-0.378723\pi$
$881$	1.32981e13	0.743702	0.371851	+	0.928292i	$0.378723\pi$
$882$	0	0
$883$	1.27657e13	0.706677	0.353338	−	0.935496i	$-0.385046\pi$
$883$	1.27657e13	0.706677	0.353338	+	0.935496i	$0.385046\pi$
$884$	8.81196e12	0.485330
$885$	0	0
$886$	−1.19789e13	−0.653079
$887$	−1.14862e13	−0.623044	−0.311522	−	0.950239i	$-0.600839\pi$
$887$	−1.14862e13	−0.623044	−0.311522	+	0.950239i	$0.600839\pi$
$888$	0	0
$889$	1.57392e13	0.845131
$890$	−9.18797e11	−0.0490868
$891$	0	0
$892$	−1.49649e13	−0.791465
$893$	−2.00814e12	−0.105673
$894$	0	0
$895$	−2.18748e13	−1.13957
$896$	−9.36146e11	−0.0485241
$897$	0	0
$898$	−1.29192e13	−0.662967
$899$	−9.25179e12	−0.472397
$900$	0	0
$901$	3.56904e12	0.180422
$902$	−1.71928e13	−0.864801
$903$	0	0
$904$	9.45303e12	0.470775
$905$	−1.37376e13	−0.680757
$906$	0	0
$907$	1.87998e13	0.922400	0.461200	−	0.887296i	$-0.347419\pi$
$907$	1.87998e13	0.922400	0.461200	+	0.887296i	$0.347419\pi$
$908$	1.23440e12	0.0602656
$909$	0	0
$910$	−4.80042e12	−0.232056
$911$	1.56523e12	0.0752914	0.0376457	−	0.999291i	$-0.488014\pi$
$911$	1.56523e12	0.0752914	0.0376457	+	0.999291i	$0.488014\pi$
$912$	0	0
$913$	−3.10249e12	−0.147772
$914$	−3.35349e12	−0.158942
$915$	0	0
$916$	−1.83253e12	−0.0860046
$917$	−8.84813e12	−0.413228
$918$	0	0
$919$	2.72891e13	1.26203	0.631014	−	0.775771i	$-0.282639\pi$
$919$	2.72891e13	1.26203	0.631014	+	0.775771i	$0.282639\pi$
$920$	−3.02885e12	−0.139390
$921$	0	0
$922$	−1.80516e13	−0.822673
$923$	−2.90694e12	−0.131834
$924$	0	0
$925$	−6.59320e12	−0.296114
$926$	−1.56082e13	−0.697595
$927$	0	0
$928$	−2.74749e12	−0.121610
$929$	3.27413e13	1.44220	0.721100	−	0.692831i	$-0.243637\pi$
$929$	3.27413e13	1.44220	0.721100	+	0.692831i	$0.243637\pi$
$930$	0	0
$931$	−3.67395e12	−0.160273
$932$	−1.15901e13	−0.503169
$933$	0	0
$934$	8.25404e12	0.354900
$935$	3.14864e13	1.34732
$936$	0	0
$937$	−2.41823e13	−1.02487	−0.512435	−	0.858726i	$-0.671256\pi$
$937$	−2.41823e13	−1.02487	−0.512435	+	0.858726i	$0.671256\pi$
$938$	−1.48015e12	−0.0624300
$939$	0	0
$940$	4.98596e12	0.208292
$941$	−7.48541e12	−0.311216	−0.155608	−	0.987819i	$-0.549734\pi$
$941$	−7.48541e12	−0.311216	−0.155608	+	0.987819i	$0.549734\pi$
$942$	0	0
$943$	−1.27622e13	−0.525562
$944$	−1.90533e12	−0.0780900
$945$	0	0
$946$	−8.88272e12	−0.360608
$947$	4.31138e13	1.74197	0.870986	−	0.491307i	$-0.163481\pi$
$947$	4.31138e13	1.74197	0.870986	+	0.491307i	$0.163481\pi$
$948$	0	0
$949$	−2.20970e13	−0.884374
$950$	−7.41394e11	−0.0295320
$951$	0	0
$952$	7.22388e12	0.285039
$953$	9.69686e12	0.380814	0.190407	−	0.981705i	$-0.439019\pi$
$953$	9.69686e12	0.380814	0.190407	+	0.981705i	$0.439019\pi$
$954$	0	0
$955$	−6.74785e12	−0.262513
$956$	1.80588e13	0.699244
$957$	0	0
$958$	−3.02745e13	−1.16127
$959$	1.40923e13	0.538019
$960$	0	0
$961$	−1.39722e13	−0.528456
$962$	−2.01942e13	−0.760221
$963$	0	0
$964$	2.00483e13	0.747708
$965$	−3.48784e13	−1.29474
$966$	0	0
$967$	2.84710e13	1.04709	0.523545	−	0.851998i	$-0.324609\pi$
$967$	2.84710e13	1.04709	0.523545	+	0.851998i	$0.324609\pi$
$968$	2.80667e11	0.0102743
$969$	0	0
$970$	−3.33337e13	−1.20896
$971$	−3.67091e13	−1.32522	−0.662609	−	0.748965i	$-0.730551\pi$
$971$	−3.67091e13	−1.32522	−0.662609	+	0.748965i	$0.730551\pi$
$972$	0	0
$973$	6.50481e12	0.232663
$974$	2.16406e13	0.770467
$975$	0	0
$976$	9.45582e12	0.333561
$977$	4.89209e13	1.71778	0.858892	−	0.512157i	$-0.171153\pi$
$977$	4.89209e13	1.71778	0.858892	+	0.512157i	$0.171153\pi$
$978$	0	0
$979$	2.23799e12	0.0778638
$980$	9.12195e12	0.315915
$981$	0	0
$982$	−1.47723e13	−0.506927
$983$	1.06278e13	0.363038	0.181519	−	0.983387i	$-0.441899\pi$
$983$	1.06278e13	0.363038	0.181519	+	0.983387i	$0.441899\pi$
$984$	0	0
$985$	−1.21472e13	−0.411162
$986$	2.12013e13	0.714360
$987$	0	0
$988$	−2.27081e12	−0.0758183
$989$	−6.59366e12	−0.219151
$990$	0	0
$991$	−9.73679e12	−0.320689	−0.160345	−	0.987061i	$-0.551261\pi$
$991$	−9.73679e12	−0.320689	−0.160345	+	0.987061i	$0.551261\pi$
$992$	3.70245e12	0.121391
$993$	0	0
$994$	−2.38305e12	−0.0774275
$995$	−3.65047e13	−1.18072
$996$	0	0
$997$	1.04996e13	0.336547	0.168273	−	0.985740i	$-0.446181\pi$
$997$	1.04996e13	0.336547	0.168273	+	0.985740i	$0.446181\pi$
$998$	3.16985e13	1.01147
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.10.a.l.1.2		4
3.2	odd	2		38.10.a.d.1.1	✓	4
12.11	even	2		304.10.a.e.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.d.1.1	✓	4	3.2	odd	2
304.10.a.e.1.4		4	12.11	even	2
342.10.a.l.1.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	342.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +256.000 q^{4} -1263.95 q^{5} -3487.42 q^{7} +4096.00 q^{8} +O(q^{10})\)	\(q+16.0000 q^{2} +256.000 q^{4} -1263.95 q^{5} -3487.42 q^{7} +4096.00 q^{8} -20223.2 q^{10} +49259.2 q^{11} -68065.3 q^{13} -55798.7 q^{14} +65536.0 q^{16} -505716. q^{17} +130321. q^{19} -323571. q^{20} +788147. q^{22} +585044. q^{23} -355562. q^{25} -1.08905e6 q^{26} -892779. q^{28} -2.62021e6 q^{29} +3.53093e6 q^{31} +1.04858e6 q^{32} -8.09145e6 q^{34} +4.40791e6 q^{35} +1.85431e7 q^{37} +2.08514e6 q^{38} -5.17713e6 q^{40} -2.18141e7 q^{41} -1.12704e7 q^{43} +1.26104e7 q^{44} +9.36070e6 q^{46} -1.54092e7 q^{47} -2.81915e7 q^{49} -5.68899e6 q^{50} -1.74247e7 q^{52} -7.05741e6 q^{53} -6.22611e7 q^{55} -1.42845e7 q^{56} -4.19234e7 q^{58} -2.90730e7 q^{59} +1.44284e8 q^{61} +5.64949e7 q^{62} +1.67772e7 q^{64} +8.60310e7 q^{65} +2.65266e7 q^{67} -1.29463e8 q^{68} +7.05266e7 q^{70} +4.27081e7 q^{71} +3.24644e8 q^{73} +2.96689e8 q^{74} +3.33622e7 q^{76} -1.71787e8 q^{77} -8.88210e7 q^{79} -8.28341e7 q^{80} -3.49026e8 q^{82} -6.29830e7 q^{83} +6.39198e8 q^{85} -1.80326e8 q^{86} +2.01766e8 q^{88} +4.54329e7 q^{89} +2.37372e8 q^{91} +1.49771e8 q^{92} -2.46547e8 q^{94} -1.64719e8 q^{95} +1.64830e9 q^{97} -4.51064e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8}+O(q^{10}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8} + 22320 q^{10} + 104249 q^{11} + 120486 q^{13} + 196912 q^{14} + 262144 q^{16} + 412139 q^{17} + 521284 q^{19} + 357120 q^{20} + 1667984 q^{22} - 3010300 q^{23} + 9760585 q^{25} + 1927776 q^{26} + 3150592 q^{28} - 6153240 q^{29} + 12774024 q^{31} + 4194304 q^{32} + 6594224 q^{34} - 9823425 q^{35} + 20506048 q^{37} + 8340544 q^{38} + 5713920 q^{40} - 11620300 q^{41} + 7698327 q^{43} + 26687744 q^{44} - 48164800 q^{46} + 31581083 q^{47} + 18970383 q^{49} + 156169360 q^{50} + 30844416 q^{52} - 72549422 q^{53} + 21332505 q^{55} + 50409472 q^{56} - 98451840 q^{58} + 149234120 q^{59} + 129004373 q^{61} + 204384384 q^{62} + 67108864 q^{64} - 124691700 q^{65} + 132595266 q^{67} + 105507584 q^{68} - 157174800 q^{70} + 47138482 q^{71} - 39332795 q^{73} + 328096768 q^{74} + 133448704 q^{76} + 165933719 q^{77} - 307010840 q^{79} + 91422720 q^{80} - 185924800 q^{82} + 746568232 q^{83} - 105005985 q^{85} + 123173232 q^{86} + 427003904 q^{88} - 286943482 q^{89} + 3155781114 q^{91} - 770636800 q^{92} + 505297328 q^{94} + 181797795 q^{95} + 793519958 q^{97} + 303526128 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8 + 22320 * q^10 + 104249 * q^11 + 120486 * q^13 + 196912 * q^14 + 262144 * q^16 + 412139 * q^17 + 521284 * q^19 + 357120 * q^20 + 1667984 * q^22 - 3010300 * q^23 + 9760585 * q^25 + 1927776 * q^26 + 3150592 * q^28 - 6153240 * q^29 + 12774024 * q^31 + 4194304 * q^32 + 6594224 * q^34 - 9823425 * q^35 + 20506048 * q^37 + 8340544 * q^38 + 5713920 * q^40 - 11620300 * q^41 + 7698327 * q^43 + 26687744 * q^44 - 48164800 * q^46 + 31581083 * q^47 + 18970383 * q^49 + 156169360 * q^50 + 30844416 * q^52 - 72549422 * q^53 + 21332505 * q^55 + 50409472 * q^56 - 98451840 * q^58 + 149234120 * q^59 + 129004373 * q^61 + 204384384 * q^62 + 67108864 * q^64 - 124691700 * q^65 + 132595266 * q^67 + 105507584 * q^68 - 157174800 * q^70 + 47138482 * q^71 - 39332795 * q^73 + 328096768 * q^74 + 133448704 * q^76 + 165933719 * q^77 - 307010840 * q^79 + 91422720 * q^80 - 185924800 * q^82 + 746568232 * q^83 - 105005985 * q^85 + 123173232 * q^86 + 427003904 * q^88 - 286943482 * q^89 + 3155781114 * q^91 - 770636800 * q^92 + 505297328 * q^94 + 181797795 * q^95 + 793519958 * q^97 + 303526128 * q^98

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