LMFDB - Embedded newform 162.10.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,10,Mod(1,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("162.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	162.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:	$83.4358054585$
Analytic rank:	$1$
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} - 656x^{2} - 2001x + 14530 $ x^4 - 656x^2 - 2001x + 14530
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 18)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-23.3115$ of defining polynomial
Character	$\chi$	$=$	162.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +256.000 q^{4} +1795.52 q^{5} -11181.7 q^{7} +4096.00 q^{8} +O(q^{10})$	\(q+16.0000 q^{2} +256.000 q^{4} +1795.52 q^{5} -11181.7 q^{7} +4096.00 q^{8} +28728.3 q^{10} +18426.2 q^{11} +21176.9 q^{13} -178907. q^{14} +65536.0 q^{16} -660849. q^{17} +522089. q^{19} +459652. q^{20} +294819. q^{22} -1.04859e6 q^{23} +1.27075e6 q^{25} +338831. q^{26} -2.86251e6 q^{28} -2.60498e6 q^{29} -53924.6 q^{31} +1.04858e6 q^{32} -1.05736e7 q^{34} -2.00769e7 q^{35} -1.93749e7 q^{37} +8.35343e6 q^{38} +7.35444e6 q^{40} +1.29777e6 q^{41} -1.47062e7 q^{43} +4.71711e6 q^{44} -1.67774e7 q^{46} +3.06582e7 q^{47} +8.46761e7 q^{49} +2.03321e7 q^{50} +5.42129e6 q^{52} -5.86557e7 q^{53} +3.30845e7 q^{55} -4.58001e7 q^{56} -4.16797e7 q^{58} -2.29677e7 q^{59} +1.80796e8 q^{61} -862794. q^{62} +1.67772e7 q^{64} +3.80235e7 q^{65} -2.37946e8 q^{67} -1.69177e8 q^{68} -3.21230e8 q^{70} -4.73186e7 q^{71} -7.05287e7 q^{73} -3.09999e8 q^{74} +1.33655e8 q^{76} -2.06036e8 q^{77} -2.57664e8 q^{79} +1.17671e8 q^{80} +2.07643e7 q^{82} -2.93491e8 q^{83} -1.18656e9 q^{85} -2.35298e8 q^{86} +7.54737e7 q^{88} -1.41522e8 q^{89} -2.36793e8 q^{91} -2.68439e8 q^{92} +4.90531e8 q^{94} +9.37420e8 q^{95} +3.28639e8 q^{97} +1.35482e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 1024 q^{4} + 171 q^{5} - 7135 q^{7} + 16384 q^{8}+O(q^{10}) $ 4 * q + 64 * q^2 + 1024 * q^4 + 171 * q^5 - 7135 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 171 q^{5} - 7135 q^{7} + 16384 q^{8} + 2736 q^{10} - 26130 q^{11} + 4163 q^{13} - 114160 q^{14} + 262144 q^{16} - 549255 q^{17} - 218191 q^{19} + 43776 q^{20} - 418080 q^{22} - 289383 q^{23} - 2947937 q^{25} + 66608 q^{26} - 1826560 q^{28} - 601707 q^{29} - 5671315 q^{31} + 4194304 q^{32} - 8788080 q^{34} - 14893965 q^{35} - 19368574 q^{37} - 3491056 q^{38} + 700416 q^{40} - 18418410 q^{41} - 35096140 q^{43} - 6689280 q^{44} - 4630128 q^{46} - 79830825 q^{47} + 40540299 q^{49} - 47166992 q^{50} + 1065728 q^{52} - 165348618 q^{53} + 28264221 q^{55} - 29224960 q^{56} - 9627312 q^{58} - 90704166 q^{59} + 122811677 q^{61} - 90741040 q^{62} + 67108864 q^{64} - 116600103 q^{65} - 221601736 q^{67} - 140609280 q^{68} - 238303440 q^{70} - 138204120 q^{71} - 494458507 q^{73} - 309897184 q^{74} - 55856896 q^{76} - 548139525 q^{77} - 592840885 q^{79} + 11206656 q^{80} - 294694560 q^{82} - 478410747 q^{83} - 1468792818 q^{85} - 561538240 q^{86} - 107028480 q^{88} - 437759976 q^{89} - 1847756531 q^{91} - 74082048 q^{92} - 1277293200 q^{94} + 813906756 q^{95} - 2679512242 q^{97} + 648644784 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 171 * q^5 - 7135 * q^7 + 16384 * q^8 + 2736 * q^10 - 26130 * q^11 + 4163 * q^13 - 114160 * q^14 + 262144 * q^16 - 549255 * q^17 - 218191 * q^19 + 43776 * q^20 - 418080 * q^22 - 289383 * q^23 - 2947937 * q^25 + 66608 * q^26 - 1826560 * q^28 - 601707 * q^29 - 5671315 * q^31 + 4194304 * q^32 - 8788080 * q^34 - 14893965 * q^35 - 19368574 * q^37 - 3491056 * q^38 + 700416 * q^40 - 18418410 * q^41 - 35096140 * q^43 - 6689280 * q^44 - 4630128 * q^46 - 79830825 * q^47 + 40540299 * q^49 - 47166992 * q^50 + 1065728 * q^52 - 165348618 * q^53 + 28264221 * q^55 - 29224960 * q^56 - 9627312 * q^58 - 90704166 * q^59 + 122811677 * q^61 - 90741040 * q^62 + 67108864 * q^64 - 116600103 * q^65 - 221601736 * q^67 - 140609280 * q^68 - 238303440 * q^70 - 138204120 * q^71 - 494458507 * q^73 - 309897184 * q^74 - 55856896 * q^76 - 548139525 * q^77 - 592840885 * q^79 + 11206656 * q^80 - 294694560 * q^82 - 478410747 * q^83 - 1468792818 * q^85 - 561538240 * q^86 - 107028480 * q^88 - 437759976 * q^89 - 1847756531 * q^91 - 74082048 * q^92 - 1277293200 * q^94 + 813906756 * q^95 - 2679512242 * q^97 + 648644784 * 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
$5$	1795.52	1.28477	0.642383	−	0.766383i	$-0.277946\pi$
$5$	1795.52	1.28477	0.642383	+	0.766383i	$0.277946\pi$
$6$	0	0
$7$	−11181.7	−1.76021	−0.880107	−	0.474776i	$-0.842529\pi$
$7$	−11181.7	−1.76021	−0.880107	+	0.474776i	$0.842529\pi$
$8$	4096.00	0.353553
$9$	0	0
$10$	28728.3	0.908467
$11$	18426.2	0.379462	0.189731	−	0.981836i	$-0.439238\pi$
$11$	18426.2	0.379462	0.189731	+	0.981836i	$0.439238\pi$
$12$	0	0
$13$	21176.9	0.205645	0.102822	−	0.994700i	$-0.467213\pi$
$13$	21176.9	0.205645	0.102822	+	0.994700i	$0.467213\pi$
$14$	−178907.	−1.24466
$15$	0	0
$16$	65536.0	0.250000
$17$	−660849.	−1.91903	−0.959515	−	0.281656i	$-0.909116\pi$
$17$	−660849.	−1.91903	−0.959515	+	0.281656i	$0.909116\pi$
$18$	0	0
$19$	522089.	0.919081	0.459540	−	0.888157i	$-0.348014\pi$
$19$	522089.	0.919081	0.459540	+	0.888157i	$0.348014\pi$
$20$	459652.	0.642383
$21$	0	0
$22$	294819.	0.268320
$23$	−1.04859e6	−0.781322	−0.390661	−	0.920535i	$-0.627754\pi$
$23$	−1.04859e6	−0.781322	−0.390661	+	0.920535i	$0.627754\pi$
$24$	0	0
$25$	1.27075e6	0.650626
$26$	338831.	0.145413
$27$	0	0
$28$	−2.86251e6	−0.880107
$29$	−2.60498e6	−0.683933	−0.341966	−	0.939712i	$-0.611093\pi$
$29$	−2.60498e6	−0.683933	−0.341966	+	0.939712i	$0.611093\pi$
$30$	0	0
$31$	−53924.6	−0.0104872	−0.00524360	−	0.999986i	$-0.501669\pi$
$31$	−53924.6	−0.0104872	−0.00524360	+	0.999986i	$0.501669\pi$
$32$	1.04858e6	0.176777
$33$	0	0
$34$	−1.05736e7	−1.35696
$35$	−2.00769e7	−2.26146
$36$	0	0
$37$	−1.93749e7	−1.69955	−0.849773	−	0.527150i	$-0.823261\pi$
$37$	−1.93749e7	−1.69955	−0.849773	+	0.527150i	$0.823261\pi$
$38$	8.35343e6	0.649888
$39$	0	0
$40$	7.35444e6	0.454234
$41$	1.29777e6	0.0717249	0.0358625	−	0.999357i	$-0.488582\pi$
$41$	1.29777e6	0.0717249	0.0358625	+	0.999357i	$0.488582\pi$
$42$	0	0
$43$	−1.47062e7	−0.655981	−0.327990	−	0.944681i	$-0.606371\pi$
$43$	−1.47062e7	−0.655981	−0.327990	+	0.944681i	$0.606371\pi$
$44$	4.71711e6	0.189731
$45$	0	0
$46$	−1.67774e7	−0.552478
$47$	3.06582e7	0.916444	0.458222	−	0.888838i	$-0.348487\pi$
$47$	3.06582e7	0.916444	0.458222	+	0.888838i	$0.348487\pi$
$48$	0	0
$49$	8.46761e7	2.09835
$50$	2.03321e7	0.460062
$51$	0	0
$52$	5.42129e6	0.102822
$53$	−5.86557e7	−1.02110	−0.510551	−	0.859848i	$-0.670558\pi$
$53$	−5.86557e7	−1.02110	−0.510551	+	0.859848i	$0.670558\pi$
$54$	0	0
$55$	3.30845e7	0.487521
$56$	−4.58001e7	−0.622330
$57$	0	0
$58$	−4.16797e7	−0.483613
$59$	−2.29677e7	−0.246765	−0.123383	−	0.992359i	$-0.539374\pi$
$59$	−2.29677e7	−0.246765	−0.123383	+	0.992359i	$0.539374\pi$
$60$	0	0
$61$	1.80796e8	1.67187	0.835937	−	0.548825i	$-0.184925\pi$
$61$	1.80796e8	1.67187	0.835937	+	0.548825i	$0.184925\pi$
$62$	−862794.	−0.00741557
$63$	0	0
$64$	1.67772e7	0.125000
$65$	3.80235e7	0.264206
$66$	0	0
$67$	−2.37946e8	−1.44259	−0.721294	−	0.692629i	$-0.756452\pi$
$67$	−2.37946e8	−1.44259	−0.721294	+	0.692629i	$0.756452\pi$
$68$	−1.69177e8	−0.959515
$69$	0	0
$70$	−3.21230e8	−1.59910
$71$	−4.73186e7	−0.220988	−0.110494	−	0.993877i	$-0.535243\pi$
$71$	−4.73186e7	−0.220988	−0.110494	+	0.993877i	$0.535243\pi$
$72$	0	0
$73$	−7.05287e7	−0.290679	−0.145339	−	0.989382i	$-0.546427\pi$
$73$	−7.05287e7	−0.290679	−0.145339	+	0.989382i	$0.546427\pi$
$74$	−3.09999e8	−1.20176
$75$	0	0
$76$	1.33655e8	0.459540
$77$	−2.06036e8	−0.667935
$78$	0	0
$79$	−2.57664e8	−0.744272	−0.372136	−	0.928178i	$-0.621374\pi$
$79$	−2.57664e8	−0.744272	−0.372136	+	0.928178i	$0.621374\pi$
$80$	1.17671e8	0.321192
$81$	0	0
$82$	2.07643e7	0.0507172
$83$	−2.93491e8	−0.678802	−0.339401	−	0.940642i	$-0.610224\pi$
$83$	−2.93491e8	−0.678802	−0.339401	+	0.940642i	$0.610224\pi$
$84$	0	0
$85$	−1.18656e9	−2.46551
$86$	−2.35298e8	−0.463848
$87$	0	0
$88$	7.54737e7	0.134160
$89$	−1.41522e8	−0.239093	−0.119547	−	0.992829i	$-0.538144\pi$
$89$	−1.41522e8	−0.239093	−0.119547	+	0.992829i	$0.538144\pi$
$90$	0	0
$91$	−2.36793e8	−0.361979
$92$	−2.68439e8	−0.390661
$93$	0	0
$94$	4.90531e8	0.648024
$95$	9.37420e8	1.18080
$96$	0	0
$97$	3.28639e8	0.376918	0.188459	−	0.982081i	$-0.439651\pi$
$97$	3.28639e8	0.376918	0.188459	+	0.982081i	$0.439651\pi$
$98$	1.35482e9	1.48376
$99$	0	0
$100$	3.25313e8	0.325313
$101$	−4.94942e8	−0.473269	−0.236635	−	0.971599i	$-0.576044\pi$
$101$	−4.94942e8	−0.473269	−0.236635	+	0.971599i	$0.576044\pi$
$102$	0	0
$103$	−3.99056e8	−0.349355	−0.174677	−	0.984626i	$-0.555888\pi$
$103$	−3.99056e8	−0.349355	−0.174677	+	0.984626i	$0.555888\pi$
$104$	8.67406e7	0.0727064
$105$	0	0
$106$	−9.38491e8	−0.722028
$107$	1.26980e8	0.0936502	0.0468251	−	0.998903i	$-0.485090\pi$
$107$	1.26980e8	0.0936502	0.0468251	+	0.998903i	$0.485090\pi$
$108$	0	0
$109$	−2.21053e9	−1.49995	−0.749974	−	0.661467i	$-0.769934\pi$
$109$	−2.21053e9	−1.49995	−0.749974	+	0.661467i	$0.769934\pi$
$110$	5.29353e8	0.344729
$111$	0	0
$112$	−7.32802e8	−0.440053
$113$	−6.67910e8	−0.385359	−0.192679	−	0.981262i	$-0.561718\pi$
$113$	−6.67910e8	−0.385359	−0.192679	+	0.981262i	$0.561718\pi$
$114$	0	0
$115$	−1.88276e9	−1.00382
$116$	−6.66875e8	−0.341966
$117$	0	0
$118$	−3.67484e8	−0.174489
$119$	7.38939e9	3.37790
$120$	0	0
$121$	−2.01842e9	−0.856008
$122$	2.89273e9	1.18219
$123$	0	0
$124$	−1.38047e7	−0.00524360
$125$	−1.22521e9	−0.448864
$126$	0	0
$127$	−2.12304e9	−0.724171	−0.362085	−	0.932145i	$-0.617935\pi$
$127$	−2.12304e9	−0.724171	−0.362085	+	0.932145i	$0.617935\pi$
$128$	2.68435e8	0.0883883
$129$	0	0
$130$	6.08376e8	0.186822
$131$	4.97425e7	0.0147573	0.00737865	−	0.999973i	$-0.497651\pi$
$131$	4.97425e7	0.0147573	0.00737865	+	0.999973i	$0.497651\pi$
$132$	0	0
$133$	−5.83783e9	−1.61778
$134$	−3.80714e9	−1.02006
$135$	0	0
$136$	−2.70684e9	−0.678480
$137$	−6.77938e9	−1.64417	−0.822087	−	0.569362i	$-0.807190\pi$
$137$	−6.77938e9	−1.64417	−0.822087	+	0.569362i	$0.807190\pi$
$138$	0	0
$139$	4.75312e9	1.07997	0.539985	−	0.841675i	$-0.318430\pi$
$139$	4.75312e9	1.07997	0.539985	+	0.841675i	$0.318430\pi$
$140$	−5.13968e9	−1.13073
$141$	0	0
$142$	−7.57098e8	−0.156262
$143$	3.90210e8	0.0780344
$144$	0	0
$145$	−4.67728e9	−0.878694
$146$	−1.12846e9	−0.205541
$147$	0	0
$148$	−4.95999e9	−0.849773
$149$	7.20294e9	1.19721	0.598606	−	0.801043i	$-0.295721\pi$
$149$	7.20294e9	1.19721	0.598606	+	0.801043i	$0.295721\pi$
$150$	0	0
$151$	4.97363e9	0.778534	0.389267	−	0.921125i	$-0.372728\pi$
$151$	4.97363e9	0.778534	0.389267	+	0.921125i	$0.372728\pi$
$152$	2.13848e9	0.324944
$153$	0	0
$154$	−3.29657e9	−0.472301
$155$	−9.68225e7	−0.0134736
$156$	0	0
$157$	−6.93521e8	−0.0910985	−0.0455493	−	0.998962i	$-0.514504\pi$
$157$	−6.93521e8	−0.0910985	−0.0455493	+	0.998962i	$0.514504\pi$
$158$	−4.12262e9	−0.526279
$159$	0	0
$160$	1.88274e9	0.227117
$161$	1.17250e10	1.37529
$162$	0	0
$163$	7.96784e9	0.884090	0.442045	−	0.896993i	$-0.354253\pi$
$163$	7.96784e9	0.884090	0.442045	+	0.896993i	$0.354253\pi$
$164$	3.32229e8	0.0358625
$165$	0	0
$166$	−4.69585e9	−0.479985
$167$	6.13828e9	0.610692	0.305346	−	0.952241i	$-0.401228\pi$
$167$	6.13828e9	0.610692	0.305346	+	0.952241i	$0.401228\pi$
$168$	0	0
$169$	−1.01560e10	−0.957710
$170$	−1.89850e10	−1.74338
$171$	0	0
$172$	−3.76477e9	−0.327990
$173$	3.74038e9	0.317474	0.158737	−	0.987321i	$-0.449258\pi$
$173$	3.74038e9	0.317474	0.158737	+	0.987321i	$0.449258\pi$
$174$	0	0
$175$	−1.42091e10	−1.14524
$176$	1.20758e9	0.0948656
$177$	0	0
$178$	−2.26434e9	−0.169065
$179$	2.42118e10	1.76274	0.881369	−	0.472429i	$-0.156623\pi$
$179$	2.42118e10	1.76274	0.881369	+	0.472429i	$0.156623\pi$
$180$	0	0
$181$	1.15322e10	0.798657	0.399328	−	0.916808i	$-0.369243\pi$
$181$	1.15322e10	0.798657	0.399328	+	0.916808i	$0.369243\pi$
$182$	−3.78869e9	−0.255958
$183$	0	0
$184$	−4.29502e9	−0.276239
$185$	−3.47880e10	−2.18352
$186$	0	0
$187$	−1.21769e10	−0.728200
$188$	7.84849e9	0.458222
$189$	0	0
$190$	1.49987e10	0.834955
$191$	−1.81715e10	−0.987963	−0.493981	−	0.869473i	$-0.664459\pi$
$191$	−1.81715e10	−0.987963	−0.493981	+	0.869473i	$0.664459\pi$
$192$	0	0
$193$	−1.91214e10	−0.991999	−0.496000	−	0.868323i	$-0.665198\pi$
$193$	−1.91214e10	−0.991999	−0.496000	+	0.868323i	$0.665198\pi$
$194$	5.25823e9	0.266521
$195$	0	0
$196$	2.16771e10	1.04918
$197$	−1.18643e10	−0.561233	−0.280617	−	0.959820i	$-0.590539\pi$
$197$	−1.18643e10	−0.561233	−0.280617	+	0.959820i	$0.590539\pi$
$198$	0	0
$199$	−2.22347e10	−1.00506	−0.502530	−	0.864560i	$-0.667598\pi$
$199$	−2.22347e10	−1.00506	−0.502530	+	0.864560i	$0.667598\pi$
$200$	5.20501e9	0.230031
$201$	0	0
$202$	−7.91907e9	−0.334652
$203$	2.91280e10	1.20387
$204$	0	0
$205$	2.33017e9	0.0921498
$206$	−6.38490e9	−0.247031
$207$	0	0
$208$	1.38785e9	0.0514112
$209$	9.62012e9	0.348757
$210$	0	0
$211$	5.60686e10	1.94737	0.973686	−	0.227896i	$-0.0731845\pi$
$211$	5.60686e10	1.94737	0.973686	+	0.227896i	$0.0731845\pi$
$212$	−1.50159e10	−0.510551
$213$	0	0
$214$	2.03168e9	0.0662207
$215$	−2.64051e10	−0.842782
$216$	0	0
$217$	6.02967e8	0.0184597
$218$	−3.53684e10	−1.06062
$219$	0	0
$220$	8.46964e9	0.243760
$221$	−1.39947e10	−0.394639
$222$	0	0
$223$	6.43413e10	1.74228	0.871139	−	0.491036i	$-0.163382\pi$
$223$	6.43413e10	1.74228	0.871139	+	0.491036i	$0.163382\pi$
$224$	−1.17248e10	−0.311165
$225$	0	0
$226$	−1.06866e10	−0.272490
$227$	−1.23768e10	−0.309379	−0.154690	−	0.987963i	$-0.549438\pi$
$227$	−1.23768e10	−0.309379	−0.154690	+	0.987963i	$0.549438\pi$
$228$	0	0
$229$	4.24749e10	1.02064	0.510321	−	0.859984i	$-0.329527\pi$
$229$	4.24749e10	1.02064	0.510321	+	0.859984i	$0.329527\pi$
$230$	−3.01241e10	−0.709806
$231$	0	0
$232$	−1.06700e10	−0.241807
$233$	−4.56572e9	−0.101486	−0.0507431	−	0.998712i	$-0.516159\pi$
$233$	−4.56572e9	−0.101486	−0.0507431	+	0.998712i	$0.516159\pi$
$234$	0	0
$235$	5.50472e10	1.17742
$236$	−5.87974e9	−0.123383
$237$	0	0
$238$	1.18230e11	2.38854
$239$	6.44635e10	1.27798	0.638989	−	0.769216i	$-0.279353\pi$
$239$	6.44635e10	1.27798	0.638989	+	0.769216i	$0.279353\pi$
$240$	0	0
$241$	−6.16283e10	−1.17680	−0.588401	−	0.808569i	$-0.700242\pi$
$241$	−6.16283e10	−1.17680	−0.588401	+	0.808569i	$0.700242\pi$
$242$	−3.22948e10	−0.605289
$243$	0	0
$244$	4.62837e10	0.835937
$245$	1.52037e11	2.69589
$246$	0	0
$247$	1.10562e10	0.189004
$248$	−2.20875e8	−0.00370778
$249$	0	0
$250$	−1.96033e10	−0.317395
$251$	−1.50155e10	−0.238785	−0.119393	−	0.992847i	$-0.538095\pi$
$251$	−1.50155e10	−0.238785	−0.119393	+	0.992847i	$0.538095\pi$
$252$	0	0
$253$	−1.93215e10	−0.296482
$254$	−3.39686e10	−0.512066
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	8.62292e10	1.23298	0.616489	−	0.787364i	$-0.288555\pi$
$257$	8.62292e10	1.23298	0.616489	+	0.787364i	$0.288555\pi$
$258$	0	0
$259$	2.16644e11	2.99156
$260$	9.73401e9	0.132103
$261$	0	0
$262$	7.95880e8	0.0104350
$263$	1.14591e11	1.47689	0.738446	−	0.674312i	$-0.235560\pi$
$263$	1.14591e11	1.47689	0.738446	+	0.674312i	$0.235560\pi$
$264$	0	0
$265$	−1.05317e11	−1.31188
$266$	−9.34053e10	−1.14394
$267$	0	0
$268$	−6.09142e10	−0.721294
$269$	1.28269e11	1.49361	0.746806	−	0.665042i	$-0.231586\pi$
$269$	1.28269e11	1.49361	0.746806	+	0.665042i	$0.231586\pi$
$270$	0	0
$271$	−7.44512e10	−0.838514	−0.419257	−	0.907868i	$-0.637709\pi$
$271$	−7.44512e10	−0.838514	−0.419257	+	0.907868i	$0.637709\pi$
$272$	−4.33094e10	−0.479758
$273$	0	0
$274$	−1.08470e11	−1.16261
$275$	2.34152e10	0.246888
$276$	0	0
$277$	−3.66117e10	−0.373647	−0.186823	−	0.982394i	$-0.559819\pi$
$277$	−3.66117e10	−0.373647	−0.186823	+	0.982394i	$0.559819\pi$
$278$	7.60499e10	0.763654
$279$	0	0
$280$	−8.22348e10	−0.799548
$281$	−7.51695e10	−0.719222	−0.359611	−	0.933102i	$-0.617091\pi$
$281$	−7.51695e10	−0.719222	−0.359611	+	0.933102i	$0.617091\pi$
$282$	0	0
$283$	3.39484e10	0.314615	0.157308	−	0.987550i	$-0.449719\pi$
$283$	3.39484e10	0.314615	0.157308	+	0.987550i	$0.449719\pi$
$284$	−1.21136e10	−0.110494
$285$	0	0
$286$	6.24336e9	0.0551787
$287$	−1.45112e10	−0.126251
$288$	0	0
$289$	3.18133e11	2.68268
$290$	−7.48365e10	−0.621330
$291$	0	0
$292$	−1.80554e10	−0.145339
$293$	8.44144e10	0.669133	0.334566	−	0.942372i	$-0.391410\pi$
$293$	8.44144e10	0.669133	0.334566	+	0.942372i	$0.391410\pi$
$294$	0	0
$295$	−4.12389e10	−0.317036
$296$	−7.93598e10	−0.600880
$297$	0	0
$298$	1.15247e11	0.846557
$299$	−2.22059e10	−0.160675
$300$	0	0
$301$	1.64439e11	1.15467
$302$	7.95781e10	0.550506
$303$	0	0
$304$	3.42157e10	0.229770
$305$	3.24622e11	2.14797
$306$	0	0
$307$	−2.60554e10	−0.167408	−0.0837039	−	0.996491i	$-0.526675\pi$
$307$	−2.60554e10	−0.167408	−0.0837039	+	0.996491i	$0.526675\pi$
$308$	−5.27451e10	−0.333967
$309$	0	0
$310$	−1.54916e9	−0.00952727
$311$	−1.50013e11	−0.909297	−0.454648	−	0.890671i	$-0.650235\pi$
$311$	−1.50013e11	−0.909297	−0.454648	+	0.890671i	$0.650235\pi$
$312$	0	0
$313$	1.73489e11	1.02170	0.510850	−	0.859670i	$-0.329331\pi$
$313$	1.73489e11	1.02170	0.510850	+	0.859670i	$0.329331\pi$
$314$	−1.10963e10	−0.0644164
$315$	0	0
$316$	−6.59619e10	−0.372136
$317$	1.91698e10	0.106623	0.0533115	−	0.998578i	$-0.483022\pi$
$317$	1.91698e10	0.106623	0.0533115	+	0.998578i	$0.483022\pi$
$318$	0	0
$319$	−4.79999e10	−0.259527
$320$	3.01238e10	0.160596
$321$	0	0
$322$	1.87600e11	0.972480
$323$	−3.45022e11	−1.76374
$324$	0	0
$325$	2.69106e10	0.133798
$326$	1.27486e11	0.625146
$327$	0	0
$328$	5.31566e9	0.0253586
$329$	−3.42809e11	−1.61314
$330$	0	0
$331$	−2.03669e11	−0.932609	−0.466305	−	0.884624i	$-0.654415\pi$
$331$	−2.03669e11	−0.932609	−0.466305	+	0.884624i	$0.654415\pi$
$332$	−7.51336e10	−0.339401
$333$	0	0
$334$	9.82125e10	0.431825
$335$	−4.27236e11	−1.85339
$336$	0	0
$337$	−1.90874e11	−0.806142	−0.403071	−	0.915169i	$-0.632057\pi$
$337$	−1.90874e11	−0.806142	−0.403071	+	0.915169i	$0.632057\pi$
$338$	−1.62497e11	−0.677203
$339$	0	0
$340$	−3.03761e11	−1.23275
$341$	−9.93625e8	−0.00397949
$342$	0	0
$343$	−4.95599e11	−1.93333
$344$	−6.02364e10	−0.231924
$345$	0	0
$346$	5.98460e10	0.224488
$347$	5.03919e11	1.86586	0.932928	−	0.360062i	$-0.117245\pi$
$347$	5.03919e11	1.86586	0.932928	+	0.360062i	$0.117245\pi$
$348$	0	0
$349$	−2.67916e11	−0.966682	−0.483341	−	0.875432i	$-0.660577\pi$
$349$	−2.67916e11	−0.966682	−0.483341	+	0.875432i	$0.660577\pi$
$350$	−2.27346e11	−0.809808
$351$	0	0
$352$	1.93213e10	0.0670801
$353$	5.43014e10	0.186134	0.0930668	−	0.995660i	$-0.470333\pi$
$353$	5.43014e10	0.186134	0.0930668	+	0.995660i	$0.470333\pi$
$354$	0	0
$355$	−8.49614e10	−0.283919
$356$	−3.62295e10	−0.119547
$357$	0	0
$358$	3.87388e11	1.24644
$359$	2.39369e11	0.760577	0.380289	−	0.924868i	$-0.375825\pi$
$359$	2.39369e11	0.760577	0.380289	+	0.924868i	$0.375825\pi$
$360$	0	0
$361$	−5.01103e10	−0.155290
$362$	1.84516e11	0.564736
$363$	0	0
$364$	−6.06191e10	−0.180989
$365$	−1.26636e11	−0.373454
$366$	0	0
$367$	−4.24872e11	−1.22253	−0.611267	−	0.791424i	$-0.709340\pi$
$367$	−4.24872e11	−1.22253	−0.611267	+	0.791424i	$0.709340\pi$
$368$	−6.87203e10	−0.195331
$369$	0	0
$370$	−5.56608e11	−1.54398
$371$	6.55868e11	1.79736
$372$	0	0
$373$	−2.21403e11	−0.592234	−0.296117	−	0.955152i	$-0.595692\pi$
$373$	−2.21403e11	−0.592234	−0.296117	+	0.955152i	$0.595692\pi$
$374$	−1.94831e11	−0.514915
$375$	0	0
$376$	1.25576e11	0.324012
$377$	−5.51654e10	−0.140647
$378$	0	0
$379$	−7.92760e10	−0.197363	−0.0986814	−	0.995119i	$-0.531462\pi$
$379$	−7.92760e10	−0.197363	−0.0986814	+	0.995119i	$0.531462\pi$
$380$	2.39980e11	0.590402
$381$	0	0
$382$	−2.90744e11	−0.698595
$383$	3.48397e11	0.827332	0.413666	−	0.910429i	$-0.364248\pi$
$383$	3.48397e11	0.827332	0.413666	+	0.910429i	$0.364248\pi$
$384$	0	0
$385$	−3.69940e11	−0.858140
$386$	−3.05942e11	−0.701449
$387$	0	0
$388$	8.41316e10	0.188459
$389$	9.30082e10	0.205943	0.102972	−	0.994684i	$-0.467165\pi$
$389$	9.30082e10	0.205943	0.102972	+	0.994684i	$0.467165\pi$
$390$	0	0
$391$	6.92959e11	1.49938
$392$	3.46833e11	0.741880
$393$	0	0
$394$	−1.89828e11	−0.396852
$395$	−4.62640e11	−0.956216
$396$	0	0
$397$	−2.16735e11	−0.437896	−0.218948	−	0.975737i	$-0.570262\pi$
$397$	−2.16735e11	−0.437896	−0.218948	+	0.975737i	$0.570262\pi$
$398$	−3.55755e11	−0.710685
$399$	0	0
$400$	8.32801e10	0.162657
$401$	−5.96305e11	−1.15164	−0.575822	−	0.817575i	$-0.695318\pi$
$401$	−5.96305e11	−1.15164	−0.575822	+	0.817575i	$0.695318\pi$
$402$	0	0
$403$	−1.14196e9	−0.00215664
$404$	−1.26705e11	−0.236635
$405$	0	0
$406$	4.66048e11	0.851263
$407$	−3.57006e11	−0.644913
$408$	0	0
$409$	4.91106e11	0.867802	0.433901	−	0.900961i	$-0.357137\pi$
$409$	4.91106e11	0.867802	0.433901	+	0.900961i	$0.357137\pi$
$410$	3.72826e10	0.0651598
$411$	0	0
$412$	−1.02158e11	−0.174677
$413$	2.56817e11	0.434360
$414$	0	0
$415$	−5.26967e11	−0.872102
$416$	2.22056e10	0.0363532
$417$	0	0
$418$	1.53922e11	0.246608
$419$	2.94006e11	0.466008	0.233004	−	0.972476i	$-0.425144\pi$
$419$	2.94006e11	0.466008	0.233004	+	0.972476i	$0.425144\pi$
$420$	0	0
$421$	−9.69340e10	−0.150386	−0.0751929	−	0.997169i	$-0.523957\pi$
$421$	−9.69340e10	−0.150386	−0.0751929	+	0.997169i	$0.523957\pi$
$422$	8.97098e11	1.37700
$423$	0	0
$424$	−2.40254e11	−0.361014
$425$	−8.39776e11	−1.24857
$426$	0	0
$427$	−2.02160e12	−2.94286
$428$	3.25069e10	0.0468251
$429$	0	0
$430$	−4.22482e11	−0.595937
$431$	1.11086e12	1.55064	0.775318	−	0.631571i	$-0.217590\pi$
$431$	1.11086e12	1.55064	0.775318	+	0.631571i	$0.217590\pi$
$432$	0	0
$433$	2.51266e11	0.343509	0.171755	−	0.985140i	$-0.445056\pi$
$433$	2.51266e11	0.343509	0.171755	+	0.985140i	$0.445056\pi$
$434$	9.64747e9	0.0130530
$435$	0	0
$436$	−5.65895e11	−0.749974
$437$	−5.47457e11	−0.718098
$438$	0	0
$439$	1.10506e12	1.42003	0.710013	−	0.704188i	$-0.248689\pi$
$439$	1.10506e12	1.42003	0.710013	+	0.704188i	$0.248689\pi$
$440$	1.35514e11	0.172365
$441$	0	0
$442$	−2.23916e11	−0.279052
$443$	−1.53318e10	−0.0189137	−0.00945687	−	0.999955i	$-0.503010\pi$
$443$	−1.53318e10	−0.0189137	−0.00945687	+	0.999955i	$0.503010\pi$
$444$	0	0
$445$	−2.54104e11	−0.307179
$446$	1.02946e12	1.23198
$447$	0	0
$448$	−1.87597e11	−0.220027
$449$	−1.10134e12	−1.27883	−0.639415	−	0.768862i	$-0.720823\pi$
$449$	−1.10134e12	−1.27883	−0.639415	+	0.768862i	$0.720823\pi$
$450$	0	0
$451$	2.39129e10	0.0272169
$452$	−1.70985e11	−0.192679
$453$	0	0
$454$	−1.98029e11	−0.218764
$455$	−4.25166e11	−0.465058
$456$	0	0
$457$	−3.48063e11	−0.373280	−0.186640	−	0.982428i	$-0.559760\pi$
$457$	−3.48063e11	−0.373280	−0.186640	+	0.982428i	$0.559760\pi$
$458$	6.79599e11	0.721702
$459$	0	0
$460$	−4.81986e11	−0.501908
$461$	−1.77076e11	−0.182603	−0.0913013	−	0.995823i	$-0.529103\pi$
$461$	−1.77076e11	−0.182603	−0.0913013	+	0.995823i	$0.529103\pi$
$462$	0	0
$463$	4.28840e10	0.0433691	0.0216846	−	0.999765i	$-0.493097\pi$
$463$	4.28840e10	0.0433691	0.0216846	+	0.999765i	$0.493097\pi$
$464$	−1.70720e11	−0.170983
$465$	0	0
$466$	−7.30515e10	−0.0717616
$467$	−1.23771e12	−1.20419	−0.602093	−	0.798426i	$-0.705666\pi$
$467$	−1.23771e12	−1.20419	−0.602093	+	0.798426i	$0.705666\pi$
$468$	0	0
$469$	2.66064e12	2.53926
$470$	8.80756e11	0.832559
$471$	0	0
$472$	−9.40758e10	−0.0872447
$473$	−2.70978e11	−0.248920
$474$	0	0
$475$	6.63447e11	0.597978
$476$	1.89168e12	1.68895
$477$	0	0
$478$	1.03142e12	0.903667
$479$	8.92232e11	0.774404	0.387202	−	0.921995i	$-0.373442\pi$
$479$	8.92232e11	0.774404	0.387202	+	0.921995i	$0.373442\pi$
$480$	0	0
$481$	−4.10301e11	−0.349502
$482$	−9.86053e11	−0.832125
$483$	0	0
$484$	−5.16716e11	−0.428004
$485$	5.90077e11	0.484251
$486$	0	0
$487$	−4.38243e11	−0.353049	−0.176524	−	0.984296i	$-0.556485\pi$
$487$	−4.38243e11	−0.353049	−0.176524	+	0.984296i	$0.556485\pi$
$488$	7.40539e11	0.591097
$489$	0	0
$490$	2.43260e12	1.90628
$491$	1.22021e12	0.947477	0.473738	−	0.880666i	$-0.342904\pi$
$491$	1.22021e12	0.947477	0.473738	+	0.880666i	$0.342904\pi$
$492$	0	0
$493$	1.72150e12	1.31249
$494$	1.76900e11	0.133646
$495$	0	0
$496$	−3.53400e9	−0.00262180
$497$	5.29101e11	0.388987
$498$	0	0
$499$	2.04494e12	1.47648	0.738242	−	0.674536i	$-0.235656\pi$
$499$	2.04494e12	1.47648	0.738242	+	0.674536i	$0.235656\pi$
$500$	−3.13653e11	−0.224432
$501$	0	0
$502$	−2.40247e11	−0.168847
$503$	−2.19466e11	−0.152866	−0.0764329	−	0.997075i	$-0.524353\pi$
$503$	−2.19466e11	−0.152866	−0.0764329	+	0.997075i	$0.524353\pi$
$504$	0	0
$505$	−8.88676e11	−0.608040
$506$	−3.09144e11	−0.209645
$507$	0	0
$508$	−5.43498e11	−0.362085
$509$	6.78625e11	0.448126	0.224063	−	0.974575i	$-0.428068\pi$
$509$	6.78625e11	0.448126	0.224063	+	0.974575i	$0.428068\pi$
$510$	0	0
$511$	7.88629e11	0.511657
$512$	6.87195e10	0.0441942
$513$	0	0
$514$	1.37967e12	0.871847
$515$	−7.16512e11	−0.448839
$516$	0	0
$517$	5.64913e11	0.347756
$518$	3.46631e12	2.11535
$519$	0	0
$520$	1.55744e11	0.0934108
$521$	−3.00159e12	−1.78477	−0.892383	−	0.451279i	$-0.850968\pi$
$521$	−3.00159e12	−1.78477	−0.892383	+	0.451279i	$0.850968\pi$
$522$	0	0
$523$	−1.25398e12	−0.732881	−0.366440	−	0.930442i	$-0.619424\pi$
$523$	−1.25398e12	−0.732881	−0.366440	+	0.930442i	$0.619424\pi$
$524$	1.27341e10	0.00737865
$525$	0	0
$526$	1.83345e12	1.04432
$527$	3.56360e10	0.0201252
$528$	0	0
$529$	−7.01613e11	−0.389536
$530$	−1.68508e12	−0.927637
$531$	0	0
$532$	−1.49448e12	−0.808889
$533$	2.74827e10	0.0147499
$534$	0	0
$535$	2.27995e11	0.120319
$536$	−9.74628e11	−0.510032
$537$	0	0
$538$	2.05231e12	1.05614
$539$	1.56026e12	0.796245
$540$	0	0
$541$	1.80539e11	0.0906113	0.0453056	−	0.998973i	$-0.485574\pi$
$541$	1.80539e11	0.0906113	0.0453056	+	0.998973i	$0.485574\pi$
$542$	−1.19122e12	−0.592919
$543$	0	0
$544$	−6.92950e11	−0.339240
$545$	−3.96904e12	−1.92708
$546$	0	0
$547$	−1.50299e12	−0.717816	−0.358908	−	0.933373i	$-0.616851\pi$
$547$	−1.50299e12	−0.717816	−0.358908	+	0.933373i	$0.616851\pi$
$548$	−1.73552e12	−0.822087
$549$	0	0
$550$	3.74643e11	0.174576
$551$	−1.36003e12	−0.628589
$552$	0	0
$553$	2.88111e12	1.31008
$554$	−5.85788e11	−0.264208
$555$	0	0
$556$	1.21680e12	0.539985
$557$	−1.28134e12	−0.564047	−0.282023	−	0.959408i	$-0.591006\pi$
$557$	−1.28134e12	−0.564047	−0.282023	+	0.959408i	$0.591006\pi$
$558$	0	0
$559$	−3.11431e11	−0.134899
$560$	−1.31576e12	−0.565366
$561$	0	0
$562$	−1.20271e12	−0.508567
$563$	−2.37619e12	−0.996768	−0.498384	−	0.866956i	$-0.666073\pi$
$563$	−2.37619e12	−0.996768	−0.498384	+	0.866956i	$0.666073\pi$
$564$	0	0
$565$	−1.19924e12	−0.495096
$566$	5.43174e11	0.222467
$567$	0	0
$568$	−1.93817e11	−0.0781312
$569$	−2.95285e11	−0.118096	−0.0590481	−	0.998255i	$-0.518807\pi$
$569$	−2.95285e11	−0.118096	−0.0590481	+	0.998255i	$0.518807\pi$
$570$	0	0
$571$	7.54059e11	0.296854	0.148427	−	0.988923i	$-0.452579\pi$
$571$	7.54059e11	0.296854	0.148427	+	0.988923i	$0.452579\pi$
$572$	9.98937e10	0.0390172
$573$	0	0
$574$	−2.32180e11	−0.0892731
$575$	−1.33250e12	−0.508349
$576$	0	0
$577$	−2.25656e12	−0.847532	−0.423766	−	0.905772i	$-0.639292\pi$
$577$	−2.25656e12	−0.847532	−0.423766	+	0.905772i	$0.639292\pi$
$578$	5.09013e12	1.89694
$579$	0	0
$580$	−1.19738e12	−0.439347
$581$	3.28172e12	1.19484
$582$	0	0
$583$	−1.08080e12	−0.387469
$584$	−2.88886e11	−0.102770
$585$	0	0
$586$	1.35063e12	0.473148
$587$	−1.10342e12	−0.383593	−0.191796	−	0.981435i	$-0.561431\pi$
$587$	−1.10342e12	−0.383593	−0.191796	+	0.981435i	$0.561431\pi$
$588$	0	0
$589$	−2.81535e10	−0.00963858
$590$	−6.59823e11	−0.224178
$591$	0	0
$592$	−1.26976e12	−0.424886
$593$	−8.96636e11	−0.297763	−0.148881	−	0.988855i	$-0.547567\pi$
$593$	−8.96636e11	−0.297763	−0.148881	+	0.988855i	$0.547567\pi$
$594$	0	0
$595$	1.32678e13	4.33982
$596$	1.84395e12	0.598606
$597$	0	0
$598$	−3.55294e11	−0.113614
$599$	−3.53494e12	−1.12192	−0.560959	−	0.827844i	$-0.689568\pi$
$599$	−3.53494e12	−1.12192	−0.560959	+	0.827844i	$0.689568\pi$
$600$	0	0
$601$	4.46317e12	1.39543	0.697715	−	0.716375i	$-0.254200\pi$
$601$	4.46317e12	1.39543	0.697715	+	0.716375i	$0.254200\pi$
$602$	2.63103e12	0.816472
$603$	0	0
$604$	1.27325e12	0.389267
$605$	−3.62411e12	−1.09977
$606$	0	0
$607$	−1.96872e12	−0.588620	−0.294310	−	0.955710i	$-0.595090\pi$
$607$	−1.96872e12	−0.588620	−0.294310	+	0.955710i	$0.595090\pi$
$608$	5.47451e11	0.162472
$609$	0	0
$610$	5.19395e12	1.51884
$611$	6.49245e11	0.188462
$612$	0	0
$613$	−5.68828e12	−1.62708	−0.813540	−	0.581509i	$-0.802463\pi$
$613$	−5.68828e12	−1.62708	−0.813540	+	0.581509i	$0.802463\pi$
$614$	−4.16887e11	−0.118375
$615$	0	0
$616$	−8.43922e11	−0.236151
$617$	2.72150e12	0.756006	0.378003	−	0.925804i	$-0.376611\pi$
$617$	2.72150e12	0.756006	0.378003	+	0.925804i	$0.376611\pi$
$618$	0	0
$619$	−8.54242e11	−0.233869	−0.116935	−	0.993140i	$-0.537307\pi$
$619$	−8.54242e11	−0.233869	−0.116935	+	0.993140i	$0.537307\pi$
$620$	−2.47866e10	−0.00673680
$621$	0	0
$622$	−2.40020e12	−0.642970
$623$	1.58245e12	0.420855
$624$	0	0
$625$	−4.68182e12	−1.22731
$626$	2.77583e12	0.722451
$627$	0	0
$628$	−1.77541e11	−0.0455493
$629$	1.28039e13	3.26148
$630$	0	0
$631$	1.82693e12	0.458764	0.229382	−	0.973336i	$-0.426330\pi$
$631$	1.82693e12	0.458764	0.229382	+	0.973336i	$0.426330\pi$
$632$	−1.05539e12	−0.263140
$633$	0	0
$634$	3.06717e11	0.0753938
$635$	−3.81195e12	−0.930391
$636$	0	0
$637$	1.79318e12	0.431515
$638$	−7.67998e11	−0.183513
$639$	0	0
$640$	4.81980e11	0.113558
$641$	−7.12089e12	−1.66599	−0.832997	−	0.553278i	$-0.813377\pi$
$641$	−7.12089e12	−1.66599	−0.832997	+	0.553278i	$0.813377\pi$
$642$	0	0
$643$	6.02641e12	1.39030	0.695151	−	0.718864i	$-0.255338\pi$
$643$	6.02641e12	1.39030	0.695151	+	0.718864i	$0.255338\pi$
$644$	3.00159e12	0.687647
$645$	0	0
$646$	−5.52036e12	−1.24716
$647$	5.11089e12	1.14664	0.573320	−	0.819332i	$-0.305655\pi$
$647$	5.11089e12	1.14664	0.573320	+	0.819332i	$0.305655\pi$
$648$	0	0
$649$	−4.23208e11	−0.0936381
$650$	4.30570e11	0.0946093
$651$	0	0
$652$	2.03977e12	0.442045
$653$	6.53913e12	1.40738	0.703689	−	0.710508i	$-0.251535\pi$
$653$	6.53913e12	1.40738	0.703689	+	0.710508i	$0.251535\pi$
$654$	0	0
$655$	8.93135e10	0.0189597
$656$	8.50506e10	0.0179312
$657$	0	0
$658$	−5.48495e12	−1.14066
$659$	1.94618e12	0.401975	0.200987	−	0.979594i	$-0.435585\pi$
$659$	1.94618e12	0.401975	0.200987	+	0.979594i	$0.435585\pi$
$660$	0	0
$661$	−1.78969e12	−0.364645	−0.182323	−	0.983239i	$-0.558362\pi$
$661$	−1.78969e12	−0.364645	−0.182323	+	0.983239i	$0.558362\pi$
$662$	−3.25871e12	−0.659454
$663$	0	0
$664$	−1.20214e12	−0.239993
$665$	−1.04819e13	−2.07847
$666$	0	0
$667$	2.73155e12	0.534372
$668$	1.57140e12	0.305346
$669$	0	0
$670$	−6.83578e12	−1.31054
$671$	3.33138e12	0.634413
$672$	0	0
$673$	−5.24986e12	−0.986460	−0.493230	−	0.869899i	$-0.664184\pi$
$673$	−5.24986e12	−0.986460	−0.493230	+	0.869899i	$0.664184\pi$
$674$	−3.05398e12	−0.570028
$675$	0	0
$676$	−2.59995e12	−0.478855
$677$	1.00326e13	1.83555	0.917774	−	0.397104i	$-0.129985\pi$
$677$	1.00326e13	1.83555	0.917774	+	0.397104i	$0.129985\pi$
$678$	0	0
$679$	−3.67473e12	−0.663456
$680$	−4.86017e12	−0.871688
$681$	0	0
$682$	−1.58980e10	−0.00281393
$683$	2.26372e12	0.398043	0.199021	−	0.979995i	$-0.436224\pi$
$683$	2.26372e12	0.398043	0.199021	+	0.979995i	$0.436224\pi$
$684$	0	0
$685$	−1.21725e13	−2.11238
$686$	−7.92959e12	−1.36707
$687$	0	0
$688$	−9.63782e11	−0.163995
$689$	−1.24215e12	−0.209984
$690$	0	0
$691$	−3.41838e12	−0.570387	−0.285193	−	0.958470i	$-0.592058\pi$
$691$	−3.41838e12	−0.570387	−0.285193	+	0.958470i	$0.592058\pi$
$692$	9.57536e11	0.158737
$693$	0	0
$694$	8.06271e12	1.31936
$695$	8.53430e12	1.38751
$696$	0	0
$697$	−8.57629e11	−0.137642
$698$	−4.28665e12	−0.683547
$699$	0	0
$700$	−3.63754e12	−0.572620
$701$	−6.70506e12	−1.04875	−0.524374	−	0.851488i	$-0.675701\pi$
$701$	−6.70506e12	−1.04875	−0.524374	+	0.851488i	$0.675701\pi$
$702$	0	0
$703$	−1.01155e13	−1.56202
$704$	3.09140e11	0.0474328
$705$	0	0
$706$	8.68822e11	0.131616
$707$	5.53428e12	0.833055
$708$	0	0
$709$	−5.01888e12	−0.745931	−0.372965	−	0.927845i	$-0.621659\pi$
$709$	−5.01888e12	−0.745931	−0.372965	+	0.927845i	$0.621659\pi$
$710$	−1.35938e12	−0.200761
$711$	0	0
$712$	−5.79672e11	−0.0845323
$713$	5.65448e10	0.00819388
$714$	0	0
$715$	7.00628e11	0.100256
$716$	6.19821e12	0.881369
$717$	0	0
$718$	3.82991e12	0.537809
$719$	9.03791e11	0.126121	0.0630606	−	0.998010i	$-0.479914\pi$
$719$	9.03791e11	0.126121	0.0630606	+	0.998010i	$0.479914\pi$
$720$	0	0
$721$	4.46211e12	0.614939
$722$	−8.01764e11	−0.109807
$723$	0	0
$724$	2.95225e12	0.399328
$725$	−3.31029e12	−0.444984
$726$	0	0
$727$	−1.45873e13	−1.93674	−0.968369	−	0.249521i	$-0.919727\pi$
$727$	−1.45873e13	−1.93674	−0.968369	+	0.249521i	$0.919727\pi$
$728$	−9.69905e11	−0.127979
$729$	0	0
$730$	−2.02617e12	−0.264072
$731$	9.71854e12	1.25885
$732$	0	0
$733$	−2.93730e12	−0.375821	−0.187911	−	0.982186i	$-0.560171\pi$
$733$	−2.93730e12	−0.375821	−0.187911	+	0.982186i	$0.560171\pi$
$734$	−6.79796e12	−0.864462
$735$	0	0
$736$	−1.09953e12	−0.138120
$737$	−4.38444e12	−0.547407
$738$	0	0
$739$	−1.26838e13	−1.56441	−0.782206	−	0.623020i	$-0.785905\pi$
$739$	−1.26838e13	−1.56441	−0.782206	+	0.623020i	$0.785905\pi$
$740$	−8.90574e12	−1.09176
$741$	0	0
$742$	1.04939e13	1.27092
$743$	−1.16847e12	−0.140659	−0.0703296	−	0.997524i	$-0.522405\pi$
$743$	−1.16847e12	−0.140659	−0.0703296	+	0.997524i	$0.522405\pi$
$744$	0	0
$745$	1.29330e13	1.53814
$746$	−3.54244e12	−0.418772
$747$	0	0
$748$	−3.11729e12	−0.364100
$749$	−1.41985e12	−0.164844
$750$	0	0
$751$	−1.18975e13	−1.36483	−0.682413	−	0.730966i	$-0.739070\pi$
$751$	−1.18975e13	−1.36483	−0.682413	+	0.730966i	$0.739070\pi$
$752$	2.00921e12	0.229111
$753$	0	0
$754$	−8.82647e11	−0.0994525
$755$	8.93024e12	1.00023
$756$	0	0
$757$	5.40853e12	0.598615	0.299308	−	0.954157i	$-0.403244\pi$
$757$	5.40853e12	0.598615	0.299308	+	0.954157i	$0.403244\pi$
$758$	−1.26842e12	−0.139557
$759$	0	0
$760$	3.83967e12	0.417478
$761$	3.40799e12	0.368356	0.184178	−	0.982893i	$-0.441038\pi$
$761$	3.40799e12	0.368356	0.184178	+	0.982893i	$0.441038\pi$
$762$	0	0
$763$	2.47174e13	2.64023
$764$	−4.65190e12	−0.493981
$765$	0	0
$766$	5.57435e12	0.585012
$767$	−4.86386e11	−0.0507460
$768$	0	0
$769$	−2.50939e12	−0.258761	−0.129381	−	0.991595i	$-0.541299\pi$
$769$	−2.50939e12	−0.258761	−0.129381	+	0.991595i	$0.541299\pi$
$770$	−5.91904e12	−0.606797
$771$	0	0
$772$	−4.89507e12	−0.496000
$773$	−1.35883e13	−1.36885	−0.684427	−	0.729082i	$-0.739948\pi$
$773$	−1.35883e13	−1.36885	−0.684427	+	0.729082i	$0.739948\pi$
$774$	0	0
$775$	−6.85249e10	−0.00682324
$776$	1.34611e12	0.133261
$777$	0	0
$778$	1.48813e12	0.145624
$779$	6.77552e11	0.0659210
$780$	0	0
$781$	−8.71902e11	−0.0838568
$782$	1.10873e13	1.06022
$783$	0	0
$784$	5.54933e12	0.524588
$785$	−1.24523e12	−0.117040
$786$	0	0
$787$	−1.34190e11	−0.0124690	−0.00623452	−	0.999981i	$-0.501985\pi$
$787$	−1.34190e11	−0.0124690	−0.00623452	+	0.999981i	$0.501985\pi$
$788$	−3.03725e12	−0.280617
$789$	0	0
$790$	−7.40223e12	−0.676146
$791$	7.46835e12	0.678313
$792$	0	0
$793$	3.82869e12	0.343812
$794$	−3.46775e12	−0.309639
$795$	0	0
$796$	−5.69208e12	−0.502530
$797$	1.51654e13	1.33135	0.665674	−	0.746243i	$-0.268144\pi$
$797$	1.51654e13	1.33135	0.665674	+	0.746243i	$0.268144\pi$
$798$	0	0
$799$	−2.02604e13	−1.75868
$800$	1.33248e12	0.115016
$801$	0	0
$802$	−9.54087e12	−0.814336
$803$	−1.29958e12	−0.110302
$804$	0	0
$805$	2.10524e13	1.76693
$806$	−1.82713e10	−0.00152497
$807$	0	0
$808$	−2.02728e12	−0.167326
$809$	4.97475e12	0.408322	0.204161	−	0.978937i	$-0.434553\pi$
$809$	4.97475e12	0.408322	0.204161	+	0.978937i	$0.434553\pi$
$810$	0	0
$811$	1.46659e13	1.19046	0.595230	−	0.803555i	$-0.297061\pi$
$811$	1.46659e13	1.19046	0.595230	+	0.803555i	$0.297061\pi$
$812$	7.45677e12	0.601934
$813$	0	0
$814$	−5.71210e12	−0.456022
$815$	1.43064e13	1.13585
$816$	0	0
$817$	−7.67793e12	−0.602899
$818$	7.85770e12	0.613628
$819$	0	0
$820$	5.96522e11	0.0460749
$821$	−2.44422e13	−1.87757	−0.938784	−	0.344507i	$-0.888046\pi$
$821$	−2.44422e13	−1.87757	−0.938784	+	0.344507i	$0.888046\pi$
$822$	0	0
$823$	−1.76460e13	−1.34075	−0.670375	−	0.742022i	$-0.733867\pi$
$823$	−1.76460e13	−1.34075	−0.670375	+	0.742022i	$0.733867\pi$
$824$	−1.63453e12	−0.123515
$825$	0	0
$826$	4.10908e12	0.307139
$827$	1.53876e13	1.14392	0.571959	−	0.820282i	$-0.306184\pi$
$827$	1.53876e13	1.14392	0.571959	+	0.820282i	$0.306184\pi$
$828$	0	0
$829$	−1.22874e13	−0.903579	−0.451789	−	0.892125i	$-0.649214\pi$
$829$	−1.22874e13	−0.903579	−0.451789	+	0.892125i	$0.649214\pi$
$830$	−8.43148e12	−0.616669
$831$	0	0
$832$	3.55290e11	0.0257056
$833$	−5.59581e13	−4.02680
$834$	0	0
$835$	1.10214e13	0.784597
$836$	2.46275e12	0.174378
$837$	0	0
$838$	4.70410e12	0.329518
$839$	5.02853e12	0.350358	0.175179	−	0.984537i	$-0.443950\pi$
$839$	5.02853e12	0.350358	0.175179	+	0.984537i	$0.443950\pi$
$840$	0	0
$841$	−7.72123e12	−0.532236
$842$	−1.55094e12	−0.106339
$843$	0	0
$844$	1.43536e13	0.973686
$845$	−1.82353e13	−1.23043
$846$	0	0
$847$	2.25693e13	1.50676
$848$	−3.84406e12	−0.255275
$849$	0	0
$850$	−1.34364e13	−0.882873
$851$	2.03164e13	1.32789
$852$	0	0
$853$	1.19222e13	0.771053	0.385526	−	0.922697i	$-0.374020\pi$
$853$	1.19222e13	0.771053	0.385526	+	0.922697i	$0.374020\pi$
$854$	−3.23456e13	−2.08091
$855$	0	0
$856$	5.20110e11	0.0331103
$857$	−5.71947e12	−0.362195	−0.181097	−	0.983465i	$-0.557965\pi$
$857$	−5.71947e12	−0.362195	−0.181097	+	0.983465i	$0.557965\pi$
$858$	0	0
$859$	−5.82113e12	−0.364786	−0.182393	−	0.983226i	$-0.558384\pi$
$859$	−5.82113e12	−0.364786	−0.182393	+	0.983226i	$0.558384\pi$
$860$	−6.75971e12	−0.421391
$861$	0	0
$862$	1.77737e13	1.09647
$863$	1.65530e13	1.01585	0.507924	−	0.861402i	$-0.330413\pi$
$863$	1.65530e13	1.01585	0.507924	+	0.861402i	$0.330413\pi$
$864$	0	0
$865$	6.71591e12	0.407880
$866$	4.02026e12	0.242898
$867$	0	0
$868$	1.54360e11	0.00922985
$869$	−4.74776e12	−0.282423
$870$	0	0
$871$	−5.03897e12	−0.296660
$872$	−9.05431e12	−0.530312
$873$	0	0
$874$	−8.75932e12	−0.507772
$875$	1.36999e13	0.790097
$876$	0	0
$877$	3.07906e13	1.75760	0.878799	−	0.477191i	$-0.158345\pi$
$877$	3.07906e13	1.75760	0.878799	+	0.477191i	$0.158345\pi$
$878$	1.76810e13	1.00411
$879$	0	0
$880$	2.16823e12	0.121880
$881$	2.43879e13	1.36390	0.681949	−	0.731399i	$-0.261132\pi$
$881$	2.43879e13	1.36390	0.681949	+	0.731399i	$0.261132\pi$
$882$	0	0
$883$	−5.39949e12	−0.298902	−0.149451	−	0.988769i	$-0.547751\pi$
$883$	−5.39949e12	−0.298902	−0.149451	+	0.988769i	$0.547751\pi$
$884$	−3.58265e12	−0.197319
$885$	0	0
$886$	−2.45310e11	−0.0133740
$887$	−2.64499e12	−0.143472	−0.0717361	−	0.997424i	$-0.522854\pi$
$887$	−2.64499e12	−0.143472	−0.0717361	+	0.997424i	$0.522854\pi$
$888$	0	0
$889$	2.37391e13	1.27470
$890$	−4.06567e12	−0.217209
$891$	0	0
$892$	1.64714e13	0.871139
$893$	1.60063e13	0.842286
$894$	0	0
$895$	4.34726e13	2.26471
$896$	−3.00156e12	−0.155582
$897$	0	0
$898$	−1.76214e13	−0.904270
$899$	1.40472e11	0.00717253
$900$	0	0
$901$	3.87625e13	1.95952
$902$	3.82607e11	0.0192453
$903$	0	0
$904$	−2.73576e12	−0.136245
$905$	2.07063e13	1.02609
$906$	0	0
$907$	5.71181e12	0.280247	0.140123	−	0.990134i	$-0.455250\pi$
$907$	5.71181e12	0.280247	0.140123	+	0.990134i	$0.455250\pi$
$908$	−3.16846e12	−0.154690
$909$	0	0
$910$	−6.80266e12	−0.328846
$911$	−1.44620e13	−0.695659	−0.347829	−	0.937558i	$-0.613081\pi$
$911$	−1.44620e13	−0.695659	−0.347829	+	0.937558i	$0.613081\pi$
$912$	0	0
$913$	−5.40792e12	−0.257580
$914$	−5.56901e12	−0.263949
$915$	0	0
$916$	1.08736e13	0.510321
$917$	−5.56204e11	−0.0259760
$918$	0	0
$919$	−3.39599e13	−1.57053	−0.785266	−	0.619158i	$-0.787474\pi$
$919$	−3.39599e13	−1.57053	−0.785266	+	0.619158i	$0.787474\pi$
$920$	−7.71178e12	−0.354903
$921$	0	0
$922$	−2.83322e12	−0.129119
$923$	−1.00206e12	−0.0454451
$924$	0	0
$925$	−2.46208e13	−1.10577
$926$	6.86144e11	0.0306666
$927$	0	0
$928$	−2.73152e12	−0.120903
$929$	2.29252e13	1.00982	0.504908	−	0.863173i	$-0.331527\pi$
$929$	2.29252e13	1.00982	0.504908	+	0.863173i	$0.331527\pi$
$930$	0	0
$931$	4.42085e13	1.92856
$932$	−1.16882e12	−0.0507431
$933$	0	0
$934$	−1.98034e13	−0.851487
$935$	−2.18639e13	−0.935567
$936$	0	0
$937$	2.69013e13	1.14010	0.570052	−	0.821608i	$-0.306923\pi$
$937$	2.69013e13	1.14010	0.570052	+	0.821608i	$0.306923\pi$
$938$	4.25702e13	1.79553
$939$	0	0
$940$	1.40921e13	0.588708
$941$	−1.78244e13	−0.741074	−0.370537	−	0.928818i	$-0.620826\pi$
$941$	−1.78244e13	−0.741074	−0.370537	+	0.928818i	$0.620826\pi$
$942$	0	0
$943$	−1.36083e12	−0.0560403
$944$	−1.50521e12	−0.0616913
$945$	0	0
$946$	−4.33565e12	−0.176013
$947$	1.67550e13	0.676971	0.338485	−	0.940972i	$-0.390085\pi$
$947$	1.67550e13	0.676971	0.338485	+	0.940972i	$0.390085\pi$
$948$	0	0
$949$	−1.49358e12	−0.0597765
$950$	1.06152e13	0.422834
$951$	0	0
$952$	3.02669e13	1.19427
$953$	−1.77293e13	−0.696263	−0.348131	−	0.937446i	$-0.613184\pi$
$953$	−1.77293e13	−0.696263	−0.348131	+	0.937446i	$0.613184\pi$
$954$	0	0
$955$	−3.26272e13	−1.26930
$956$	1.65027e13	0.638989
$957$	0	0
$958$	1.42757e13	0.547587
$959$	7.58048e13	2.89410
$960$	0	0
$961$	−2.64367e13	−0.999890
$962$	−6.56482e12	−0.247136
$963$	0	0
$964$	−1.57768e13	−0.588401
$965$	−3.43328e13	−1.27449
$966$	0	0
$967$	−3.85334e13	−1.41716	−0.708578	−	0.705632i	$-0.750663\pi$
$967$	−3.85334e13	−1.41716	−0.708578	+	0.705632i	$0.750663\pi$
$968$	−8.26746e12	−0.302645
$969$	0	0
$970$	9.44123e12	0.342417
$971$	1.91351e13	0.690786	0.345393	−	0.938458i	$-0.387746\pi$
$971$	1.91351e13	0.690786	0.345393	+	0.938458i	$0.387746\pi$
$972$	0	0
$973$	−5.31478e13	−1.90098
$974$	−7.01189e12	−0.249643
$975$	0	0
$976$	1.18486e13	0.417969
$977$	1.13181e13	0.397417	0.198708	−	0.980059i	$-0.436325\pi$
$977$	1.13181e13	0.397417	0.198708	+	0.980059i	$0.436325\pi$
$978$	0	0
$979$	−2.60770e12	−0.0907269
$980$	3.89215e13	1.34795
$981$	0	0
$982$	1.95234e13	0.669967
$983$	2.72852e13	0.932045	0.466023	−	0.884773i	$-0.345687\pi$
$983$	2.72852e13	0.932045	0.466023	+	0.884773i	$0.345687\pi$
$984$	0	0
$985$	−2.13025e13	−0.721054
$986$	2.75440e13	0.928069
$987$	0	0
$988$	2.83040e12	0.0945021
$989$	1.54207e13	0.512532
$990$	0	0
$991$	2.96159e13	0.975423	0.487711	−	0.873005i	$-0.337832\pi$
$991$	2.96159e13	0.975423	0.487711	+	0.873005i	$0.337832\pi$
$992$	−5.65440e10	−0.00185389
$993$	0	0
$994$	8.46562e12	0.275055
$995$	−3.99228e13	−1.29127
$996$	0	0
$997$	2.24297e13	0.718943	0.359471	−	0.933156i	$-0.382957\pi$
$997$	2.24297e13	0.718943	0.359471	+	0.933156i	$0.382957\pi$
$998$	3.27191e13	1.04403
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.10.a.h.1.4		4
3.2	odd	2		162.10.a.e.1.1		4
9.2	odd	6		18.10.c.a.13.1	yes	8
9.4	even	3		54.10.c.a.19.1		8
9.5	odd	6		18.10.c.a.7.1	✓	8
9.7	even	3		54.10.c.a.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.10.c.a.7.1	✓	8	9.5	odd	6
18.10.c.a.13.1	yes	8	9.2	odd	6
54.10.c.a.19.1		8	9.4	even	3
54.10.c.a.37.1		8	9.7	even	3
162.10.a.e.1.1		4	3.2	odd	2
162.10.a.h.1.4		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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	162.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +256.000 q^{4} +1795.52 q^{5} -11181.7 q^{7} +4096.00 q^{8} +O(q^{10})\)	\(q+16.0000 q^{2} +256.000 q^{4} +1795.52 q^{5} -11181.7 q^{7} +4096.00 q^{8} +28728.3 q^{10} +18426.2 q^{11} +21176.9 q^{13} -178907. q^{14} +65536.0 q^{16} -660849. q^{17} +522089. q^{19} +459652. q^{20} +294819. q^{22} -1.04859e6 q^{23} +1.27075e6 q^{25} +338831. q^{26} -2.86251e6 q^{28} -2.60498e6 q^{29} -53924.6 q^{31} +1.04858e6 q^{32} -1.05736e7 q^{34} -2.00769e7 q^{35} -1.93749e7 q^{37} +8.35343e6 q^{38} +7.35444e6 q^{40} +1.29777e6 q^{41} -1.47062e7 q^{43} +4.71711e6 q^{44} -1.67774e7 q^{46} +3.06582e7 q^{47} +8.46761e7 q^{49} +2.03321e7 q^{50} +5.42129e6 q^{52} -5.86557e7 q^{53} +3.30845e7 q^{55} -4.58001e7 q^{56} -4.16797e7 q^{58} -2.29677e7 q^{59} +1.80796e8 q^{61} -862794. q^{62} +1.67772e7 q^{64} +3.80235e7 q^{65} -2.37946e8 q^{67} -1.69177e8 q^{68} -3.21230e8 q^{70} -4.73186e7 q^{71} -7.05287e7 q^{73} -3.09999e8 q^{74} +1.33655e8 q^{76} -2.06036e8 q^{77} -2.57664e8 q^{79} +1.17671e8 q^{80} +2.07643e7 q^{82} -2.93491e8 q^{83} -1.18656e9 q^{85} -2.35298e8 q^{86} +7.54737e7 q^{88} -1.41522e8 q^{89} -2.36793e8 q^{91} -2.68439e8 q^{92} +4.90531e8 q^{94} +9.37420e8 q^{95} +3.28639e8 q^{97} +1.35482e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 1024 q^{4} + 171 q^{5} - 7135 q^{7} + 16384 q^{8}+O(q^{10}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 171 * q^5 - 7135 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 171 q^{5} - 7135 q^{7} + 16384 q^{8} + 2736 q^{10} - 26130 q^{11} + 4163 q^{13} - 114160 q^{14} + 262144 q^{16} - 549255 q^{17} - 218191 q^{19} + 43776 q^{20} - 418080 q^{22} - 289383 q^{23} - 2947937 q^{25} + 66608 q^{26} - 1826560 q^{28} - 601707 q^{29} - 5671315 q^{31} + 4194304 q^{32} - 8788080 q^{34} - 14893965 q^{35} - 19368574 q^{37} - 3491056 q^{38} + 700416 q^{40} - 18418410 q^{41} - 35096140 q^{43} - 6689280 q^{44} - 4630128 q^{46} - 79830825 q^{47} + 40540299 q^{49} - 47166992 q^{50} + 1065728 q^{52} - 165348618 q^{53} + 28264221 q^{55} - 29224960 q^{56} - 9627312 q^{58} - 90704166 q^{59} + 122811677 q^{61} - 90741040 q^{62} + 67108864 q^{64} - 116600103 q^{65} - 221601736 q^{67} - 140609280 q^{68} - 238303440 q^{70} - 138204120 q^{71} - 494458507 q^{73} - 309897184 q^{74} - 55856896 q^{76} - 548139525 q^{77} - 592840885 q^{79} + 11206656 q^{80} - 294694560 q^{82} - 478410747 q^{83} - 1468792818 q^{85} - 561538240 q^{86} - 107028480 q^{88} - 437759976 q^{89} - 1847756531 q^{91} - 74082048 q^{92} - 1277293200 q^{94} + 813906756 q^{95} - 2679512242 q^{97} + 648644784 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 171 * q^5 - 7135 * q^7 + 16384 * q^8 + 2736 * q^10 - 26130 * q^11 + 4163 * q^13 - 114160 * q^14 + 262144 * q^16 - 549255 * q^17 - 218191 * q^19 + 43776 * q^20 - 418080 * q^22 - 289383 * q^23 - 2947937 * q^25 + 66608 * q^26 - 1826560 * q^28 - 601707 * q^29 - 5671315 * q^31 + 4194304 * q^32 - 8788080 * q^34 - 14893965 * q^35 - 19368574 * q^37 - 3491056 * q^38 + 700416 * q^40 - 18418410 * q^41 - 35096140 * q^43 - 6689280 * q^44 - 4630128 * q^46 - 79830825 * q^47 + 40540299 * q^49 - 47166992 * q^50 + 1065728 * q^52 - 165348618 * q^53 + 28264221 * q^55 - 29224960 * q^56 - 9627312 * q^58 - 90704166 * q^59 + 122811677 * q^61 - 90741040 * q^62 + 67108864 * q^64 - 116600103 * q^65 - 221601736 * q^67 - 140609280 * q^68 - 238303440 * q^70 - 138204120 * q^71 - 494458507 * q^73 - 309897184 * q^74 - 55856896 * q^76 - 548139525 * q^77 - 592840885 * q^79 + 11206656 * q^80 - 294694560 * q^82 - 478410747 * q^83 - 1468792818 * q^85 - 561538240 * q^86 - 107028480 * q^88 - 437759976 * q^89 - 1847756531 * q^91 - 74082048 * q^92 - 1277293200 * q^94 + 813906756 * q^95 - 2679512242 * q^97 + 648644784 * q^98

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